LMFDB - Embedded newform 252.4.i.a.25.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(25,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 4]))

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

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

chi := DirichletCharacter("252.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.6
Character	$\chi$	$=$	252.25
Dual form			252.4.i.a.121.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.01985 - 3.29253i) q^{3} +(3.23563 - 5.60427i) q^{5} +(4.58917 + 17.9427i) q^{7} +(5.31845 + 26.4710i) q^{9} +O(q^{10})$	\(q+(-4.01985 - 3.29253i) q^{3} +(3.23563 - 5.60427i) q^{5} +(4.58917 + 17.9427i) q^{7} +(5.31845 + 26.4710i) q^{9} +(-2.23163 - 3.86530i) q^{11} +(-20.7145 - 35.8785i) q^{13} +(-31.4590 + 11.8749i) q^{15} +(-50.9198 + 88.1956i) q^{17} +(75.6705 + 131.065i) q^{19} +(40.6291 - 87.2369i) q^{21} +(60.2473 - 104.351i) q^{23} +(41.5614 + 71.9865i) q^{25} +(65.7773 - 123.921i) q^{27} +(114.801 - 198.841i) q^{29} +296.677 q^{31} +(-3.75579 + 22.8856i) q^{33} +(115.404 + 32.3369i) q^{35} +(-89.8577 - 155.638i) q^{37} +(-34.8620 + 212.429i) q^{39} +(242.341 + 419.748i) q^{41} +(-57.7297 + 99.9908i) q^{43} +(165.559 + 55.8443i) q^{45} +507.677 q^{47} +(-300.879 + 164.684i) q^{49} +(495.077 - 186.878i) q^{51} +(-57.0200 + 98.7615i) q^{53} -28.8829 q^{55} +(127.352 - 776.011i) q^{57} -297.103 q^{59} +10.5273 q^{61} +(-450.553 + 216.907i) q^{63} -268.097 q^{65} +322.893 q^{67} +(-585.766 + 221.111i) q^{69} +799.850 q^{71} +(-417.999 + 723.996i) q^{73} +(69.9471 - 426.218i) q^{75} +(59.1124 - 57.7799i) q^{77} -933.660 q^{79} +(-672.428 + 281.569i) q^{81} +(625.063 - 1082.64i) q^{83} +(329.515 + 570.737i) q^{85} +(-1116.17 + 421.326i) q^{87} +(-248.345 - 430.147i) q^{89} +(548.694 - 536.325i) q^{91} +(-1192.60 - 976.818i) q^{93} +979.367 q^{95} +(-735.318 + 1273.61i) q^{97} +(90.4495 - 79.6309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9}+O(q^{10}) $ 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9	$ 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9} + 4 q^{11} - 12 q^{13} - 26 q^{15} + 112 q^{17} + 60 q^{19} - 80 q^{21} + 10 q^{23} - 600 q^{25} + 194 q^{29} + 60 q^{31} - 472 q^{33} + 394 q^{35} - 84 q^{37} + 604 q^{39} + 210 q^{41} + 42 q^{43} + 254 q^{45} - 132 q^{47} - 78 q^{49} - 58 q^{51} - 468 q^{53} + 612 q^{55} + 1476 q^{57} - 916 q^{59} - 804 q^{61} - 444 q^{63} + 1656 q^{65} - 588 q^{67} - 28 q^{69} - 2228 q^{71} - 336 q^{73} - 668 q^{75} - 1216 q^{77} - 768 q^{79} - 104 q^{81} + 1024 q^{83} + 360 q^{85} + 2188 q^{87} + 2922 q^{89} - 120 q^{91} - 1292 q^{93} + 2428 q^{95} - 264 q^{97} - 2246 q^{99}+O(q^{100}) $ 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9 + 4 * q^11 - 12 * q^13 - 26 * q^15 + 112 * q^17 + 60 * q^19 - 80 * q^21 + 10 * q^23 - 600 * q^25 + 194 * q^29 + 60 * q^31 - 472 * q^33 + 394 * q^35 - 84 * q^37 + 604 * q^39 + 210 * q^41 + 42 * q^43 + 254 * q^45 - 132 * q^47 - 78 * q^49 - 58 * q^51 - 468 * q^53 + 612 * q^55 + 1476 * q^57 - 916 * q^59 - 804 * q^61 - 444 * q^63 + 1656 * q^65 - 588 * q^67 - 28 * q^69 - 2228 * q^71 - 336 * q^73 - 668 * q^75 - 1216 * q^77 - 768 * q^79 - 104 * q^81 + 1024 * q^83 + 360 * q^85 + 2188 * q^87 + 2922 * q^89 - 120 * q^91 - 1292 * q^93 + 2428 * q^95 - 264 * q^97 - 2246 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−4.01985	−	3.29253i	−0.773621	−	0.633648i
$3$	−4.01985	−	3.29253i	−0.773621	−	0.633648i
$4$		0			0
$5$	3.23563	−	5.60427i	0.289403	−	0.501261i	−0.684264	−	0.729234i	$-0.739876\pi$
$5$	3.23563	−	5.60427i	0.289403	−	0.501261i	0.973667	+	0.227973i	$0.0732098\pi$
$6$		0			0
$7$	4.58917	+	17.9427i	0.247792	+	0.968813i
$7$	4.58917	+	17.9427i	0.247792	+	0.968813i
$8$		0			0
$9$	5.31845	+	26.4710i	0.196980	+	0.980408i
$10$		0			0
$11$	−2.23163	−	3.86530i	−0.0611692	−	0.105948i	0.833819	−	0.552038i	$-0.186150\pi$
$11$	−2.23163	−	3.86530i	−0.0611692	−	0.105948i	−0.894988	+	0.446090i	$0.852816\pi$
$12$		0			0
$13$	−20.7145	−	35.8785i	−0.441935	−	0.765454i	0.555898	−	0.831250i	$-0.312374\pi$
$13$	−20.7145	−	35.8785i	−0.441935	−	0.765454i	−0.997833	+	0.0657966i	$0.979041\pi$
$14$		0			0
$15$	−31.4590	+	11.8749i	−0.541512	+	0.204406i
$16$		0			0
$17$	−50.9198	+	88.1956i	−0.726462	+	1.25827i	0.231907	+	0.972738i	$0.425503\pi$
$17$	−50.9198	+	88.1956i	−0.726462	+	1.25827i	−0.958369	+	0.285532i	$0.907830\pi$
$18$		0			0
$19$	75.6705	+	131.065i	0.913685	+	1.58255i	0.808815	+	0.588063i	$0.200109\pi$
$19$	75.6705	+	131.065i	0.913685	+	1.58255i	0.104869	+	0.994486i	$0.466558\pi$
$20$		0			0
$21$	40.6291	−	87.2369i	0.422190	−	0.906507i
$22$		0			0
$23$	60.2473	−	104.351i	0.546193	−	0.946034i	−0.452338	−	0.891847i	$-0.649410\pi$
$23$	60.2473	−	104.351i	0.546193	−	0.946034i	0.998531	−	0.0541873i	$-0.0172568\pi$
$24$		0			0
$25$	41.5614	+	71.9865i	0.332491	+	0.575892i
$26$		0			0
$27$	65.7773	−	123.921i	0.468846	−	0.883280i
$28$		0			0
$29$	114.801	−	198.841i	0.735104	−	1.27324i	−0.219574	−	0.975596i	$-0.570467\pi$
$29$	114.801	−	198.841i	0.735104	−	1.27324i	0.954678	−	0.297641i	$-0.0961998\pi$
$30$		0			0
$31$	296.677			1.71886			0.859431	−	0.511252i	$-0.170818\pi$
$31$	296.677			1.71886			0.859431	+	0.511252i	$0.170818\pi$
$32$		0			0
$33$	−3.75579	+	22.8856i	−0.0198121	+	0.120724i
$34$		0			0
$35$	115.404	+	32.3369i	0.557340	+	0.156170i
$36$		0			0
$37$	−89.8577	−	155.638i	−0.399257	−	0.691534i	0.594377	−	0.804186i	$-0.297399\pi$
$37$	−89.8577	−	155.638i	−0.399257	−	0.691534i	−0.993634	+	0.112653i	$0.964065\pi$
$38$		0			0
$39$	−34.8620	+	212.429i	−0.143138	+	0.872203i
$40$		0			0
$41$	242.341	+	419.748i	0.923107	+	1.59887i	0.794578	+	0.607162i	$0.207692\pi$
$41$	242.341	+	419.748i	0.923107	+	1.59887i	0.128528	+	0.991706i	$0.458975\pi$
$42$		0			0
$43$	−57.7297	+	99.9908i	−0.204737	+	0.354615i	−0.950049	−	0.312101i	$-0.898967\pi$
$43$	−57.7297	+	99.9908i	−0.204737	+	0.354615i	0.745312	+	0.666716i	$0.232301\pi$
$44$		0			0
$45$	165.559	+	55.8443i	0.548447	+	0.184995i
$46$		0			0
$47$	507.677			1.57558			0.787790	−	0.615944i	$-0.211225\pi$
$47$	507.677			1.57558			0.787790	+	0.615944i	$0.211225\pi$
$48$		0			0
$49$	−300.879	+	164.684i	−0.877199	+	0.480128i
$50$		0			0
$51$	495.077	−	186.878i	1.35931	−	0.513102i
$52$		0			0
$53$	−57.0200	+	98.7615i	−0.147779	+	0.255961i	−0.930406	−	0.366530i	$-0.880546\pi$
$53$	−57.0200	+	98.7615i	−0.147779	+	0.255961i	0.782627	+	0.622491i	$0.213879\pi$
$54$		0			0
$55$	−28.8829			−0.0708104
$56$		0			0
$57$	127.352	−	776.011i	0.295933	−	1.80325i
$58$		0			0
$59$	−297.103			−0.655586			−0.327793	−	0.944750i	$-0.606305\pi$
$59$	−297.103			−0.655586			−0.327793	+	0.944750i	$0.606305\pi$
$60$		0			0
$61$	10.5273			0.0220965			0.0110483	−	0.999939i	$-0.496483\pi$
$61$	10.5273			0.0220965			0.0110483	+	0.999939i	$0.496483\pi$
