LMFDB - Embedded newform 184.4.i.a.9.6

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			9.6
Character	$\chi$	$=$	184.9
Dual form			184.4.i.a.41.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.658159 + 0.759556i) q^{3} +(-1.68723 - 11.7349i) q^{5} +(-15.1088 + 33.0837i) q^{7} +(3.69875 - 25.7254i) q^{9} +(68.8010 + 20.2018i) q^{11} +(8.11313 + 17.7653i) q^{13} +(7.80288 - 9.00501i) q^{15} +(59.0342 + 37.9390i) q^{17} +(54.4857 - 35.0158i) q^{19} +(-35.0729 + 10.2983i) q^{21} +(25.1929 - 107.389i) q^{23} +(-14.9255 + 4.38253i) q^{25} +(44.8025 - 28.7928i) q^{27} +(115.270 + 74.0793i) q^{29} +(-127.201 + 146.798i) q^{31} +(29.9376 + 65.5543i) q^{33} +(413.727 + 121.481i) q^{35} +(-14.5321 + 101.073i) q^{37} +(-8.15400 + 17.8548i) q^{39} +(17.3882 + 120.938i) q^{41} +(207.528 + 239.500i) q^{43} -308.126 q^{45} +367.725 q^{47} +(-641.637 - 740.488i) q^{49} +(10.0371 + 69.8096i) q^{51} +(-22.1707 + 48.5472i) q^{53} +(120.984 - 841.461i) q^{55} +(62.4567 + 18.3389i) q^{57} +(-193.862 - 424.498i) q^{59} +(89.7639 - 103.593i) q^{61} +(795.206 + 511.048i) q^{63} +(194.786 - 125.181i) q^{65} +(-804.280 + 236.158i) q^{67} +(98.1487 - 51.5433i) q^{69} +(-877.383 + 257.623i) q^{71} +(176.420 - 113.378i) q^{73} +(-13.1521 - 8.45237i) q^{75} +(-1707.85 + 1970.97i) q^{77} +(115.785 + 253.534i) q^{79} +(-621.946 - 182.620i) q^{81} +(10.6358 - 73.9737i) q^{83} +(345.607 - 756.775i) q^{85} +(19.5984 + 136.310i) q^{87} +(-247.380 - 285.492i) q^{89} -710.321 q^{91} -195.220 q^{93} +(-502.838 - 580.307i) q^{95} +(-64.5225 - 448.764i) q^{97} +(774.176 - 1695.21i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/184\mathbb{Z}\right)^\times$.

$n$	$47$	$93$	$97$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{11}\right)$

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
$3$	0.658159	+	0.759556i	0.126663	+	0.146177i	0.815538	−	0.578703i	$-0.196441\pi$
$3$	0.658159	+	0.759556i	0.126663	+	0.146177i	−0.688876	+	0.724879i	$0.741895\pi$
$4$		0			0
$5$	−1.68723	−	11.7349i	−0.150910	−	1.04961i	−0.914698	−	0.404138i	$-0.867572\pi$
$5$	−1.68723	−	11.7349i	−0.150910	−	1.04961i	0.763788	−	0.645468i	$-0.223337\pi$
$6$		0			0
$7$	−15.1088	+	33.0837i	−0.815799	+	1.78635i	−0.235656	+	0.971837i	$0.575724\pi$
$7$	−15.1088	+	33.0837i	−0.815799	+	1.78635i	−0.580144	+	0.814514i	$0.697004\pi$
$8$		0			0
$9$	3.69875	−	25.7254i	0.136991	−	0.952791i
$10$		0			0
$11$	68.8010	+	20.2018i	1.88584	+	0.553734i	0.995056	+	0.0993166i	$0.0316656\pi$
$11$	68.8010	+	20.2018i	1.88584	+	0.553734i	0.890789	+	0.454417i	$0.150153\pi$
$12$		0			0
$13$	8.11313	+	17.7653i	0.173091	+	0.379016i	0.976218	−	0.216792i	$-0.0695594\pi$
$13$	8.11313	+	17.7653i	0.173091	+	0.379016i	−0.803127	+	0.595808i	$0.796832\pi$
$14$		0			0
$15$	7.80288	−	9.00501i	0.134313	−	0.155006i
$16$		0			0
$17$	59.0342	+	37.9390i	0.842229	+	0.541268i	0.889142	−	0.457631i	$-0.151302\pi$
$17$	59.0342	+	37.9390i	0.842229	+	0.541268i	−0.0469131	+	0.998899i	$0.514938\pi$
$18$		0			0
$19$	54.4857	−	35.0158i	0.657888	−	0.422799i	−0.168653	−	0.985675i	$-0.553942\pi$
$19$	54.4857	−	35.0158i	0.657888	−	0.422799i	0.826541	+	0.562877i	$0.190305\pi$
$20$		0			0
$21$	−35.0729	+	10.2983i	−0.364454	+	0.107013i
$22$		0			0
$23$	25.1929	−	107.389i	0.228395	−	0.973568i
$23$	25.1929	−	107.389i	0.228395	−	0.973568i
$24$		0			0
$25$	−14.9255	+	4.38253i	−0.119404	+	0.0350602i
$26$		0			0
$27$	44.8025	−	28.7928i	0.319342	−	0.205229i
$28$		0			0
$29$	115.270	+	74.0793i	0.738105	+	0.474351i	0.854892	−	0.518806i	$-0.173623\pi$
$29$	115.270	+	74.0793i	0.738105	+	0.474351i	−0.116787	+	0.993157i	$0.537260\pi$
$30$		0			0
$31$	−127.201	+	146.798i	−0.736969	+	0.850508i	−0.993238	−	0.116098i	$-0.962961\pi$
$31$	−127.201	+	146.798i	−0.736969	+	0.850508i	0.256269	+	0.966606i	$0.417507\pi$
$32$		0			0
$33$	29.9376	+	65.5543i	0.157923	+	0.345804i
$34$		0			0
$35$	413.727	+	121.481i	1.99808	+	0.586688i
$36$		0			0
$37$	−14.5321	+	101.073i	−0.0645693	+	0.449089i	0.931731	+	0.363149i	$0.118298\pi$
$37$	−14.5321	+	101.073i	−0.0645693	+	0.449089i	−0.996300	+	0.0859400i	$0.972611\pi$
$38$		0			0
$39$	−8.15400	+	17.8548i	−0.0334791	+	0.0733090i
$40$		0			0
$41$	17.3882	+	120.938i	0.0662339	+	0.460667i	0.995766	+	0.0919253i	$0.0293021\pi$
$41$	17.3882	+	120.938i	0.0662339	+	0.460667i	−0.929532	+	0.368741i	$0.879789\pi$
$42$		0			0
$43$	207.528	+	239.500i	0.735993	+	0.849381i	0.993133	−	0.116993i	$-0.0373256\pi$
$43$	207.528	+	239.500i	0.735993	+	0.849381i	−0.257140	+	0.966374i	$0.582780\pi$
$44$		0			0
$45$	−308.126			−1.02073
$46$		0			0
$47$	367.725			1.14124			0.570619	−	0.821215i	$-0.306703\pi$
$47$	367.725			1.14124			0.570619	+	0.821215i	$0.306703\pi$
$48$		0			0
$49$	−641.637	−	740.488i	−1.87066	−	2.15886i
$50$		0			0
$51$	10.0371	+	69.8096i	0.0275584	+	0.191673i
$52$		0			0
$53$	−22.1707	+	48.5472i	−0.0574601	+	0.125820i	−0.936184	−	0.351510i	$-0.885668\pi$
$53$	−22.1707	+	48.5472i	−0.0574601	+	0.125820i	0.878724	+	0.477330i	$0.158395\pi$
$54$		0			0
$55$	120.984	−	841.461i	0.296608	−	2.06296i
$56$		0			0
$57$	62.4567	+	18.3389i	0.145133	+	0.0426150i
$58$		0			0
$59$	−193.862	−	424.498i	−0.427774	−	0.936694i	−0.993683	−	0.112226i	$-0.964202\pi$
$59$	−193.862	−	424.498i	−0.427774	−	0.936694i	0.565909	−	0.824468i	$-0.308525\pi$
$60$		0			0
$61$	89.7639	−	103.593i	0.188411	−	0.217438i	−0.653683	−	0.756768i	$-0.726777\pi$
$61$	89.7639	−	103.593i	0.188411	−	0.217438i	0.842094	+	0.539330i	$0.181323\pi$
$62$		0			0
$63$	795.206	+	511.048i	1.59026	+	1.02200i
$64$		0			0
$65$	194.786	−	125.181i	0.371696	−	0.238874i
$66$		0			0
$67$	−804.280	+	236.158i	−1.46654	+	0.430616i	−0.914974	−	0.403513i	$-0.867789\pi$
$67$	−804.280	+	236.158i	−1.46654	+	0.430616i	−0.551570	+	0.834129i	$0.685971\pi$
$68$		0			0
$69$	98.1487	−	51.5433i	0.171242	−	0.0899288i
$70$		0			0
$71$	−877.383	+	257.623i	−1.46657	+	0.430623i	−0.914981	−	0.403497i	$-0.867795\pi$
$71$	−877.383	+	257.623i	−1.46657	+	0.430623i	−0.551584	+	0.834119i	$0.685977\pi$
$72$		0			0
$73$	176.420	−	113.378i	0.282854	−	0.181779i	−0.391519	−	0.920170i	$-0.628050\pi$
$73$	176.420	−	113.378i	0.282854	−	0.181779i	0.674373	+	0.738391i	$0.264414\pi$
$74$		0			0
$75$	−13.1521	−	8.45237i	−0.0202491	−	0.0130133i
$76$		0			0
$77$	−1707.85	+	1970.97i	−2.52763	+	2.91704i
$78$		0			0
$79$	115.785	+	253.534i	0.164897	+	0.361073i	0.973985	−	0.226614i	$-0.0727657\pi$
$79$	115.785	+	253.534i	0.164897	+	0.361073i	−0.809088	+	0.587688i	$0.800038\pi$
$80$		0			0
$81$	−621.946	−	182.620i	−0.853149	−	0.250507i
$82$		0			0
$83$	10.6358	−	73.9737i	0.0140654	−	0.0978273i	−0.981579	−	0.191055i	$-0.938809\pi$
