LMFDB - Embedded newform 184.4.i.a.25.8

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			25.8
Character	$\chi$	$=$	184.25
Dual form			184.4.i.a.81.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.961609 + 6.68814i) q^{3} +(-17.3126 - 5.08343i) q^{5} +(23.0068 - 26.5513i) q^{7} +(-17.9002 + 5.25597i) q^{9} +(-3.18916 + 2.04955i) q^{11} +(-4.30168 - 4.96440i) q^{13} +(17.3508 - 120.677i) q^{15} +(33.6407 - 73.6628i) q^{17} +(-25.8795 - 56.6682i) q^{19} +(199.702 + 128.341i) q^{21} +(86.3597 + 68.6222i) q^{23} +(168.727 + 108.434i) q^{25} +(23.4213 + 51.2855i) q^{27} +(9.92531 - 21.7334i) q^{29} +(36.0043 - 250.416i) q^{31} +(-16.7744 - 19.3587i) q^{33} +(-533.278 + 342.717i) q^{35} +(370.177 - 108.694i) q^{37} +(29.0661 - 33.5440i) q^{39} +(-323.173 - 94.8922i) q^{41} +(3.75057 + 26.0858i) q^{43} +336.617 q^{45} -44.9208 q^{47} +(-126.843 - 882.210i) q^{49} +(525.016 + 154.159i) q^{51} +(-38.5510 + 44.4902i) q^{53} +(65.6313 - 19.2711i) q^{55} +(354.119 - 227.578i) q^{57} +(-421.079 - 485.951i) q^{59} +(-7.67877 + 53.4070i) q^{61} +(-272.273 + 596.195i) q^{63} +(49.2369 + 107.814i) q^{65} +(-727.606 - 467.604i) q^{67} +(-375.910 + 643.573i) q^{69} +(227.836 + 146.422i) q^{71} +(152.196 + 333.263i) q^{73} +(-562.974 + 1232.74i) q^{75} +(-18.9542 + 131.830i) q^{77} +(-581.283 - 670.836i) q^{79} +(-744.229 + 478.287i) q^{81} +(-497.557 + 146.096i) q^{83} +(-956.866 + 1104.28i) q^{85} +(154.900 + 45.4828i) q^{87} +(37.3154 + 259.534i) q^{89} -230.779 q^{91} +1709.44 q^{93} +(159.972 + 1112.63i) q^{95} +(1257.48 + 369.229i) q^{97} +(46.3142 - 53.4494i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.961609	+	6.68814i	0.185062	+	1.28713i	0.844574	+	0.535439i	$0.179854\pi$
$3$	0.961609	+	6.68814i	0.185062	+	1.28713i	−0.659512	+	0.751694i	$0.729237\pi$
$4$		0			0
$5$	−17.3126	−	5.08343i	−1.54848	−	0.454676i	−0.607836	−	0.794062i	$-0.707962\pi$
$5$	−17.3126	−	5.08343i	−1.54848	−	0.454676i	−0.940647	+	0.339387i	$0.889780\pi$
$6$		0			0
$7$	23.0068	−	26.5513i	1.24225	−	1.43363i	0.381685	−	0.924292i	$-0.375344\pi$
$7$	23.0068	−	26.5513i	1.24225	−	1.43363i	0.860565	−	0.509340i	$-0.170111\pi$
$8$		0			0
$9$	−17.9002	+	5.25597i	−0.662970	+	0.194666i
$10$		0			0
$11$	−3.18916	+	2.04955i	−0.0874152	+	0.0561784i	−0.583618	−	0.812028i	$-0.698364\pi$
$11$	−3.18916	+	2.04955i	−0.0874152	+	0.0561784i	0.496203	+	0.868207i	$0.334727\pi$
$12$		0			0
$13$	−4.30168	−	4.96440i	−0.0917747	−	0.105914i	0.708005	−	0.706208i	$-0.249596\pi$
$13$	−4.30168	−	4.96440i	−0.0917747	−	0.105914i	−0.799779	+	0.600294i	$0.795050\pi$
$14$		0			0
$15$	17.3508	−	120.677i	0.298663	−	2.07725i
$16$		0			0
$17$	33.6407	−	73.6628i	0.479945	−	1.05093i	−0.502534	−	0.864558i	$-0.667599\pi$
$17$	33.6407	−	73.6628i	0.479945	−	1.05093i	0.982479	−	0.186375i	$-0.0596740\pi$
$18$		0			0
$19$	−25.8795	−	56.6682i	−0.312482	−	0.684240i	0.686602	−	0.727034i	$-0.259102\pi$
$19$	−25.8795	−	56.6682i	−0.312482	−	0.684240i	−0.999084	+	0.0427933i	$0.986374\pi$
$20$		0			0
$21$	199.702	+	128.341i	2.07517	+	1.33363i
$22$		0			0
$23$	86.3597	+	68.6222i	0.782923	+	0.622118i
$23$	86.3597	+	68.6222i	0.782923	+	0.622118i
$24$		0			0
$25$	168.727	+	108.434i	1.34982	+	0.867474i
$26$		0			0
$27$	23.4213	+	51.2855i	0.166942	+	0.365552i
$28$		0			0
$29$	9.92531	−	21.7334i	0.0635546	−	0.139165i	−0.875189	−	0.483780i	$-0.839263\pi$
$29$	9.92531	−	21.7334i	0.0635546	−	0.139165i	0.938744	+	0.344615i	$0.111991\pi$
$30$		0			0
$31$	36.0043	−	250.416i	0.208599	−	1.45084i	−0.569135	−	0.822244i	$-0.692722\pi$
$31$	36.0043	−	250.416i	0.208599	−	1.45084i	0.777734	−	0.628593i	$-0.216369\pi$
$32$		0			0
$33$	−16.7744	−	19.3587i	−0.0884862	−	0.102119i
$34$		0			0
$35$	−533.278	+	342.717i	−2.57544	+	1.65514i
$36$		0			0
$37$	370.177	−	108.694i	1.64478	−	0.482950i	0.677257	−	0.735747i	$-0.263169\pi$
$37$	370.177	−	108.694i	1.64478	−	0.482950i	0.967519	+	0.252797i	$0.0813506\pi$
$38$		0			0
$39$	29.0661	−	33.5440i	0.119341	−	0.137727i
$40$		0			0
$41$	−323.173	−	94.8922i	−1.23100	−	0.361455i	−0.399375	−	0.916788i	$-0.630773\pi$
$41$	−323.173	−	94.8922i	−1.23100	−	0.361455i	−0.831629	+	0.555332i	$0.812591\pi$
$42$		0			0
$43$	3.75057	+	26.0858i	0.0133013	+	0.0925127i	0.995391	−	0.0959030i	$-0.0305739\pi$
$43$	3.75057	+	26.0858i	0.0133013	+	0.0925127i	−0.982089	+	0.188416i	$0.939665\pi$
$44$		0			0
$45$	336.617			1.11511
$46$		0			0
$47$	−44.9208			−0.139412			−0.0697062	−	0.997568i	$-0.522206\pi$
$47$	−44.9208			−0.139412			−0.0697062	+	0.997568i	$0.522206\pi$
$48$		0			0
$49$	−126.843	−	882.210i	−0.369803	−	2.57204i
$50$		0			0
$51$	525.016	+	154.159i	1.44151	+	0.423265i
$52$		0			0
$53$	−38.5510	+	44.4902i	−0.0999129	+	0.115306i	−0.803504	−	0.595300i	$-0.797033\pi$
$53$	−38.5510	+	44.4902i	−0.0999129	+	0.115306i	0.703591	+	0.710605i	$0.251579\pi$
$54$		0			0
$55$	65.6313	−	19.2711i	0.160904	−	0.0472457i
$56$		0			0
$57$	354.119	−	227.578i	0.822880	−	0.528833i
$58$		0			0
$59$	−421.079	−	485.951i	−0.929149	−	1.07230i	−0.997212	−	0.0746141i	$-0.976228\pi$
$59$	−421.079	−	485.951i	−0.929149	−	1.07230i	0.0680635	−	0.997681i	$-0.478318\pi$
$60$		0			0
$61$	−7.67877	+	53.4070i	−0.0161175	+	0.112099i	−0.996292	−	0.0860368i	$-0.972580\pi$
$61$	−7.67877	+	53.4070i	−0.0161175	+	0.112099i	0.980174	+	0.198136i	$0.0634888\pi$
$62$		0			0
$63$	−272.273	+	596.195i	−0.544496	+	1.19228i
$64$		0			0
$65$	49.2369	+	107.814i	0.0939552	+	0.205733i
$66$		0			0
$67$	−727.606	−	467.604i	−1.32673	−	0.852640i	−0.330886	−	0.943671i	$-0.607347\pi$
$67$	−727.606	−	467.604i	−1.32673	−	0.852640i	−0.995848	+	0.0910308i	$0.970984\pi$
$68$		0			0
$69$	−375.910	+	643.573i	−0.655859	+	1.12286i
$70$		0			0
$71$	227.836	+	146.422i	0.380834	+	0.244747i	0.717026	−	0.697046i	$-0.245503\pi$
$71$	227.836	+	146.422i	0.380834	+	0.244747i	−0.336192	+	0.941793i	$0.609139\pi$
$72$		0			0
$73$	152.196	+	333.263i	0.244016	+	0.534322i	0.991523	−	0.129933i	$-0.0414763\pi$
$73$	152.196	+	333.263i	0.244016	+	0.534322i	−0.747506	+	0.664255i	$0.768749\pi$
$74$		0			0
$75$	−562.974	+	1232.74i	−0.866755	+	1.89793i
$76$		0			0
$77$	−18.9542	+	131.830i	−0.0280524	+	0.195109i
$78$		0			0
$79$	−581.283	−	670.836i	−0.827841	−	0.955379i	0.171716	−	0.985147i	$-0.445069\pi$
$79$	−581.283	−	670.836i	−0.827841	−	0.955379i	−0.999557	+	0.0297671i	$0.990523\pi$
$80$		0			0
$81$	−744.229	+	478.287i	−1.02089	+	0.656086i
$82$		0			0
$83$	−497.557	+	146.096i	−0.658000	+	0.193206i	−0.593653	−	0.804721i	$-0.702315\pi$
$83$	−497.557	+	146.096i	−0.658000	+	0.193206i	−0.0643471	+	0.997928i	$0.520496\pi$
$84$		0			0
$85$	−956.866	+	1104.28i	−1.22102	+	1.40913i
