LMFDB - Embedded newform 124.3.o.a.53.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,3,Mod(13,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 11]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("124.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	124.o (of order $30$, degree $8$, 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:	$3.37875527807$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			53.3
Character	$\chi$	$=$	124.53
Dual form			124.3.o.a.117.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.257314 + 1.21057i) q^{3} +(-1.69238 - 2.93128i) q^{5} +(9.33225 - 4.15499i) q^{7} +(6.82265 + 3.03764i) q^{9} +O(q^{10})$	\(q+(-0.257314 + 1.21057i) q^{3} +(-1.69238 - 2.93128i) q^{5} +(9.33225 - 4.15499i) q^{7} +(6.82265 + 3.03764i) q^{9} +(3.52941 + 0.370956i) q^{11} +(11.8413 + 10.6620i) q^{13} +(3.98399 - 1.29448i) q^{15} +(-7.31731 + 0.769080i) q^{17} +(-1.19025 - 1.32191i) q^{19} +(2.62857 + 12.3665i) q^{21} +(-20.0883 - 27.6492i) q^{23} +(6.77172 - 11.7290i) q^{25} +(-11.9799 + 16.4889i) q^{27} +(29.1982 + 9.48706i) q^{29} +(-21.4898 - 22.3425i) q^{31} +(-1.35723 + 4.17714i) q^{33} +(-27.9731 - 20.3237i) q^{35} +(20.0330 + 11.5661i) q^{37} +(-15.9540 + 11.5913i) q^{39} +(-71.7116 + 15.2428i) q^{41} +(-47.0628 + 42.3756i) q^{43} +(-2.64231 - 25.1399i) q^{45} +(3.20690 + 9.86983i) q^{47} +(37.0396 - 41.1366i) q^{49} +(0.951822 - 9.05598i) q^{51} +(-16.3449 + 36.7113i) q^{53} +(-4.88572 - 10.9735i) q^{55} +(1.90652 - 1.10073i) q^{57} +(9.27114 + 1.97064i) q^{59} +73.5627i q^{61} +76.2920 q^{63} +(11.2133 - 52.7544i) q^{65} +(-29.7583 - 51.5429i) q^{67} +(38.6403 - 17.2038i) q^{69} +(-18.1714 - 8.09043i) q^{71} +(33.4019 + 3.51068i) q^{73} +(12.4562 + 11.2156i) q^{75} +(34.4787 - 11.2028i) q^{77} +(-14.7231 + 1.54746i) q^{79} +(28.0972 + 31.2051i) q^{81} +(-21.4378 - 100.857i) q^{83} +(14.6380 + 20.1475i) q^{85} +(-18.9978 + 32.9052i) q^{87} +(-32.9589 + 45.3640i) q^{89} +(154.807 + 50.2997i) q^{91} +(32.5767 - 20.2658i) q^{93} +(-1.86053 + 5.72612i) q^{95} +(81.3575 + 59.1097i) q^{97} +(22.9531 + 13.2520i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{3} - 3 q^{5} + 19 q^{7} - 2 q^{9}+O(q^{10}) $ 40 * q - 3 * q^3 - 3 * q^5 + 19 * q^7 - 2 * q^9	$ 40 q - 3 q^{3} - 3 q^{5} + 19 q^{7} - 2 q^{9} + 2 q^{11} - 18 q^{13} + 35 q^{15} + 25 q^{17} - 11 q^{19} + 54 q^{21} + 25 q^{23} - 75 q^{25} + 225 q^{27} + 20 q^{29} + 59 q^{31} - 303 q^{33} - 66 q^{35} - 222 q^{37} - 169 q^{39} + q^{41} + 122 q^{43} + 54 q^{45} - 120 q^{47} - 118 q^{49} - 515 q^{51} + 61 q^{53} - 121 q^{55} - 201 q^{57} - 257 q^{59} - 158 q^{63} + 182 q^{65} - q^{67} + 510 q^{69} + 459 q^{71} + 253 q^{73} + 651 q^{75} + 670 q^{77} + 385 q^{79} + 974 q^{81} + 375 q^{83} - 370 q^{85} - 344 q^{87} + 245 q^{89} + 960 q^{91} - 212 q^{93} - 851 q^{95} - 797 q^{97} - 21 q^{99}+O(q^{100}) $ 40 * q - 3 * q^3 - 3 * q^5 + 19 * q^7 - 2 * q^9 + 2 * q^11 - 18 * q^13 + 35 * q^15 + 25 * q^17 - 11 * q^19 + 54 * q^21 + 25 * q^23 - 75 * q^25 + 225 * q^27 + 20 * q^29 + 59 * q^31 - 303 * q^33 - 66 * q^35 - 222 * q^37 - 169 * q^39 + q^41 + 122 * q^43 + 54 * q^45 - 120 * q^47 - 118 * q^49 - 515 * q^51 + 61 * q^53 - 121 * q^55 - 201 * q^57 - 257 * q^59 - 158 * q^63 + 182 * q^65 - q^67 + 510 * q^69 + 459 * q^71 + 253 * q^73 + 651 * q^75 + 670 * q^77 + 385 * q^79 + 974 * q^81 + 375 * q^83 - 370 * q^85 - 344 * q^87 + 245 * q^89 + 960 * q^91 - 212 * q^93 - 851 * q^95 - 797 * q^97 - 21 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{17}{30}\right)$