$83$	10.6358	−	73.9737i	0.0140654	−	0.0978273i	0.995645	+	0.0932273i	$0.0297183\pi$
$84$		0			0
$85$	345.607	−	756.775i	0.441016	−	0.965691i
$86$		0			0
$87$	19.5984	+	136.310i	0.0241514	+	0.167976i
$88$		0			0
$89$	−247.380	−	285.492i	−0.294632	−	0.340024i	0.589062	−	0.808088i	$-0.299497\pi$
$89$	−247.380	−	285.492i	−0.294632	−	0.340024i	−0.883695	+	0.468064i	$0.844952\pi$
$90$		0			0
$91$	−710.321			−0.818262
$92$		0			0
$93$	−195.220			−0.217671
$94$		0			0
$95$	−502.838	−	580.307i	−0.543054	−	0.626718i
$96$		0			0
$97$	−64.5225	−	448.764i	−0.0675388	−	0.469743i	−0.995321	−	0.0966212i	$-0.969196\pi$
$97$	−64.5225	−	448.764i	−0.0675388	−	0.469743i	0.927782	−	0.373122i	$-0.121713\pi$
$98$		0			0
$99$	774.176	−	1695.21i	0.785936	−	1.72096i
$100$		0			0
$101$	147.146	−	1023.42i	0.144966	−	1.00826i	−0.779339	−	0.626603i	$-0.784445\pi$
$101$	147.146	−	1023.42i	0.144966	−	1.00826i	0.924304	−	0.381656i	$-0.124646\pi$
$102$		0			0
$103$	1639.53	+	481.410i	1.56843	+	0.460531i	0.946543	−	0.322579i	$-0.104550\pi$
$103$	1639.53	+	481.410i	1.56843	+	0.460531i	0.621883	+	0.783110i	$0.286368\pi$
$104$		0			0
$105$	180.026	+	394.203i	0.167322	+	0.366384i
$106$		0			0
$107$	368.269	−	425.005i	0.332728	−	0.383989i	−0.564591	−	0.825371i	$-0.690966\pi$
$107$	368.269	−	425.005i	0.332728	−	0.383989i	0.897319	+	0.441382i	$0.145512\pi$
$108$		0			0
$109$	−1227.67	−	788.973i	−1.07880	−	0.693302i	−0.124519	−	0.992217i	$-0.539739\pi$
$109$	−1227.67	−	788.973i	−1.07880	−	0.693302i	−0.954280	+	0.298915i	$0.903375\pi$
$110$		0			0
$111$	−86.3350	+	55.4842i	−0.0738249	+	0.0474444i
$112$		0			0
$113$	−475.381	+	139.584i	−0.395753	+	0.116203i	−0.473553	−	0.880765i	$-0.657029\pi$
$113$	−475.381	+	139.584i	−0.395753	+	0.116203i	0.0777999	+	0.996969i	$0.475210\pi$
$114$		0			0
$115$	−1302.71	−	114.448i	−1.05633	−	0.0928032i
$116$		0			0
$117$	487.027	−	143.004i	0.384834	−	0.112998i
$118$		0			0
$119$	−2147.10	+	1379.86i	−1.65398	+	1.06295i
$120$		0			0
$121$	3205.76	+	2060.22i	2.40854	+	1.54787i
$122$		0			0
$123$	−80.4149	+	92.8037i	−0.0589493	+	0.0680312i
$124$		0			0
$125$	−539.014	−	1180.28i	−0.385687	−	0.844536i
$126$		0			0
$127$	1355.19	+	397.919i	0.946878	+	0.278029i	0.718487	−	0.695541i	$-0.244835\pi$
$127$	1355.19	+	397.919i	0.946878	+	0.278029i	0.228392	+	0.973569i	$0.426653\pi$
$128$		0			0
$129$	−45.3273	+	315.258i	−0.0309368	+	0.215170i
$130$		0			0
$131$	−531.051	+	1162.84i	−0.354184	+	0.775555i	0.645744	+	0.763554i	$0.276547\pi$
$131$	−531.051	+	1162.84i	−0.354184	+	0.775555i	−0.999928	+	0.0120010i	$0.996180\pi$
$132$		0			0
$133$	335.238	+	2331.63i	0.218563	+	1.52014i
$134$		0			0
$135$	−413.474	−	477.174i	−0.263601	−	0.304212i
$136$		0			0
$137$	1644.88			1.02578			0.512890	−	0.858454i	$-0.328575\pi$
$137$	1644.88			1.02578			0.512890	+	0.858454i	$0.328575\pi$
$138$		0			0
$139$	195.877			0.119525			0.0597627	−	0.998213i	$-0.480966\pi$
$139$	195.877			0.119525			0.0597627	+	0.998213i	$0.480966\pi$
$140$		0			0
$141$	242.021	+	279.308i	0.144552	+	0.166822i
$142$		0			0
$143$	199.301	+	1386.17i	0.116548	+	0.810611i
$144$		0			0
$145$	674.830	−	1477.67i	0.386494	−	0.846303i
$146$		0			0
$147$	140.143	−	974.718i	0.0786315	−	0.546894i
$148$		0			0
$149$	140.702	+	41.3137i	0.0773606	+	0.0227151i	0.320184	−	0.947355i	$-0.396255\pi$
$149$	140.702	+	41.3137i	0.0773606	+	0.0227151i	−0.242823	+	0.970071i	$0.578074\pi$
$150$		0			0
$151$	−634.731	−	1389.87i	−0.342077	−	0.749044i	0.657915	−	0.753092i	$-0.271439\pi$
$151$	−634.731	−	1389.87i	−0.342077	−	0.749044i	−0.999992	+	0.00404809i	$0.998711\pi$
$152$		0			0
$153$	1194.35	−	1378.35i	0.631093	−	0.728320i
$154$		0			0
$155$	1937.29	+	1245.02i	1.00391	+	0.645176i
$156$		0			0
$157$	−196.367	+	126.197i	−0.0998202	+	0.0641505i	−0.589599	−	0.807696i	$-0.700714\pi$
$157$	−196.367	+	126.197i	−0.0998202	+	0.0641505i	0.489778	+	0.871847i	$0.337078\pi$
$158$		0			0
$159$	−51.4662	+	15.1118i	−0.0256700	+	0.00753740i
$160$		0			0
$161$	3172.18	+	2455.99i	1.55281	+	1.20223i
$162$		0			0
$163$	517.617	−	151.986i	0.248730	−	0.0730336i	−0.154991	−	0.987916i	$-0.549535\pi$
$163$	517.617	−	151.986i	0.248730	−	0.0730336i	0.403721	+	0.914882i	$0.367717\pi$
$164$		0			0
$165$	718.764	−	461.921i	0.339125	−	0.217943i
$166$		0			0
$167$	−2895.65	−	1860.92i	−1.34175	−	0.862290i	−0.344675	−	0.938722i	$-0.612011\pi$
$167$	−2895.65	−	1860.92i	−1.34175	−	0.862290i	−0.997075	+	0.0764321i	$0.975647\pi$
$168$		0			0
$169$	1188.95	−	1372.12i	0.541168	−	0.624541i
$170$		0			0
$171$	−699.266	−	1531.18i	−0.312715	−	0.684749i
$172$		0			0
$173$	−2999.71	−	880.795i	−1.31829	−	0.387084i	−0.454413	−	0.890791i	$-0.650151\pi$
$173$	−2999.71	−	880.795i	−1.31829	−	0.387084i	−0.863875	+	0.503707i	$0.831969\pi$
$174$		0			0
$175$	80.5167	−	560.006i	0.0347800	−	0.241900i
$176$		0			0
$177$	194.838	−	426.636i	0.0827398	−	0.181175i
$178$		0			0
$179$	433.458	+	3014.77i	0.180996	+	1.25885i	0.854415	+	0.519591i	$0.173916\pi$
$179$	433.458	+	3014.77i	0.180996	+	1.25885i	−0.673420	+	0.739260i	$0.735175\pi$
$180$		0			0
$181$	307.276	+	354.616i	0.126186	+	0.145626i	0.815327	−	0.579001i	$-0.196557\pi$
$181$	307.276	+	354.616i	0.126186	+	0.145626i	−0.689141	+	0.724627i	$0.742012\pi$
$182$		0			0
$183$	137.764			0.0556491
$184$		0			0
$185$	1210.60			0.481110
$186$		0			0
$187$	3295.18	+	3802.84i	1.28859	+	1.48712i
$188$		0			0
$189$	275.660	+	1917.26i	0.106092	+	0.737883i
$190$		0			0
$191$	444.557	−	973.445i	0.168414	−	0.368775i	−0.806541	−	0.591178i	$-0.798663\pi$
$191$	444.557	−	973.445i	0.168414	−	0.368775i	0.974955	+	0.222403i	$0.0713902\pi$
$192$		0			0
$193$	−131.728	+	916.185i	−0.0491293	+	0.341702i	0.950400	+	0.311030i	$0.100674\pi$
$193$	−131.728	+	916.185i	−0.0491293	+	0.341702i	−0.999530	+	0.0306721i	$0.990235\pi$
$194$		0			0
$195$	223.282	+	65.5616i	0.0819978	+	0.0240767i
$196$		0			0
$197$	1773.56	+	3883.55i	0.641425	+	1.40452i	0.898863	+	0.438230i	$0.144394\pi$
$197$	1773.56	+	3883.55i	0.641425	+	1.40452i	−0.257438	+	0.966295i	$0.582878\pi$
$198$		0			0
$199$	1658.97	−	1914.55i	0.590961	−	0.682005i	−0.378963	−	0.925412i	$-0.623719\pi$
$199$	1658.97	−	1914.55i	0.590961	−	0.682005i	0.969924	+	0.243406i	$0.0782648\pi$
$200$		0			0
$201$	−708.719	−	455.466i	−0.248702	−	0.159831i
$202$		0			0
$203$	−4192.41	+	2694.30i	−1.44950	+	0.931539i
$204$		0			0
$205$	1389.86	−	408.100i	0.473523	−	0.139039i
$206$		0			0
$207$	−2669.43	−	1045.30i	−0.896319	−	0.350983i
$208$		0			0
$209$	4456.05	−	1308.42i	1.47479	−	0.433038i
$210$		0			0
$211$	−1728.83	+	1111.05i	−0.564065	+	0.362503i	−0.791385	−	0.611317i	$-0.790640\pi$
$211$	−1728.83	+	1111.05i	−0.564065	+	0.362503i	0.227321	+	0.973820i	$0.427003\pi$