$62$		0			0
$63$	−450.553	+	216.907i	−0.901022	+	0.433773i
$64$		0			0
$65$	−268.097			−0.511590
$66$		0			0
$67$	322.893			0.588771			0.294386	−	0.955687i	$-0.404885\pi$
$67$	322.893			0.588771			0.294386	+	0.955687i	$0.404885\pi$
$68$		0			0
$69$	−585.766	+	221.111i	−1.02200	+	0.385778i
$70$		0			0
$71$	799.850			1.33697			0.668484	−	0.743726i	$-0.266943\pi$
$71$	799.850			1.33697			0.668484	+	0.743726i	$0.266943\pi$
$72$		0			0
$73$	−417.999	+	723.996i	−0.670180	+	1.16079i	0.307673	+	0.951492i	$0.400450\pi$
$73$	−417.999	+	723.996i	−0.670180	+	1.16079i	−0.977853	+	0.209293i	$0.932884\pi$
$74$		0			0
$75$	69.9471	−	426.218i	0.107691	−	0.656205i
$76$		0			0
$77$	59.1124	−	57.7799i	0.0874868	−	0.0855147i
$78$		0			0
$79$	−933.660			−1.32968			−0.664842	−	0.746984i	$-0.731501\pi$
$79$	−933.660			−1.32968			−0.664842	+	0.746984i	$0.731501\pi$
$80$		0			0
$81$	−672.428	+	281.569i	−0.922398	+	0.386240i
$82$		0			0
$83$	625.063	−	1082.64i	0.826622	−	1.43175i	−0.0740517	−	0.997254i	$-0.523593\pi$
$83$	625.063	−	1082.64i	0.826622	−	1.43175i	0.900673	−	0.434497i	$-0.143074\pi$
$84$		0			0
$85$	329.515	+	570.737i	0.420481	+	0.728295i
$86$		0			0
$87$	−1116.17	+	421.326i	−1.37548	+	0.519206i
$88$		0			0
$89$	−248.345	−	430.147i	−0.295782	−	0.512309i	0.679385	−	0.733782i	$-0.262247\pi$
$89$	−248.345	−	430.147i	−0.295782	−	0.512309i	−0.975166	+	0.221473i	$0.928913\pi$
$90$		0			0
$91$	548.694	−	536.325i	0.632074	−	0.617826i
$92$		0			0
$93$	−1192.60	−	976.818i	−1.32975	−	1.08915i
$94$		0			0
$95$	979.367			1.05769
$96$		0			0
$97$	−735.318	+	1273.61i	−0.769693	+	1.33315i	0.168036	+	0.985781i	$0.446257\pi$
$97$	−735.318	+	1273.61i	−0.769693	+	1.33315i	−0.937729	+	0.347367i	$0.887076\pi$
$98$		0			0
$99$	90.4495	−	79.6309i	0.0918234	−	0.0808404i
$100$		0			0
$101$	−124.068	−	214.893i	−0.122230	−	0.211709i	0.798417	−	0.602106i	$-0.205671\pi$
$101$	−124.068	−	214.893i	−0.122230	−	0.211709i	−0.920647	+	0.390396i	$0.872338\pi$
$102$		0			0
$103$	−614.345	+	1064.08i	−0.587701	+	1.01793i	0.406832	+	0.913503i	$0.366633\pi$
$103$	−614.345	+	1064.08i	−0.587701	+	1.01793i	−0.994533	+	0.104425i	$0.966700\pi$
$104$		0			0
$105$	−357.439	−	509.963i	−0.332214	−	0.473974i
$106$		0			0
$107$	595.501	+	1031.44i	0.538030	+	0.931896i	0.999010	+	0.0444852i	$0.0141648\pi$
$107$	595.501	+	1031.44i	0.538030	+	0.931896i	−0.460980	+	0.887411i	$0.652502\pi$
$108$		0			0
$109$	18.7648	−	32.5016i	0.0164894	−	0.0285604i	−0.857663	−	0.514212i	$-0.828084\pi$
$109$	18.7648	−	32.5016i	0.0164894	−	0.0285604i	0.874152	+	0.485652i	$0.161418\pi$
$110$		0			0
$111$	−151.229	+	921.502i	−0.129315	+	0.787974i
$112$		0			0
$113$	−92.2655	−	159.809i	−0.0768107	−	0.133040i	0.825062	−	0.565043i	$-0.191140\pi$
$113$	−92.2655	−	159.809i	−0.0768107	−	0.133040i	−0.901872	+	0.432003i	$0.857807\pi$
$114$		0			0
$115$	−389.876	−	675.285i	−0.316140	−	0.547571i
$116$		0			0
$117$	839.571	−	739.150i	0.663405	−	0.584055i
$118$		0			0
$119$	−1816.14	−	508.893i	−1.39904	−	0.392018i
$120$		0			0
$121$	655.540	−	1135.43i	0.492517	−	0.853064i
$122$		0			0
$123$	407.856	−	2485.24i	0.298985	−	1.82184i
$124$		0			0
$125$	1346.82			0.963703
$126$		0			0
$127$	−195.325			−0.136475			−0.0682375	−	0.997669i	$-0.521738\pi$
$127$	−195.325			−0.136475			−0.0682375	+	0.997669i	$0.521738\pi$
$128$		0			0
$129$	561.288	−	211.871i	0.383090	−	0.144606i
$130$		0			0
$131$	−735.750	+	1274.36i	−0.490708	+	0.849931i	−0.999943	−	0.0106964i	$-0.996595\pi$
$131$	−735.750	+	1274.36i	−0.490708	+	0.849931i	0.509235	+	0.860628i	$0.329928\pi$
$132$		0			0
$133$	−2004.40	+	1959.21i	−1.30679	+	1.27733i
$134$		0			0
$135$	−481.655	−	769.595i	−0.307068	−	0.490639i
$136$		0			0
$137$	−279.211	−	483.608i	−0.174121	−	0.301587i	0.765735	−	0.643156i	$-0.222375\pi$
$137$	−279.211	−	483.608i	−0.174121	−	0.301587i	−0.939857	+	0.341568i	$0.889042\pi$
$138$		0			0
$139$	1370.00	+	2372.91i	0.835986	+	1.44797i	0.893225	+	0.449609i	$0.148437\pi$
$139$	1370.00	+	2372.91i	0.835986	+	1.44797i	−0.0572395	+	0.998360i	$0.518230\pi$
$140$		0			0
$141$	−2040.79	−	1671.54i	−1.21890	−	0.998364i
$142$		0			0
$143$	−92.4540	+	160.135i	−0.0540657	+	0.0936445i
$144$		0			0
$145$	−742.907	−	1286.75i	−0.425483	−	0.736958i
$146$		0			0
$147$	1751.72	+	328.650i	0.982852	+	0.184399i
$148$		0			0
$149$	558.641	−	967.594i	0.307152	−	0.532003i	−0.670586	−	0.741832i	$-0.733957\pi$
$149$	558.641	−	967.594i	0.307152	−	0.532003i	0.977738	+	0.209829i	$0.0672907\pi$
$150$		0			0
$151$	535.364	+	927.277i	0.288525	+	0.499740i	0.973458	−	0.228866i	$-0.0735018\pi$
$151$	535.364	+	927.277i	0.288525	+	0.499740i	−0.684933	+	0.728606i	$0.740168\pi$
$152$		0			0
$153$	−2605.44	−	878.834i	−1.37672	−	0.464376i
$154$		0			0
$155$	959.936	−	1662.66i	0.497445	−	0.861599i
$156$		0			0
$157$	−1361.29			−0.691993			−0.345996	−	0.938236i	$-0.612459\pi$
$157$	−1361.29			−0.691993			−0.345996	+	0.938236i	$0.612459\pi$
$158$		0			0
$159$	554.387	−	209.267i	0.276514	−	0.104377i
$160$		0			0
$161$	2148.83	+	602.112i	1.05187	+	0.294740i
$162$		0			0
$163$	−199.390	−	345.353i	−0.0958123	−	0.165952i	0.814135	−	0.580676i	$-0.197212\pi$
$163$	−199.390	−	345.353i	−0.0958123	−	0.165952i	−0.909947	+	0.414724i	$0.863878\pi$
$164$		0			0
$165$	116.105	+	95.0979i	0.0547804	+	0.0448689i
$166$		0			0
$167$	232.578	+	402.837i	0.107769	+	0.186661i	0.914866	−	0.403757i	$-0.132296\pi$
$167$	232.578	+	402.837i	0.107769	+	0.186661i	−0.807097	+	0.590419i	$0.798963\pi$
$168$		0			0
$169$	240.323	−	416.252i	0.109387	−	0.189464i
$170$		0			0
$171$	−3066.98	+	2700.14i	−1.37157	+	1.20751i
$172$		0			0
$173$	1078.07			0.473780			0.236890	−	0.971536i	$-0.423872\pi$
$173$	1078.07			0.473780			0.236890	+	0.971536i	$0.423872\pi$
$174$		0			0
$175$	−1100.90	+	1076.08i	−0.475543	+	0.464823i
$176$		0			0
$177$	1194.31	+	978.223i	0.507175	+	0.415411i
$178$		0			0
$179$	−1581.28	+	2738.86i	−0.660282	+	1.14364i	0.320260	+	0.947330i	$0.396230\pi$
$179$	−1581.28	+	2738.86i	−0.660282	+	1.14364i	−0.980542	+	0.196311i	$0.937104\pi$
$180$		0			0
$181$	−1402.76			−0.576055			−0.288028	−	0.957622i	$-0.593000\pi$
$181$	−1402.76			−0.576055			−0.288028	+	0.957622i	$0.593000\pi$
$182$		0			0
$183$	−42.3184	−	34.6616i	−0.0170943	−	0.0140014i
$184$		0			0
$185$	−1162.98			−0.462186
$186$		0			0
$187$	454.536			0.177749
$188$		0			0
$189$	2525.33	+	611.528i	0.971909	+	0.235355i
$190$		0			0
$191$	1801.27			0.682383			0.341191	−	0.939994i	$-0.389170\pi$
$191$	1801.27			0.682383			0.341191	+	0.939994i	$0.389170\pi$
$192$		0			0
$193$	826.260			0.308163			0.154082	−	0.988058i	$-0.450758\pi$
$193$	826.260			0.308163			0.154082	+	0.988058i	$0.450758\pi$
$194$		0			0
$195$	1077.71	+	882.719i	0.395777	+	0.324168i
$196$		0			0
$197$	−2737.36			−0.989995			−0.494998	−	0.868894i	$-0.664831\pi$