$86$		0			0
$87$	154.900	+	45.4828i	0.190886	+	0.0560491i
$88$		0			0
$89$	37.3154	+	259.534i	0.0444429	+	0.309107i	0.999902	+	0.0139845i	$0.00445154\pi$
$89$	37.3154	+	259.534i	0.0444429	+	0.309107i	−0.955459	+	0.295123i	$0.904639\pi$
$90$		0			0
$91$	−230.779			−0.265848
$92$		0			0
$93$	1709.44			1.90602
$94$		0			0
$95$	159.972	+	1112.63i	0.172766	+	1.20161i
$96$		0			0
$97$	1257.48	+	369.229i	1.31626	+	0.386490i	0.863143	−	0.504960i	$-0.168493\pi$
$97$	1257.48	+	369.229i	1.31626	+	0.386490i	0.453120	+	0.891450i	$0.350311\pi$
$98$		0			0
$99$	46.3142	−	53.4494i	0.0470177	−	0.0542613i
$100$		0			0
$101$	756.114	−	222.015i	0.744912	−	0.218726i	0.112816	−	0.993616i	$-0.464013\pi$
$101$	756.114	−	222.015i	0.744912	−	0.218726i	0.632096	+	0.774890i	$0.282195\pi$
$102$		0			0
$103$	1706.83	−	1096.91i	1.63281	−	1.04934i	0.685970	−	0.727630i	$-0.259378\pi$
$103$	1706.83	−	1096.91i	1.63281	−	1.04934i	0.946838	−	0.321712i	$-0.104258\pi$
$104$		0			0
$105$	−2804.94	−	3237.08i	−2.60700	−	3.00863i
$106$		0			0
$107$	−68.3755	+	475.562i	−0.0617767	+	0.429666i	0.935338	+	0.353756i	$0.115096\pi$
$107$	−68.3755	+	475.562i	−0.0617767	+	0.429666i	−0.997115	+	0.0759109i	$0.975814\pi$
$108$		0			0
$109$	−299.023	+	654.769i	−0.262763	+	0.575371i	−0.994323	−	0.106406i	$-0.966066\pi$
$109$	−299.023	+	654.769i	−0.262763	+	0.575371i	0.731559	+	0.681778i	$0.238793\pi$
$110$		0			0
$111$	1082.92	+	2371.27i	0.926006	+	2.02767i
$112$		0			0
$113$	1840.46	+	1182.79i	1.53218	+	0.984669i	0.989469	+	0.144747i	$0.0462367\pi$
$113$	1840.46	+	1182.79i	1.53218	+	0.984669i	0.542706	+	0.839923i	$0.317400\pi$
$114$		0			0
$115$	−1146.27	−	1627.03i	−0.929482	−	1.31932i
$116$		0			0
$117$	103.094	+	66.2542i	0.0814616	+	0.0523522i
$118$		0			0
$119$	−1181.88	−	2587.95i	−0.910440	−	1.99359i
$120$		0			0
$121$	−546.947	+	1197.65i	−0.410930	+	0.899810i
$122$		0			0
$123$	323.886	−	2252.67i	0.237429	−	1.65136i
$124$		0			0
$125$	−892.887	−	1030.45i	−0.638898	−	0.737328i
$126$		0			0
$127$	−2111.11	+	1356.73i	−1.47505	+	0.947955i	−0.477450	+	0.878659i	$0.658439\pi$
$127$	−2111.11	+	1356.73i	−1.47505	+	0.947955i	−0.997596	+	0.0692962i	$0.977925\pi$
$128$		0			0
$129$	−170.859	+	50.1686i	−0.116615	+	0.0342411i
$130$		0			0
$131$	−260.043	+	300.105i	−0.173435	+	0.200155i	−0.835812	−	0.549016i	$-0.815003\pi$
$131$	−260.043	+	300.105i	−0.173435	+	0.200155i	0.662376	+	0.749171i	$0.269548\pi$
$132$		0			0
$133$	−2100.01	−	616.620i	−1.36913	−	0.402013i
$134$		0			0
$135$	−144.777	−	1006.94i	−0.0922992	−	0.641955i
$136$		0			0
$137$	−907.321			−0.565823			−0.282911	−	0.959146i	$-0.591300\pi$
$137$	−907.321			−0.565823			−0.282911	+	0.959146i	$0.591300\pi$
$138$		0			0
$139$	2830.06			1.72692			0.863462	−	0.504414i	$-0.168291\pi$
$139$	2830.06			1.72692			0.863462	+	0.504414i	$0.168291\pi$
$140$		0			0
$141$	−43.1963	−	300.437i	−0.0257999	−	0.179442i
$142$		0			0
$143$	23.8935	+	7.01577i	0.0139726	+	0.00410271i
$144$		0			0
$145$	−282.313	+	325.806i	−0.161688	+	0.186598i
$146$		0			0
$147$	5778.37	−	1696.68i	3.24212	−	0.951972i
$148$		0			0
$149$	742.090	−	476.913i	0.408016	−	0.262216i	−0.320495	−	0.947250i	$-0.603849\pi$
$149$	742.090	−	476.913i	0.408016	−	0.262216i	0.728511	+	0.685034i	$0.240213\pi$
$150$		0			0
$151$	886.322	+	1022.87i	0.477668	+	0.551258i	0.942529	−	0.334126i	$-0.108441\pi$
$151$	886.322	+	1022.87i	0.477668	+	0.551258i	−0.464860	+	0.885384i	$0.653896\pi$
$152$		0			0
$153$	−215.005	+	1495.39i	−0.113609	+	0.790166i
$154$		0			0
$155$	−1896.30	+	4152.31i	−0.982672	+	2.15175i
$156$		0			0
$157$	−512.185	−	1121.53i	−0.260362	−	0.570113i	0.733632	−	0.679547i	$-0.237824\pi$
$157$	−512.185	−	1121.53i	−0.260362	−	0.570113i	−0.993994	+	0.109434i	$0.965096\pi$
$158$		0			0
$159$	−334.628	−	215.052i	−0.166904	−	0.107263i
$160$		0			0
$161$	3808.86	−	714.181i	1.86448	−	0.349599i
$162$		0			0
$163$	−27.3953	−	17.6059i	−0.0131642	−	0.00846012i	0.534042	−	0.845458i	$-0.320672\pi$
$163$	−27.3953	−	17.6059i	−0.0131642	−	0.00846012i	−0.547206	+	0.836998i	$0.684309\pi$
$164$		0			0
$165$	191.999	+	420.420i	0.0905886	+	0.198361i
$166$		0			0
$167$	1411.67	−	3091.12i	0.654120	−	1.43232i	−0.233782	−	0.972289i	$-0.575110\pi$
$167$	1411.67	−	3091.12i	0.654120	−	1.43232i	0.887902	−	0.460034i	$-0.152163\pi$
$168$		0			0
$169$	306.525	−	2131.93i	0.139520	−	0.970381i
$170$		0			0
$171$	761.094	+	878.349i	0.340364	+	0.392801i
$172$		0			0
$173$	−2007.69	+	1290.26i	−0.882322	+	0.567034i	−0.901499	−	0.432782i	$-0.857532\pi$
$173$	−2007.69	+	1290.26i	−0.882322	+	0.567034i	0.0191763	+	0.999816i	$0.493896\pi$
$174$		0			0
$175$	6760.94	−	1985.19i	2.92045	−	0.857521i
$176$		0			0
$177$	2845.19	−	3283.53i	1.20824	−	1.39438i
$178$		0			0
$179$	958.182	+	281.348i	0.400100	+	0.117480i	0.475591	−	0.879667i	$-0.342234\pi$
$179$	958.182	+	281.348i	0.400100	+	0.117480i	−0.0754911	+	0.997146i	$0.524052\pi$
$180$		0			0
$181$	275.971	+	1919.42i	0.113330	+	0.788228i	0.964641	+	0.263567i	$0.0848988\pi$
$181$	275.971	+	1919.42i	0.113330	+	0.788228i	−0.851311	+	0.524661i	$0.824192\pi$
$182$		0			0
$183$	−364.577			−0.147270
$184$		0			0
$185$	−6961.25			−2.76649
$186$		0			0
$187$	43.6900	+	303.871i	0.0170852	+	0.118830i
$188$		0			0
$189$	1900.54	+	558.050i	0.731451	+	0.214773i
$190$		0			0
$191$	−2410.96	+	2782.39i	−0.913355	+	1.05407i	0.0849798	+	0.996383i	$0.472917\pi$
$191$	−2410.96	+	2782.39i	−0.913355	+	1.05407i	−0.998335	+	0.0576852i	$0.981628\pi$
$192$		0			0
$193$	−1864.73	+	547.533i	−0.695471	+	0.204209i	−0.610315	−	0.792159i	$-0.708957\pi$
$193$	−1864.73	+	547.533i	−0.695471	+	0.204209i	−0.0851562	+	0.996368i	$0.527139\pi$
$194$		0			0
$195$	−673.727	+	432.978i	−0.247418	+	0.159006i
$196$		0			0
$197$	−425.734	−	491.323i	−0.153971	−	0.177692i	0.673524	−	0.739166i	$-0.264780\pi$
$197$	−425.734	−	491.323i	−0.153971	−	0.177692i	−0.827495	+	0.561474i	$0.810235\pi$
$198$		0			0
$199$	−280.996	+	1954.37i	−0.100097	+	0.696189i	0.876546	+	0.481319i	$0.159842\pi$
$199$	−280.996	+	1954.37i	−0.100097	+	0.696189i	−0.976643	+	0.214870i	$0.931067\pi$
$200$		0			0
$201$	2427.73	−	5315.98i	0.851933	−	1.86547i
$202$		0			0
$203$	−348.699	−	763.545i	−0.120561	−	0.263992i
$204$		0			0
$205$	5112.58	+	3285.65i	1.74184	+	1.11941i
$206$		0			0
$207$	−1906.53	−	774.446i	−0.640160	−	0.260037i
$208$		0			0
$209$	198.678	+	127.683i	0.0657552	+	0.0422583i
$210$		0			0
$211$	612.017	+	1340.13i	0.199682	+	0.437243i	0.982811	−	0.184617i	$-0.0591045\pi$
$211$	612.017	+	1340.13i	0.199682	+	0.437243i	−0.783128	+	0.621860i	$0.786377\pi$
$212$		0			0
$213$	−760.198	+	1664.60i	−0.244544	+	0.535477i
$214$		0			0