$212$		0			0
$213$	−773.136	−	496.865i	−0.248706	−	0.159834i
$214$		0			0
$215$	2460.37	−	2839.42i	0.780446	−	0.900682i
$216$		0			0
$217$	−2934.76	−	6426.24i	−0.918086	−	2.01033i
$218$		0			0
$219$	202.229	+	59.3799i	0.0623990	+	0.0183220i
$220$		0			0
$221$	−195.044	+	1356.56i	−0.0593670	+	0.412906i
$222$		0			0
$223$	−482.552	+	1056.64i	−0.144906	+	0.317300i	−0.968143	−	0.250398i	$-0.919439\pi$
$223$	−482.552	+	1056.64i	−0.144906	+	0.317300i	0.823237	+	0.567698i	$0.192166\pi$
$224$		0			0
$225$	57.5364	+	400.174i	0.0170478	+	0.118570i
$226$		0			0
$227$	−1979.71	−	2284.71i	−0.578847	−	0.668025i	0.388510	−	0.921445i	$-0.372990\pi$
$227$	−1979.71	−	2284.71i	−0.578847	−	0.668025i	−0.967356	+	0.253420i	$0.918445\pi$
$228$		0			0
$229$	−4445.95			−1.28295			−0.641477	−	0.767143i	$-0.721678\pi$
$229$	−4445.95			−1.28295			−0.641477	+	0.767143i	$0.721678\pi$
$230$		0			0
$231$	−2621.10			−0.746561
$232$		0			0
$233$	840.045	+	969.464i	0.236194	+	0.272582i	0.861456	−	0.507833i	$-0.169553\pi$
$233$	840.045	+	969.464i	0.236194	+	0.272582i	−0.625262	+	0.780415i	$0.715008\pi$
$234$		0			0
$235$	−620.436	−	4315.23i	−0.172225	−	1.19785i
$236$		0			0
$237$	−116.368	+	254.811i	−0.0318942	+	0.0698386i
$238$		0			0
$239$	−611.697	+	4254.44i	−0.165554	+	1.15145i	0.722385	+	0.691491i	$0.243046\pi$
$239$	−611.697	+	4254.44i	−0.165554	+	1.15145i	−0.887939	+	0.459961i	$0.847863\pi$
$240$		0			0
$241$	−3804.72	−	1117.17i	−1.01694	−	0.298602i	−0.269553	−	0.962986i	$-0.586876\pi$
$241$	−3804.72	−	1117.17i	−1.01694	−	0.298602i	−0.747391	+	0.664384i	$0.768694\pi$
$242$		0			0
$243$	−867.968	−	1900.59i	−0.229137	−	0.501739i
$244$		0			0
$245$	−7607.00	+	8778.94i	−1.98365	+	2.28925i
$246$		0			0
$247$	1064.12	+	683.865i	0.274122	+	0.176167i
$248$		0			0
$249$	63.1872	−	40.6080i	0.0160816	−	0.0103350i
$250$		0			0
$251$	5468.20	−	1605.61i	1.37510	−	0.403765i	0.491038	−	0.871138i	$-0.336618\pi$
$251$	5468.20	−	1605.61i	1.37510	−	0.403765i	0.884060	+	0.467373i	$0.154799\pi$
$252$		0			0
$253$	3902.74	−	6879.51i	0.969816	−	1.70953i
$254$		0			0
$255$	802.277	−	235.570i	0.197022	−	0.0578508i
$256$		0			0
$257$	−852.015	+	547.557i	−0.206799	+	0.132901i	−0.639941	−	0.768424i	$-0.721041\pi$
$257$	−852.015	+	547.557i	−0.206799	+	0.132901i	0.433142	+	0.901326i	$0.357405\pi$
$258$		0			0
$259$	−3124.30	−	2007.87i	−0.749555	−	0.481710i
$260$		0			0
$261$	2332.07	−	2691.35i	0.553071	−	0.638278i
$262$		0			0
$263$	1049.87	+	2298.90i	0.246152	+	0.538997i	0.991869	−	0.127266i	$-0.0406202\pi$
$263$	1049.87	+	2298.90i	0.246152	+	0.538997i	−0.745717	+	0.666263i	$0.767893\pi$
$264$		0			0
$265$	607.105	+	178.262i	0.140733	+	0.0413229i
$266$		0			0
$267$	54.0317	−	375.799i	0.0123846	−	0.0861367i
$268$		0			0
$269$	−2702.04	+	5916.64i	−0.612440	+	1.34106i	0.308453	+	0.951240i	$0.400189\pi$
$269$	−2702.04	+	5916.64i	−0.612440	+	1.34106i	−0.920893	+	0.389816i	$0.872539\pi$
$270$		0			0
$271$	−487.316	−	3389.36i	−0.109234	−	0.759738i	−0.968644	−	0.248452i	$-0.920078\pi$
$271$	−487.316	−	3389.36i	−0.109234	−	0.759738i	0.859411	−	0.511286i	$-0.170831\pi$
$272$		0			0
$273$	−467.504	−	539.528i	−0.103643	−	0.119611i
$274$		0			0
$275$	−1115.43			−0.244592
$276$		0			0
$277$	1155.56			0.250653			0.125327	−	0.992116i	$-0.460002\pi$
$277$	1155.56			0.250653			0.125327	+	0.992116i	$0.460002\pi$
$278$		0			0
$279$	3305.95	+	3815.27i	0.709398	+	0.818689i
$280$		0			0
$281$	−1067.50	−	7424.63i	−0.226625	−	1.57621i	−0.712173	−	0.702004i	$-0.752289\pi$
$281$	−1067.50	−	7424.63i	−0.226625	−	1.57621i	0.485548	−	0.874210i	$-0.338620\pi$
$282$		0			0
$283$	−1090.42	+	2387.70i	−0.229042	+	0.501533i	−0.988905	−	0.148551i	$-0.952539\pi$
$283$	−1090.42	+	2387.70i	−0.229042	+	0.501533i	0.759862	+	0.650084i	$0.225266\pi$
$284$		0			0
$285$	109.828	−	763.868i	0.0228268	−	0.158764i
$286$		0			0
$287$	−4263.79	−	1251.96i	−0.876946	−	0.257494i
$288$		0			0
$289$	4.73546	+	10.3692i	0.000963863	+	0.00211057i
$290$		0			0
$291$	298.395	−	344.366i	0.0601108	−	0.0693715i
$292$		0			0
$293$	−3844.61	−	2470.78i	−0.766568	−	0.492643i	0.0979832	−	0.995188i	$-0.468761\pi$
$293$	−3844.61	−	2470.78i	−0.766568	−	0.492643i	−0.864551	+	0.502545i	$0.832397\pi$
$294$		0			0
$295$	−4654.37	+	2991.18i	−0.918604	+	0.590351i
$296$		0			0
$297$	3664.12	−	1075.88i	0.715872	−	0.210199i
$298$		0			0
$299$	2112.18	−	423.698i	0.408531	−	0.0819502i
$300$		0			0
$301$	−11059.0	+	3247.23i	−2.11771	+	0.621817i
$302$		0			0
$303$	874.191	−	561.808i	0.165746	−	0.106518i
$304$		0			0
$305$	−1367.11	−	878.589i	−0.256658	−	0.164944i
$306$		0			0
$307$	−5432.85	+	6269.84i	−1.01000	+	1.16560i	−0.0238519	+	0.999716i	$0.507593\pi$
$307$	−5432.85	+	6269.84i	−1.01000	+	1.16560i	−0.986145	+	0.165884i	$0.946952\pi$
$308$		0			0
$309$	713.415	+	1562.16i	0.131342	+	0.287599i
$310$		0			0
$311$	−3494.70	−	1026.14i	−0.637191	−	0.187096i	−0.0528473	−	0.998603i	$-0.516830\pi$
$311$	−3494.70	−	1026.14i	−0.637191	−	0.187096i	−0.584343	+	0.811507i	$0.698648\pi$
$312$		0			0
$313$	1330.17	−	9251.50i	0.240209	−	1.67069i	−0.410881	−	0.911689i	$-0.634779\pi$
$313$	1330.17	−	9251.50i	0.240209	−	1.67069i	0.651090	−	0.759001i	$-0.274312\pi$
$314$		0			0
$315$	4655.42	−	10194.0i	0.832709	−	1.82338i
$316$		0			0
$317$	−277.552	−	1930.41i	−0.0491762	−	0.342028i	−0.999524	−	0.0308393i	$-0.990182\pi$
$317$	−277.552	−	1930.41i	−0.0491762	−	0.342028i	0.950348	−	0.311189i	$-0.100727\pi$
$318$		0			0
$319$	6434.14	+	7425.39i	1.12929	+	1.30327i
$320$		0			0
$321$	565.195			0.0982744
$322$		0			0
$323$	4544.98			0.782940
$324$		0			0
$325$	−198.950	−	229.600i	−0.0339561	−	0.0391875i
$326$		0			0
$327$	−208.730	−	1451.75i	−0.0352991	−	0.245511i
$328$		0			0
$329$	−5555.88	+	12165.7i	−0.931020	+	2.03865i
$330$		0			0
$331$	413.129	−	2873.37i	0.0686030	−	0.477145i	−0.926339	−	0.376691i	$-0.877062\pi$
$331$	413.129	−	2873.37i	0.0686030	−	0.477145i	0.994942	−	0.100453i	$-0.0320292\pi$
$332$		0			0
$333$	2546.39	+	747.687i	0.419043	+	0.123042i
$334$		0			0
$335$	4128.30	+	9039.72i	0.673294	+	1.47431i
$336$		0			0
$337$	−331.111	+	382.123i	−0.0535216	+	0.0617672i	−0.781879	−	0.623430i	$-0.785739\pi$
$337$	−331.111	+	382.123i	−0.0535216	+	0.0617672i	0.728357	+	0.685197i	$0.240284\pi$
$338$		0			0
$339$	−418.898	−	269.210i	−0.0671134	−	0.0431312i
$340$		0			0
$341$	−11717.2	+	7530.17i	−1.86076	+	1.19584i
$342$		0			0
$343$	22222.7	−	6525.18i	3.49829	−	1.02719i
$344$		0			0
$345$	−770.458	−	1064.80i	−0.120232	−	0.166165i
$346$		0			0
$347$	448.061	−	131.562i	0.0693174	−	0.0203534i	−0.246890	−	0.969044i	$-0.579409\pi$
$347$	448.061	−	131.562i	0.0693174	−	0.0203534i	0.316207	+	0.948690i	$0.397590\pi$