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
$3$	−0.257314	+	1.21057i	−0.0857713	+	0.403522i	−0.999999	−	0.00167946i	$-0.999465\pi$
$3$	−0.257314	+	1.21057i	−0.0857713	+	0.403522i	0.914227	+	0.405202i	$0.132799\pi$
$4$		0			0
$5$	−1.69238	−	2.93128i	−0.338475	−	0.586257i	0.645671	−	0.763616i	$-0.276578\pi$
$5$	−1.69238	−	2.93128i	−0.338475	−	0.586257i	−0.984146	+	0.177359i	$0.943245\pi$
$6$		0			0
$7$	9.33225	−	4.15499i	1.33318	−	0.593569i	0.388464	−	0.921464i	$-0.373006\pi$
$7$	9.33225	−	4.15499i	1.33318	−	0.593569i	0.944714	+	0.327894i	$0.106339\pi$
$8$		0			0
$9$	6.82265	+	3.03764i	0.758072	+	0.337515i
$10$		0			0
$11$	3.52941	+	0.370956i	0.320856	+	0.0337233i	0.263587	−	0.964636i	$-0.415094\pi$
$11$	3.52941	+	0.370956i	0.320856	+	0.0337233i	0.0572683	+	0.998359i	$0.481761\pi$
$12$		0			0
$13$	11.8413	+	10.6620i	0.910872	+	0.820153i	0.984183	−	0.177156i	$-0.0566898\pi$
$13$	11.8413	+	10.6620i	0.910872	+	0.820153i	−0.0733108	+	0.997309i	$0.523357\pi$
$14$		0			0
$15$	3.98399	−	1.29448i	0.265599	−	0.0862984i
$16$		0			0
$17$	−7.31731	+	0.769080i	−0.430430	+	0.0452400i	−0.317266	−	0.948336i	$-0.602765\pi$
$17$	−7.31731	+	0.769080i	−0.430430	+	0.0452400i	−0.113163	+	0.993576i	$0.536098\pi$
$18$		0			0
$19$	−1.19025	−	1.32191i	−0.0626447	−	0.0695740i	0.711008	−	0.703184i	$-0.248239\pi$
$19$	−1.19025	−	1.32191i	−0.0626447	−	0.0695740i	−0.773653	+	0.633610i	$0.781572\pi$
$20$		0			0
$21$	2.62857	+	12.3665i	0.125170	+	0.588879i
$22$		0			0
$23$	−20.0883	−	27.6492i	−0.873406	−	1.20214i	−0.978204	−	0.207647i	$-0.933419\pi$
$23$	−20.0883	−	27.6492i	−0.873406	−	1.20214i	0.104798	−	0.994494i	$-0.466581\pi$
$24$		0			0
$25$	6.77172	−	11.7290i	0.270869	−	0.469159i
$26$		0			0
$27$	−11.9799	+	16.4889i	−0.443699	+	0.610699i
$28$		0			0
$29$	29.1982	+	9.48706i	1.00683	+	0.327140i	0.765593	−	0.643325i	$-0.222446\pi$
$29$	29.1982	+	9.48706i	1.00683	+	0.327140i	0.241240	+	0.970465i	$0.422446\pi$
$30$		0			0
$31$	−21.4898	−	22.3425i	−0.693219	−	0.720727i
$31$	−21.4898	−	22.3425i	−0.693219	−	0.720727i
$32$		0			0
$33$	−1.35723	+	4.17714i	−0.0411283	+	0.126580i
$34$		0			0
$35$	−27.9731	−	20.3237i	−0.799232	−	0.580676i
$36$		0			0
$37$	20.0330	+	11.5661i	0.541433	+	0.312597i	0.745660	−	0.666327i	$-0.232135\pi$
$37$	20.0330	+	11.5661i	0.541433	+	0.312597i	−0.204226	+	0.978924i	$0.565468\pi$
$38$		0			0
$39$	−15.9540	+	11.5913i	−0.409077	+	0.297212i
$40$		0			0
$41$	−71.7116	+	15.2428i	−1.74906	+	0.371775i	−0.967661	−	0.252253i	$-0.918828\pi$
$41$	−71.7116	+	15.2428i	−1.74906	+	0.371775i	−0.781402	+	0.624028i	$0.785495\pi$
$42$		0			0
$43$	−47.0628	+	42.3756i	−1.09448	+	0.985478i	−0.999950	−	0.0100431i	$-0.996803\pi$
$43$	−47.0628	+	42.3756i	−1.09448	+	0.985478i	−0.0945351	+	0.995522i	$0.530136\pi$
$44$		0			0
$45$	−2.64231	−	25.1399i	−0.0587181	−	0.558665i
$46$		0			0
$47$	3.20690	+	9.86983i	0.0682320	+	0.209996i	0.979359	−	0.202130i	$-0.0647863\pi$
$47$	3.20690	+	9.86983i	0.0682320	+	0.209996i	−0.911127	+	0.412126i	$0.864786\pi$
$48$		0			0
$49$	37.0396	−	41.1366i	0.755910	−	0.839523i
$50$		0			0
$51$	0.951822	−	9.05598i	0.0186632	−	0.177568i
$52$		0			0
$53$	−16.3449	+	36.7113i	−0.308395	+	0.692667i	−0.999549	−	0.0300411i	$-0.990436\pi$
$53$	−16.3449	+	36.7113i	−0.308395	+	0.692667i	0.691153	+	0.722708i	$0.257103\pi$
$54$		0			0
$55$	−4.88572	−	10.9735i	−0.0888312	−	0.199518i
$56$		0			0
$57$	1.90652	−	1.10073i	0.0334478	−	0.0193111i