$197$	−2737.36			−0.989995			−0.494998	+	0.868894i	$0.664831\pi$
$198$		0			0
$199$	283.565	−	491.148i	0.101012	−	0.174958i	−0.811090	−	0.584921i	$-0.801125\pi$
$199$	283.565	−	491.148i	0.101012	−	0.174958i	0.912102	+	0.409964i	$0.134459\pi$
$200$		0			0
$201$	−1297.98	−	1063.14i	−0.455486	−	0.373074i
$202$		0			0
$203$	4094.58	+	1147.32i	1.41568	+	0.396681i
$204$		0			0
$205$	3136.51			1.06860
$206$		0			0
$207$	3082.71	+	1039.82i	1.03509	+	0.349142i
$208$		0			0
$209$	337.737	−	584.978i	0.111779	−	0.193607i
$210$		0			0
$211$	−374.139	−	648.028i	−0.122070	−	0.211432i	0.798514	−	0.601977i	$-0.205620\pi$
$211$	−374.139	−	648.028i	−0.122070	−	0.211432i	−0.920584	+	0.390545i	$0.872287\pi$
$212$		0			0
$213$	−3215.28	−	2633.53i	−1.03431	−	0.847168i
$214$		0			0
$215$	373.584	+	647.066i	0.118503	+	0.205254i
$216$		0			0
$217$	1361.50	+	5323.18i	0.425920	+	1.66526i
$218$		0			0
$219$	4064.08	−	1534.08i	1.25400	−	0.473350i
$220$		0			0
$221$	4219.10			1.28420
$222$		0			0
$223$	1845.88	−	3197.15i	0.554301	−	0.960077i	−0.443657	−	0.896197i	$-0.646319\pi$
$223$	1845.88	−	3197.15i	0.554301	−	0.960077i	0.997958	−	0.0638805i	$-0.0203476\pi$
$224$		0			0
$225$	−1684.51	+	1483.03i	−0.499115	+	0.439416i
$226$		0			0
$227$	−1926.25	−	3336.36i	−0.563215	−	0.975516i	−0.997213	−	0.0746028i	$-0.976231\pi$
$227$	−1926.25	−	3336.36i	−0.563215	−	0.975516i	0.433999	−	0.900913i	$-0.357102\pi$
$228$		0			0
$229$	−245.275	+	424.829i	−0.0707783	+	0.122592i	−0.899243	−	0.437450i	$-0.855882\pi$
$229$	−245.275	+	424.829i	−0.0707783	+	0.122592i	0.828464	+	0.560042i	$0.189215\pi$
$230$		0			0
$231$	−427.866	+	37.6370i	−0.121868	+	0.0107201i
$232$		0			0
$233$	−1367.83	−	2369.15i	−0.384591	−	0.666131i	0.607122	−	0.794609i	$-0.292324\pi$
$233$	−1367.83	−	2369.15i	−0.384591	−	0.666131i	−0.991712	+	0.128478i	$0.958991\pi$
$234$		0			0
$235$	1642.65	−	2845.16i	0.455978	−	0.789778i
$236$		0			0
$237$	3753.18	+	3074.11i	1.02867	+	0.842551i
$238$		0			0
$239$	97.3137	+	168.552i	0.0263377	+	0.0456182i	0.878894	−	0.477017i	$-0.158282\pi$
$239$	97.3137	+	168.552i	0.0263377	+	0.0456182i	−0.852556	+	0.522636i	$0.824949\pi$
$240$		0			0
$241$	863.677	+	1495.93i	0.230848	+	0.399840i	0.958058	−	0.286575i	$-0.0925167\pi$
$241$	863.677	+	1495.93i	0.230848	+	0.399840i	−0.727210	+	0.686415i	$0.759183\pi$
$242$		0			0
$243$	3630.14	+	1082.13i	0.958327	+	0.285672i
$244$		0			0
$245$	−50.6002	+	2219.06i	−0.0131948	+	0.578656i
$246$		0			0
$247$	3134.95	−	5429.89i	0.807579	−	1.39877i
$248$		0			0
$249$	−6077.30	+	2294.02i	−1.54672	+	0.583845i
$250$		0			0
$251$	491.910			0.123701			0.0618507	−	0.998085i	$-0.480300\pi$
$251$	491.910			0.123701			0.0618507	+	0.998085i	$0.480300\pi$
$252$		0			0
$253$	−537.799			−0.133641
$254$		0			0
$255$	554.568	−	3379.22i	0.136190	−	0.829862i
$256$		0			0
$257$	3662.22	−	6343.15i	0.888884	−	1.53959i	0.0476867	−	0.998862i	$-0.484815\pi$
$257$	3662.22	−	6343.15i	0.888884	−	1.53959i	0.841197	−	0.540729i	$-0.181852\pi$
$258$		0			0
$259$	2380.19	−	2326.54i	0.571035	−	0.558162i
$260$		0			0
$261$	5874.09	+	1981.37i	1.39309	+	0.469900i
$262$		0			0
$263$	−531.789	−	921.086i	−0.124683	−	0.215957i	0.796926	−	0.604077i	$-0.206458\pi$
$263$	−531.789	−	921.086i	−0.124683	−	0.215957i	−0.921609	+	0.388120i	$0.873125\pi$
$264$		0			0
$265$	368.991	+	639.111i	0.0855356	+	0.148152i
$266$		0			0
$267$	−417.961	+	2546.81i	−0.0958007	+	0.583755i
$268$		0			0
$269$	−2333.10	+	4041.06i	−0.528817	+	0.915939i	0.470618	+	0.882337i	$0.344031\pi$
$269$	−2333.10	+	4041.06i	−0.528817	+	0.915939i	−0.999435	+	0.0336015i	$0.989302\pi$
$270$		0			0
$271$	1433.87	+	2483.53i	0.321407	+	0.556693i	0.980779	−	0.195124i	$-0.0625109\pi$
$271$	1433.87	+	2483.53i	0.321407	+	0.556693i	−0.659372	+	0.751817i	$0.729178\pi$
$272$		0			0
$273$	−3971.54	+	349.355i	−0.880470	+	0.0774502i
$274$		0			0
$275$	185.499	−	321.294i	0.0406765	−	0.0704537i
$276$		0			0
$277$	−499.792	−	865.665i	−0.108410	−	0.187772i	0.806716	−	0.590939i	$-0.201243\pi$
$277$	−499.792	−	865.665i	−0.108410	−	0.187772i	−0.915126	+	0.403167i	$0.867909\pi$
$278$		0			0
$279$	1577.86	+	7853.33i	0.338581	+	1.68519i
$280$		0			0
$281$	853.086	−	1477.59i	0.181106	−	0.313685i	−0.761151	−	0.648574i	$-0.775366\pi$
$281$	853.086	−	1477.59i	0.181106	−	0.313685i	0.942257	+	0.334889i	$0.108699\pi$
$282$		0			0
$283$	−4841.65			−1.01698			−0.508491	−	0.861067i	$-0.669797\pi$
$283$	−4841.65			−1.01698			−0.508491	+	0.861067i	$0.669797\pi$
$284$		0			0
$285$	−3936.91	−	3224.60i	−0.818255	−	0.670206i
$286$		0			0
$287$	−6419.25	+	6274.54i	−1.32027	+	1.29050i
$288$		0			0
$289$	−2729.15	−	4727.02i	−0.555495	−	0.962145i
$290$		0			0
$291$	7149.27	−	2698.66i	1.44020	−	0.543636i
$292$		0			0
$293$	2899.31	+	5021.75i	0.578087	+	1.00128i	0.995699	+	0.0926506i	$0.0295340\pi$
$293$	2899.31	+	5021.75i	0.578087	+	1.00128i	−0.417612	+	0.908626i	$0.637133\pi$
$294$		0			0
$295$	−961.316	+	1665.05i	−0.189729	+	0.328620i
$296$		0			0
$297$	−625.781	+	22.2965i	−0.122261	+	0.00435614i
$298$		0			0
$299$	−4991.96			−0.965527
$300$		0			0
$301$	−2059.03	−	576.951i	−0.394288	−	0.110481i
$302$		0			0
$303$	−208.805	+	1272.34i	−0.0395892	+	0.241234i
$304$		0			0
$305$	34.0626	−	58.9981i	0.00639481	−	0.0110761i
$306$		0			0
$307$	4827.31			0.897424			0.448712	−	0.893676i	$-0.351883\pi$
$307$	4827.31			0.897424			0.448712	+	0.893676i	$0.351883\pi$
$308$		0			0
$309$	5973.08	−	2254.68i	1.09967	−	0.415095i
$310$		0			0
$311$	−8487.28			−1.54749			−0.773745	−	0.633497i	$-0.781619\pi$
$311$	−8487.28			−1.54749			−0.773745	+	0.633497i	$0.781619\pi$
$312$		0			0
$313$	−1337.68			−0.241566			−0.120783	−	0.992679i	$-0.538541\pi$
$313$	−1337.68			−0.241566			−0.120783	+	0.992679i	$0.538541\pi$
$314$		0			0
$315$	−242.218	+	3226.85i	−0.0433251	+	0.577183i
$316$		0			0
$317$	−6538.30			−1.15845			−0.579223	−	0.815169i	$-0.696644\pi$
$317$	−6538.30			−1.15845			−0.579223	+	0.815169i	$0.696644\pi$
$318$		0			0
$319$	−1024.77			−0.179863
$320$		0			0
$321$	1002.22	−	6106.94i	0.174263	−	1.06186i
$322$		0			0
$323$	−15412.5			−2.65503
$324$		0			0
$325$	1721.84	−	2982.32i	0.293879	−	0.509014i
$326$		0			0
$327$	−182.444	+	68.8679i	−0.0308538	+	0.0116465i
$328$		0			0
$329$	2329.81	+	9109.08i	0.390416	+	1.52644i
$330$		0			0
$331$	4273.56			0.709656			0.354828	−	0.934932i	$-0.384539\pi$
$331$	4273.56			0.709656			0.354828	+	0.934932i	$0.384539\pi$
$332$		0			0
$333$	3641.99	−	3206.38i	0.599340	−	0.527653i
$334$		0			0
$335$	1044.76	−	1809.58i	0.170392	−	0.295128i
$336$		0			0
$337$	−3408.45	−	5903.61i	−0.550950	−	0.954273i	−0.998206	−	0.0598672i	$-0.980932\pi$
$337$	−3408.45	−	5903.61i	−0.550950	−	0.954273i	0.447257	−	0.894406i	$-0.352401\pi$
$338$		0			0
$339$	−155.281	+	946.194i	−0.0248782	+	0.151594i