$348$		0			0
$349$	8381.49	−	5386.46i	1.28553	−	0.826162i	0.293973	−	0.955814i	$-0.405022\pi$
$349$	8381.49	−	5386.46i	1.28553	−	0.826162i	0.991560	+	0.129652i	$0.0413861\pi$
$350$		0			0
$351$	875.001	+	562.329i	0.133060	+	0.0855125i
$352$		0			0
$353$	−432.848	+	499.534i	−0.0652640	+	0.0753187i	−0.787443	−	0.616388i	$-0.788595\pi$
$353$	−432.848	+	499.534i	−0.0652640	+	0.0753187i	0.722179	+	0.691707i	$0.243141\pi$
$354$		0			0
$355$	4503.53	+	9861.37i	0.673304	+	1.47433i
$356$		0			0
$357$	−2461.21	−	722.676i	−0.364877	−	0.107137i
$358$		0			0
$359$	1101.69	−	7662.40i	0.161963	−	1.12648i	−0.732964	−	0.680267i	$-0.761864\pi$
$359$	1101.69	−	7662.40i	0.161963	−	1.12648i	0.894927	−	0.446212i	$-0.147227\pi$
$360$		0			0
$361$	−1106.75	+	2423.45i	−0.161357	+	0.353323i
$362$		0			0
$363$	545.050	+	3790.91i	0.0788091	+	0.548129i
$364$		0			0
$365$	−1628.15	−	1878.98i	−0.233482	−	0.269453i
$366$		0			0
$367$	−8772.23			−1.24770			−0.623851	−	0.781544i	$-0.714433\pi$
$367$	−8772.23			−1.24770			−0.623851	+	0.781544i	$0.714433\pi$
$368$		0			0
$369$	3175.49			0.447992
$370$		0			0
$371$	−1271.15	−	1466.98i	−0.177883	−	0.205288i
$372$		0			0
$373$	−220.234	−	1531.76i	−0.0305718	−	0.212632i	0.968809	−	0.247807i	$-0.0797100\pi$
$373$	−220.234	−	1531.76i	−0.0305718	−	0.212632i	−0.999381	+	0.0351757i	$0.988801\pi$
$374$		0			0
$375$	541.728	−	1186.22i	0.0745993	−	0.163350i
$376$		0			0
$377$	−380.842	+	2648.81i	−0.0520275	+	0.361859i
$378$		0			0
$379$	−9160.42	−	2689.74i	−1.24153	−	0.364546i	−0.405939	−	0.913900i	$-0.633056\pi$
$379$	−9160.42	−	2689.74i	−1.24153	−	0.364546i	−0.835590	+	0.549354i	$0.814874\pi$
$380$		0			0
$381$	589.688	+	1291.24i	0.0792930	+	0.173627i
$382$		0			0
$383$	4169.90	−	4812.32i	0.556324	−	0.642032i	−0.406021	−	0.913864i	$-0.633084\pi$
$383$	4169.90	−	4812.32i	0.556324	−	0.642032i	0.962345	+	0.271832i	$0.0876294\pi$
$384$		0			0
$385$	26010.7	+	16716.1i	3.44319	+	2.21281i
$386$		0			0
$387$	6928.81	−	4452.88i	0.910107	−	0.584890i
$388$		0			0
$389$	2561.36	−	752.083i	0.333846	−	0.0980260i	−0.110513	−	0.993875i	$-0.535250\pi$
$389$	2561.36	−	752.083i	0.333846	−	0.0980260i	0.444359	+	0.895849i	$0.353431\pi$
$390$		0			0
$391$	5561.46	−	5383.80i	0.719322	−	0.696345i
$392$		0			0
$393$	−1232.76	+	361.970i	−0.158230	+	0.0464605i
$394$		0			0
$395$	2779.85	−	1786.50i	0.354100	−	0.227566i
$396$		0			0
$397$	−2857.12	−	1836.16i	−0.361196	−	0.232127i	0.347438	−	0.937703i	$-0.387052\pi$
$397$	−2857.12	−	1836.16i	−0.361196	−	0.232127i	−0.708634	+	0.705576i	$0.750688\pi$
$398$		0			0
$399$	−1550.37	+	1789.22i	−0.194525	+	0.224494i
$400$		0			0
$401$	−3660.17	−	8014.65i	−0.455811	−	0.998086i	−0.988422	−	0.151727i	$-0.951517\pi$
$401$	−3660.17	−	8014.65i	−0.455811	−	0.998086i	0.532612	−	0.846360i	$-0.321211\pi$
$402$		0			0
$403$	−3639.91	−	1068.77i	−0.449918	−	0.132108i
$404$		0			0
$405$	−1093.67	+	7606.62i	−0.134184	+	0.933274i
$406$		0			0
$407$	−3041.68	+	6660.35i	−0.370444	+	0.811158i
$408$		0			0
$409$	−680.807	−	4735.12i	−0.0823074	−	0.572461i	−0.988687	−	0.149996i	$-0.952074\pi$
$409$	−680.807	−	4735.12i	−0.0823074	−	0.572461i	0.906379	−	0.422465i	$-0.138835\pi$
$410$		0			0
$411$	1082.60	+	1249.38i	0.129928	+	0.149945i
$412$		0			0
$413$	16973.0			2.02224
$414$		0			0
$415$	−886.022			−0.104803
$416$		0			0
$417$	128.918	+	148.779i	0.0151394	+	0.0174718i
$418$		0			0
$419$	679.878	+	4728.66i	0.0792702	+	0.551337i	0.990295	+	0.138984i	$0.0443837\pi$
$419$	679.878	+	4728.66i	0.0792702	+	0.551337i	−0.911024	+	0.412353i	$0.864707\pi$
$420$		0			0
$421$	3727.98	−	8163.13i	0.431569	−	0.945004i	−0.561501	−	0.827476i	$-0.689776\pi$
$421$	3727.98	−	8163.13i	0.431569	−	0.945004i	0.993070	−	0.117528i	$-0.0374970\pi$
$422$		0			0
$423$	1360.12	−	9459.85i	0.156339	−	1.08736i
$424$		0			0
$425$	−1047.38	−	307.540i	−0.119543	−	0.0351009i
$426$		0			0
$427$	2071.01	+	4534.89i	0.234715	+	0.513955i
$428$		0			0
$429$	−921.702	+	1063.70i	−0.103730	+	0.119711i
$430$		0			0
$431$	42.8501	+	27.5381i	0.00478890	+	0.00307764i	0.543033	−	0.839711i	$-0.317276\pi$
$431$	42.8501	+	27.5381i	0.00478890	+	0.00307764i	−0.538244	+	0.842789i	$0.680912\pi$
$432$		0			0
$433$	7315.93	−	4701.66i	0.811966	−	0.521819i	−0.0675344	−	0.997717i	$-0.521513\pi$
$433$	7315.93	−	4701.66i	0.811966	−	0.521819i	0.879500	+	0.475898i	$0.157877\pi$
$434$		0			0
$435$	1566.52	−	459.972i	0.172664	−	0.0506988i
$436$		0			0
$437$	−2387.65	−	6733.29i	−0.261365	−	0.737064i
$438$		0			0
$439$	−15849.0	+	4653.70i	−1.72308	+	0.505943i	−0.985552	−	0.169371i	$-0.945826\pi$
$439$	−15849.0	+	4653.70i	−1.72308	+	0.505943i	−0.737530	+	0.675314i	$0.764008\pi$
$440$		0			0
$441$	−21422.6	+	13767.5i	−2.31320	+	1.48661i
$442$		0			0
$443$	10145.5	+	6520.15i	1.08810	+	0.699281i	0.956415	−	0.292010i	$-0.0943240\pi$
$443$	10145.5	+	6520.15i	1.08810	+	0.699281i	0.131688	+	0.991291i	$0.457960\pi$
$444$		0			0
$445$	−2932.85	+	3384.69i	−0.312428	+	0.360561i
$446$		0			0
$447$	61.2240	+	134.062i	0.00647829	+	0.0141855i
$448$		0			0
$449$	−4384.08	−	1287.28i	−0.460796	−	0.135302i	0.0430917	−	0.999071i	$-0.486279\pi$
$449$	−4384.08	−	1287.28i	−0.460796	−	0.135302i	−0.503888	+	0.863769i	$0.668097\pi$
$450$		0			0
$451$	−1246.84	+	8671.93i	−0.130180	+	0.905422i
$452$		0			0
$453$	637.928	−	1396.87i	0.0661644	−	0.144880i
$454$		0			0
$455$	1198.47	+	8335.57i	0.123484	+	0.858852i
$456$		0			0
$457$	−273.221	−	315.314i	−0.0279666	−	0.0322752i	0.741594	−	0.670849i	$-0.234070\pi$
$457$	−273.221	−	315.314i	−0.0279666	−	0.0322752i	−0.769561	+	0.638574i	$0.779525\pi$
$458$		0			0
$459$	3737.25			0.380043
$460$		0			0
$461$	−3064.26			−0.309581			−0.154790	−	0.987947i	$-0.549470\pi$
$461$	−3064.26			−0.309581			−0.154790	+	0.987947i	$0.549470\pi$
$462$		0			0
$463$	−5853.22	−	6754.98i	−0.587521	−	0.678036i	0.381683	−	0.924293i	$-0.375345\pi$
$463$	−5853.22	−	6754.98i	−0.587521	−	0.678036i	−0.969204	+	0.246257i	$0.920799\pi$
$464$		0			0
$465$	329.381	+	2290.90i	0.0328488	+	0.228468i
$466$		0			0
$467$	−4152.02	+	9091.65i	−0.411418	+	0.900881i	0.584565	+	0.811347i	$0.301265\pi$
$467$	−4152.02	+	9091.65i	−0.411418	+	0.900881i	−0.995984	+	0.0895340i	$0.971462\pi$
$468$		0			0
$469$	4338.74	−	30176.6i	0.427174	−	2.97106i
$470$		0			0
$471$	−225.094	−	66.0937i	−0.0220208	−	0.00646589i
$472$		0			0
$473$	9439.80	+	20670.3i	0.917637	+	2.00934i
$474$		0			0
$475$	−659.770	+	761.415i	−0.0637312	+	0.0735497i
$476$		0			0
$477$	1166.89	+	749.914i	0.112009	+	0.0719837i
$478$		0			0
$479$	−1759.13	+	1130.53i	−0.167801	+	0.107839i	−0.621846	−	0.783140i	$-0.713617\pi$
$479$	−1759.13	+	1130.53i	−0.167801	+	0.107839i	0.454045	+	0.890979i	$0.349981\pi$