$215$	67.6732	−	470.678i	0.0214664	−	0.149302i
$216$		0			0
$217$	−5820.50	−	6717.22i	−1.82084	−	2.10136i
$218$		0			0
$219$	−2082.56	+	1338.38i	−0.642585	+	0.412964i
$220$		0			0
$221$	−510.403	+	149.868i	−0.155355	+	0.0456163i
$222$		0			0
$223$	−697.786	+	805.287i	−0.209539	+	0.241821i	−0.850784	−	0.525515i	$-0.823873\pi$
$223$	−697.786	+	805.287i	−0.209539	+	0.241821i	0.641245	+	0.767336i	$0.278418\pi$
$224$		0			0
$225$	−3590.17	−	1054.17i	−1.06376	−	0.312347i
$226$		0			0
$227$	322.778	+	2244.97i	0.0943767	+	0.656405i	0.981014	+	0.193938i	$0.0621262\pi$
$227$	322.778	+	2244.97i	0.0943767	+	0.656405i	−0.886637	+	0.462466i	$0.846965\pi$
$228$		0			0
$229$	3931.50			1.13450			0.567251	−	0.823545i	$-0.308007\pi$
$229$	3931.50			1.13450			0.567251	+	0.823545i	$0.308007\pi$
$230$		0			0
$231$	−899.922			−0.256323
$232$		0			0
$233$	631.441	+	4391.77i	0.177541	+	1.23483i	0.862429	+	0.506178i	$0.168942\pi$
$233$	631.441	+	4391.77i	0.177541	+	1.23483i	−0.684888	+	0.728648i	$0.740149\pi$
$234$		0			0
$235$	777.695	+	228.352i	0.215878	+	0.0633874i
$236$		0			0
$237$	3927.68	−	4532.78i	1.07650	−	1.24235i
$238$		0			0
$239$	−952.822	+	279.774i	−0.257878	+	0.0757199i	−0.408116	−	0.912930i	$-0.633814\pi$
$239$	−952.822	+	279.774i	−0.257878	+	0.0757199i	0.150238	+	0.988650i	$0.451996\pi$
$240$		0			0
$241$	−3766.64	+	2420.67i	−1.00677	+	0.647009i	−0.936554	−	0.350523i	$-0.886004\pi$
$241$	−3766.64	+	2420.67i	−1.00677	+	0.647009i	−0.0702113	+	0.997532i	$0.522367\pi$
$242$		0			0
$243$	−2917.63	−	3367.12i	−0.770231	−	0.888894i
$244$		0			0
$245$	−2288.68	+	15918.1i	−0.596809	+	4.15090i
$246$		0			0
$247$	−169.998	+	372.244i	−0.0437924	+	0.0958920i
$248$		0			0
$249$	−1455.56	−	3187.24i	−0.370453	−	0.811178i
$250$		0			0
$251$	1655.08	+	1063.66i	0.416207	+	0.267480i	0.731941	−	0.681368i	$-0.238614\pi$
$251$	1655.08	+	1063.66i	0.416207	+	0.267480i	−0.315734	+	0.948848i	$0.602251\pi$
$252$		0			0
$253$	−416.059	−	41.8488i	−0.103389	−	0.0103992i
$254$		0			0
$255$	−8305.73	−	5337.77i	−2.03970	−	1.31084i
$256$		0			0
$257$	897.265	+	1964.74i	0.217781	+	0.476875i	0.986716	−	0.162452i	$-0.0519403\pi$
$257$	897.265	+	1964.74i	0.217781	+	0.476875i	−0.768935	+	0.639327i	$0.779213\pi$
$258$		0			0
$259$	5630.63	−	12329.4i	1.35085	−	2.95795i
$260$		0			0
$261$	−63.4348	+	441.199i	−0.0150441	+	0.104634i
$262$		0			0
$263$	−3908.47	−	4510.61i	−0.916374	−	1.05755i	−0.998144	−	0.0609010i	$-0.980603\pi$
$263$	−3908.47	−	4510.61i	−0.916374	−	1.05755i	0.0817696	−	0.996651i	$-0.473943\pi$
$264$		0			0
$265$	893.579	−	574.269i	0.207140	−	0.133121i
$266$		0			0
$267$	−1699.92	+	499.141i	−0.389638	+	0.114408i
$268$		0			0
$269$	−4023.71	+	4643.61i	−0.912007	+	1.05251i	0.0864094	+	0.996260i	$0.472461\pi$
$269$	−4023.71	+	4643.61i	−0.912007	+	1.05251i	−0.998417	+	0.0562526i	$0.982085\pi$
$270$		0			0
$271$	695.177	+	204.122i	0.155827	+	0.0457548i	0.358715	−	0.933447i	$-0.383215\pi$
$271$	695.177	+	204.122i	0.155827	+	0.0457548i	−0.202889	+	0.979202i	$0.565033\pi$
$272$		0			0
$273$	−221.919	−	1543.48i	−0.0491984	−	0.342182i
$274$		0			0
$275$	−760.339			−0.166728
$276$		0			0
$277$	3912.32			0.848624			0.424312	−	0.905516i	$-0.360516\pi$
$277$	3912.32			0.848624			0.424312	+	0.905516i	$0.360516\pi$
$278$		0			0
$279$	671.692	+	4671.72i	0.144133	+	1.00247i
$280$		0			0
$281$	3747.53	+	1100.37i	0.795582	+	0.233604i	0.654171	−	0.756347i	$-0.273018\pi$
$281$	3747.53	+	1100.37i	0.795582	+	0.233604i	0.141411	+	0.989951i	$0.454836\pi$
$282$		0			0
$283$	3815.09	−	4402.84i	0.801355	−	0.924813i	−0.197100	−	0.980383i	$-0.563152\pi$
$283$	3815.09	−	4402.84i	0.801355	−	0.924813i	0.998455	+	0.0555709i	$0.0176979\pi$
$284$		0			0
$285$	−7287.58	+	2139.83i	−1.51466	+	0.444745i
$286$		0			0
$287$	−9954.68	+	6397.48i	−2.04741	+	1.31579i
$288$		0			0
$289$	−1077.19	−	1243.14i	−0.219252	−	0.253030i
$290$		0			0
$291$	−1260.25	+	8765.24i	−0.253874	+	1.76573i
$292$		0			0
$293$	4156.13	−	9100.65i	0.828681	−	1.81456i	0.348963	−	0.937136i	$-0.386534\pi$
$293$	4156.13	−	9100.65i	0.828681	−	1.81456i	0.479718	−	0.877423i	$-0.340739\pi$
$294$		0			0
$295$	4819.66	+	10553.6i	0.951225	+	2.08289i
$296$		0			0
$297$	−179.806	−	115.554i	−0.0351294	−	0.0225763i
$298$		0			0
$299$	−30.8235	−	723.914i	−0.00596176	−	0.140017i
$300$		0			0
$301$	778.899	+	500.568i	0.149153	+	0.0958547i
$302$		0			0
$303$	2211.95	+	4843.50i	0.419384	+	0.918323i
$304$		0			0
$305$	404.430	−	885.578i	0.0759265	−	0.166256i
$306$		0			0
$307$	−88.3275	+	614.331i	−0.0164206	+	0.114208i	−0.996383	−	0.0849740i	$-0.972919\pi$
$307$	−88.3275	+	614.331i	−0.0164206	+	0.114208i	0.979963	+	0.199182i	$0.0638284\pi$
$308$		0			0
$309$	8977.62	+	10360.7i	1.65281	+	1.90745i
$310$		0			0
$311$	1163.41	−	747.678i	0.212125	−	0.136324i	−0.430264	−	0.902703i	$-0.641580\pi$
$311$	1163.41	−	747.678i	0.212125	−	0.136324i	0.642389	+	0.766379i	$0.277943\pi$
$312$		0			0
$313$	−2801.71	+	822.657i	−0.505949	+	0.148560i	−0.524739	−	0.851263i	$-0.675837\pi$
$313$	−2801.71	+	822.657i	−0.505949	+	0.148560i	0.0187894	+	0.999823i	$0.494019\pi$
$314$		0			0
$315$	7744.47	−	8937.59i	1.38524	−	1.59865i
$316$		0			0
$317$	3831.56	+	1125.05i	0.678869	+	0.199334i	0.602949	−	0.797780i	$-0.293992\pi$
$317$	3831.56	+	1125.05i	0.678869	+	0.199334i	0.0759205	+	0.997114i	$0.475810\pi$
$318$		0			0
$319$	12.8902	+	89.6536i	0.00226243	+	0.0157355i
$320$		0			0
$321$	−3246.37			−0.564470
$322$		0			0
$323$	−5044.94			−0.869065
$324$		0			0
$325$	−187.498	−	1304.08i	−0.0320016	−	0.222576i
$326$		0			0
$327$	−4666.73	−	1370.27i	−0.789207	−	0.231732i
$328$		0			0
$329$	−1033.48	+	1192.70i	−0.173185	+	0.199866i
$330$		0			0
$331$	438.503	−	128.756i	0.0728166	−	0.0213809i	−0.245121	−	0.969492i	$-0.578828\pi$
$331$	438.503	−	128.756i	0.0728166	−	0.0213809i	0.317938	+	0.948112i	$0.397010\pi$
$332$		0			0
$333$	−6054.95	+	3891.28i	−0.996423	+	0.640362i
$334$		0			0
$335$	10219.7	+	11794.2i	1.66675	+	1.92353i
$336$		0			0
$337$	632.880	−	4401.78i	0.102300	−	0.711513i	−0.872529	−	0.488562i	$-0.837522\pi$
$337$	632.880	−	4401.78i	0.102300	−	0.711513i	0.974830	−	0.222952i	$-0.0715692\pi$
$338$		0			0
$339$	−6140.87	+	13446.6i	−0.983853	+	2.15434i
$340$		0			0
$341$	398.415	+	872.408i	0.0632709	+	0.138544i
$342$		0			0
$343$	−16204.6	−	10414.0i	−2.55092	−	1.63938i
$344$		0			0
$345$	9779.53	−	9230.99i	1.52612	−	1.44052i
$346$		0			0
$347$	−5525.55	−	3551.05i	−0.854833	−	0.549368i	0.0382460	−	0.999268i	$-0.487823\pi$
$347$	−5525.55	−	3551.05i	−0.854833	−	0.549368i	−0.893079	+	0.449901i	$0.851459\pi$
$348$		0			0
$349$	−1825.80	−	3997.95i	−0.280037	−	0.613196i	0.716385	−	0.697705i	$-0.245795\pi$