$340$		0			0
$341$	−662.073	−	1146.74i	−0.105142	−	0.182110i
$342$		0			0
$343$	−4335.65	−	4642.82i	−0.682517	−	0.730870i
$344$		0			0
$345$	−656.154	+	3998.23i	−0.102395	+	0.623934i
$346$		0			0
$347$	4564.91			0.706217			0.353108	−	0.935582i	$-0.385125\pi$
$347$	4564.91			0.706217			0.353108	+	0.935582i	$0.385125\pi$
$348$		0			0
$349$	632.524	−	1095.56i	0.0970150	−	0.168035i	−0.813433	−	0.581659i	$-0.802404\pi$
$349$	632.524	−	1095.56i	0.0970150	−	0.168035i	0.910448	+	0.413624i	$0.135737\pi$
$350$		0			0
$351$	−5808.63	+	206.961i	−0.883310	+	0.0314722i
$352$		0			0
$353$	−5809.54	−	10062.4i	−0.875950	−	1.51719i	−0.855747	−	0.517394i	$-0.826902\pi$
$353$	−5809.54	−	10062.4i	−0.875950	−	1.51719i	−0.0202030	−	0.999796i	$-0.506431\pi$
$354$		0			0
$355$	2588.02	−	4482.58i	0.386923	−	0.670171i
$356$		0			0
$357$	5625.09	+	8025.39i	0.833925	+	1.18977i
$358$		0			0
$359$	−2288.30	−	3963.46i	−0.336412	−	0.582683i	0.647343	−	0.762199i	$-0.275880\pi$
$359$	−2288.30	−	3963.46i	−0.336412	−	0.582683i	−0.983755	+	0.179516i	$0.942547\pi$
$360$		0			0
$361$	−8022.56	+	13895.5i	−1.16964	+	2.02588i
$362$		0			0
$363$	−6373.61	+	2405.87i	−0.921564	+	0.347866i
$364$		0			0
$365$	2704.98	+	4685.16i	0.387905	+	0.671871i
$366$		0			0
$367$	−6256.33	−	10836.3i	−0.889858	−	1.54128i	−0.840043	−	0.542520i	$-0.817470\pi$
$367$	−6256.33	−	10836.3i	−0.889858	−	1.54128i	−0.0498148	−	0.998758i	$-0.515863\pi$
$368$		0			0
$369$	−9822.26	+	8647.43i	−1.38571	+	1.21996i
$370$		0			0
$371$	−2033.72	−	569.858i	−0.284597	−	0.0797454i
$372$		0			0
$373$	3440.80	−	5959.64i	0.477635	−	0.827288i	−0.522036	−	0.852923i	$-0.674827\pi$
$373$	3440.80	−	5959.64i	0.477635	−	0.827288i	0.999671	+	0.0256351i	$0.00816079\pi$
$374$		0			0
$375$	−5414.00	−	4434.44i	−0.745541	−	0.610649i
$376$		0			0
$377$	−9512.16			−1.29947
$378$		0			0
$379$	5620.19			0.761714			0.380857	−	0.924634i	$-0.375629\pi$
$379$	5620.19			0.761714			0.380857	+	0.924634i	$0.375629\pi$
$380$		0			0
$381$	785.179	+	643.115i	0.105580	+	0.0864771i
$382$		0			0
$383$	1718.87	−	2977.16i	0.229321	−	0.397196i	−0.728286	−	0.685273i	$-0.759683\pi$
$383$	1718.87	−	2977.16i	0.229321	−	0.397196i	0.957607	+	0.288078i	$0.0930161\pi$
$384$		0			0
$385$	−132.548	−	518.236i	−0.0175462	−	0.0686020i
$386$		0			0
$387$	−2953.89	−	996.368i	−0.387996	−	0.130874i
$388$		0			0
$389$	4726.94	+	8187.30i	0.616106	+	1.06713i	0.990189	+	0.139732i	$0.0446242\pi$
$389$	4726.94	+	8187.30i	0.616106	+	1.06713i	−0.374083	+	0.927395i	$0.622042\pi$
$390$		0			0
$391$	6135.56	+	10627.1i	0.793577	+	1.37452i
$392$		0			0
$393$	7153.47	−	2700.24i	0.918180	−	0.346588i
$394$		0			0
$395$	−3020.98	+	5232.49i	−0.384815	+	0.666519i
$396$		0			0
$397$	1096.47	+	1899.14i	0.138615	+	0.240089i	0.926973	−	0.375129i	$-0.122401\pi$
$397$	1096.47	+	1899.14i	0.138615	+	0.240089i	−0.788357	+	0.615218i	$0.789068\pi$
$398$		0			0
$399$	14508.1	−	1276.20i	1.82034	−	0.160126i
$400$		0			0
$401$	3263.56	−	5652.65i	0.406420	−	0.703940i	−0.588066	−	0.808813i	$-0.700110\pi$
$401$	3263.56	−	5652.65i	0.406420	−	0.703940i	0.994486	+	0.104873i	$0.0334437\pi$
$402$		0			0
$403$	−6145.50	−	10644.3i	−0.759625	−	1.31571i
$404$		0			0
$405$	−597.737	+	4679.52i	−0.0733377	+	0.574142i
$406$		0			0
$407$	−401.058	+	694.653i	−0.0488445	+	0.0846012i
$408$		0			0
$409$	−2409.38			−0.291286			−0.145643	−	0.989337i	$-0.546525\pi$
$409$	−2409.38			−0.291286			−0.145643	+	0.989337i	$0.546525\pi$
$410$		0			0
$411$	−469.908	+	2863.35i	−0.0563962	+	0.343646i
$412$		0			0
$413$	−1363.46	−	5330.83i	−0.162449	−	0.635140i
$414$		0			0
$415$	−4044.95	−	7006.05i	−0.478454	−	0.828707i
$416$		0			0
$417$	2305.69	−	14049.5i	0.270767	−	1.64990i
$418$		0			0
$419$	−4262.00	−	7382.00i	−0.496927	−	0.860702i	0.503067	−	0.864247i	$-0.332205\pi$
$419$	−4262.00	−	7382.00i	−0.496927	−	0.860702i	−0.999994	+	0.00354511i	$0.998872\pi$
$420$		0			0
$421$	1612.75	−	2793.37i	0.186700	−	0.323374i	−0.757448	−	0.652896i	$-0.773554\pi$
$421$	1612.75	−	2793.37i	0.186700	−	0.323374i	0.944148	+	0.329521i	$0.106887\pi$
$422$		0			0
$423$	2700.05	+	13438.7i	0.310357	+	1.54471i
$424$		0			0
$425$	−8465.19			−0.966170
$426$		0			0
$427$	48.3117	+	188.889i	0.00547534	+	0.0214074i
$428$		0			0
$429$	898.901	−	339.311i	0.101164	−	0.0381867i
$430$		0			0
$431$	454.920	−	787.944i	0.0508416	−	0.0880602i	−0.839485	−	0.543383i	$-0.817143\pi$
$431$	454.920	−	787.944i	0.0508416	−	0.0880602i	0.890326	+	0.455323i	$0.150476\pi$
$432$		0			0
$433$	13706.1			1.52119			0.760593	−	0.649229i	$-0.224908\pi$
$433$	13706.1			1.52119			0.760593	+	0.649229i	$0.224908\pi$
$434$		0			0
$435$	−1250.30	+	7618.60i	−0.137810	+	0.839733i
$436$		0			0
$437$	18235.8			1.99619
$438$		0			0
$439$	11761.0			1.27864			0.639319	−	0.768941i	$-0.279216\pi$
$439$	11761.0			1.27864			0.639319	+	0.768941i	$0.279216\pi$
$440$		0			0
$441$	−5959.56	−	7088.71i	−0.643511	−	0.765437i
$442$		0			0
$443$	−16064.2			−1.72287			−0.861437	−	0.507864i	$-0.830435\pi$
$443$	−16064.2			−1.72287			−0.861437	+	0.507864i	$0.830435\pi$
$444$		0			0
$445$	−3214.21			−0.342401
$446$		0			0
$447$	−5431.49	+	2050.24i	−0.574722	+	0.216942i
$448$		0			0
$449$	16413.8			1.72520			0.862602	−	0.505884i	$-0.168833\pi$
$449$	16413.8			1.72520			0.862602	+	0.505884i	$0.168833\pi$
$450$		0			0
$451$	1081.63	−	1873.44i	0.112931	−	0.195603i
$452$		0			0
$453$	901.007	−	5490.22i	0.0934504	−	0.569433i
$454$		0			0
$455$	−1230.34	−	4810.38i	−0.126768	−	0.495635i
$456$		0			0
$457$	5631.28			0.576412			0.288206	−	0.957568i	$-0.406941\pi$
$457$	5631.28			0.576412			0.288206	+	0.957568i	$0.406941\pi$
$458$		0			0
$459$	7579.90	+	12111.3i	0.770805	+	1.23160i
$460$		0			0
$461$	4684.26	−	8113.37i	0.473248	−	0.819690i	−0.526283	−	0.850310i	$-0.676415\pi$
$461$	4684.26	−	8113.37i	0.473248	−	0.819690i	0.999531	+	0.0306194i	$0.00974797\pi$
$462$		0			0
$463$	−7043.73	−	12200.1i	−0.707020	−	1.22459i	−0.965958	−	0.258700i	$-0.916706\pi$
$463$	−7043.73	−	12200.1i	−0.707020	−	1.22459i	0.258938	−	0.965894i	$-0.416627\pi$
$464$		0			0
$465$	−9333.16	+	3523.02i	−0.930785	+	0.351347i
$466$		0			0
$467$	5780.79	+	10012.6i	0.572811	+	0.992138i	0.996276	+	0.0862257i	$0.0274806\pi$
$467$	5780.79	+	10012.6i	0.572811	+	0.992138i	−0.423464	+	0.905913i	$0.639186\pi$
$468$		0			0
$469$	1481.81	+	5793.56i	0.145893	+	0.570409i
$470$		0			0
$471$	5472.19	+	4482.10i	0.535340	+	0.438480i
$472$		0			0
$473$	515.325			0.0500945
$474$		0			0
$475$	−6289.95	+	10894.5i	−0.607585	+	1.05237i
$476$		0			0
$477$	−2917.57	−	984.118i	−0.280056	−	0.0944647i
$478$		0			0
$479$	−165.544	−	286.731i	−0.0157911	−	0.0273509i	0.858022	−	0.513613i	$-0.171693\pi$
$479$	−165.544	−	286.731i	−0.0157911	−	0.0273509i	−0.873813	+	0.486262i	$0.838360\pi$
$480$		0			0
$481$	−3722.71	+	6447.92i	−0.352892	+	0.611226i