$480$		0			0
$481$	−1913.49	+	561.852i	−0.181388	+	0.0532604i
$482$		0			0
$483$	222.334	+	4025.88i	0.0209453	+	0.379262i
$484$		0			0
$485$	−5157.35	+	1514.34i	−0.482852	+	0.141778i
$486$		0			0
$487$	−10119.2	+	6503.22i	−0.941572	+	0.605111i	−0.918840	−	0.394630i	$-0.870873\pi$
$487$	−10119.2	+	6503.22i	−0.941572	+	0.605111i	−0.0227316	+	0.999742i	$0.507236\pi$
$488$		0			0
$489$	456.117	+	293.128i	0.0421806	+	0.0271078i
$490$		0			0
$491$	1120.43	−	1293.05i	0.102982	−	0.118848i	−0.701919	−	0.712257i	$-0.747673\pi$
$491$	1120.43	−	1293.05i	0.102982	−	0.118848i	0.804901	+	0.593409i	$0.202218\pi$
$492$		0			0
$493$	3994.36	+	8746.43i	0.364902	+	0.799025i
$494$		0			0
$495$	−21199.4	−	6224.71i	−1.92493	−	0.565212i
$496$		0			0
$497$	4733.10	−	32919.4i	0.427180	−	2.97110i
$498$		0			0
$499$	4576.91	−	10022.0i	0.410602	−	0.899093i	−0.585482	−	0.810685i	$-0.699095\pi$
$499$	4576.91	−	10022.0i	0.410602	−	0.899093i	0.996084	−	0.0884080i	$-0.0281779\pi$
$500$		0			0
$501$	−492.324	−	3424.19i	−0.0439031	−	0.305353i
$502$		0			0
$503$	−155.458	−	179.408i	−0.0137804	−	0.0159034i	0.748818	−	0.662776i	$-0.230622\pi$
$503$	−155.458	−	179.408i	−0.0137804	−	0.0159034i	−0.762598	+	0.646873i	$0.776076\pi$
$504$		0			0
$505$	−12258.1			−1.08015
$506$		0			0
$507$	1824.72			0.159839
$508$		0			0
$509$	10566.6	+	12194.5i	0.920148	+	1.06191i	0.997890	+	0.0649340i	$0.0206837\pi$
$509$	10566.6	+	12194.5i	0.920148	+	1.06191i	−0.0777415	+	0.996974i	$0.524771\pi$
$510$		0			0
$511$	1085.47	+	7549.62i	0.0939695	+	0.653573i
$512$		0			0
$513$	1432.89	−	3137.59i	0.123321	−	0.270035i
$514$		0			0
$515$	2883.05	−	20052.1i	0.246684	−	1.71573i
$516$		0			0
$517$	25299.8	+	7428.70i	2.15220	+	0.631942i
$518$		0			0
$519$	−1305.27	−	2858.15i	−0.110395	−	0.241732i
$520$		0			0
$521$	10634.6	−	12272.9i	0.894258	−	1.03203i	−0.105037	−	0.994468i	$-0.533496\pi$
$521$	10634.6	−	12272.9i	0.894258	−	1.03203i	0.999294	−	0.0375599i	$-0.0119585\pi$
$522$		0			0
$523$	−38.0081	−	24.4263i	−0.00317778	−	0.00204223i	0.539051	−	0.842273i	$-0.318783\pi$
$523$	−38.0081	−	24.4263i	−0.00317778	−	0.00204223i	−0.542229	+	0.840231i	$0.682419\pi$
$524$		0			0
$525$	478.349	−	307.416i	0.0397654	−	0.0255557i
$526$		0			0
$527$	−13078.6	+	3840.22i	−1.08105	+	0.317425i
$528$		0			0
$529$	−10897.6	−	5410.87i	−0.895671	−	0.444717i
$530$		0			0
$531$	−11637.4	+	3417.05i	−0.951075	+	0.279261i
$532$		0			0
$533$	−2007.42	+	1290.09i	−0.163135	+	0.104841i
$534$		0			0
$535$	−5608.76	−	3604.53i	−0.453249	−	0.291285i
$536$		0			0
$537$	−2004.60	+	2313.43i	−0.161089	+	0.185907i
$538$		0			0
$539$	−29186.1	−	63908.6i	−2.33234	−	5.10712i
$540$		0			0
$541$	−12859.0	−	3775.76i	−1.02191	−	0.300060i	−0.272493	−	0.962158i	$-0.587848\pi$
$541$	−12859.0	−	3775.76i	−1.02191	−	0.300060i	−0.749417	+	0.662098i	$0.769666\pi$
$542$		0			0
$543$	−67.1139	+	466.787i	−0.00530411	+	0.0368909i
$544$		0			0
$545$	−7187.20	+	15737.8i	−0.564891	+	1.23694i
$546$		0			0
$547$	2614.27	+	18182.7i	0.204348	+	1.42127i	0.791191	+	0.611570i	$0.209462\pi$
$547$	2614.27	+	18182.7i	0.204348	+	1.42127i	−0.586843	+	0.809701i	$0.699629\pi$
$548$		0			0
$549$	−2332.96	−	2692.37i	−0.181363	−	0.209304i
$550$		0			0
$551$	8874.50			0.686146
$552$		0			0
$553$	−10137.2			−0.779526
$554$		0			0
$555$	796.771	+	919.522i	0.0609388	+	0.0703271i
$556$		0			0
$557$	2652.03	+	18445.3i	0.201742	+	1.40315i	0.799113	+	0.601181i	$0.205303\pi$
$557$	2652.03	+	18445.3i	0.201742	+	1.40315i	−0.597371	+	0.801965i	$0.703788\pi$
$558$		0			0
$559$	−2571.08	+	5629.88i	−0.194535	+	0.425973i
$560$		0			0
$561$	−719.717	+	5005.74i	−0.0541649	+	0.376725i
$562$		0			0
$563$	−10052.2	−	2951.59i	−0.752485	−	0.220949i	−0.117073	−	0.993123i	$-0.537351\pi$
$563$	−10052.2	−	2951.59i	−0.752485	−	0.220949i	−0.635411	+	0.772174i	$0.719169\pi$
$564$		0			0
$565$	2440.09	+	5343.06i	0.181691	+	0.397848i
$566$		0			0
$567$	15438.6	−	17817.1i	1.14349	−	1.31966i
$568$		0			0
$569$	15875.5	+	10202.5i	1.16966	+	0.751692i	0.973457	−	0.228872i	$-0.0735036\pi$
$569$	15875.5	+	10202.5i	1.16966	+	0.751692i	0.196199	+	0.980564i	$0.437140\pi$
$570$		0			0
$571$	−14435.6	+	9277.18i	−1.05799	+	0.679926i	−0.949371	−	0.314158i	$-0.898278\pi$
$571$	−14435.6	+	9277.18i	−1.05799	+	0.679926i	−0.108615	+	0.994084i	$0.534642\pi$
$572$		0			0
$573$	1031.98	−	303.015i	0.0752381	−	0.0220919i
$574$		0			0
$575$	94.6159	+	1713.24i	0.00686219	+	0.124256i
$576$		0			0
$577$	−8475.10	+	2488.51i	−0.611479	+	0.179546i	−0.572786	−	0.819705i	$-0.694137\pi$
$577$	−8475.10	+	2488.51i	−0.611479	+	0.179546i	−0.0386925	+	0.999251i	$0.512319\pi$
$578$		0			0
$579$	−782.592	+	502.941i	−0.0561717	+	0.0360993i
$580$		0			0
$581$	2286.63	+	1469.53i	0.163279	+	0.104933i
$582$		0			0
$583$	−2506.11	+	2892.21i	−0.178032	+	0.205460i
$584$		0			0
$585$	−2499.87	−	5473.95i	−0.176678	−	0.386872i
$586$		0			0
$587$	−24217.9	−	7111.02i	−1.70286	−	0.500005i	−0.721539	−	0.692373i	$-0.756565\pi$
$587$	−24217.9	−	7111.02i	−1.70286	−	0.500005i	−0.981323	+	0.192368i	$0.938383\pi$
$588$		0			0
$589$	−1790.39	+	12452.5i	−0.125249	+	0.871128i
$590$		0			0
$591$	−1782.49	+	3903.11i	−0.124064	+	0.271662i
$592$		0			0
$593$	2690.86	+	18715.3i	0.186341	+	1.29603i	0.841383	+	0.540439i	$0.181742\pi$
$593$	2690.86	+	18715.3i	0.186341	+	1.29603i	−0.655042	+	0.755593i	$0.727349\pi$
$594$		0			0
$595$	19815.2	+	22867.9i	1.36528	+	1.57562i
$596$		0			0
$597$	2546.08			0.174546
$598$		0			0
$599$	23226.9			1.58435			0.792173	−	0.610296i	$-0.208950\pi$
$599$	23226.9			1.58435			0.792173	+	0.610296i	$0.208950\pi$
$600$		0			0
$601$	−1978.09	−	2282.83i	−0.134256	−	0.154940i	0.684640	−	0.728881i	$-0.259959\pi$
$601$	−1978.09	−	2282.83i	−0.134256	−	0.154940i	−0.818896	+	0.573941i	$0.805414\pi$
$602$		0			0
$603$	3100.42	+	21563.9i	0.209384	+	1.45630i
$604$		0			0
$605$	18767.7	−	41095.5i	1.26118	−	2.76160i
$606$		0			0
$607$	−275.273	+	1914.57i	−0.0184069	+	0.128023i	−0.996953	−	0.0780056i	$-0.975145\pi$
$607$	−275.273	+	1914.57i	−0.0184069	+	0.128023i	0.978546	+	0.206028i	$0.0660539\pi$
$608$		0			0
$609$	−4805.74	−	1411.09i	−0.319767	−	0.0938922i
$610$		0			0
$611$	2983.40	+	6532.73i	0.197537	+	0.432547i
$612$		0			0
$613$	6380.29	−	7363.25i	0.420388	−	0.485153i	−0.505567	−	0.862787i	$-0.668717\pi$
$613$	6380.29	−	7363.25i	0.420388	−	0.485153i	0.925955	+	0.377634i	$0.123262\pi$
$614$		0			0
$615$	1224.73	+	787.083i	0.0803019	+	0.0516069i
$616$		0			0
$617$	−13592.1	+	8735.11i	−0.886868	+	0.569955i	−0.902869	−	0.429917i	$-0.858543\pi$
$617$	−13592.1	+	8735.11i	−0.886868	+	0.569955i	0.0160007	+	0.999872i	$0.494907\pi$
$618$		0			0