$349$	−1825.80	−	3997.95i	−0.280037	−	0.613196i	−0.996423	+	0.0845084i	$0.973068\pi$
$350$		0			0
$351$	153.851	−	336.886i	0.0233959	−	0.0512298i
$352$		0			0
$353$	385.513	−	2681.30i	0.0581269	−	0.404281i	−0.939898	−	0.341456i	$-0.889080\pi$
$353$	385.513	−	2681.30i	0.0581269	−	0.404281i	0.998025	−	0.0628250i	$-0.0200110\pi$
$354$		0			0
$355$	−3200.11	−	3693.12i	−0.478434	−	0.552143i
$356$		0			0
$357$	16172.0	−	10393.1i	2.39752	−	1.54079i
$358$		0			0
$359$	11200.1	−	3288.66i	1.64658	−	0.483479i	0.678598	−	0.734510i	$-0.262588\pi$
$359$	11200.1	−	3288.66i	1.64658	−	0.483479i	0.967979	+	0.251031i	$0.0807698\pi$
$360$		0			0
$361$	1950.16	−	2250.60i	0.284321	−	0.328124i
$362$		0			0
$363$	−8535.98	−	2506.39i	−1.23422	−	0.362400i
$364$		0			0
$365$	−940.787	−	6543.31i	−0.134912	−	0.938336i
$366$		0			0
$367$	−4095.67			−0.582540			−0.291270	−	0.956641i	$-0.594078\pi$
$367$	−4095.67			−0.582540			−0.291270	+	0.956641i	$0.594078\pi$
$368$		0			0
$369$	6283.61			0.886481
$370$		0			0
$371$	294.336	+	2047.15i	0.0411892	+	0.286477i
$372$		0			0
$373$	8172.61	+	2399.70i	1.13448	+	0.333114i	0.794468	−	0.607306i	$-0.207750\pi$
$373$	8172.61	+	2399.70i	1.13448	+	0.333114i	0.340014	+	0.940420i	$0.389568\pi$
$374$		0			0
$375$	6033.16	−	6962.64i	0.830803	−	0.958798i
$376$		0			0
$377$	−150.589	+	44.2168i	−0.0205722	+	0.00604054i
$378$		0			0
$379$	−5017.29	+	3224.42i	−0.680002	+	0.437011i	−0.834519	−	0.550979i	$-0.814254\pi$
$379$	−5017.29	+	3224.42i	−0.680002	+	0.437011i	0.154517	+	0.987990i	$0.450618\pi$
$380$		0			0
$381$	−11104.1	−	12814.8i	−1.49312	−	1.72315i
$382$		0			0
$383$	964.135	−	6705.71i	0.128629	−	0.894636i	−0.818665	−	0.574271i	$-0.805285\pi$
$383$	964.135	−	6705.71i	0.128629	−	0.894636i	0.947294	−	0.320365i	$-0.103806\pi$
$384$		0			0
$385$	998.293	−	2185.96i	0.132150	−	0.289368i
$386$		0			0
$387$	−204.242	−	447.228i	−0.0268274	−	0.0587438i
$388$		0			0
$389$	2181.41	+	1401.91i	0.284323	+	0.182724i	0.675027	−	0.737793i	$-0.264132\pi$
$389$	2181.41	+	1401.91i	0.284323	+	0.182724i	−0.390704	+	0.920517i	$0.627768\pi$
$390$		0			0
$391$	7960.10	−	4053.00i	1.02956	−	0.524218i
$392$		0			0
$393$	−2257.21	−	1450.62i	−0.289723	−	0.186193i
$394$		0			0
$395$	6653.35	+	14568.8i	0.847510	+	1.85579i
$396$		0			0
$397$	1355.07	−	2967.19i	0.171307	−	0.375110i	−0.804433	−	0.594044i	$-0.797531\pi$
$397$	1355.07	−	2967.19i	0.171307	−	0.375110i	0.975740	+	0.218934i	$0.0702578\pi$
$398$		0			0
$399$	2104.65	−	14638.1i	0.264070	−	1.83665i
$400$		0			0
$401$	4219.66	+	4869.74i	0.525485	+	0.606442i	0.954996	−	0.296620i	$-0.0958593\pi$
$401$	4219.66	+	4869.74i	0.525485	+	0.606442i	−0.429511	+	0.903062i	$0.641314\pi$
$402$		0			0
$403$	−1398.04	+	898.467i	−0.172808	+	0.111057i
$404$		0			0
$405$	15315.9	−	4497.14i	1.87914	−	0.551765i
$406$		0			0
$407$	−957.780	+	1105.34i	−0.116647	+	0.134618i
$408$		0			0
$409$	3492.90	+	1025.61i	0.422280	+	0.123993i	0.485967	−	0.873977i	$-0.338468\pi$
$409$	3492.90	+	1025.61i	0.422280	+	0.123993i	−0.0636866	+	0.997970i	$0.520286\pi$
$410$		0			0
$411$	−872.489	−	6068.29i	−0.104712	−	0.728289i
$412$		0			0
$413$	−22590.3			−2.69151
$414$		0			0
$415$	9356.66			1.10675
$416$		0			0
$417$	2721.41	+	18927.8i	0.319588	+	2.22278i
$418$		0			0
$419$	−4452.93	−	1307.50i	−0.519188	−	0.152447i	0.0116313	−	0.999932i	$-0.496298\pi$
$419$	−4452.93	−	1307.50i	−0.519188	−	0.152447i	−0.530819	+	0.847485i	$0.678116\pi$
$420$		0			0
$421$	−9105.30	+	10508.1i	−1.05407	+	1.21647i	−0.0784721	+	0.996916i	$0.525004\pi$
$421$	−9105.30	+	10508.1i	−1.05407	+	1.21647i	−0.975601	+	0.219549i	$0.929541\pi$
$422$		0			0
$423$	804.092	−	236.103i	0.0924262	−	0.0271388i
$424$		0			0
$425$	13663.7	−	8781.11i	1.55950	−	1.00223i
$426$		0			0
$427$	1241.36	+	1432.61i	0.140688	+	0.162362i
$428$		0			0
$429$	−23.9462	+	166.549i	−0.00269495	+	0.0187438i
$430$		0			0
$431$	1454.03	−	3183.89i	0.162502	−	0.355830i	−0.810812	−	0.585306i	$-0.800974\pi$
$431$	1454.03	−	3183.89i	0.162502	−	0.355830i	0.973314	+	0.229477i	$0.0737015\pi$
$432$		0			0
$433$	3702.79	+	8107.97i	0.410957	+	0.899871i	0.996041	+	0.0888978i	$0.0283345\pi$
$433$	3702.79	+	8107.97i	0.410957	+	0.899871i	−0.585083	+	0.810973i	$0.698938\pi$
$434$		0			0
$435$	−2450.51	−	1574.85i	−0.270099	−	0.173582i
$436$		0			0
$437$	1653.75	−	6669.75i	0.181029	−	0.730109i
$438$		0			0
$439$	8265.38	+	5311.84i	0.898600	+	0.577495i	0.906375	−	0.422475i	$-0.138839\pi$
$439$	8265.38	+	5311.84i	0.898600	+	0.577495i	−0.00777494	+	0.999970i	$0.502475\pi$
$440$		0			0
$441$	6907.37	+	15125.0i	0.745856	+	1.63320i
$442$		0			0
$443$	−4181.41	+	9156.02i	−0.448454	+	0.981976i	0.541515	+	0.840691i	$0.317851\pi$
$443$	−4181.41	+	9156.02i	−0.448454	+	0.981976i	−0.989969	+	0.141286i	$0.954876\pi$
$444$		0			0
$445$	673.298	−	4682.89i	0.0717245	−	0.498855i
$446$		0			0
$447$	3903.26	+	4504.60i	0.413015	+	0.476645i
$448$		0			0
$449$	−10932.0	+	7025.60i	−1.14903	+	0.738437i	−0.969446	−	0.245305i	$-0.921112\pi$
$449$	−10932.0	+	7025.60i	−1.14903	+	0.738437i	−0.179585	+	0.983742i	$0.557476\pi$
$450$		0			0
$451$	1225.14	−	359.732i	0.127914	−	0.0375591i
$452$		0			0
$453$	−5988.80	+	6911.45i	−0.621145	+	0.716839i
$454$		0			0
$455$	3995.37	+	1173.15i	0.411662	+	0.120875i
$456$		0			0
$457$	1337.51	+	9302.57i	0.136906	+	0.952201i	0.936252	+	0.351330i	$0.114270\pi$
$457$	1337.51	+	9302.57i	0.136906	+	0.952201i	−0.799346	+	0.600871i	$0.794821\pi$
$458$		0			0
$459$	4565.74			0.464293
$460$		0			0
$461$	3882.86			0.392283			0.196142	−	0.980576i	$-0.437159\pi$
$461$	3882.86			0.392283			0.196142	+	0.980576i	$0.437159\pi$
$462$		0			0
$463$	1159.57	+	8064.96i	0.116392	+	0.809526i	0.961475	+	0.274891i	$0.0886417\pi$
$463$	1159.57	+	8064.96i	0.116392	+	0.809526i	−0.845083	+	0.534635i	$0.820449\pi$
$464$		0			0
$465$	−29594.7	−	8689.80i	−2.95145	−	0.866623i
$466$		0			0
$467$	6099.28	−	7038.95i	0.604371	−	0.697481i	−0.368290	−	0.929711i	$-0.620057\pi$
$467$	6099.28	−	7038.95i	0.604371	−	0.697481i	0.972661	+	0.232230i	$0.0746022\pi$
$468$		0			0
$469$	−29155.3	+	8560.78i	−2.87051	+	0.842857i
$470$		0			0
$471$	7008.42	−	4504.04i	0.685628	−	0.440627i
$472$		0			0
$473$	−65.4252	−	75.5047i	−0.00635995	−	0.00733977i
$474$		0			0
$475$	1778.20	−	12367.7i	0.171768	−	1.19467i
$476$		0			0
$477$	456.231	−	999.006i	0.0437932	−	0.0958938i
$478$		0			0
$479$	−5827.33	−	12760.1i	−0.555861	−	1.21717i	−0.953991	−	0.299837i	$-0.903068\pi$
$479$	−5827.33	−	12760.1i	−0.555861	−	1.21717i	0.398130	−	0.917329i	$-0.369659\pi$
$480$		0			0
$481$	−2131.98	−	1370.14i	−0.202100	−	0.129882i