$58$		0			0
$59$	9.27114	+	1.97064i	0.157138	+	0.0334007i	0.285809	−	0.958287i	$-0.407738\pi$
$59$	9.27114	+	1.97064i	0.157138	+	0.0334007i	−0.128671	+	0.991687i	$0.541071\pi$
$60$		0			0
$61$			73.5627i			1.20595i	0.797762	+	0.602973i	$0.206017\pi$
$61$			73.5627i			1.20595i	−0.797762	+	0.602973i	$0.793983\pi$
$62$		0			0
$63$	76.2920			1.21098
$64$		0			0
$65$	11.2133	−	52.7544i	0.172512	−	0.811606i
$66$		0			0
$67$	−29.7583	−	51.5429i	−0.444154	−	0.769298i	0.553839	−	0.832624i	$-0.313162\pi$
$67$	−29.7583	−	51.5429i	−0.444154	−	0.769298i	−0.997993	+	0.0633263i	$0.979829\pi$
$68$		0			0
$69$	38.6403	−	17.2038i	0.560004	−	0.249330i
$70$		0			0
$71$	−18.1714	−	8.09043i	−0.255935	−	0.113950i	0.274759	−	0.961513i	$-0.411402\pi$
$71$	−18.1714	−	8.09043i	−0.255935	−	0.113950i	−0.530694	+	0.847563i	$0.678069\pi$
$72$		0			0
$73$	33.4019	+	3.51068i	0.457560	+	0.0480915i	0.330505	−	0.943804i	$-0.392781\pi$
$73$	33.4019	+	3.51068i	0.457560	+	0.0480915i	0.127055	+	0.991896i	$0.459448\pi$
$74$		0			0
$75$	12.4562	+	11.2156i	0.166083	+	0.149542i
$76$		0			0
$77$	34.4787	−	11.2028i	0.447775	−	0.145491i
$78$		0			0
$79$	−14.7231	+	1.54746i	−0.186368	+	0.0195881i	−0.197253	−	0.980353i	$-0.563202\pi$
$79$	−14.7231	+	1.54746i	−0.186368	+	0.0195881i	0.0108844	+	0.999941i	$0.496535\pi$
$80$		0			0
$81$	28.0972	+	31.2051i	0.346879	+	0.385248i
$82$		0			0
$83$	−21.4378	−	100.857i	−0.258286	−	1.21514i	−0.895714	−	0.444631i	$-0.853335\pi$
$83$	−21.4378	−	100.857i	−0.258286	−	1.21514i	0.637428	−	0.770510i	$-0.279999\pi$
$84$		0			0
$85$	14.6380	+	20.1475i	0.172212	+	0.237030i
$86$		0			0
$87$	−18.9978	+	32.9052i	−0.218366	+	0.378220i
$88$		0			0
$89$	−32.9589	+	45.3640i	−0.370325	+	0.509708i	−0.952989	−	0.303005i	$-0.902010\pi$
$89$	−32.9589	+	45.3640i	−0.370325	+	0.509708i	0.582664	+	0.812713i	$0.302010\pi$
$90$		0			0
$91$	154.807	+	50.2997i	1.70117	+	0.552744i
$92$		0			0
$93$	32.5767	−	20.2658i	0.350288	−	0.217912i
$94$		0			0
$95$	−1.86053	+	5.72612i	−0.0195845	+	0.0602750i
$96$		0			0
$97$	81.3575	+	59.1097i	0.838738	+	0.609378i	0.922018	−	0.387148i	$-0.126540\pi$
$97$	81.3575	+	59.1097i	0.838738	+	0.609378i	−0.0832802	+	0.996526i	$0.526540\pi$
$98$		0			0
$99$	22.9531	+	13.2520i	0.231849	+	0.133858i
$100$		0			0
$101$	−79.8015	+	57.9792i	−0.790114	+	0.574051i	−0.907997	−	0.418976i	$-0.862389\pi$
$101$	−79.8015	+	57.9792i	−0.790114	+	0.574051i	0.117883	+	0.993027i	$0.462389\pi$
$102$		0			0
$103$	93.9054	−	19.9602i	0.911703	−	0.193789i	0.271898	−	0.962326i	$-0.412349\pi$
$103$	93.9054	−	19.9602i	0.911703	−	0.193789i	0.639805	+	0.768537i	$0.279015\pi$
$104$		0			0
$105$	31.8010	−	28.6338i	0.302867	−	0.272703i
$106$		0			0
$107$	−9.60317	−	91.3681i	−0.0897493	−	0.853907i	−0.943086	−	0.332548i	$-0.892092\pi$
$107$	−9.60317	−	91.3681i	−0.0897493	−	0.853907i	0.853337	−	0.521359i	$-0.174575\pi$
$108$		0			0
$109$	−19.4334	−	59.8100i	−0.178288	−	0.548716i	0.821480	−	0.570237i	$-0.193149\pi$
$109$	−19.4334	−	59.8100i	−0.178288	−	0.548716i	−0.999768	+	0.0215220i	$0.993149\pi$
$110$		0			0
$111$	−19.1563	+	21.2752i	−0.172579	+	0.191669i
$112$		0			0
$113$	20.1629	−	191.838i	0.178433	−	1.69768i	−0.428998	−	0.903306i	$-0.641133\pi$
$113$	20.1629	−	191.838i	0.178433	−	1.69768i	0.607431	−	0.794373i	$-0.292200\pi$
$114$		0			0
$115$	−47.0507	+	105.678i	−0.409136	+	0.918935i
$116$		0			0
$117$	48.4020	+	108.713i	0.413692	+	0.929168i
$118$		0			0
$119$	−65.0914	+	37.5805i	−0.546987	+	0.315803i
$120$		0			0