$619$	−749.036	+	219.937i	−0.0486370	+	0.0142811i	−0.305961	−	0.952044i	$-0.598978\pi$
$619$	−749.036	+	219.937i	−0.0486370	+	0.0142811i	0.257324	+	0.966325i	$0.417159\pi$
$620$		0			0
$621$	−1963.31	−	5536.65i	−0.126868	−	0.357775i
$622$		0			0
$623$	13182.8	−	3870.81i	0.847763	−	0.248926i
$624$		0			0
$625$	−14576.8	+	9367.94i	−0.932915	+	0.599548i
$626$		0			0
$627$	3926.61	+	2523.48i	0.250101	+	0.160730i
$628$		0			0
$629$	−4692.50	+	5415.43i	−0.297460	+	0.343287i
$630$		0			0
$631$	1728.11	+	3784.04i	0.109025	+	0.238732i	0.956279	−	0.292457i	$-0.0944727\pi$
$631$	1728.11	+	3784.04i	0.109025	+	0.238732i	−0.847253	+	0.531189i	$0.821745\pi$
$632$		0			0
$633$	−1981.75	−	581.895i	−0.124435	−	0.0365375i
$634$		0			0
$635$	2383.05	−	16574.4i	0.148926	−	1.03581i
$636$		0			0
$637$	7949.30	−	17406.5i	0.494447	−	1.08269i
$638$		0			0
$639$	3382.22	+	23523.9i	0.209387	+	1.45632i
$640$		0			0
$641$	−10598.9	−	12231.8i	−0.653092	−	0.753708i	0.328541	−	0.944490i	$-0.393443\pi$
$641$	−10598.9	−	12231.8i	−0.653092	−	0.753708i	−0.981633	+	0.190782i	$0.938898\pi$
$642$		0			0
$643$	−23941.3			−1.46836			−0.734178	−	0.678957i	$-0.762432\pi$
$643$	−23941.3			−1.46836			−0.734178	+	0.678957i	$0.762432\pi$
$644$		0			0
$645$	3776.01			0.230512
$646$		0			0
$647$	−11060.9	−	12765.0i	−0.672103	−	0.775648i	0.312601	−	0.949885i	$-0.398800\pi$
$647$	−11060.9	−	12765.0i	−0.672103	−	0.775648i	−0.984704	+	0.174237i	$0.944254\pi$
$648$		0			0
$649$	−4762.26	−	33122.3i	−0.288036	−	2.00333i
$650$		0			0
$651$	2949.55	−	6458.60i	0.177576	−	0.388837i
$652$		0			0
$653$	2191.62	−	15243.1i	0.131340	−	0.913488i	−0.812471	−	0.583001i	$-0.801878\pi$
$653$	2191.62	−	15243.1i	0.131340	−	0.913488i	0.943811	−	0.330486i	$-0.107213\pi$
$654$		0			0
$655$	14541.9	+	4269.87i	0.867477	+	0.254714i
$656$		0			0
$657$	−2264.16	−	4957.82i	−0.134449	−	0.294403i
$658$		0			0
$659$	−13976.0	+	16129.1i	−0.826139	+	0.953415i	−0.999506	−	0.0314420i	$-0.989990\pi$
$659$	−13976.0	+	16129.1i	−0.826139	+	0.953415i	0.173366	+	0.984857i	$0.444536\pi$
$660$		0			0
$661$	−10721.8	−	6890.45i	−0.630905	−	0.405458i	0.185740	−	0.982599i	$-0.440532\pi$
$661$	−10721.8	−	6890.45i	−0.630905	−	0.405458i	−0.816644	+	0.577141i	$0.804168\pi$
$662$		0			0
$663$	−1158.76	+	744.687i	−0.0678768	+	0.0436218i
$664$		0			0
$665$	26796.0	−	7868.01i	1.56256	−	0.458809i
$666$		0			0
$667$	10859.3	−	10512.4i	0.630393	−	0.610256i
$668$		0			0
$669$	−1120.18	+	328.913i	−0.0647361	+	0.0190082i
$670$		0			0
$671$	8268.62	−	5313.92i	0.475717	−	0.305725i
$672$		0			0
$673$	25395.6	+	16320.8i	1.45457	+	0.934799i	0.999005	+	0.0445986i	$0.0142009\pi$
$673$	25395.6	+	16320.8i	1.45457	+	0.934799i	0.455570	+	0.890200i	$0.349435\pi$
$674$		0			0
$675$	−542.515	+	626.096i	−0.0309354	+	0.0357014i
$676$		0			0
$677$	2171.79	+	4755.55i	0.123292	+	0.269971i	0.961206	−	0.275830i	$-0.0889527\pi$
$677$	2171.79	+	4755.55i	0.123292	+	0.269971i	−0.837915	+	0.545801i	$0.816225\pi$
$678$		0			0
$679$	15821.6	+	4645.65i	0.894224	+	0.262568i
$680$		0			0
$681$	432.400	−	3007.41i	0.0243313	−	0.169228i
$682$		0			0
$683$	1022.23	−	2238.37i	0.0572688	−	0.125401i	−0.878834	−	0.477128i	$-0.841678\pi$
$683$	1022.23	−	2238.37i	0.0572688	−	0.125401i	0.936103	+	0.351726i	$0.114405\pi$
$684$		0			0
$685$	−2775.30	−	19302.6i	−0.154801	−	1.07667i
$686$		0			0
$687$	−2926.14	−	3376.94i	−0.162502	−	0.187538i
$688$		0			0
$689$	−1042.33			−0.0576336
$690$		0			0
$691$	15011.6			0.826437			0.413218	−	0.910632i	$-0.364405\pi$
$691$	15011.6			0.826437			0.413218	+	0.910632i	$0.364405\pi$
$692$		0			0
$693$	44386.9	+	51225.2i	2.43307	+	2.80791i
$694$		0			0
$695$	−330.489	−	2298.60i	−0.0180376	−	0.125455i
$696$		0			0
$697$	−3561.76	+	7799.16i	−0.193560	+	0.423837i
$698$		0			0
$699$	−183.479	+	1276.12i	−0.00992819	+	0.0690521i
$700$		0			0
$701$	8489.08	+	2492.62i	0.457387	+	0.134301i	0.502306	−	0.864690i	$-0.332485\pi$
$701$	8489.08	+	2492.62i	0.457387	+	0.134301i	−0.0449195	+	0.998991i	$0.514303\pi$
$702$		0			0
$703$	2747.36	+	6015.88i	0.147395	+	0.322750i
$704$		0			0
$705$	2869.31	−	3311.36i	0.153283	−	0.176898i
$706$		0			0
$707$	31635.3	+	20330.8i	1.68284	+	1.08150i
$708$		0			0
$709$	−5656.43	+	3635.17i	−0.299622	+	0.192555i	−0.681810	−	0.731529i	$-0.738807\pi$
$709$	−5656.43	+	3635.17i	−0.299622	+	0.192555i	0.382188	+	0.924084i	$0.375171\pi$
$710$		0			0
$711$	6950.51	−	2040.85i	0.366617	−	0.107648i
$712$		0			0
$713$	12559.9	+	17358.3i	0.659707	+	0.911742i
$714$		0			0
$715$	15930.4	−	4677.57i	0.833233	−	0.244659i
$716$		0			0
$717$	−3634.08	+	2335.48i	−0.189285	+	0.121646i
$718$		0			0
$719$	−10788.6	−	6933.41i	−0.559592	−	0.359628i	0.230066	−	0.973175i	$-0.426106\pi$
$719$	−10788.6	−	6933.41i	−0.559592	−	0.359628i	−0.789658	+	0.613547i	$0.789742\pi$
$720$		0			0
$721$	−40698.2	+	46968.2i	−2.10219	+	2.42606i
$722$		0			0
$723$	−1655.56	−	3625.17i	−0.0851604	−	0.186475i
$724$		0			0
$725$	−2045.12	−	600.500i	−0.104764	−	0.0307614i
$726$		0			0
$727$	3584.82	−	24933.0i	0.182880	−	1.27196i	−0.667031	−	0.745030i	$-0.732435\pi$
$727$	3584.82	−	24933.0i	0.182880	−	1.27196i	0.849911	−	0.526927i	$-0.176656\pi$
$728$		0			0
$729$	−6398.03	+	14009.7i	−0.325054	+	0.711768i
$730$		0			0
$731$	3164.86	+	22012.1i	0.160132	+	1.11374i
$732$		0			0
$733$	12672.3	+	14624.6i	0.638557	+	0.736934i	0.979119	−	0.203288i	$-0.0651627\pi$
$733$	12672.3	+	14624.6i	0.638557	+	0.736934i	−0.340562	+	0.940222i	$0.610617\pi$
$734$		0			0
$735$	−11674.7			−0.585889
$736$		0			0
$737$	−60106.1			−3.00412
$738$		0			0
$739$	6532.08	+	7538.42i	0.325151	+	0.375244i	0.894665	−	0.446737i	$-0.147414\pi$
$739$	6532.08	+	7538.42i	0.325151	+	0.375244i	−0.569514	+	0.821981i	$0.692869\pi$
$740$		0			0
$741$	180.923	+	1258.35i	0.00896947	+	0.0623840i
$742$		0			0
$743$	4852.83	−	10626.2i	0.239614	−	0.524681i	−0.751174	−	0.660104i	$-0.770512\pi$
$743$	4852.83	−	10626.2i	0.239614	−	0.524681i	0.990788	+	0.135423i	$0.0432394\pi$
$744$		0			0
$745$	247.418	−	1720.83i	0.0121674	−	0.0846260i
$746$		0			0
$747$	−1863.66	−	547.220i	−0.0912822	−	0.0268029i
$748$		0			0
$749$	8496.62	+	18605.0i	0.414499	+	0.907627i
$750$		0			0
$751$	−12304.7	+	14200.4i	−0.597875	+	0.689985i	−0.971349	−	0.237656i	$-0.923621\pi$
$751$	−12304.7	+	14200.4i	−0.597875	+	0.689985i	0.373474	+	0.927641i	$0.378166\pi$
$752$		0			0
$753$	4818.50	+	3096.66i	0.233195	+	0.149865i
$754$		0			0
$755$	−15239.1	+	9793.55i	−0.734578	+	0.472085i
$756$		0			0
$757$	24100.7	−	7076.62i	1.15714	−	0.339767i	0.353820	−	0.935313i	$-0.384882\pi$
$757$	24100.7	−	7076.62i	1.15714	−	0.339767i	0.803321	+	0.595546i	$0.203064\pi$
$758$		0			0