$482$		0			0
$483$	−6655.50	−	9495.50i	−0.626989	−	0.894534i
$484$		0			0
$485$	4758.43	+	8241.84i	0.445504	+	0.771635i
$486$		0			0
$487$	−3747.29	+	6490.49i	−0.348677	+	0.603927i	−0.986015	−	0.166658i	$-0.946702\pi$
$487$	−3747.29	+	6490.49i	−0.348677	+	0.603927i	0.637338	+	0.770585i	$0.280036\pi$
$488$		0			0
$489$	−335.569	+	2044.77i	−0.0310326	+	0.189095i
$490$		0			0
$491$	−4121.41	−	7138.49i	−0.378812	−	0.656121i	0.612078	−	0.790797i	$-0.290334\pi$
$491$	−4121.41	−	7138.49i	−0.378812	−	0.656121i	−0.990890	+	0.134676i	$0.957001\pi$
$492$		0			0
$493$	11691.3	+	20249.9i	1.06805	+	1.84992i
$494$		0			0
$495$	−153.612	−	764.559i	−0.0139482	−	0.0694230i
$496$		0			0
$497$	3670.64	+	14351.5i	0.331290	+	1.29527i
$498$		0			0
$499$	1905.09	−	3299.72i	0.170909	−	0.296023i	−0.767829	−	0.640655i	$-0.778663\pi$
$499$	1905.09	−	3299.72i	0.170909	−	0.296023i	0.938738	+	0.344632i	$0.111996\pi$
$500$		0			0
$501$	391.424	−	2385.12i	0.0349053	−	0.212693i
$502$		0			0
$503$	−12157.8			−1.07771			−0.538855	−	0.842398i	$-0.681143\pi$
$503$	−12157.8			−1.07771			−0.538855	+	0.842398i	$0.681143\pi$
$504$		0			0
$505$	−1605.76			−0.141496
$506$		0			0
$507$	−2336.59	+	881.999i	−0.204677	+	0.0772603i
$508$		0			0
$509$	3389.25	−	5870.35i	0.295139	−	0.511196i	−0.679878	−	0.733325i	$-0.737967\pi$
$509$	3389.25	−	5870.35i	0.295139	−	0.511196i	0.975017	+	0.222129i	$0.0713007\pi$
$510$		0			0
$511$	−14908.7	−	4177.49i	−1.29065	−	0.361646i
$512$		0			0
$513$	21219.1	−	756.033i	1.82621	−	0.0650676i
$514$		0			0
$515$	3975.58	+	6885.91i	0.340165	+	0.589183i
$516$		0			0
$517$	−1132.95	−	1962.32i	−0.0963771	−	0.166930i
$518$		0			0
$519$	−4333.68	−	3549.57i	−0.366526	−	0.300210i
$520$		0			0
$521$	−4431.22	+	7675.10i	−0.372620	+	0.645398i	−0.989968	−	0.141293i	$-0.954874\pi$
$521$	−4431.22	+	7675.10i	−0.372620	+	0.645398i	0.617347	+	0.786691i	$0.288207\pi$
$522$		0			0
$523$	−5447.80	−	9435.87i	−0.455479	−	0.788914i	0.543236	−	0.839580i	$-0.317199\pi$
$523$	−5447.80	−	9435.87i	−0.455479	−	0.788914i	−0.998716	+	0.0506664i	$0.983865\pi$
$524$		0			0
$525$	7968.48	−	700.944i	0.662425	−	0.0582699i
$526$		0			0
$527$	−15106.7	+	26165.6i	−1.24869	+	2.16279i
$528$		0			0
$529$	−1175.98	−	2036.86i	−0.0966536	−	0.167409i
$530$		0			0
$531$	−1580.13	−	7864.62i	−0.129137	−	0.642741i
$532$		0			0
$533$	10039.9	−	17389.7i	0.815906	−	1.41319i
$534$		0			0
$535$	7707.28			0.622831
$536$		0			0
$537$	15374.3	−	5803.39i	1.23547	−	0.466359i
$538$		0			0
$539$	1308.00	+	795.474i	0.104526	+	0.0635686i
$540$		0			0
$541$	−1428.87	−	2474.87i	−0.113552	−	0.196678i	0.803648	−	0.595105i	$-0.202890\pi$
$541$	−1428.87	−	2474.87i	−0.113552	−	0.196678i	−0.917200	+	0.398427i	$0.869556\pi$
$542$		0			0
$543$	5638.87	+	4618.62i	0.445649	+	0.365017i
$544$		0			0
$545$	−121.432	−	210.326i	−0.00954416	−	0.0165310i
$546$		0			0
$547$	1509.55	−	2614.61i	0.117996	−	0.204374i	−0.800978	−	0.598694i	$-0.795686\pi$
$547$	1509.55	−	2614.61i	0.117996	−	0.204374i	0.918973	+	0.394320i	$0.129020\pi$
$548$		0			0
$549$	55.9891	+	278.669i	0.00435256	+	0.0216636i
$550$		0			0
$551$	34748.2			2.68661
$552$		0			0
$553$	−4284.72	−	16752.4i	−0.329484	−	1.28821i
$554$		0			0
$555$	4675.03	+	3829.17i	0.357557	+	0.292863i
$556$		0			0
$557$	2968.07	−	5140.84i	0.225783	−	0.391067i	−0.730771	−	0.682622i	$-0.760839\pi$
$557$	2968.07	−	5140.84i	0.225783	−	0.391067i	0.956554	+	0.291555i	$0.0941727\pi$
$558$		0			0
$559$	4783.36			0.361922
$560$		0			0
$561$	−1827.17	−	1496.58i	−0.137510	−	0.112630i
$562$		0			0
$563$	−9401.46			−0.703773			−0.351887	−	0.936043i	$-0.614460\pi$
$563$	−9401.46			−0.703773			−0.351887	+	0.936043i	$0.614460\pi$
$564$		0			0
$565$	−1194.15			−0.0889171
$566$		0			0
$567$	−8137.99	−	10773.0i	−0.602757	−	0.797924i
$568$		0			0
$569$	−11687.4			−0.861091			−0.430546	−	0.902569i	$-0.641679\pi$
$569$	−11687.4			−0.861091			−0.430546	+	0.902569i	$0.641679\pi$
$570$		0			0
$571$	11144.7			0.816798			0.408399	−	0.912804i	$-0.366087\pi$
$571$	11144.7			0.816798			0.408399	+	0.912804i	$0.366087\pi$
$572$		0			0
$573$	−7240.83	−	5930.73i	−0.527906	−	0.432391i
$574$		0			0
$575$	10015.9			0.726418
$576$		0			0
$577$	−2767.21	+	4792.94i	−0.199654	+	0.345811i	−0.948416	−	0.317028i	$-0.897315\pi$
$577$	−2767.21	+	4792.94i	−0.199654	+	0.345811i	0.748762	+	0.662839i	$0.230648\pi$
$578$		0			0
$579$	−3321.44	−	2720.49i	−0.238402	−	0.195267i
$580$		0			0
$581$	22294.0	+	6246.89i	1.59193	+	0.446066i
$582$		0			0
$583$	508.990			0.0361582
$584$		0			0
$585$	−1425.86	−	7096.80i	−0.100773	−	0.501567i
$586$		0			0
$587$	7322.72	−	12683.3i	0.514891	−	0.891818i	−0.484959	−	0.874537i	$-0.661166\pi$
$587$	7322.72	−	12683.3i	0.514891	−	0.891818i	0.999851	−	0.0172811i	$-0.00550101\pi$
$588$		0			0
$589$	22449.7	+	38884.0i	1.57050	+	2.72018i
$590$		0			0
$591$	11003.8	+	9012.86i	0.765881	+	0.627309i
$592$		0			0
$593$	6892.61	+	11938.4i	0.477311	+	0.826727i	0.999662	−	0.0260034i	$-0.00827807\pi$
$593$	6892.61	+	11938.4i	0.477311	+	0.826727i	−0.522351	+	0.852731i	$0.674945\pi$
$594$		0			0
$595$	−8728.34	+	8531.58i	−0.601390	+	0.587833i
$596$		0			0
$597$	−2757.01	+	1040.70i	−0.189007	+	0.0713450i
$598$		0			0
$599$	5747.04			0.392016			0.196008	−	0.980602i	$-0.437202\pi$
$599$	5747.04			0.392016			0.196008	+	0.980602i	$0.437202\pi$
$600$		0			0
$601$	−5646.18	+	9779.46i	−0.383215	+	0.663748i	−0.991520	−	0.129955i	$-0.958517\pi$
$601$	−5646.18	+	9779.46i	−0.383215	+	0.663748i	0.608305	+	0.793704i	$0.291850\pi$
$602$		0			0
$603$	1717.29	+	8547.30i	0.115976	+	0.577236i
$604$		0			0
$605$	−4242.17	−	7347.65i	−0.285072	−	0.493759i
$606$		0			0
$607$	−10253.6	+	17759.7i	−0.685633	+	1.18755i	0.287604	+	0.957749i	$0.407141\pi$
$607$	−10253.6	+	17759.7i	−0.685633	+	1.18755i	−0.973237	+	0.229802i	$0.926192\pi$
$608$		0			0
$609$	−12682.0	−	18093.6i	−0.843845	−	1.20392i
$610$		0			0
$611$	−10516.2	−	18214.7i	−0.696304	−	1.20603i
$612$		0			0
$613$	−3006.68	+	5207.73i	−0.198106	+	0.343129i	−0.947914	−	0.318526i	$-0.896812\pi$
$613$	−3006.68	+	5207.73i	−0.198106	+	0.343129i	0.749809	+	0.661655i	$0.230146\pi$
$614$		0			0
$615$	−12608.3	−	10327.1i	−0.826692	−	0.677117i
$616$		0			0
$617$	−5309.80	−	9196.84i	−0.346458	−	0.600082i	0.639160	−	0.769074i	$-0.279282\pi$
$617$	−5309.80	−	9196.84i	−0.346458	−	0.600082i	−0.985617	+	0.168992i	$0.945949\pi$
$618$		0			0
$619$	2644.98	+	4581.24i	0.171746	+	0.297473i	0.939030	−	0.343834i	$-0.111726\pi$
$619$	2644.98	+	4581.24i	0.171746	+	0.297473i	−0.767284	+	0.641307i	$0.778393\pi$
$620$		0			0
$621$	−8968.40	−	14329.9i	−0.579532	−	0.925986i
$622$		0			0
$623$	6578.29	−	6430.00i	0.423039	−	0.413503i
$624$		0			0
$625$	−837.380	+	1450.38i	−0.0535923	+	0.0928246i
$626$		0			0
$627$	−3283.71	+	1239.52i	−0.209153	+	0.0789497i