$121$	−106.037	−	22.5388i	−0.876337	−	0.186271i
$122$		0			0
$123$		−	90.7339i		−	0.737674i
$124$		0			0
$125$	−130.460			−1.04368
$126$		0			0
$127$	−36.1232	+	169.946i	−0.284435	+	1.33816i	0.571298	+	0.820743i	$0.306440\pi$
$127$	−36.1232	+	169.946i	−0.284435	+	1.33816i	−0.855733	+	0.517418i	$0.826893\pi$
$128$		0			0
$129$	−39.1885	−	67.8766i	−0.303787	−	0.526175i
$130$		0			0
$131$	−100.720	+	44.8435i	−0.768856	+	0.342317i	−0.753399	−	0.657564i	$-0.771587\pi$
$131$	−100.720	+	44.8435i	−0.768856	+	0.342317i	−0.0154571	+	0.999881i	$0.504920\pi$
$132$		0			0
$133$	−16.6002	−	7.39089i	−0.124814	−	0.0555706i
$134$		0			0
$135$	68.6080	+	7.21100i	0.508208	+	0.0534148i
$136$		0			0
$137$	−93.1128	−	83.8392i	−0.679656	−	0.611965i	0.255244	−	0.966877i	$-0.417844\pi$
$137$	−93.1128	−	83.8392i	−0.679656	−	0.611965i	−0.934900	+	0.354912i	$0.884511\pi$
$138$		0			0
$139$	−1.28954	+	0.418997i	−0.00927726	+	0.00301436i	−0.313652	−	0.949538i	$-0.601553\pi$
$139$	−1.28954	+	0.418997i	−0.00927726	+	0.00301436i	0.304375	+	0.952552i	$0.401553\pi$
$140$		0			0
$141$	−12.7733	+	1.34252i	−0.0905906	+	0.00952145i
$142$		0			0
$143$	37.8378	+	42.0232i	0.264600	+	0.293868i
$144$		0			0
$145$	−21.6050	−	101.644i	−0.149000	−	0.700991i
$146$		0			0
$147$	40.2679	+	55.4239i	0.273931	+	0.377034i
$148$		0			0
$149$	−101.974	+	176.624i	−0.684388	+	1.18540i	0.289240	+	0.957256i	$0.406597\pi$
$149$	−101.974	+	176.624i	−0.684388	+	1.18540i	−0.973629	+	0.228139i	$0.926736\pi$
$150$		0			0
$151$	152.286	−	209.603i	1.00852	−	1.38810i	0.0885640	−	0.996070i	$-0.471772\pi$
$151$	152.286	−	209.603i	1.00852	−	1.38810i	0.919952	−	0.392032i	$-0.128228\pi$
$152$		0			0
$153$	−52.2596	−	16.9802i	−0.341566	−	0.110981i
$154$		0			0
$155$	−29.1234	+	100.805i	−0.187893	+	0.650353i
$156$		0			0
$157$	−33.6009	+	103.413i	−0.214019	+	0.658682i	0.785203	+	0.619238i	$0.212559\pi$
$157$	−33.6009	+	103.413i	−0.214019	+	0.658682i	−0.999222	+	0.0394435i	$0.987441\pi$
$158$		0			0
$159$	−40.2358	−	29.2330i	−0.253055	−	0.183855i
$160$		0			0
$161$	−302.352	−	174.563i	−1.87796	−	1.08424i
$162$		0			0
$163$	86.1892	−	62.6201i	0.528768	−	0.384172i	−0.291129	−	0.956684i	$-0.594031\pi$
$163$	86.1892	−	62.6201i	0.528768	−	0.384172i	0.819897	+	0.572511i	$0.194031\pi$
$164$		0			0
$165$	14.5413	−	3.09085i	0.0881292	−	0.0187324i
$166$		0			0
$167$	−118.346	+	106.559i	−0.708659	+	0.638079i	−0.942504	−	0.334195i	$-0.891536\pi$
$167$	−118.346	+	106.559i	−0.708659	+	0.638079i	0.233845	+	0.972274i	$0.424869\pi$
$168$		0			0
$169$	8.87396	+	84.4301i	0.0525086	+	0.499586i
$170$		0			0
$171$	−4.10518	−	12.6345i	−0.0240069	−	0.0738857i
$172$		0			0
$173$	167.146	−	185.634i	0.966161	−	1.07303i	−0.0311329	−	0.999515i	$-0.509912\pi$
$173$	167.146	−	185.634i	0.966161	−	1.07303i	0.997294	−	0.0735154i	$-0.0234218\pi$
$174$		0			0
$175$	14.4617	−	137.594i	0.0826384	−	0.786252i
$176$		0			0
$177$	−4.77119	+	10.7163i	−0.0269559	+	0.0605438i
$178$		0			0
$179$	53.8120	+	120.864i	0.300626	+	0.675217i	0.999186	−	0.0403344i	$-0.0128423\pi$
$179$	53.8120	+	120.864i	0.300626	+	0.675217i	−0.698560	+	0.715551i	$0.746176\pi$
$180$		0			0
$181$	−131.228	+	75.7648i	−0.725019	+	0.418590i	−0.816597	−	0.577208i	$-0.804142\pi$
$181$	−131.228	+	75.7648i	−0.725019	+	0.418590i	0.0915781	+	0.995798i	$0.470809\pi$
$182$		0			0
$183$	−89.0526	−	18.9287i	−0.486626	−	0.103436i
$184$		0			0
$185$		−	78.2966i		−	0.423225i
$186$		0			0
$187$	−26.1111			−0.139631
$188$		0			0