$482$		0			0
$483$	8439.18	+	24787.4i	0.795023	+	2.33513i
$484$		0			0
$485$	−19893.2	−	12784.6i	−1.86248	−	1.19695i
$486$		0			0
$487$	1410.63	+	3088.85i	0.131256	+	0.287411i	0.963837	−	0.266493i	$-0.0858649\pi$
$487$	1410.63	+	3088.85i	0.131256	+	0.287411i	−0.832581	+	0.553904i	$0.813138\pi$
$488$		0			0
$489$	91.4070	−	200.153i	0.00845311	−	0.0185097i
$490$		0			0
$491$	1132.93	−	7879.70i	0.104131	−	0.724248i	−0.869136	−	0.494573i	$-0.835324\pi$
$491$	1132.93	−	7879.70i	0.104131	−	0.724248i	0.973267	−	0.229675i	$-0.0737664\pi$
$492$		0			0
$493$	−1267.05	−	1462.25i	−0.115751	−	0.133583i
$494$		0			0
$495$	−1073.52	+	689.912i	−0.0974774	+	0.0626449i
$496$		0			0
$497$	9129.46	−	2680.65i	0.823968	−	0.241939i
$498$		0			0
$499$	155.342	−	179.274i	0.0139360	−	0.0160830i	−0.748739	−	0.662865i	$-0.769340\pi$
$499$	155.342	−	179.274i	0.0139360	−	0.0160830i	0.762675	+	0.646782i	$0.223886\pi$
$500$		0			0
$501$	22031.3	+	6468.97i	1.96464	+	0.576871i
$502$		0			0
$503$	290.965	+	2023.71i	0.0257923	+	0.179389i	0.998645	−	0.0520348i	$-0.0165707\pi$
$503$	290.965	+	2023.71i	0.0257923	+	0.179389i	−0.972853	+	0.231424i	$0.925662\pi$
$504$		0			0
$505$	−14218.9			−1.25293
$506$		0			0
$507$	14553.4			1.27483
$508$		0			0
$509$	−1936.80	−	13470.8i	−0.168659	−	1.17305i	−0.881660	−	0.471885i	$-0.843574\pi$
$509$	−1936.80	−	13470.8i	−0.168659	−	1.17305i	0.713001	−	0.701163i	$-0.247335\pi$
$510$		0			0
$511$	12350.1	+	3626.31i	1.06915	+	0.313931i
$512$		0			0
$513$	2300.12	−	2654.48i	0.197959	−	0.228457i
$514$		0			0
$515$	−35125.7	+	10313.8i	−3.00548	+	0.882490i
$516$		0			0
$517$	143.260	−	92.0674i	0.0121868	−	0.00783196i
$518$		0			0
$519$	−10560.1	−	12187.0i	−0.893132	−	1.03073i
$520$		0			0
$521$	2904.54	−	20201.5i	0.244242	−	1.69874i	−0.386127	−	0.922446i	$-0.626187\pi$
$521$	2904.54	−	20201.5i	0.244242	−	1.69874i	0.630369	−	0.776295i	$-0.282904\pi$
$522$		0			0
$523$	−317.755	+	695.787i	−0.0265669	+	0.0581733i	−0.922450	−	0.386116i	$-0.873816\pi$
$523$	−317.755	+	695.787i	−0.0265669	+	0.0581733i	0.895883	+	0.444289i	$0.146544\pi$
$524$		0			0
$525$	19778.6	+	43309.1i	1.64421	+	3.60031i
$526$		0			0
$527$	−17235.1	−	11076.3i	−1.42462	−	0.915546i
$528$		0			0
$529$	2748.99	+	11852.4i	0.225938	+	0.974142i
$530$		0			0
$531$	10091.5	+	6485.43i	0.824737	+	0.530026i
$532$		0			0
$533$	919.103	+	2012.56i	0.0746919	+	0.163552i
$534$		0			0
$535$	3601.24	−	7885.62i	0.291019	−	0.637243i
$536$		0			0
$537$	−960.295	+	6679.00i	−0.0771691	+	0.536723i
$538$		0			0
$539$	2212.65	+	2553.54i	0.176819	+	0.204060i
$540$		0			0
$541$	9247.66	−	5943.11i	0.734913	−	0.472300i	−0.118883	−	0.992908i	$-0.537931\pi$
$541$	9247.66	−	5943.11i	0.734913	−	0.472300i	0.853796	+	0.520608i	$0.174295\pi$
$542$		0			0
$543$	−12572.0	+	3691.46i	−0.993580	+	0.291742i
$544$		0			0
$545$	8505.33	−	9815.67i	0.668492	−	0.771481i
$546$		0			0
$547$	2473.75	+	726.358i	0.193364	+	0.0567767i	0.376980	−	0.926221i	$-0.376962\pi$
$547$	2473.75	+	726.358i	0.193364	+	0.0567767i	−0.183617	+	0.982998i	$0.558781\pi$
$548$		0			0
$549$	−143.254	−	996.355i	−0.0111365	−	0.0774561i
$550$		0			0
$551$	−1488.45			−0.115082
$552$		0			0
$553$	−31185.0			−2.39805
$554$		0			0
$555$	−6694.00	−	46557.8i	−0.511972	−	3.56084i
$556$		0			0
$557$	7336.74	+	2154.26i	0.558111	+	0.163876i	0.548609	−	0.836079i	$-0.315157\pi$
$557$	7336.74	+	2154.26i	0.558111	+	0.163876i	0.00950130	+	0.999955i	$0.496976\pi$
$558$		0			0
$559$	113.367	−	130.832i	0.00857762	−	0.00989911i
$560$		0			0
$561$	−1990.32	+	584.410i	−0.149788	+	0.0439818i
$562$		0			0
$563$	−14851.5	+	9544.51i	−1.11175	+	0.714481i	−0.961675	−	0.274192i	$-0.911589\pi$
$563$	−14851.5	+	9544.51i	−1.11175	+	0.714481i	−0.150080	+	0.988674i	$0.547953\pi$
$564$		0			0
$565$	−25850.4	−	29833.0i	−1.92484	−	2.22139i
$566$		0			0
$567$	−4423.21	+	30764.1i	−0.327614	+	2.27861i
$568$		0			0
$569$	−7675.59	+	16807.2i	−0.565514	+	1.23830i	0.383637	+	0.923484i	$0.374671\pi$
$569$	−7675.59	+	16807.2i	−0.565514	+	1.23830i	−0.949152	+	0.314819i	$0.898056\pi$
$570$		0			0
$571$	−4506.11	−	9867.01i	−0.330254	−	0.723155i	0.669554	−	0.742763i	$-0.266485\pi$
$571$	−4506.11	−	9867.01i	−0.330254	−	0.723155i	−0.999808	+	0.0196085i	$0.993758\pi$
$572$		0			0
$573$	−20927.4	−	13449.2i	−1.52575	−	0.980542i
$574$		0			0
$575$	7130.22	+	20942.8i	0.517131	+	1.51891i
$576$		0			0
$577$	15165.6	+	9746.36i	1.09420	+	0.703200i	0.957795	−	0.287453i	$-0.0928087\pi$
$577$	15165.6	+	9746.36i	1.09420	+	0.703200i	0.136405	+	0.990653i	$0.456445\pi$
$578$		0			0
$579$	−5455.11	−	11945.0i	−0.391549	−	0.857372i
$580$		0			0
$581$	−7568.16	+	16572.0i	−0.540413	+	1.18334i
$582$		0			0
$583$	31.7604	−	220.898i	0.00225623	−	0.0156924i
$584$		0			0
$585$	−1448.02	−	1671.10i	−0.102339	−	0.118105i
$586$		0			0
$587$	−9873.34	+	6345.21i	−0.694236	+	0.446158i	−0.839589	−	0.543221i	$-0.817204\pi$
$587$	−9873.34	+	6345.21i	−0.694236	+	0.446158i	0.145354	+	0.989380i	$0.453568\pi$
$588$		0			0
$589$	−15122.4	+	4440.33i	−1.05790	+	0.310629i
$590$		0			0
$591$	2876.65	−	3319.83i	0.200219	−	0.231065i
$592$		0			0
$593$	14094.7	+	4138.59i	0.976056	+	0.286596i	0.730596	−	0.682810i	$-0.239243\pi$
$593$	14094.7	+	4138.59i	0.976056	+	0.286596i	0.245461	+	0.969406i	$0.421061\pi$
$594$		0			0
$595$	7305.66	+	50812.0i	0.503366	+	3.50099i
$596$		0			0
$597$	−13341.3			−0.914612
$598$		0			0
$599$	14379.4			0.980844			0.490422	−	0.871485i	$-0.336843\pi$
$599$	14379.4			0.980844			0.490422	+	0.871485i	$0.336843\pi$
$600$		0			0
$601$	434.055	+	3018.92i	0.0294600	+	0.204899i	0.999235	−	0.0391010i	$-0.0124494\pi$
$601$	434.055	+	3018.92i	0.0294600	+	0.204899i	−0.969775	+	0.244000i	$0.921540\pi$
$602$		0			0
$603$	15482.0	+	4545.92i	1.04556	+	0.307005i
$604$		0			0
$605$	15557.2	−	17954.0i	1.04544	−	1.20650i
$606$		0			0
$607$	2886.71	−	847.615i	0.193028	−	0.0566781i	−0.183790	−	0.982966i	$-0.558837\pi$
$607$	2886.71	−	847.615i	0.193028	−	0.0566781i	0.376818	+	0.926287i	$0.377018\pi$
$608$		0			0
$609$	4771.38	−	3066.38i	0.317481	−	0.204033i
$610$		0			0
$611$	193.235	+	223.005i	0.0127945	+	0.0147657i
$612$		0			0
$613$	1761.88	−	12254.1i	0.116087	−	0.807405i	−0.845710	−	0.533643i	$-0.820823\pi$
$613$	1761.88	−	12254.1i	0.116087	−	0.807405i	0.961797	−	0.273763i	$-0.0882682\pi$
$614$		0			0
$615$	−17058.6	+	37353.1i	−1.11849	+	2.44914i
$616$		0			0
$617$	−5097.92	−	11162.9i	−0.332633	−	0.728364i	0.667231	−	0.744851i	$-0.267479\pi$
$617$	−5097.92	−	11162.9i	−0.332633	−	0.728364i	−0.999864	+	0.0164864i	$0.994752\pi$
$618$		0			0
$619$	−3940.59	−	2532.46i	−0.255873	−	0.164440i	0.406416	−	0.913688i	$-0.366778\pi$