$759$	7794.00	−	1563.46i	0.372733	−	0.0747692i
$760$		0			0
$761$	28476.0	−	8361.30i	1.35644	−	0.398288i	0.478936	−	0.877850i	$-0.341023\pi$
$761$	28476.0	−	8361.30i	1.35644	−	0.398288i	0.877508	+	0.479562i	$0.159205\pi$
$762$		0			0
$763$	44650.7	−	28695.3i	2.11856	−	1.36152i
$764$		0			0
$765$	−18190.0	−	11690.0i	−0.859687	−	0.552487i
$766$		0			0
$767$	5968.50	−	6888.02i	0.280978	−	0.324266i
$768$		0			0
$769$	−9844.86	−	21557.2i	−0.461658	−	1.01089i	−0.987107	−	0.160064i	$-0.948830\pi$
$769$	−9844.86	−	21557.2i	−0.461658	−	1.01089i	0.525449	−	0.850825i	$-0.323897\pi$
$770$		0			0
$771$	−976.662	−	286.774i	−0.0456208	−	0.0133955i
$772$		0			0
$773$	3202.66	−	22275.0i	0.149019	−	1.03645i	−0.768811	−	0.639476i	$-0.779151\pi$
$773$	3202.66	−	22275.0i	0.149019	−	1.03645i	0.917830	−	0.396974i	$-0.129940\pi$
$774$		0			0
$775$	1255.20	−	2748.50i	0.0581782	−	0.127392i
$776$		0			0
$777$	−531.201	−	3694.58i	−0.0245260	−	0.170582i
$778$		0			0
$779$	5182.15	+	5980.52i	0.238344	+	0.275063i
$780$		0			0
$781$	−65569.3			−3.00417
$782$		0			0
$783$	7297.32			0.333059
$784$		0			0
$785$	1812.23	+	2091.43i	0.0823966	+	0.0950908i
$786$		0			0
$787$	−5017.92	−	34900.4i	−0.227280	−	1.58077i	−0.709491	−	0.704714i	$-0.751075\pi$
$787$	−5017.92	−	34900.4i	−0.227280	−	1.58077i	0.482211	−	0.876055i	$-0.339834\pi$
$788$		0			0
$789$	−1055.16	+	2310.48i	−0.0476105	+	0.104252i
$790$		0			0
$791$	2564.47	−	17836.3i	0.115275	−	0.801752i
$792$		0			0
$793$	2568.63	+	754.217i	0.115025	+	0.0337743i
$794$		0			0
$795$	264.172	+	578.455i	0.0117852	+	0.0258059i
$796$		0			0
$797$	−3847.80	+	4440.60i	−0.171011	+	0.197358i	−0.834785	−	0.550576i	$-0.814408\pi$
$797$	−3847.80	+	4440.60i	−0.171011	+	0.197358i	0.663774	+	0.747933i	$0.268954\pi$
$798$		0			0
$799$	21708.3	+	13951.1i	0.961183	+	0.617715i
$800$		0			0
$801$	−8259.39	+	5307.99i	−0.364334	+	0.234143i
$802$		0			0
$803$	14428.3	−	4236.53i	0.634077	−	0.186182i
$804$		0			0
$805$	23468.7	−	41369.1i	1.02753	−	1.81127i
$806$		0			0
$807$	−6272.39	+	1841.74i	−0.273604	+	0.0803375i
$808$		0			0
$809$	−8132.75	+	5226.60i	−0.353439	+	0.227142i	−0.705297	−	0.708912i	$-0.749186\pi$
$809$	−8132.75	+	5226.60i	−0.353439	+	0.227142i	0.351858	+	0.936053i	$0.385550\pi$
$810$		0			0
$811$	−12917.3	−	8301.44i	−0.559294	−	0.359437i	0.230249	−	0.973132i	$-0.426046\pi$
$811$	−12917.3	−	8301.44i	−0.559294	−	0.359437i	−0.789543	+	0.613695i	$0.789682\pi$
$812$		0			0
$813$	2253.68	−	2600.88i	0.0972200	−	0.112198i
$814$		0			0
$815$	−2656.89	−	5817.77i	−0.114192	−	0.250046i
$816$		0			0
$817$	19693.6	+	5782.55i	0.843318	+	0.247621i
$818$		0			0
$819$	−2627.30	+	18273.3i	−0.112094	+	0.779633i
$820$		0			0
$821$	5385.70	−	11793.0i	0.228943	−	0.501316i	−0.759943	−	0.649990i	$-0.774773\pi$
$821$	5385.70	−	11793.0i	0.228943	−	0.501316i	0.988886	+	0.148674i	$0.0475005\pi$
$822$		0			0
$823$	1308.14	+	9098.29i	0.0554055	+	0.385354i	0.998590	+	0.0530845i	$0.0169053\pi$
$823$	1308.14	+	9098.29i	0.0554055	+	0.385354i	−0.943184	+	0.332270i	$0.892186\pi$
$824$		0			0
$825$	−734.128	−	847.229i	−0.0309807	−	0.0357536i
$826$		0			0
$827$	31708.9			1.33329			0.666643	−	0.745377i	$-0.267731\pi$
$827$	31708.9			1.33329			0.666643	+	0.745377i	$0.267731\pi$
$828$		0			0
$829$	16023.2			0.671301			0.335650	−	0.941987i	$-0.391044\pi$
$829$	16023.2			0.671301			0.335650	+	0.941987i	$0.391044\pi$
$830$		0			0
$831$	760.544	+	877.714i	0.0317485	+	0.0366397i
$832$		0			0
$833$	−9785.14	−	68057.1i	−0.407005	−	2.83078i
$834$		0			0
$835$	−16952.2	+	37120.1i	−0.702580	+	1.53844i
$836$		0			0
$837$	−1472.20	+	10239.4i	−0.0607967	+	0.422850i
$838$		0			0
$839$	4182.24	+	1228.02i	0.172094	+	0.0505314i	0.366645	−	0.930361i	$-0.380507\pi$
$839$	4182.24	+	1228.02i	0.172094	+	0.0505314i	−0.194550	+	0.980893i	$0.562325\pi$
$840$		0			0
$841$	−2332.20	−	5106.81i	−0.0956252	−	0.209390i
$842$		0			0
$843$	4936.83	−	5697.41i	0.201701	−	0.232775i
$844$		0			0
$845$	−18107.7	−	11637.1i	−0.737190	−	0.473763i
$846$		0			0
$847$	−116595.	+	74930.9i	−4.72992	+	3.03974i
$848$		0			0
$849$	−2531.26	+	743.246i	−0.102324	+	0.0300449i
$850$		0			0
$851$	10488.0	+	4106.91i	0.422472	+	0.165432i
$852$		0			0
$853$	−19751.2	+	5799.47i	−0.792810	+	0.232790i	−0.652970	−	0.757384i	$-0.726477\pi$
$853$	−19751.2	+	5799.47i	−0.792810	+	0.232790i	−0.139840	+	0.990174i	$0.544659\pi$
$854$		0			0
$855$	−16788.5	+	10789.3i	−0.671525	+	0.431563i
$856$		0			0
$857$	−18194.8	−	11693.1i	−0.725232	−	0.466078i	0.125221	−	0.992129i	$-0.460036\pi$
$857$	−18194.8	−	11693.1i	−0.725232	−	0.466078i	−0.850453	+	0.526050i	$0.823672\pi$
$858$		0			0
$859$	9367.81	−	10811.0i	0.372090	−	0.429415i	−0.538564	−	0.842585i	$-0.681033\pi$
$859$	9367.81	−	10811.0i	0.372090	−	0.429415i	0.910654	+	0.413170i	$0.135578\pi$
$860$		0			0
$861$	−1855.32	−	4062.58i	−0.0734367	−	0.160804i
$862$		0			0
$863$	26514.4	+	7785.33i	1.04584	+	0.307087i	0.759136	−	0.650932i	$-0.225622\pi$
$863$	26514.4	+	7785.33i	1.04584	+	0.307087i	0.286705	+	0.958019i	$0.407440\pi$
$864$		0			0
$865$	−5274.87	+	36687.5i	−0.207342	+	1.44210i
$866$		0			0
$867$	−4.75931	+	10.4214i	−0.000186430	+	0.000408225i
$868$		0			0
$869$	2844.29	+	19782.5i	0.111031	+	0.772237i
$870$		0			0
$871$	−10720.6	−	12372.3i	−0.417055	−	0.481307i
$872$		0			0
$873$	−11783.3			−0.456819
$874$		0			0
$875$	47191.7			1.82328
$876$		0			0
$877$	−469.877	−	542.267i	−0.0180919	−	0.0208792i	0.746631	−	0.665238i	$-0.231670\pi$
$877$	−469.877	−	542.267i	−0.0180919	−	0.0208792i	−0.764723	+	0.644359i	$0.777124\pi$
$878$		0			0
$879$	−653.668	−	4546.36i	−0.0250827	−	0.174454i
$880$		0			0
$881$	−18452.1	+	40404.5i	−0.705639	+	1.54513i	0.127358	+	0.991857i	$0.459350\pi$
$881$	−18452.1	+	40404.5i	−0.705639	+	1.54513i	−0.832997	+	0.553277i	$0.813377\pi$
$882$		0			0
$883$	−399.375	+	2777.71i	−0.0152209	+	0.105864i	−0.996016	−	0.0891794i	$-0.971576\pi$
$883$	−399.375	+	2777.71i	−0.0152209	+	0.105864i	0.980795	+	0.195043i	$0.0624846\pi$
$884$		0			0
$885$	−5335.29	−	1566.58i	−0.202648	−	0.0595029i
$886$		0			0
$887$	−13622.3	−	29828.6i	−0.515661	−	1.12914i	−0.971056	−	0.238851i	$-0.923229\pi$
$887$	−13622.3	−	29828.6i	−0.515661	−	1.12914i	0.455395	−	0.890289i	$-0.349498\pi$
$888$		0			0
$889$	−33639.9	+	38822.5i	−1.26912	+	1.46464i
$890$		0			0
$891$	−39101.2	−	25128.8i	−1.47019	−	0.944835i
$892$		0			0
$893$	20035.7	−	12876.2i	0.750806	−	0.482514i
$894$		0			0
$895$	34646.8	−	10173.2i	1.29398	−	0.379948i
$896$		0			0
$897$	1711.98	+	1325.46i	0.0637248	+	0.0493376i
$898$		0			0
$899$	−25537.2	+	7498.39i	−0.947400	+	0.278182i
$900$		0			0
$901$	−3150.66	+	2024.81i	−0.116497	+	0.0748680i
$902$		0			0