$189$	−43.2881	+	203.655i	−0.229038	+	1.07754i
$190$		0			0
$191$	184.289	+	319.198i	0.964865	+	1.67120i	0.709978	+	0.704224i	$0.248705\pi$
$191$	184.289	+	319.198i	0.964865	+	1.67120i	0.254887	+	0.966971i	$0.417962\pi$
$192$		0			0
$193$	184.257	−	82.0365i	0.954699	−	0.425060i	0.130556	−	0.991441i	$-0.458324\pi$
$193$	184.257	−	82.0365i	0.954699	−	0.425060i	0.824143	+	0.566381i	$0.191657\pi$
$194$		0			0
$195$	60.9774	+	27.1489i	0.312705	+	0.139225i
$196$		0			0
$197$	275.796	+	28.9873i	1.39998	+	0.147144i	0.774242	−	0.632890i	$-0.218132\pi$
$197$	275.796	+	28.9873i	1.39998	+	0.147144i	0.625737	+	0.780034i	$0.284798\pi$
$198$		0			0
$199$	−194.854	−	175.447i	−0.979165	−	0.881644i	0.0138174	−	0.999905i	$-0.495602\pi$
$199$	−194.854	−	175.447i	−0.979165	−	0.881644i	−0.992983	+	0.118260i	$0.962268\pi$
$200$		0			0
$201$	70.0534	−	22.7617i	0.348525	−	0.113242i
$202$		0			0
$203$	311.903	−	32.7823i	1.53647	−	0.161489i
$204$		0			0
$205$	166.044	+	184.410i	0.809970	+	0.899563i
$206$		0			0
$207$	−53.0673	−	249.662i	−0.256364	−	1.20610i
$208$		0			0
$209$	−3.71051	−	5.10708i	−0.0177537	−	0.0244358i
$210$		0			0
$211$	−111.516	+	193.151i	−0.528512	+	0.915409i	0.470936	+	0.882168i	$0.343916\pi$
$211$	−111.516	+	193.151i	−0.528512	+	0.915409i	−0.999447	+	0.0332415i	$0.989417\pi$
$212$		0			0
$213$	14.4698	−	19.9159i	0.0679331	−	0.0935019i
$214$		0			0
$215$	203.863	+	66.2391i	0.948199	+	0.308089i
$216$		0			0
$217$	−293.381	−	119.216i	−1.35199	−	0.549383i
$218$		0			0
$219$	−12.8447	+	39.5319i	−0.0586515	+	0.180511i
$220$		0			0
$221$	−94.8466	−	68.9101i	−0.429170	−	0.311810i
$222$		0			0
$223$	45.6129	+	26.3346i	0.204542	+	0.118093i	0.598772	−	0.800919i	$-0.295655\pi$
$223$	45.6129	+	26.3346i	0.204542	+	0.118093i	−0.394230	+	0.919012i	$0.628989\pi$
$224$		0			0
$225$	81.8294	−	59.4526i	0.363686	−	0.264234i
$226$		0			0
$227$	255.336	−	54.2733i	1.12483	−	0.239089i	0.392307	−	0.919834i	$-0.371677\pi$
$227$	255.336	−	54.2733i	1.12483	−	0.239089i	0.732521	+	0.680745i	$0.238344\pi$
$228$		0			0
$229$	214.531	−	193.164i	0.936816	−	0.843513i	−0.0510701	−	0.998695i	$-0.516263\pi$
$229$	214.531	−	193.164i	0.936816	−	0.843513i	0.987886	+	0.155182i	$0.0495965\pi$
$230$		0			0
$231$	4.68990	+	44.6214i	0.0203026	+	0.193166i
$232$		0			0
$233$	−123.639	−	380.521i	−0.530638	−	1.63314i	−0.752889	−	0.658147i	$-0.771340\pi$
$233$	−123.639	−	380.521i	−0.530638	−	1.63314i	0.222251	−	0.974990i	$-0.428660\pi$
$234$		0			0
$235$	23.5040	−	26.1038i	0.100017	−	0.111080i
$236$		0			0
$237$	1.91516	−	18.2215i	0.00808083	−	0.0768839i
$238$		0			0
$239$	15.1381	−	34.0008i	0.0633395	−	0.142263i	−0.879102	−	0.476633i	$-0.841857\pi$
$239$	15.1381	−	34.0008i	0.0633395	−	0.142263i	0.942442	+	0.334370i	$0.108524\pi$
$240$		0			0
$241$	140.914	+	316.498i	0.584706	+	1.31327i	0.927487	+	0.373856i	$0.121965\pi$
$241$	140.914	+	316.498i	0.584706	+	1.31327i	−0.342780	+	0.939416i	$0.611369\pi$
$242$		0			0
$243$	−203.863	+	117.700i	−0.838942	+	0.484363i
$244$		0			0
$245$	−183.268	−	38.9548i	−0.748033	−	0.158999i
$246$		0			0
$247$		−	28.3436i		−	0.114751i
$248$		0			0
$249$	127.610			0.512490
$250$		0			0
$251$	−28.5841	+	134.478i	−0.113881	+	0.535767i	0.883810	+	0.467846i	$0.154970\pi$
$251$	−28.5841	+	134.478i	−0.113881	+	0.535767i	−0.997691	+	0.0679210i	$0.978363\pi$
$252$		0			0
$253$	−60.6434	−	105.037i	−0.239697	−	0.415168i
$254$		0			0
$255$	−28.1565	+	12.5361i	−0.110418	+	0.0491611i
$256$		0			0