$619$	−3940.59	−	2532.46i	−0.255873	−	0.164440i	−0.662289	+	0.749249i	$0.730415\pi$
$620$		0			0
$621$	−1496.67	+	6036.22i	−0.0967136	+	0.390057i
$622$		0			0
$623$	7749.46	+	4980.28i	0.498356	+	0.320274i
$624$		0			0
$625$	−194.812	−	426.579i	−0.0124680	−	0.0273010i
$626$		0			0
$627$	−662.908	+	1451.57i	−0.0422233	+	0.0924561i
$628$		0			0
$629$	4446.32	−	30924.8i	0.281854	−	1.96034i
$630$		0			0
$631$	−3230.92	−	3728.68i	−0.203837	−	0.235240i	0.644622	−	0.764501i	$-0.277015\pi$
$631$	−3230.92	−	3728.68i	−0.203837	−	0.235240i	−0.848459	+	0.529261i	$0.822469\pi$
$632$		0			0
$633$	−8374.45	+	5381.93i	−0.525836	+	0.337935i
$634$		0			0
$635$	43445.6	−	12756.8i	2.71510	−	0.797224i
$636$		0			0
$637$	−3834.01	+	4424.68i	−0.238475	+	0.275215i
$638$		0			0
$639$	−4847.90	−	1423.47i	−0.300125	−	0.0881247i
$640$		0			0
$641$	1446.16	+	10058.2i	0.0891104	+	0.619776i	0.984617	+	0.174728i	$0.0559045\pi$
$641$	1446.16	+	10058.2i	0.0891104	+	0.619776i	−0.895506	+	0.445049i	$0.853186\pi$
$642$		0			0
$643$	12736.3			0.781139			0.390570	−	0.920573i	$-0.372278\pi$
$643$	12736.3			0.781139			0.390570	+	0.920573i	$0.372278\pi$
$644$		0			0
$645$	3213.03			0.196144
$646$		0			0
$647$	−1120.28	−	7791.75i	−0.0680725	−	0.473455i	−0.995133	−	0.0985426i	$-0.968582\pi$
$647$	−1120.28	−	7791.75i	−0.0680725	−	0.473455i	0.927060	−	0.374912i	$-0.122327\pi$
$648$		0			0
$649$	2338.87	+	686.753i	0.141462	+	0.0415369i
$650$		0			0
$651$	39328.6	−	45387.7i	2.36776	−	2.73254i
$652$		0			0
$653$	21089.3	−	6192.37i	1.26384	−	0.371097i	0.419918	−	0.907562i	$-0.362059\pi$
$653$	21089.3	−	6192.37i	1.26384	−	0.371097i	0.843922	+	0.536465i	$0.180241\pi$
$654$		0			0
$655$	6027.57	−	3873.69i	0.359568	−	0.231080i
$656$		0			0
$657$	−4475.96	−	5165.53i	−0.265790	−	0.306738i
$658$		0			0
$659$	−1352.73	+	9408.42i	−0.0799617	+	0.556146i	0.909978	+	0.414656i	$0.136098\pi$
$659$	−1352.73	+	9408.42i	−0.0799617	+	0.556146i	−0.989940	+	0.141489i	$0.954811\pi$
$660$		0			0
$661$	17.1956	−	37.6532i	0.00101185	−	0.00221564i	−0.909125	−	0.416523i	$-0.863249\pi$
$661$	17.1956	−	37.6532i	0.00101185	−	0.00221564i	0.910137	+	0.414307i	$0.135976\pi$
$662$		0			0
$663$	−1493.15	−	3269.53i	−0.0874645	−	0.191520i
$664$		0			0
$665$	33222.1	+	21350.5i	1.93729	+	1.24502i
$666$		0			0
$667$	2348.54	−	1195.79i	0.136336	−	0.0694172i
$668$		0			0
$669$	−6056.87	−	3892.51i	−0.350033	−	0.224953i
$670$		0			0
$671$	−84.9714	−	186.061i	−0.00488865	−	0.0107047i
$672$		0			0
$673$	−2598.23	+	5689.33i	−0.148818	+	0.325866i	−0.969330	−	0.245764i	$-0.920961\pi$
$673$	−2598.23	+	5689.33i	−0.148818	+	0.325866i	0.820512	+	0.571629i	$0.193688\pi$
$674$		0			0
$675$	−1609.30	+	11192.9i	−0.0917659	+	0.638246i
$676$		0			0
$677$	8695.36	+	10035.0i	0.493633	+	0.569683i	0.946833	−	0.321726i	$-0.104263\pi$
$677$	8695.36	+	10035.0i	0.493633	+	0.569683i	−0.453200	+	0.891409i	$0.649717\pi$
$678$		0			0
$679$	38734.0	−	24892.8i	2.18921	−	1.40692i
$680$		0			0
$681$	−14704.3	+	4317.57i	−0.827414	+	0.242951i
$682$		0			0
$683$	15163.6	−	17499.7i	0.849515	−	0.980392i	−0.150451	−	0.988617i	$-0.548073\pi$
$683$	15163.6	−	17499.7i	0.849515	−	0.980392i	0.999966	+	0.00822516i	$0.00261818\pi$
$684$		0			0
$685$	15708.1	+	4612.30i	0.876167	+	0.257266i
$686$		0			0
$687$	3780.57	+	26294.4i	0.209953	+	1.46025i
$688$		0			0
$689$	386.701			0.0213819
$690$		0			0
$691$	−11372.4			−0.626085			−0.313043	−	0.949739i	$-0.601348\pi$
$691$	−11372.4			−0.626085			−0.313043	+	0.949739i	$0.601348\pi$
$692$		0			0
$693$	−353.608	−	2459.40i	−0.0193831	−	0.134812i
$694$		0			0
$695$	−48995.6	−	14386.4i	−2.67411	−	0.785190i
$696$		0			0
$697$	−17861.8	+	20613.6i	−0.970679	+	1.12022i
$698$		0			0
$699$	−28765.6	+	8446.33i	−1.55653	+	0.457038i
$700$		0			0
$701$	19074.9	−	12258.7i	1.02775	−	0.660492i	0.0858194	−	0.996311i	$-0.472649\pi$
$701$	19074.9	−	12258.7i	1.02775	−	0.660492i	0.941927	+	0.335818i	$0.109013\pi$
$702$		0			0
$703$	−15739.5	−	18164.3i	−0.844417	−	0.974509i
$704$		0			0
$705$	−779.410	+	5420.92i	−0.0416373	+	0.289594i
$706$		0			0
$707$	11501.0	−	25183.6i	0.611794	−	1.33964i
$708$		0			0
$709$	1637.37	+	3585.34i	0.0867316	+	0.189916i	0.948028	−	0.318187i	$-0.103074\pi$
$709$	1637.37	+	3585.34i	0.0867316	+	0.189916i	−0.861296	+	0.508103i	$0.830347\pi$
$710$		0			0
$711$	13931.0	+	8952.89i	0.734813	+	0.472236i
$712$		0			0
$713$	20293.4	−	19155.1i	1.06591	−	1.00612i
$714$		0			0
$715$	−377.994	−	242.922i	−0.0197709	−	0.0127060i
$716$		0			0
$717$	−2787.41	−	6103.57i	−0.145185	−	0.317911i
$718$		0			0
$719$	−7395.32	+	16193.5i	−0.383587	+	0.839938i	0.615087	+	0.788459i	$0.289121\pi$
$719$	−7395.32	+	16193.5i	−0.383587	+	0.839938i	−0.998674	+	0.0514791i	$0.983606\pi$
$720$		0			0
$721$	10144.3	−	70555.0i	0.523984	−	3.64439i
$722$		0			0
$723$	−19811.8	−	22864.1i	−1.01910	−	1.17610i
$724$		0			0
$725$	4031.31	−	2590.77i	0.206509	−	0.132715i
$726$		0			0
$727$	−5859.88	+	1720.62i	−0.298942	+	0.0877774i	−0.427764	−	0.903890i	$-0.640699\pi$
$727$	−5859.88	+	1720.62i	−0.298942	+	0.0877774i	0.128822	+	0.991668i	$0.458880\pi$
$728$		0			0
$729$	4072.17	−	4699.53i	0.206888	−	0.238761i
$730$		0			0
$731$	2047.72	+	601.266i	0.103608	+	0.0304222i
$732$		0			0
$733$	5169.48	+	35954.5i	0.260490	+	1.81175i	0.529169	+	0.848517i	$0.322504\pi$
$733$	5169.48	+	35954.5i	0.260490	+	1.81175i	−0.268679	+	0.963230i	$0.586587\pi$
$734$		0			0
$735$	−108663.			−5.45321
$736$		0			0
$737$	3278.83			0.163877
$738$		0			0
$739$	−1044.26	−	7263.00i	−0.0519807	−	0.361534i	−0.999165	−	0.0408456i	$-0.986995\pi$
$739$	−1044.26	−	7263.00i	−0.0519807	−	0.361534i	0.947185	−	0.320688i	$-0.103914\pi$
$740$		0			0
$741$	−2653.09	−	779.018i	−0.131530	−	0.0386207i
$742$		0			0
$743$	−4797.62	+	5536.75i	−0.236888	+	0.273383i	−0.861729	−	0.507369i	$-0.830618\pi$
$743$	−4797.62	+	5536.75i	−0.236888	+	0.273383i	0.624841	+	0.780752i	$0.285164\pi$
$744$		0			0
$745$	−15271.8	+	4484.22i	−0.751029	+	0.220522i
$746$		0			0
$747$	8138.49	−	5230.29i	0.398623	−	0.256180i
$748$		0			0
$749$	11053.7	+	12756.6i	0.539242	+	0.622318i
$750$		0			0
$751$	1441.99	−	10029.3i	0.0700653	−	0.487315i	−0.924330	−	0.381593i	$-0.875376\pi$
$751$	1441.99	−	10029.3i	0.0700653	−	0.487315i	0.994396	−	0.105722i	$-0.0337154\pi$
$752$		0			0
$753$	−5522.35	+	12092.3i	−0.267258	+	0.585214i
$754$		0			0
$755$	−10144.8	−	22214.1i	−0.489017	−	1.07080i
$756$		0			0
$757$	−1989.87	−	1278.81i	−0.0955391	−	0.0613992i	0.491999	−	0.870596i	$-0.336266\pi$
$757$	−1989.87	−	1278.81i	−0.0955391	−	0.0613992i	−0.587538	+	0.809197i	$0.699903\pi$
$758$		0			0
$759$	−120.196	−	2822.90i	−0.00574814	−	0.135000i