$628$		0			0
$629$	18302.1			1.16018
$630$		0			0
$631$	16123.2			1.01720			0.508601	−	0.861002i	$-0.330163\pi$
$631$	16123.2			1.01720			0.508601	+	0.861002i	$0.330163\pi$
$632$		0			0
$633$	−629.670	+	3836.85i	−0.0395373	+	0.240918i
$634$		0			0
$635$	−632.000	+	1094.66i	−0.0394963	+	0.0684096i
$636$		0			0
$637$	12141.2	+	7383.75i	0.755180	+	0.459270i
$638$		0			0
$639$	4253.96	+	21172.8i	0.263355	+	1.31077i
$640$		0			0
$641$	−7840.30	−	13579.8i	−0.483109	−	0.836770i	0.516702	−	0.856165i	$-0.327159\pi$
$641$	−7840.30	−	13579.8i	−0.483109	−	0.836770i	−0.999812	+	0.0193949i	$0.993826\pi$
$642$		0			0
$643$	6480.16	+	11224.0i	0.397438	+	0.688383i	0.993409	−	0.114623i	$-0.0365660\pi$
$643$	6480.16	+	11224.0i	0.397438	+	0.688383i	−0.595971	+	0.803006i	$0.703233\pi$
$644$		0			0
$645$	628.735	−	3831.15i	0.0383820	−	0.233878i
$646$		0			0
$647$	8862.45	−	15350.2i	0.538514	−	0.932734i	−0.460470	−	0.887675i	$-0.652319\pi$
$647$	8862.45	−	15350.2i	0.538514	−	0.932734i	0.998984	−	0.0450590i	$-0.0143476\pi$
$648$		0			0
$649$	663.025	+	1148.39i	0.0401017	+	0.0694582i
$650$		0			0
$651$	12053.7	−	25881.2i	0.725687	−	1.55816i
$652$		0			0
$653$	−1257.30	+	2177.70i	−0.0753473	+	0.130505i	−0.901237	−	0.433326i	$-0.857340\pi$
$653$	−1257.30	+	2177.70i	−0.0753473	+	0.130505i	0.825890	+	0.563831i	$0.190673\pi$
$654$		0			0
$655$	4761.23	+	8246.68i	0.284025	+	0.491946i
$656$		0			0
$657$	−21388.0	−	7214.33i	−1.27005	−	0.428398i
$658$		0			0
$659$	−9628.10	+	16676.4i	−0.569131	+	0.985764i	0.427521	+	0.904005i	$0.359387\pi$
$659$	−9628.10	+	16676.4i	−0.569131	+	0.985764i	−0.996652	+	0.0817588i	$0.973946\pi$
$660$		0			0
$661$	28649.8			1.68585			0.842926	−	0.538029i	$-0.180831\pi$
$661$	28649.8			1.68585			0.842926	+	0.538029i	$0.180831\pi$
$662$		0			0
$663$	−16960.2	−	13891.5i	−0.993482	−	0.813729i
$664$		0			0
$665$	4494.48	+	17572.5i	0.262088	+	1.02471i
$666$		0			0
$667$	−13832.9	−	23959.3i	−0.803017	−	1.39087i
$668$		0			0
$669$	−17946.9	+	6774.48i	−1.03717	+	0.391504i
$670$		0			0
$671$	−23.4931	−	40.6913i	−0.00135163	−	0.00234109i
$672$		0			0
$673$	−4689.26	+	8122.03i	−0.268585	+	0.465203i	−0.968497	−	0.249027i	$-0.919889\pi$
$673$	−4689.26	+	8122.03i	−0.268585	+	0.465203i	0.699912	+	0.714229i	$0.253223\pi$
$674$		0			0
$675$	11654.4	−	415.245i	0.664561	−	0.0236782i
$676$		0			0
$677$	−13981.6			−0.793732			−0.396866	−	0.917876i	$-0.629902\pi$
$677$	−13981.6			−0.793732			−0.396866	+	0.917876i	$0.629902\pi$
$678$		0			0
$679$	−26226.4	−	7348.77i	−1.48229	−	0.415346i
$680$		0			0
$681$	−3241.84	+	19753.9i	−0.182420	+	1.11156i
$682$		0			0
$683$	−8705.82	+	15078.9i	−0.487729	+	0.844771i	−0.999900	−	0.0141120i	$-0.995508\pi$
$683$	−8705.82	+	15078.9i	−0.487729	+	0.844771i	0.512172	+	0.858883i	$0.328841\pi$
$684$		0			0
$685$	−3613.70			−0.201565
$686$		0			0
$687$	2384.73	−	900.173i	0.132436	−	0.0499909i
$688$		0			0
$689$	4724.55			0.261235
$690$		0			0
$691$	−19048.8			−1.04870			−0.524348	−	0.851504i	$-0.675691\pi$
$691$	−19048.8			−1.04870			−0.524348	+	0.851504i	$0.675691\pi$
$692$		0			0
$693$	1843.88	+	1257.47i	0.101072	+	0.0689281i
$694$		0			0
$695$	17731.3			0.967749
$696$		0			0
$697$	−49359.9			−2.68241
$698$		0			0
$699$	−2302.04	+	14027.3i	−0.124565	+	0.759028i
$700$		0			0
$701$	8141.11			0.438638			0.219319	−	0.975653i	$-0.429616\pi$
$701$	8141.11			0.438638			0.219319	+	0.975653i	$0.429616\pi$
$702$		0			0
$703$	13599.2	−	23554.4i	0.729591	−	1.26369i
$704$		0			0
$705$	−15971.0	+	6028.63i	−0.853196	+	0.322059i
$706$		0			0
$707$	3286.38	−	3212.30i	0.174819	−	0.170878i
$708$		0			0
$709$	−29720.6			−1.57430			−0.787151	−	0.616761i	$-0.788445\pi$
$709$	−29720.6			−1.57430			−0.787151	+	0.616761i	$0.788445\pi$
$710$		0			0
$711$	−4965.62	−	24714.9i	−0.261920	−	1.30363i
$712$		0			0
$713$	17874.0	−	30958.7i	0.938830	−	1.62610i
$714$		0			0
$715$	598.293	+	1036.27i	0.0312936	+	0.0542021i
$716$		0			0
$717$	163.777	−	997.964i	0.00853050	−	0.0519800i
$718$		0			0
$719$	−6373.33	−	11038.9i	−0.330577	−	0.572577i	0.652048	−	0.758178i	$-0.273910\pi$
$719$	−6373.33	−	11038.9i	−0.330577	−	0.572577i	−0.982625	+	0.185601i	$0.940577\pi$
$720$		0			0
$721$	−21911.7	−	6139.77i	−1.13181	−	0.317138i
$722$		0			0
$723$	1453.55	−	8857.12i	0.0747693	−	0.455601i
$724$		0			0
$725$	19085.2			0.977662
$726$		0			0
$727$	9357.28	−	16207.3i	0.477362	−	0.826815i	−0.522301	−	0.852761i	$-0.674926\pi$
$727$	9357.28	−	16207.3i	0.477362	−	0.826815i	0.999663	+	0.0259458i	$0.00825972\pi$
$728$		0			0
$729$	−11029.7	−	16302.3i	−0.560367	−	0.828245i
$730$		0			0
$731$	−5879.17	−	10183.0i	−0.297468	−	0.515229i
$732$		0			0
$733$	−8884.58	+	15388.6i	−0.447694	+	0.775429i	−0.998236	−	0.0593792i	$-0.981088\pi$
$733$	−8884.58	+	15388.6i	−0.447694	+	0.775429i	0.550542	+	0.834808i	$0.314421\pi$
$734$		0			0
$735$	7509.75	−	8753.71i	0.376872	−	0.439300i
$736$		0			0
$737$	−720.578	−	1248.08i	−0.0360147	−	0.0623793i
$738$		0			0
$739$	−3089.53	+	5351.22i	−0.153789	+	0.266371i	−0.932617	−	0.360866i	$-0.882481\pi$
$739$	−3089.53	+	5351.22i	−0.153789	+	0.266371i	0.778828	+	0.627237i	$0.215814\pi$
$740$		0			0
$741$	−30480.1	+	11505.4i	−1.51109	+	0.570395i
$742$		0			0
$743$	561.005	+	971.689i	0.0277002	+	0.0479782i	0.879543	−	0.475819i	$-0.157848\pi$
$743$	561.005	+	971.689i	0.0277002	+	0.0479782i	−0.851843	+	0.523797i	$0.824515\pi$
$744$		0			0
$745$	−3615.11	−	6261.55i	−0.177782	−	0.307927i
$746$		0			0
$747$	31983.0	+	10788.1i	1.56653	+	0.528401i
$748$		0			0
$749$	−15773.9	+	15418.3i	−0.769514	+	0.752167i
$750$		0			0
$751$	821.916	−	1423.60i	0.0399363	−	0.0691717i	−0.845366	−	0.534187i	$-0.820618\pi$
$751$	821.916	−	1423.60i	0.0399363	−	0.0691717i	0.885303	+	0.465015i	$0.153951\pi$
$752$		0			0
$753$	−1977.41	−	1619.63i	−0.0956981	−	0.0783832i
$754$		0			0
$755$	6928.95			0.334001
$756$		0			0
$757$	−16462.4			−0.790404			−0.395202	−	0.918594i	$-0.629325\pi$
$757$	−16462.4			−0.790404			−0.395202	+	0.918594i	$0.629325\pi$
$758$		0			0
$759$	2161.87	+	1770.72i	0.103387	+	0.0846813i
$760$		0			0
$761$	−8028.31	+	13905.4i	−0.382426	+	0.662381i	−0.991408	−	0.130803i	$-0.958245\pi$
$761$	−8028.31	+	13905.4i	−0.382426	+	0.662381i	0.608983	+	0.793184i	$0.291578\pi$
$762$		0			0
$763$	669.280	+	187.536i	0.0317557	+	0.00889809i
$764$		0			0
$765$	−13355.5	+	11758.0i	−0.631200	+	0.555702i
$766$		0			0
$767$	6154.33	+	10659.6i	0.289726	+	0.501821i
$768$		0			0
$769$	17919.1	+	31036.7i	0.840283	+	1.45541i	0.889655	+	0.456633i	$0.150945\pi$
$769$	17919.1	+	31036.7i	0.840283	+	1.45541i	−0.0493722	+	0.998780i	$0.515722\pi$
$770$		0			0
$771$	−35606.6	+	13440.6i	−1.66322	+	0.627821i
$772$		0			0
$773$	9517.66	−	16485.1i	0.442854	−	0.767046i	−0.555046	−	0.831820i	$-0.687299\pi$