$257$	60.2668	+	26.8325i	0.234501	+	0.104407i	0.520623	−	0.853787i	$-0.325700\pi$
$257$	60.2668	+	26.8325i	0.234501	+	0.104407i	−0.286122	+	0.958193i	$0.592366\pi$
$258$		0			0
$259$	235.010	+	24.7006i	0.907375	+	0.0953689i
$260$		0			0
$261$	170.391	+	153.420i	0.652837	+	0.587817i
$262$		0			0
$263$	212.325	−	68.9886i	0.807320	−	0.262314i	0.123858	−	0.992300i	$-0.460473\pi$
$263$	212.325	−	68.9886i	0.807320	−	0.262314i	0.683462	+	0.729986i	$0.260473\pi$
$264$		0			0
$265$	135.273	−	14.2178i	0.510465	−	0.0536520i
$266$		0			0
$267$	−46.4354	−	51.5718i	−0.173915	−	0.193153i
$268$		0			0
$269$	20.3560	+	95.7673i	0.0756727	+	0.356012i	0.999651	−	0.0264338i	$-0.00841511\pi$
$269$	20.3560	+	95.7673i	0.0756727	+	0.356012i	−0.923978	+	0.382446i	$0.875082\pi$
$270$		0			0
$271$	75.6307	+	104.097i	0.279080	+	0.384121i	0.925429	−	0.378921i	$-0.123705\pi$
$271$	75.6307	+	104.097i	0.279080	+	0.384121i	−0.646349	+	0.763042i	$0.723705\pi$
$272$		0			0
$273$	−100.725	+	174.461i	−0.368957	+	0.639052i
$274$		0			0
$275$	28.2511	−	38.8843i	0.102731	−	0.141398i
$276$		0			0
$277$	−96.8691	−	31.4747i	−0.349708	−	0.113627i	0.128896	−	0.991658i	$-0.458857\pi$
$277$	−96.8691	−	31.4747i	−0.349708	−	0.113627i	−0.478603	+	0.878031i	$0.658857\pi$
$278$		0			0
$279$	−78.7488	−	217.713i	−0.282254	−	0.780335i
$280$		0			0
$281$	−31.4241	+	96.7136i	−0.111830	+	0.344176i	−0.991273	−	0.131828i	$-0.957915\pi$
$281$	−31.4241	+	96.7136i	−0.111830	+	0.344176i	0.879443	+	0.476004i	$0.157915\pi$
$282$		0			0
$283$	−351.054	−	255.056i	−1.24048	−	0.901258i	−0.242845	−	0.970065i	$-0.578081\pi$
$283$	−351.054	−	255.056i	−1.24048	−	0.901258i	−0.997630	+	0.0688072i	$0.978081\pi$
$284$		0			0
$285$	−6.45312	−	3.72571i	−0.0226425	−	0.0130727i
$286$		0			0
$287$	−605.897	+	440.210i	−2.11114	+	1.53383i
$288$		0			0
$289$	−229.733	+	48.8313i	−0.794925	+	0.168966i
$290$		0			0
$291$	−92.4907	+	83.2790i	−0.317837	+	0.286182i
$292$		0			0
$293$	12.0129	+	114.295i	0.0409995	+	0.390085i	0.995709	+	0.0925437i	$0.0294998\pi$
$293$	12.0129	+	114.295i	0.0409995	+	0.390085i	−0.954709	+	0.297541i	$0.903834\pi$
$294$		0			0
$295$	−9.91375	−	30.5114i	−0.0336059	−	0.103428i
$296$		0			0
$297$	−48.3986	+	53.7521i	−0.162958	+	0.180983i
$298$		0			0
$299$	56.9229	−	541.585i	0.190378	−	1.81132i
$300$		0			0
$301$	−263.132	+	591.005i	−0.874194	+	1.96347i
$302$		0			0
$303$	−49.6537	−	111.524i	−0.163873	−	0.368066i
$304$		0			0
$305$	215.633	−	124.496i	0.706994	−	0.408183i
$306$		0			0
$307$	−556.751	−	118.341i	−1.81352	−	0.385476i	−0.828789	−	0.559561i	$-0.810970\pi$
$307$	−556.751	−	118.341i	−1.81352	−	0.385476i	−0.984731	+	0.174085i	$0.944303\pi$
$308$		0			0
$309$			118.815i			0.384514i
$310$		0			0
$311$	−302.500			−0.972670			−0.486335	−	0.873772i	$-0.661667\pi$
$311$	−302.500			−0.972670			−0.486335	+	0.873772i	$0.661667\pi$
$312$		0			0
$313$	47.4376	−	223.176i	0.151558	−	0.713023i	−0.835085	−	0.550122i	$-0.814581\pi$
$313$	47.4376	−	223.176i	0.151558	−	0.713023i	0.986642	−	0.162902i	$-0.0520853\pi$
$314$		0			0
$315$	−129.115	−	223.633i	−0.409888	−	0.709947i
$316$		0			0
$317$	452.917	−	201.651i	1.42876	−	0.636124i	0.460862	−	0.887472i	$-0.347540\pi$
$317$	452.917	−	201.651i	1.42876	−	0.636124i	0.967897	+	0.251348i	$0.0808737\pi$
$318$		0			0
$319$	99.5330	+	44.3150i	0.312016	+	0.138918i
$320$		0			0
$321$	113.078	+	11.8850i	0.352269	+	0.0370249i
$322$		0			0
$323$	9.72608	+	8.75740i	0.0301117	+	0.0271127i
$324$		0			0
$325$	205.240	−	66.6866i	0.631509	−	0.205190i