$760$		0			0
$761$	9485.02	+	6095.65i	0.451816	+	0.290364i	0.746691	−	0.665172i	$-0.231642\pi$
$761$	9485.02	+	6095.65i	0.451816	+	0.290364i	−0.294875	+	0.955536i	$0.595278\pi$
$762$		0			0
$763$	10505.4	+	23003.6i	0.498454	+	1.09146i
$764$		0			0
$765$	11324.0	−	24796.1i	0.535190	−	1.17190i
$766$		0			0
$767$	−601.109	+	4180.81i	−0.0282983	+	0.196819i
$768$		0			0
$769$	23998.1	+	27695.3i	1.12535	+	1.29872i	0.949311	+	0.314338i	$0.101782\pi$
$769$	23998.1	+	27695.3i	1.12535	+	1.29872i	0.176037	+	0.984384i	$0.443672\pi$
$770$		0			0
$771$	−12277.6	+	7890.34i	−0.573498	+	0.368565i
$772$		0			0
$773$	−30136.3	+	8848.80i	−1.40223	+	0.411733i	−0.893450	−	0.449162i	$-0.851722\pi$
$773$	−30136.3	+	8848.80i	−1.40223	+	0.411733i	−0.508783	+	0.860895i	$0.669904\pi$
$774$		0			0
$775$	33228.5	−	38347.8i	1.54013	−	1.77741i
$776$		0			0
$777$	87874.9	+	25802.4i	4.05726	+	1.19132i
$778$		0			0
$779$	2986.19	+	20769.4i	0.137344	+	0.955251i
$780$		0			0
$781$	−1026.70			−0.0470402
$782$		0			0
$783$	1347.07			0.0614820
$784$		0			0
$785$	3166.03	+	22020.2i	0.143950	+	1.00119i
$786$		0			0
$787$	17104.0	+	5022.18i	0.774703	+	0.227473i	0.645106	−	0.764093i	$-0.276813\pi$
$787$	17104.0	+	5022.18i	0.774703	+	0.227473i	0.129597	+	0.991567i	$0.458631\pi$
$788$		0			0
$789$	26409.2	−	30477.8i	1.19162	−	1.37521i
$790$		0			0
$791$	73747.6	−	21654.3i	3.31500	−	0.973371i
$792$		0			0
$793$	298.165	−	191.619i	0.0133520	−	0.00858083i
$794$		0			0
$795$	4700.06	+	5424.16i	0.209678	+	0.241981i
$796$		0			0
$797$	1804.16	−	12548.2i	0.0801841	−	0.557693i	−0.909640	−	0.415397i	$-0.863643\pi$
$797$	1804.16	−	12548.2i	0.0801841	−	0.557693i	0.989824	−	0.142296i	$-0.0454483\pi$
$798$		0			0
$799$	−1511.17	+	3309.00i	−0.0669102	+	0.146513i
$800$		0			0
$801$	−2032.06	−	4449.58i	−0.0896369	−	0.196277i
$802$		0			0
$803$	−1168.42	−	750.895i	−0.0513481	−	0.0329994i
$804$		0			0
$805$	−69571.7	−	6997.78i	−3.04606	−	0.306384i
$806$		0			0
$807$	−34926.3	−	22445.8i	−1.52350	−	0.979095i
$808$		0			0
$809$	2704.51	+	5922.05i	0.117535	+	0.257365i	0.959251	−	0.282555i	$-0.0911819\pi$
$809$	2704.51	+	5922.05i	0.117535	+	0.257365i	−0.841717	+	0.539920i	$0.818455\pi$
$810$		0			0
$811$	−3863.11	+	8459.02i	−0.167265	+	0.366260i	−0.974640	−	0.223780i	$-0.928160\pi$
$811$	−3863.11	+	8459.02i	−0.167265	+	0.366260i	0.807375	+	0.590039i	$0.200888\pi$
$812$		0			0
$813$	−696.710	+	4845.73i	−0.0300550	+	0.209037i
$814$		0			0
$815$	384.785	+	444.065i	0.0165379	+	0.0190858i
$816$		0			0
$817$	1381.17	−	887.624i	0.0591445	−	0.0380098i
$818$		0			0
$819$	4130.98	−	1212.97i	0.176249	−	0.0517515i
$820$		0			0
$821$	28083.4	−	32409.9i	1.19381	−	1.37773i	0.286059	−	0.958212i	$-0.407655\pi$
$821$	28083.4	−	32409.9i	1.19381	−	1.37773i	0.907748	−	0.419515i	$-0.137800\pi$
$822$		0			0
$823$	−25657.5	−	7533.73i	−1.08671	−	0.319088i	−0.311152	−	0.950360i	$-0.600715\pi$
$823$	−25657.5	−	7533.73i	−1.08671	−	0.319088i	−0.775561	+	0.631272i	$0.782533\pi$
$824$		0			0
$825$	−731.149	−	5085.25i	−0.0308549	−	0.214601i
$826$		0			0
$827$	−37323.6			−1.56937			−0.784685	−	0.619894i	$-0.787176\pi$
$827$	−37323.6			−1.56937			−0.784685	+	0.619894i	$0.787176\pi$
$828$		0			0
$829$	17948.3			0.751953			0.375976	−	0.926629i	$-0.377307\pi$
$829$	17948.3			0.751953			0.375976	+	0.926629i	$0.377307\pi$
$830$		0			0
$831$	3762.13	+	26166.2i	0.157048	+	1.09229i
$832$		0			0
$833$	−69253.1	−	20334.6i	−2.88053	−	0.845799i
$834$		0			0
$835$	−40153.0	+	46339.1i	−1.66414	+	1.92052i
$836$		0			0
$837$	13686.0	−	4018.56i	0.565180	−	0.165952i
$838$		0			0
$839$	22665.9	−	14566.5i	0.932675	−	0.599394i	0.0163661	−	0.999866i	$-0.494790\pi$
$839$	22665.9	−	14566.5i	0.932675	−	0.599394i	0.916309	+	0.400472i	$0.131154\pi$
$840$		0			0
$841$	15597.6	+	18000.6i	0.639533	+	0.738060i
$842$		0			0
$843$	−3755.79	+	26122.1i	−0.153448	+	1.06725i
$844$		0			0
$845$	−16144.2	+	35350.9i	−0.657253	+	1.43918i
$846$		0			0
$847$	19215.5	+	42076.2i	0.779520	+	1.70691i
$848$		0			0
$849$	33115.5	+	21282.0i	1.33866	+	0.860302i
$850$		0			0
$851$	39427.2	+	16015.6i	1.58819	+	0.645132i
$852$		0			0
$853$	−27775.5	−	17850.2i	−1.11491	−	0.716507i	−0.152550	−	0.988296i	$-0.548749\pi$
$853$	−27775.5	−	17850.2i	−1.11491	−	0.716507i	−0.962357	+	0.271789i	$0.912385\pi$
$854$		0			0
$855$	−8711.46	−	19075.4i	−0.348451	−	0.763002i
$856$		0			0
$857$	−236.239	+	517.292i	−0.00941631	+	0.0206188i	−0.914282	−	0.405079i	$-0.867244\pi$
$857$	−236.239	+	517.292i	−0.00941631	+	0.0206188i	0.904865	+	0.425698i	$0.139971\pi$
$858$		0			0
$859$	−3350.23	+	23301.3i	−0.133071	+	0.925531i	0.808447	+	0.588569i	$0.200309\pi$
$859$	−3350.23	+	23301.3i	−0.133071	+	0.925531i	−0.941518	+	0.336962i	$0.890601\pi$
$860$		0			0
$861$	−52359.8	−	60426.4i	−2.07249	−	2.39178i
$862$		0			0
$863$	−20009.9	+	12859.6i	−0.789277	+	0.507237i	−0.872100	−	0.489327i	$-0.837242\pi$
$863$	−20009.9	+	12859.6i	−0.789277	+	0.507237i	0.0828238	+	0.996564i	$0.473606\pi$
$864$		0			0
$865$	41317.2	−	12131.8i	1.62408	−	0.476872i
$866$		0			0
$867$	7278.45	−	8399.78i	0.285108	−	0.329033i
$868$		0			0
$869$	3228.71	+	948.036i	0.126038	+	0.0370080i
$870$		0			0
$871$	808.552	+	5623.60i	0.0314544	+	0.218770i
$872$		0			0
$873$	−24449.7			−0.947879
$874$		0			0
$875$	−47902.1			−1.85073
$876$		0			0
$877$	−1191.57	−	8287.53i	−0.0458796	−	0.319099i	−0.999818	−	0.0190959i	$-0.993921\pi$
$877$	−1191.57	−	8287.53i	−0.0458796	−	0.319099i	0.953938	−	0.300004i	$-0.0969879\pi$
$878$		0			0
$879$	64863.0	+	19045.5i	2.48894	+	0.730817i
$880$		0			0
$881$	−4576.92	+	5282.05i	−0.175029	+	0.201994i	−0.836485	−	0.547990i	$-0.815393\pi$
$881$	−4576.92	+	5282.05i	−0.175029	+	0.201994i	0.661456	+	0.749984i	$0.269939\pi$
$882$		0			0
$883$	−12896.6	+	3786.78i	−0.491512	+	0.144321i	−0.518090	−	0.855326i	$-0.673357\pi$
$883$	−12896.6	+	3786.78i	−0.491512	+	0.144321i	0.0265787	+	0.999647i	$0.491539\pi$
$884$		0			0
$885$	−65949.2	+	42383.0i	−2.50492	+	1.60982i
$886$		0			0
$887$	−6001.96	−	6926.63i	−0.227200	−	0.262203i	0.630692	−	0.776034i	$-0.282771\pi$
$887$	−6001.96	−	6926.63i	−0.227200	−	0.262203i	−0.857891	+	0.513831i	$0.828226\pi$
$888$		0			0
$889$	−12547.1	+	87266.7i	−0.473357	+	3.29227i
$890$		0			0
$891$	1393.19	−	3050.67i	0.0523835	−	0.114704i
$892$		0			0
$893$	1162.53	+	2545.58i	0.0435639	+	0.0953915i
$894$		0			0
$895$	−15158.4	−	9741.70i	−0.566133	−	0.363831i
$896$		0			0
$897$	4812.00	−	902.274i	0.179117	−	0.0335854i
$898$		0			0
$899$	−5085.03	−	3267.95i	−0.188649	−	0.121237i
$900$		0			0
$901$	1980.39	+	4336.46i	0.0732258	+	0.160342i
$902$		0			0