$773$	9517.66	−	16485.1i	0.442854	−	0.767046i	0.997900	+	0.0647738i	$0.0206326\pi$
$774$		0			0
$775$	12330.3	+	21356.7i	0.571507	+	0.989879i
$776$		0			0
$777$	−17228.2	+	1515.47i	−0.795443	+	0.0699708i
$778$		0			0
$779$	−36676.2	+	63525.1i	−1.68686	+	2.92172i
$780$		0			0
$781$	−1784.97	−	3091.66i	−0.0817814	−	0.141649i
$782$		0			0
$783$	−17089.2	−	27305.5i	−0.779974	−	1.24625i
$784$		0			0
$785$	−4404.63	+	7629.05i	−0.200265	+	0.346869i
$786$		0			0
$787$	35845.9			1.62360			0.811798	−	0.583939i	$-0.198489\pi$
$787$	35845.9			1.62360			0.811798	+	0.583939i	$0.198489\pi$
$788$		0			0
$789$	−894.991	+	5453.56i	−0.0403834	+	0.246074i
$790$		0			0
$791$	2443.97	−	2388.88i	0.109858	−	0.107381i
$792$		0			0
$793$	−218.068	−	377.705i	−0.00976523	−	0.0169139i
$794$		0			0
$795$	621.005	−	3784.05i	0.0277041	−	0.168813i
$796$		0			0
$797$	−16354.3	−	28326.5i	−0.726850	−	1.25894i	−0.958208	−	0.286073i	$-0.907650\pi$
$797$	−16354.3	−	28326.5i	−0.726850	−	1.25894i	0.231358	−	0.972869i	$-0.425683\pi$
$798$		0			0
$799$	−25850.8	+	44774.9i	−1.14460	+	1.98251i
$800$		0			0
$801$	10065.6	−	8861.67i	0.444009	−	0.390901i
$802$		0			0
$803$	3731.28			0.163978
$804$		0			0
$805$	10327.2	−	10094.4i	0.452157	−	0.441964i
$806$		0			0
$807$	22684.0	−	8562.63i	0.989487	−	0.373505i
$808$		0			0
$809$	4633.70	−	8025.80i	0.201375	−	0.348791i	−0.747597	−	0.664153i	$-0.768792\pi$
$809$	4633.70	−	8025.80i	0.201375	−	0.348791i	0.948972	+	0.315362i	$0.102126\pi$
$810$		0			0
$811$	2535.42			0.109779			0.0548894	−	0.998492i	$-0.482519\pi$
$811$	2535.42			0.109779			0.0548894	+	0.998492i	$0.482519\pi$
$812$		0			0
$813$	2413.17	−	14704.5i	0.104101	−	0.634329i
$814$		0			0
$815$	−2580.60			−0.110914
$816$		0			0
$817$	−17473.8			−0.748261
$818$		0			0
$819$	17115.3	+	11672.1i	0.730227	+	0.497991i
$820$		0			0
$821$	−34226.6			−1.45495			−0.727477	−	0.686132i	$-0.759307\pi$
$821$	−34226.6			−1.45495			−0.727477	+	0.686132i	$0.759307\pi$
$822$		0			0
$823$	−26566.0			−1.12519			−0.562596	−	0.826732i	$-0.690197\pi$
$823$	−26566.0			−1.12519			−0.562596	+	0.826732i	$0.690197\pi$
$824$		0			0
$825$	−1803.55	+	680.793i	−0.0761111	+	0.0287299i
$826$		0			0
$827$	32490.0			1.36613			0.683064	−	0.730358i	$-0.260647\pi$
$827$	32490.0			1.36613			0.683064	+	0.730358i	$0.260647\pi$
$828$		0			0
$829$	1977.57	−	3425.25i	0.0828513	−	0.143503i	−0.821622	−	0.570032i	$-0.806931\pi$
$829$	1977.57	−	3425.25i	0.0828513	−	0.143503i	0.904474	+	0.426530i	$0.140264\pi$
$830$		0			0
$831$	−841.140	+	5125.43i	−0.0351129	+	0.213958i
$832$		0			0
$833$	796.306	−	34921.9i	0.0331217	−	1.45255i
$834$		0			0
$835$	3010.14			0.124755
$836$		0			0
$837$	19514.6	−	36764.4i	0.805882	−	1.51824i
$838$		0			0
$839$	22845.8	−	39570.1i	0.940078	−	1.62826i	0.174759	−	0.984611i	$-0.444085\pi$
$839$	22845.8	−	39570.1i	0.940078	−	1.62826i	0.765319	−	0.643651i	$-0.222581\pi$
$840$		0			0
$841$	−14164.0	−	24532.8i	−0.580755	−	1.00590i
$842$		0			0
$843$	−8294.29	+	3130.87i	−0.338874	+	0.127916i
$844$		0			0
$845$	−1555.19	−	2693.67i	−0.0633139	−	0.109663i
$846$		0			0
$847$	23381.0	+	6551.47i	0.948501	+	0.265775i
$848$		0			0
$849$	19462.7	+	15941.3i	0.786759	+	0.644409i
$850$		0			0
$851$	−21654.8			−0.872286
$852$		0			0
$853$	9568.93	−	16573.9i	0.384096	−	0.665274i	−0.607547	−	0.794284i	$-0.707846\pi$
$853$	9568.93	−	16573.9i	0.384096	−	0.665274i	0.991643	+	0.129010i	$0.0411798\pi$
$854$		0			0
$855$	5208.71	+	25924.8i	0.208344	+	1.03697i
$856$		0			0
$857$	23956.1	+	41493.1i	0.954870	+	1.65388i	0.734666	+	0.678429i	$0.237339\pi$
$857$	23956.1	+	41493.1i	0.954870	+	1.65388i	0.220203	+	0.975454i	$0.429328\pi$
$858$		0			0
$859$	7280.67	−	12610.5i	0.289189	−	0.500890i	−0.684427	−	0.729081i	$-0.739948\pi$
$859$	7280.67	−	12610.5i	0.289189	−	0.500890i	0.973616	+	0.228191i	$0.0732811\pi$
$860$		0			0
$861$	46463.6	−	4087.15i	1.83911	−	0.161777i
$862$		0			0
$863$	6159.68	+	10668.9i	0.242964	+	0.420826i	0.961557	−	0.274605i	$-0.0885470\pi$
$863$	6159.68	+	10668.9i	0.242964	+	0.420826i	−0.718593	+	0.695431i	$0.755214\pi$
$864$		0			0
$865$	3488.23	−	6041.79i	0.137114	−	0.237488i
$866$		0			0
$867$	−4593.10	+	27987.7i	−0.179919	+	1.09632i
$868$		0			0
$869$	2083.58	+	3608.87i	0.0813357	+	0.140878i
$870$		0			0
$871$	−6688.55	−	11584.9i	−0.260199	−	0.450677i
$872$		0			0
$873$	−37624.4	−	12691.0i	−1.45864	−	0.492010i
$874$		0			0
$875$	6180.76	+	24165.5i	0.238798	+	0.933649i
$876$		0			0
$877$	21743.2	−	37660.3i	0.837189	−	1.45005i	−0.0550473	−	0.998484i	$-0.517531\pi$
$877$	21743.2	−	37660.3i	0.837189	−	1.45005i	0.892236	−	0.451569i	$-0.149136\pi$
$878$		0			0
$879$	4879.49	−	29732.8i	0.187237	−	1.14091i
$880$		0			0
$881$	−10762.9			−0.411590			−0.205795	−	0.978595i	$-0.565978\pi$
$881$	−10762.9			−0.411590			−0.205795	+	0.978595i	$0.565978\pi$
$882$		0			0
$883$	13595.9			0.518163			0.259081	−	0.965856i	$-0.416580\pi$
$883$	13595.9			0.518163			0.259081	+	0.965856i	$0.416580\pi$
$884$		0			0
$885$	9346.58	−	3528.08i	0.355008	−	0.134006i
$886$		0			0
$887$	14202.0	−	24598.5i	0.537605	−	0.931159i	−0.461428	−	0.887178i	$-0.652663\pi$
$887$	14202.0	−	24598.5i	0.537605	−	0.931159i	0.999032	−	0.0439808i	$-0.0140041\pi$
$888$		0			0
$889$	−896.380	−	3504.66i	−0.0338174	−	0.132219i
$890$		0			0
$891$	2588.96	+	1970.78i	0.0973439	+	0.0741004i
$892$		0			0
$893$	38416.2	+	66538.8i	1.43958	+	2.49343i
$894$		0			0
$895$	10232.9	+	17723.8i	0.382175	+	0.661947i
$896$		0			0
$897$	20067.0	+	16436.2i	0.746952	+	0.611805i
$898$		0			0
$899$	34058.8	−	58991.5i	1.26354	−	2.18852i
$900$		0			0
$901$	−5806.89	−	10057.8i	−0.214712	−	0.371892i
$902$		0			0
$903$	6377.38	+	9098.69i	0.235023	+	0.335311i
$904$		0			0
$905$	−4538.80	+	7861.43i	−0.166712	+	0.288754i
$906$		0			0
$907$	5022.83	+	8699.79i	0.183881	+	0.318492i	0.943199	−	0.332228i	$-0.107801\pi$
$907$	5022.83	+	8699.79i	0.183881	+	0.318492i	−0.759318	+	0.650720i	$0.774467\pi$
$908$		0			0
$909$	5028.58	−	4427.11i	0.183485	−	0.161538i
$910$		0			0
$911$	−14368.7	+	24887.3i	−0.522564	+	0.905107i	0.477091	+	0.878854i	$0.341691\pi$
$911$	−14368.7	+	24887.3i	−0.522564	+	0.905107i	−0.999655	+	0.0262535i	$0.991642\pi$
$912$		0			0
$913$	−5579.64			−0.202255
$914$		0			0
$915$	−331.180	+	125.012i	−0.0119655	+	0.00451667i
$916$		0			0
$917$	−26241.8	−	7353.09i	−0.945018	−	0.264799i
$918$		0			0
$919$	12166.5	+	21073.1i	0.436711	+	0.756405i	0.997434	−	0.0715985i	$-0.0228100\pi$
$919$	12166.5	+	21073.1i	0.436711	+	0.756405i	−0.560723	+	0.828004i	$0.689477\pi$
$920$		0			0
$921$	−19405.1	−	15894.1i	−0.694266	−	0.568651i
$922$		0			0
$923$	−16568.5	−	28697.4i	−0.590853	−	1.02339i
$924$		0			0
$925$	7469.23	−	12937.1i	0.265499	−	0.459858i
$926$		0			0
$927$	−31434.5	−	10603.1i	−1.11375	−	0.375675i
$928$		0			0
$929$	−3808.98			−0.134520			−0.0672598	−	0.997735i	$-0.521426\pi$