$326$		0			0
$327$	77.4045	−	8.13554i	0.236711	−	0.0248793i
$328$		0			0
$329$	70.9366	+	78.7831i	0.215613	+	0.239462i
$330$		0			0
$331$	−112.113	−	527.449i	−0.338709	−	1.59350i	−0.736771	−	0.676142i	$-0.763651\pi$
$331$	−112.113	−	527.449i	−0.338709	−	1.59350i	0.398062	−	0.917358i	$-0.369683\pi$
$332$		0			0
$333$	101.545	+	139.764i	0.304939	+	0.419713i
$334$		0			0
$335$	−100.725	+	174.460i	−0.300671	+	0.520777i
$336$		0			0
$337$	−119.233	+	164.109i	−0.353806	+	0.486972i	−0.948410	−	0.317047i	$-0.897309\pi$
$337$	−119.233	+	164.109i	−0.353806	+	0.486972i	0.594604	+	0.804019i	$0.297309\pi$
$338$		0			0
$339$	227.044	+	73.7711i	0.669747	+	0.217614i
$340$		0			0
$341$	−67.5583	−	86.8277i	−0.198118	−	0.254627i
$342$		0			0
$343$	20.0605	−	61.7398i	0.0584853	−	0.179999i
$344$		0			0
$345$	−115.823	−	84.1503i	−0.335719	−	0.243914i
$346$		0			0
$347$	284.895	+	164.484i	0.821023	+	0.474018i	0.850769	−	0.525540i	$-0.176137\pi$
$347$	284.895	+	164.484i	0.821023	+	0.474018i	−0.0297462	+	0.999557i	$0.509470\pi$
$348$		0			0
$349$	−534.791	+	388.548i	−1.53235	+	1.11332i	−0.577439	+	0.816434i	$0.695948\pi$
$349$	−534.791	+	388.548i	−1.53235	+	1.11332i	−0.954913	+	0.296885i	$0.904052\pi$
$350$		0			0
$351$	−317.662	+	67.5211i	−0.905020	+	0.192368i
$352$		0			0
$353$	−263.626	+	237.370i	−0.746816	+	0.672436i	−0.951935	−	0.306301i	$-0.900909\pi$
$353$	−263.626	+	237.370i	−0.746816	+	0.672436i	0.205119	+	0.978737i	$0.434242\pi$
$354$		0			0
$355$	7.03752	+	66.9576i	0.0198240	+	0.188613i
$356$		0			0
$357$	−28.7448	−	88.4675i	−0.0805178	−	0.247808i
$358$		0			0
$359$	127.225	−	141.298i	0.354388	−	0.393587i	−0.539421	−	0.842036i	$-0.681357\pi$
$359$	127.225	−	141.298i	0.354388	−	0.393587i	0.893808	+	0.448449i	$0.148023\pi$
$360$		0			0
$361$	37.4040	−	355.876i	0.103612	−	0.985805i
$362$		0			0
$363$	54.5695	−	122.565i	0.150329	−	0.337645i
$364$		0			0
$365$	−46.2378	−	103.852i	−0.126679	−	0.284525i
$366$		0			0
$367$	−37.5418	+	21.6748i	−0.102294	+	0.0590594i	−0.550274	−	0.834984i	$-0.685477\pi$
$367$	−37.5418	+	21.6748i	−0.102294	+	0.0590594i	0.447980	+	0.894043i	$0.352143\pi$
$368$		0			0
$369$	−535.565	−	113.838i	−1.45140	−	0.308504i
$370$		0			0
$371$			410.512i			1.10650i
$372$		0			0
$373$	392.547			1.05241			0.526203	−	0.850359i	$-0.323615\pi$
$373$	392.547			1.05241			0.526203	+	0.850359i	$0.323615\pi$
$374$		0			0
$375$	33.5692	−	157.931i	0.0895179	−	0.421148i
$376$		0			0
$377$	244.594	+	423.650i	0.648791	+	1.12374i
$378$		0			0
$379$	23.7759	−	10.5857i	0.0627333	−	0.0279306i	−0.375130	−	0.926972i	$-0.622402\pi$
$379$	23.7759	−	10.5857i	0.0627333	−	0.0279306i	0.437863	+	0.899041i	$0.355735\pi$
$380$		0			0
$381$	−196.437	−	87.4592i	−0.515581	−	0.229552i
$382$		0			0
$383$	571.732	+	60.0914i	1.49277	+	0.156897i	0.815466	−	0.578805i	$-0.196481\pi$
$383$	571.732	+	60.0914i	1.49277	+	0.156897i	0.677306	+	0.735702i	$0.263147\pi$
$384$		0			0
$385$	−91.1895	−	82.1074i	−0.236856	−	0.213266i
$386$		0			0
$387$	−449.815	+	146.154i	−1.16231	+	0.377658i
$388$		0			0
$389$	631.959	−	66.4216i	1.62457	−	0.170750i	0.751976	−	0.659190i	$-0.229101\pi$
$389$	631.959	−	66.4216i	1.62457	−	0.170750i	0.872597	+	0.488441i	$0.162434\pi$
$390$		0			0
$391$	168.257	+	186.868i	0.430325	+	0.477924i
$392$		0			0
$393$	−28.3694	−	133.467i	−0.0721867	−	0.339612i
$394$		0			0
$395$	29.4531	+	40.5387i	0.0745648	+	0.102630i
$396$		0			0
$397$	187.797	−	325.274i	0.473040	−	0.819330i	−0.526484	−	0.850185i	$-0.676490\pi$