$903$	−2598.87	+	5690.73i	−0.0957752	+	0.209718i
$904$		0			0
$905$	4979.46	−	34632.9i	0.182898	−	1.27209i
$906$		0			0
$907$	1691.13	+	1951.67i	0.0619109	+	0.0714490i	0.785860	−	0.618404i	$-0.212221\pi$
$907$	1691.13	+	1951.67i	0.0619109	+	0.0714490i	−0.723949	+	0.689853i	$0.757675\pi$
$908$		0			0
$909$	−12367.7	+	7948.22i	−0.451276	+	0.290017i
$910$		0			0
$911$	48713.5	−	14303.6i	1.77163	−	0.520196i	0.777544	−	0.628829i	$-0.216465\pi$
$911$	48713.5	−	14303.6i	1.77163	−	0.520196i	0.994082	+	0.108633i	$0.0346472\pi$
$912$		0			0
$913$	1287.36	−	1485.69i	0.0466652	−	0.0538545i
$914$		0			0
$915$	6311.77	+	1853.30i	0.228045	+	0.0669599i
$916$		0			0
$917$	1985.42	+	13808.9i	0.0714989	+	0.497286i
$918$		0			0
$919$	−42333.9			−1.51955			−0.759776	−	0.650185i	$-0.774691\pi$
$919$	−42333.9			−1.51955			−0.759776	+	0.650185i	$0.774691\pi$
$920$		0			0
$921$	−4193.67			−0.150039
$922$		0			0
$923$	−253.183	−	1760.93i	−0.00902886	−	0.0627971i
$924$		0			0
$925$	74245.0	+	21800.3i	2.63909	+	0.774907i
$926$		0			0
$927$	−24787.3	+	28606.0i	−0.878232	+	1.01353i
$928$		0			0
$929$	−30922.4	+	9079.63i	−1.09207	+	0.320660i	−0.777696	−	0.628640i	$-0.783612\pi$
$929$	−30922.4	+	9079.63i	−1.09207	+	0.320660i	−0.314371	+	0.949300i	$0.601794\pi$
$930$		0			0
$931$	−46710.6	+	30019.1i	−1.64434	+	1.05675i
$932$		0			0
$933$	6119.32	+	7062.07i	0.214724	+	0.247805i
$934$		0			0
$935$	788.319	−	5482.88i	0.0275730	−	0.191775i
$936$		0			0
$937$	3215.99	−	7042.03i	0.112126	−	0.245521i	−0.845247	−	0.534375i	$-0.820547\pi$
$937$	3215.99	−	7042.03i	0.112126	−	0.245521i	0.957373	+	0.288854i	$0.0932743\pi$
$938$		0			0
$939$	−8196.19	−	17947.2i	−0.284848	−	0.623731i
$940$		0			0
$941$	−11927.8	−	7665.53i	−0.413215	−	0.265557i	0.317475	−	0.948267i	$-0.397165\pi$
$941$	−11927.8	−	7665.53i	−0.413215	−	0.265557i	−0.730690	+	0.682710i	$0.760801\pi$
$942$		0			0
$943$	−21397.4	−	30371.7i	−0.738914	−	1.04882i
$944$		0			0
$945$	−30066.5	−	19322.5i	−1.03499	−	0.665146i
$946$		0			0
$947$	−13659.2	−	29909.4i	−0.468705	−	1.02632i	−0.985416	−	0.170161i	$-0.945571\pi$
$947$	−13659.2	−	29909.4i	−0.468705	−	1.02632i	0.516711	−	0.856160i	$-0.327156\pi$
$948$		0			0
$949$	999.752	−	2189.15i	0.0341974	−	0.0748818i
$950$		0			0
$951$	−3840.01	+	26707.8i	−0.130937	+	0.910684i
$952$		0			0
$953$	3894.82	+	4494.86i	0.132388	+	0.152784i	0.818073	−	0.575115i	$-0.195043\pi$
$953$	3894.82	+	4494.86i	0.132388	+	0.152784i	−0.685685	+	0.727898i	$0.740497\pi$
$954$		0			0
$955$	55884.0	−	35914.5i	1.89357	−	1.21693i
$956$		0			0
$957$	−587.220	+	172.423i	−0.0198350	+	0.00582410i
$958$		0			0
$959$	−20874.6	+	24090.5i	−0.702893	+	0.811182i
$960$		0			0
$961$	−32827.4	−	9638.99i	−1.10192	−	0.323554i
$962$		0			0
$963$	−1275.61	−	8872.03i	−0.0426852	−	0.296882i
$964$		0			0
$965$	35066.5			1.16977
$966$		0			0
$967$	32809.8			1.09110			0.545549	−	0.838079i	$-0.316321\pi$
$967$	32809.8			1.09110			0.545549	+	0.838079i	$0.316321\pi$
$968$		0			0
$969$	−4851.26	−	33741.3i	−0.160831	−	1.11860i
$970$		0			0
$971$	11970.9	+	3514.97i	0.395638	+	0.116170i	0.473499	−	0.880795i	$-0.342991\pi$
$971$	11970.9	+	3514.97i	0.395638	+	0.116170i	−0.0778610	+	0.996964i	$0.524809\pi$
$972$		0			0
$973$	65110.6	−	75141.6i	2.14527	−	2.47577i
$974$		0			0
$975$	8541.55	−	2508.03i	0.280563	−	0.0823806i
$976$		0			0
$977$	5163.70	−	3318.51i	0.169091	−	0.108668i	−0.453358	−	0.891328i	$-0.649774\pi$
$977$	5163.70	−	3318.51i	0.169091	−	0.108668i	0.622449	+	0.782660i	$0.286138\pi$
$978$		0			0
$979$	−650.932	−	751.216i	−0.0212501	−	0.0245240i
$980$		0			0
$981$	1911.12	−	13292.1i	0.0621992	−	0.432605i
$982$		0			0
$983$	1712.03	−	3748.83i	0.0555498	−	0.121637i	−0.879822	−	0.475304i	$-0.842338\pi$
$983$	1712.03	−	3748.83i	0.0555498	−	0.121637i	0.935371	+	0.353667i	$0.115065\pi$
$984$		0			0
$985$	4872.94	+	10670.3i	0.157629	+	0.345160i
$986$		0			0
$987$	−8970.78	−	5765.17i	−0.289304	−	0.185924i
$988$		0			0
$989$	−1466.17	+	2510.13i	−0.0471399	+	0.0807053i
$990$		0			0
$991$	−8397.18	−	5396.54i	−0.269168	−	0.172984i	0.399094	−	0.916910i	$-0.369325\pi$
$991$	−8397.18	−	5396.54i	−0.269168	−	0.172984i	−0.668261	+	0.743927i	$0.732961\pi$
$992$		0			0
$993$	1282.81	+	2808.95i	0.0409956	+	0.0897678i
$994$		0			0
$995$	14799.7	−	32406.7i	0.471539	−	1.03253i
$996$		0			0
$997$	−1418.16	+	9863.51i	−0.0450487	+	0.313320i	0.954821	+	0.297181i	$0.0960466\pi$
$997$	−1418.16	+	9863.51i	−0.0450487	+	0.313320i	−0.999870	+	0.0161391i	$0.994863\pi$
$998$		0			0
$999$	14244.4	+	16439.0i	0.451125	+	0.520626i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	184.4.i.a.25.8	✓	90
23.12	even	11	inner	184.4.i.a.81.8	yes	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.4.i.a.25.8	✓	90	1.1	even	1	trivial
184.4.i.a.81.8	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)

\(f(q)\)	\(=\)	\(q+(0.961609 + 6.68814i) q^{3} +(-17.3126 - 5.08343i) q^{5} +(23.0068 - 26.5513i) q^{7} +(-17.9002 + 5.25597i) q^{9} +(-3.18916 + 2.04955i) q^{11} +(-4.30168 - 4.96440i) q^{13} +(17.3508 - 120.677i) q^{15} +(33.6407 - 73.6628i) q^{17} +(-25.8795 - 56.6682i) q^{19} +(199.702 + 128.341i) q^{21} +(86.3597 + 68.6222i) q^{23} +(168.727 + 108.434i) q^{25} +(23.4213 + 51.2855i) q^{27} +(9.92531 - 21.7334i) q^{29} +(36.0043 - 250.416i) q^{31} +(-16.7744 - 19.3587i) q^{33} +(-533.278 + 342.717i) q^{35} +(370.177 - 108.694i) q^{37} +(29.0661 - 33.5440i) q^{39} +(-323.173 - 94.8922i) q^{41} +(3.75057 + 26.0858i) q^{43} +336.617 q^{45} -44.9208 q^{47} +(-126.843 - 882.210i) q^{49} +(525.016 + 154.159i) q^{51} +(-38.5510 + 44.4902i) q^{53} +(65.6313 - 19.2711i) q^{55} +(354.119 - 227.578i) q^{57} +(-421.079 - 485.951i) q^{59} +(-7.67877 + 53.4070i) q^{61} +(-272.273 + 596.195i) q^{63} +(49.2369 + 107.814i) q^{65} +(-727.606 - 467.604i) q^{67} +(-375.910 + 643.573i) q^{69} +(227.836 + 146.422i) q^{71} +(152.196 + 333.263i) q^{73} +(-562.974 + 1232.74i) q^{75} +(-18.9542 + 131.830i) q^{77} +(-581.283 - 670.836i) q^{79} +(-744.229 + 478.287i) q^{81} +(-497.557 + 146.096i) q^{83} +(-956.866 + 1104.28i) q^{85} +(154.900 + 45.4828i) q^{87} +(37.3154 + 259.534i) q^{89} -230.779 q^{91} +1709.44 q^{93} +(159.972 + 1112.63i) q^{95} +(1257.48 + 369.229i) q^{97} +(46.3142 - 53.4494i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 2 q^{3} - 87 q^{7} - 113 q^{9} - 6 q^{11} - 8 q^{13} - 6 q^{15} + 306 q^{17} + 275 q^{19} + 350 q^{21} - 23 q^{23} - 289 q^{25} + 511 q^{27} + 309 q^{29} - 314 q^{31} - 1444 q^{33} - 1895 q^{35}+ \cdots + 5967 q^{99}+O(q^{100}) \) 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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