$903$	−9745.05	−	6262.77i	−0.359131	−	0.230799i
$904$		0			0
$905$	3642.95	−	4204.19i	0.133807	−	0.154422i
$906$		0			0
$907$	17409.6	+	38121.7i	0.637349	+	1.39560i	0.902203	+	0.431311i	$0.141949\pi$
$907$	17409.6	+	38121.7i	0.637349	+	1.39560i	−0.264854	+	0.964288i	$0.585324\pi$
$908$		0			0
$909$	−25783.6	−	7570.75i	−0.940802	−	0.276244i
$910$		0			0
$911$	3825.80	−	26609.0i	0.139138	−	0.967724i	−0.793926	−	0.608014i	$-0.791967\pi$
$911$	3825.80	−	26609.0i	0.139138	−	0.967724i	0.933064	−	0.359710i	$-0.117124\pi$
$912$		0			0
$913$	2226.16	−	4874.60i	0.0806955	−	0.176699i
$914$		0			0
$915$	−232.439	−	1616.65i	−0.00839803	−	0.0584096i
$916$		0			0
$917$	−30447.5	−	35138.2i	−1.09647	−	1.26539i
$918$		0			0
$919$	−13821.8			−0.496127			−0.248063	−	0.968744i	$-0.579794\pi$
$919$	−13821.8			−0.496127			−0.248063	+	0.968744i	$0.579794\pi$
$920$		0			0
$921$	−8337.98			−0.298312
$922$		0			0
$923$	−11695.1	−	13496.8i	−0.417061	−	0.481314i
$924$		0			0
$925$	−226.056	−	1572.26i	−0.00803533	−	0.0558869i
$926$		0			0
$927$	18448.7	−	40396.9i	0.653650	−	1.43129i
$928$		0			0
$929$	2370.49	−	16487.1i	0.0837173	−	0.582266i	−0.904179	−	0.427153i	$-0.859517\pi$
$929$	2370.49	−	16487.1i	0.0837173	−	0.582266i	0.987897	−	0.155114i	$-0.0495743\pi$
$930$		0			0
$931$	−60888.8	−	17878.6i	−2.14345	−	0.629373i
$932$		0			0
$933$	−1520.66	−	3329.78i	−0.0533593	−	0.116840i
$934$		0			0
$935$	39066.4	−	45085.0i	1.36642	−	1.57694i
$936$		0			0
$937$	47314.1	+	30406.9i	1.64961	+	1.06014i	0.931194	+	0.364525i	$0.118768\pi$
$937$	47314.1	+	30406.9i	1.64961	+	1.06014i	0.718415	+	0.695615i	$0.244868\pi$
$938$		0			0
$939$	7902.50	−	5078.63i	0.274641	−	0.176501i
$940$		0			0
$941$	11010.5	−	3232.96i	0.381435	−	0.112000i	−0.0853933	−	0.996347i	$-0.527215\pi$
$941$	11010.5	−	3232.96i	0.381435	−	0.112000i	0.466829	+	0.884348i	$0.345397\pi$
$942$		0			0
$943$	13425.4	+	1179.48i	0.463618	+	0.0407309i
$944$		0			0
$945$	22033.8	−	6469.70i	0.758475	−	0.222708i
$946$		0			0
$947$	−19351.2	+	12436.3i	−0.664024	+	0.426743i	−0.828767	−	0.559594i	$-0.810957\pi$
$947$	−19351.2	+	12436.3i	−0.664024	+	0.426743i	0.164743	+	0.986337i	$0.447321\pi$
$948$		0			0
$949$	3445.51	+	2214.29i	0.117857	+	0.0757419i
$950$		0			0
$951$	1283.58	−	1481.34i	0.0437677	−	0.0505106i
$952$		0			0
$953$	−1852.19	−	4055.74i	−0.0629574	−	0.137858i	0.875538	−	0.483149i	$-0.160507\pi$
$953$	−1852.19	−	4055.74i	−0.0629574	−	0.137858i	−0.938495	+	0.345292i	$0.887780\pi$
$954$		0			0
$955$	−12173.4	−	3574.43i	−0.412484	−	0.121116i
$956$		0			0
$957$	−1405.31	+	9774.18i	−0.0474685	+	0.330151i
$958$		0			0
$959$	−24852.3	+	54418.8i	−0.836831	+	1.83240i
$960$		0			0
$961$	−1129.82	−	7858.09i	−0.0379249	−	0.263774i
$962$		0			0
$963$	−9571.27	−	11045.8i	−0.320280	−	0.369623i
$964$		0			0
$965$	10973.6			0.366066
$966$		0			0
$967$	−3713.80			−0.123503			−0.0617517	−	0.998092i	$-0.519669\pi$
$967$	−3713.80			−0.123503			−0.0617517	+	0.998092i	$0.519669\pi$
$968$		0			0
$969$	2991.32	+	3452.17i	0.0991693	+	0.114447i
$970$		0			0
$971$	2320.14	+	16136.9i	0.0766805	+	0.533324i	0.991565	+	0.129609i	$0.0413723\pi$
$971$	2320.14	+	16136.9i	0.0766805	+	0.533324i	−0.914885	+	0.403715i	$0.867719\pi$
$972$		0			0
$973$	−2959.46	+	6480.32i	−0.0975087	+	0.213514i
$974$		0			0
$975$	43.4537	−	302.227i	0.00142731	−	0.00992719i
$976$		0			0
$977$	19993.0	+	5870.48i	0.654691	+	0.192235i	0.592175	−	0.805809i	$-0.298269\pi$
$977$	19993.0	+	5870.48i	0.654691	+	0.192235i	0.0625162	+	0.998044i	$0.480088\pi$
$978$		0			0
$979$	−11252.6	−	24639.7i	−0.367348	−	0.804380i
$980$		0			0
$981$	−24837.4	+	28663.9i	−0.808357	+	0.932894i
$982$		0			0
$983$	4299.99	+	2763.43i	0.139520	+	0.0896642i	0.608539	−	0.793524i	$-0.291756\pi$
$983$	4299.99	+	2763.43i	0.139520	+	0.0896642i	−0.469019	+	0.883188i	$0.655392\pi$
$984$		0			0
$985$	42580.8	−	27365.0i	1.37740	−	0.885201i
$986$		0			0
$987$	−12897.2	+	3786.95i	−0.415929	+	0.122128i
$988$		0			0
$989$	30947.8	−	16252.4i	0.995028	−	0.522545i
$990$		0			0
$991$	−24438.3	+	7175.74i	−0.783359	+	0.230015i	−0.648869	−	0.760900i	$-0.724758\pi$
$991$	−24438.3	+	7175.74i	−0.783359	+	0.230015i	−0.134490	+	0.990915i	$0.542940\pi$
$992$		0			0
$993$	2454.39	−	1577.34i	0.0784368	−	0.0504083i
$994$		0			0
$995$	−25266.2	−	16237.6i	−0.805019	−	0.517354i
$996$		0			0
$997$	2418.90	−	2791.56i	0.0768378	−	0.0886756i	−0.716029	−	0.698071i	$-0.754042\pi$
$997$	2418.90	−	2791.56i	0.0768378	−	0.0886756i	0.792867	+	0.609395i	$0.208588\pi$
$998$		0			0
$999$	2259.10	+	4946.74i	0.0715463	+	0.156665i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	184.4.i.a.9.6	✓	90
23.18	even	11	inner	184.4.i.a.41.6	yes	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.4.i.a.9.6	✓	90	1.1	even	1	trivial
184.4.i.a.41.6	yes	90	23.18	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)

\(f(q)\)	\(=\)	\(q+(0.658159 + 0.759556i) q^{3} +(-1.68723 - 11.7349i) q^{5} +(-15.1088 + 33.0837i) q^{7} +(3.69875 - 25.7254i) q^{9} +(68.8010 + 20.2018i) q^{11} +(8.11313 + 17.7653i) q^{13} +(7.80288 - 9.00501i) q^{15} +(59.0342 + 37.9390i) q^{17} +(54.4857 - 35.0158i) q^{19} +(-35.0729 + 10.2983i) q^{21} +(25.1929 - 107.389i) q^{23} +(-14.9255 + 4.38253i) q^{25} +(44.8025 - 28.7928i) q^{27} +(115.270 + 74.0793i) q^{29} +(-127.201 + 146.798i) q^{31} +(29.9376 + 65.5543i) q^{33} +(413.727 + 121.481i) q^{35} +(-14.5321 + 101.073i) q^{37} +(-8.15400 + 17.8548i) q^{39} +(17.3882 + 120.938i) q^{41} +(207.528 + 239.500i) q^{43} -308.126 q^{45} +367.725 q^{47} +(-641.637 - 740.488i) q^{49} +(10.0371 + 69.8096i) q^{51} +(-22.1707 + 48.5472i) q^{53} +(120.984 - 841.461i) q^{55} +(62.4567 + 18.3389i) q^{57} +(-193.862 - 424.498i) q^{59} +(89.7639 - 103.593i) q^{61} +(795.206 + 511.048i) q^{63} +(194.786 - 125.181i) q^{65} +(-804.280 + 236.158i) q^{67} +(98.1487 - 51.5433i) q^{69} +(-877.383 + 257.623i) q^{71} +(176.420 - 113.378i) q^{73} +(-13.1521 - 8.45237i) q^{75} +(-1707.85 + 1970.97i) q^{77} +(115.785 + 253.534i) q^{79} +(-621.946 - 182.620i) q^{81} +(10.6358 - 73.9737i) q^{83} +(345.607 - 756.775i) q^{85} +(19.5984 + 136.310i) q^{87} +(-247.380 - 285.492i) q^{89} -710.321 q^{91} -195.220 q^{93} +(-502.838 - 580.307i) q^{95} +(-64.5225 - 448.764i) q^{97} +(774.176 - 1695.21i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 2 q^{3} - 87 q^{7} - 113 q^{9} - 6 q^{11} - 8 q^{13} - 6 q^{15} + 306 q^{17} + 275 q^{19} + 350 q^{21} - 23 q^{23} - 289 q^{25} + 511 q^{27} + 309 q^{29} - 314 q^{31} - 1444 q^{33} - 1895 q^{35}+ \cdots + 5967 q^{99}+O(q^{100}) \) 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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