$929$	−3808.98			−0.134520			−0.0672598	+	0.997735i	$0.521426\pi$
$930$		0			0
$931$	−44352.0	−	26973.1i	−1.56131	−	0.949524i
$932$		0			0
$933$	34117.6	+	27944.7i	1.19717	+	0.980565i
$934$		0			0
$935$	1470.71	−	2547.35i	0.0514411	−	0.0890985i
$936$		0			0
$937$	−10256.6			−0.357597			−0.178799	−	0.983886i	$-0.557221\pi$
$937$	−10256.6			−0.357597			−0.178799	+	0.983886i	$0.557221\pi$
$938$		0			0
$939$	5377.28	+	4404.36i	0.186881	+	0.153068i
$940$		0			0
$941$	−54025.7			−1.87161			−0.935806	−	0.352516i	$-0.885326\pi$
$941$	−54025.7			−1.87161			−0.935806	+	0.352516i	$0.885326\pi$
$942$		0			0
$943$	58401.7			2.01678
$944$		0			0
$945$	11598.2	−	12174.0i	0.399248	−	0.419068i
$946$		0			0
$947$	−14884.5			−0.510750			−0.255375	−	0.966842i	$-0.582199\pi$
$947$	−14884.5			−0.510750			−0.255375	+	0.966842i	$0.582199\pi$
$948$		0			0
$949$	34634.5			1.18470
$950$		0			0
$951$	26283.0	+	21527.6i	0.896199	+	0.734048i
$952$		0			0
$953$	−17355.4			−0.589922			−0.294961	−	0.955509i	$-0.595307\pi$
$953$	−17355.4			−0.589922			−0.294961	+	0.955509i	$0.595307\pi$
$954$		0			0
$955$	5828.23	−	10094.8i	0.197484	−	0.342052i
$956$		0			0
$957$	4119.44	+	3374.10i	0.139146	+	0.113970i
$958$		0			0
$959$	7395.88	−	7229.16i	0.249036	−	0.243422i
$960$		0			0
$961$	58226.1			1.95449
$962$		0			0
$963$	−24136.1	+	21249.2i	−0.807657	+	0.711053i
$964$		0			0
$965$	2673.47	−	4630.59i	0.0891835	−	0.154470i
$966$		0			0
$967$	21366.8	+	37008.3i	0.710557	+	1.23072i	0.964648	+	0.263540i	$0.0848903\pi$
$967$	21366.8	+	37008.3i	0.710557	+	1.23072i	−0.254091	+	0.967180i	$0.581776\pi$
$968$		0			0
$969$	61956.0	+	50746.2i	2.05399	+	1.68236i
$970$		0			0
$971$	1870.85	+	3240.41i	0.0618315	+	0.107095i	0.895284	−	0.445496i	$-0.146973\pi$
$971$	1870.85	+	3240.41i	0.0618315	+	0.107095i	−0.833453	+	0.552591i	$0.813639\pi$
$972$		0			0
$973$	−36289.2	+	35471.2i	−1.19566	+	1.16871i
$974$		0			0
$975$	−16741.0	+	6319.27i	−0.549887	+	0.207568i
$976$		0			0
$977$	−24369.1			−0.797991			−0.398996	−	0.916953i	$-0.630641\pi$
$977$	−24369.1			−0.797991			−0.398996	+	0.916953i	$0.630641\pi$
$978$		0			0
$979$	−1108.43	+	1919.86i	−0.0361855	+	0.0626751i
$980$		0			0
$981$	960.149	+	323.865i	0.0312489	+	0.0105405i
$982$		0			0
$983$	6606.56	+	11442.9i	0.214361	+	0.371284i	0.953075	−	0.302735i	$-0.0978999\pi$
$983$	6606.56	+	11442.9i	0.214361	+	0.371284i	−0.738714	+	0.674019i	$0.764567\pi$
$984$		0			0
$985$	−8857.09	+	15340.9i	−0.286508	+	0.496246i
$986$		0			0
$987$	20626.4	−	44288.2i	0.665195	−	1.42828i
$988$		0			0
$989$	6956.12	+	12048.4i	0.223652	+	0.387377i
$990$		0			0
$991$	−15594.4	+	27010.4i	−0.499873	+	0.865805i	−1.00000		0.000147065i	$-0.999953\pi$
$991$	−15594.4	+	27010.4i	−0.499873	+	0.865805i	0.500127	+	0.865952i	$0.333287\pi$
$992$		0			0
$993$	−17179.1	−	14070.8i	−0.549005	−	0.449672i
$994$		0			0
$995$	−1835.02	−	3178.35i	−0.0584663	−	0.101267i
$996$		0			0
$997$	10496.9	+	18181.2i	0.333440	+	0.577536i	0.983184	−	0.182618i	$-0.0584571\pi$
$997$	10496.9	+	18181.2i	0.333440	+	0.577536i	−0.649744	+	0.760153i	$0.725124\pi$
$998$		0			0
$999$	−25197.4	+	897.779i	−0.798008	+	0.0284329i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.i.a.25.6	✓	48
3.2	odd	2		756.4.i.a.613.9		48
7.2	even	3		252.4.l.a.205.21	yes	48
9.4	even	3		252.4.l.a.193.21	yes	48
9.5	odd	6		756.4.l.a.361.16		48
21.2	odd	6		756.4.l.a.289.16		48
63.23	odd	6		756.4.i.a.37.9		48
63.58	even	3	inner	252.4.i.a.121.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.i.a.25.6	✓	48	1.1	even	1	trivial
252.4.i.a.121.6	yes	48	63.58	even	3	inner
252.4.l.a.193.21	yes	48	9.4	even	3
252.4.l.a.205.21	yes	48	7.2	even	3
756.4.i.a.37.9		48	63.23	odd	6
756.4.i.a.613.9		48	3.2	odd	2
756.4.l.a.289.16		48	21.2	odd	6
756.4.l.a.361.16		48	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.01985 - 3.29253i) q^{3} +(3.23563 - 5.60427i) q^{5} +(4.58917 + 17.9427i) q^{7} +(5.31845 + 26.4710i) q^{9} +O(q^{10})\)	\(q+(-4.01985 - 3.29253i) q^{3} +(3.23563 - 5.60427i) q^{5} +(4.58917 + 17.9427i) q^{7} +(5.31845 + 26.4710i) q^{9} +(-2.23163 - 3.86530i) q^{11} +(-20.7145 - 35.8785i) q^{13} +(-31.4590 + 11.8749i) q^{15} +(-50.9198 + 88.1956i) q^{17} +(75.6705 + 131.065i) q^{19} +(40.6291 - 87.2369i) q^{21} +(60.2473 - 104.351i) q^{23} +(41.5614 + 71.9865i) q^{25} +(65.7773 - 123.921i) q^{27} +(114.801 - 198.841i) q^{29} +296.677 q^{31} +(-3.75579 + 22.8856i) q^{33} +(115.404 + 32.3369i) q^{35} +(-89.8577 - 155.638i) q^{37} +(-34.8620 + 212.429i) q^{39} +(242.341 + 419.748i) q^{41} +(-57.7297 + 99.9908i) q^{43} +(165.559 + 55.8443i) q^{45} +507.677 q^{47} +(-300.879 + 164.684i) q^{49} +(495.077 - 186.878i) q^{51} +(-57.0200 + 98.7615i) q^{53} -28.8829 q^{55} +(127.352 - 776.011i) q^{57} -297.103 q^{59} +10.5273 q^{61} +(-450.553 + 216.907i) q^{63} -268.097 q^{65} +322.893 q^{67} +(-585.766 + 221.111i) q^{69} +799.850 q^{71} +(-417.999 + 723.996i) q^{73} +(69.9471 - 426.218i) q^{75} +(59.1124 - 57.7799i) q^{77} -933.660 q^{79} +(-672.428 + 281.569i) q^{81} +(625.063 - 1082.64i) q^{83} +(329.515 + 570.737i) q^{85} +(-1116.17 + 421.326i) q^{87} +(-248.345 - 430.147i) q^{89} +(548.694 - 536.325i) q^{91} +(-1192.60 - 976.818i) q^{93} +979.367 q^{95} +(-735.318 + 1273.61i) q^{97} +(90.4495 - 79.6309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9}+O(q^{10}) \) 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9	\( 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9} + 4 q^{11} - 12 q^{13} - 26 q^{15} + 112 q^{17} + 60 q^{19} - 80 q^{21} + 10 q^{23} - 600 q^{25} + 194 q^{29} + 60 q^{31} - 472 q^{33} + 394 q^{35} - 84 q^{37} + 604 q^{39} + 210 q^{41} + 42 q^{43} + 254 q^{45} - 132 q^{47} - 78 q^{49} - 58 q^{51} - 468 q^{53} + 612 q^{55} + 1476 q^{57} - 916 q^{59} - 804 q^{61} - 444 q^{63} + 1656 q^{65} - 588 q^{67} - 28 q^{69} - 2228 q^{71} - 336 q^{73} - 668 q^{75} - 1216 q^{77} - 768 q^{79} - 104 q^{81} + 1024 q^{83} + 360 q^{85} + 2188 q^{87} + 2922 q^{89} - 120 q^{91} - 1292 q^{93} + 2428 q^{95} - 264 q^{97} - 2246 q^{99}+O(q^{100}) \) 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9 + 4 * q^11 - 12 * q^13 - 26 * q^15 + 112 * q^17 + 60 * q^19 - 80 * q^21 + 10 * q^23 - 600 * q^25 + 194 * q^29 + 60 * q^31 - 472 * q^33 + 394 * q^35 - 84 * q^37 + 604 * q^39 + 210 * q^41 + 42 * q^43 + 254 * q^45 - 132 * q^47 - 78 * q^49 - 58 * q^51 - 468 * q^53 + 612 * q^55 + 1476 * q^57 - 916 * q^59 - 804 * q^61 - 444 * q^63 + 1656 * q^65 - 588 * q^67 - 28 * q^69 - 2228 * q^71 - 336 * q^73 - 668 * q^75 - 1216 * q^77 - 768 * q^79 - 104 * q^81 + 1024 * q^83 + 360 * q^85 + 2188 * q^87 + 2922 * q^89 - 120 * q^91 - 1292 * q^93 + 2428 * q^95 - 264 * q^97 - 2246 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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