$397$	187.797	−	325.274i	0.473040	−	0.819330i	0.999524	+	0.0308556i	$0.00982321\pi$
$398$		0			0
$399$	13.2186	−	18.1939i	0.0331294	−	0.0455987i
$400$		0			0
$401$	669.518	+	217.540i	1.66962	+	0.542493i	0.982854	−	0.184385i	$-0.0590294\pi$
$401$	669.518	+	217.540i	1.66962	+	0.542493i	0.686767	+	0.726878i	$0.259029\pi$
$402$		0			0
$403$	−16.2523	−	493.689i	−0.0403282	−	1.22504i
$404$		0			0
$405$	43.9199	−	135.172i	0.108444	−	0.333757i
$406$		0			0
$407$	66.4143	+	48.2528i	0.163180	+	0.118557i
$408$		0			0
$409$	425.734	+	245.798i	1.04092	+	0.600973i	0.920092	−	0.391701i	$-0.128113\pi$
$409$	425.734	+	245.798i	1.04092	+	0.600973i	0.120823	+	0.992674i	$0.461447\pi$
$410$		0			0
$411$	125.452	−	91.1463i	0.305236	−	0.221767i
$412$		0			0
$413$	94.7086	−	20.1309i	0.229319	−	0.0487432i
$414$		0			0
$415$	−259.359	+	233.528i	−0.624961	+	0.562717i
$416$		0			0
$417$	−0.175407	−	1.66889i	−0.000420641	−	0.00400213i
$418$		0			0
$419$	83.7841	+	257.861i	0.199962	+	0.615420i	0.999883	+	0.0153143i	$0.00487487\pi$
$419$	83.7841	+	257.861i	0.199962	+	0.615420i	−0.799921	+	0.600106i	$0.795125\pi$
$420$		0			0
$421$	87.5064	−	97.1857i	0.207854	−	0.230845i	−0.630200	−	0.776433i	$-0.717027\pi$
$421$	87.5064	−	97.1857i	0.207854	−	0.230845i	0.838053	+	0.545588i	$0.183694\pi$
$422$		0			0
$423$	−8.10141	+	77.0798i	−0.0191523	+	0.182222i
$424$		0			0
$425$	−40.5302	+	91.0324i	−0.0953653	+	0.214194i
$426$		0			0
$427$	305.652	+	686.505i	0.715812	+	1.60774i
$428$		0			0
$429$	−60.6080	+	34.9921i	−0.141277	+	0.0815666i
$430$		0			0
$431$	268.864	+	57.1487i	0.623813	+	0.132596i	0.508965	−	0.860787i	$-0.330028\pi$
$431$	268.864	+	57.1487i	0.623813	+	0.132596i	0.114849	+	0.993383i	$0.463362\pi$
$432$		0			0
$433$		−	434.943i		−	1.00449i	−0.864726	−	0.502243i	$-0.832508\pi$
$433$		−	434.943i		−	1.00449i	0.864726	−	0.502243i	$-0.167492\pi$
$434$		0			0
$435$	128.606			0.295646
$436$		0			0
$437$	−12.6396	+	59.4644i	−0.0289235	+	0.136074i
$438$		0			0
$439$	−373.021	−	646.091i	−0.849706	−	1.47173i	−0.881471	−	0.472239i	$-0.843446\pi$
$439$	−373.021	−	646.091i	−0.849706	−	1.47173i	0.0317647	−	0.999495i	$-0.489887\pi$
$440$		0			0
$441$	377.666	−	168.148i	0.856386	−	0.381288i
$442$		0			0
$443$	−181.916	−	80.9944i	−0.410646	−	0.182832i	0.191007	−	0.981589i	$-0.438825\pi$
$443$	−181.916	−	80.9944i	−0.410646	−	0.182832i	−0.601654	+	0.798757i	$0.705491\pi$
$444$		0			0
$445$	188.754	+	19.8388i	0.424166	+	0.0445816i
$446$		0			0
$447$	−187.576	−	168.894i	−0.419633	−	0.377839i
$448$		0			0
$449$	307.941	−	100.056i	0.685837	−	0.222842i	0.0546878	−	0.998504i	$-0.482584\pi$
$449$	307.941	−	100.056i	0.685837	−	0.222842i	0.631149	+	0.775662i	$0.282584\pi$
$450$		0			0
$451$	−258.754	+	27.1961i	−0.573734	+	0.0603019i
$452$		0			0
$453$	214.554	+	238.286i	0.473629	+	0.526018i
$454$		0			0
$455$	−114.548	−	538.908i	−0.251755	−	1.18441i
$456$		0			0
$457$	69.3569	+	95.4616i	0.151766	+	0.208888i	0.878130	−	0.478423i	$-0.158791\pi$
$457$	69.3569	+	95.4616i	0.151766	+	0.208888i	−0.726364	+	0.687310i	$0.758791\pi$
$458$		0			0
$459$	74.9791	−	129.868i	0.163353	−	0.282936i
$460$		0			0
$461$	−252.424	+	347.432i	−0.547557	+	0.753648i	−0.989678	−	0.143308i	$-0.954226\pi$
$461$	−252.424	+	347.432i	−0.547557	+	0.753648i	0.442121	+	0.896955i	$0.354226\pi$
$462$		0			0
$463$	203.856	+	66.2368i	0.440293	+	0.143060i	0.520771	−	0.853696i	$-0.325645\pi$
$463$	203.856	+	66.2368i	0.440293	+	0.143060i	−0.0804776	+	0.996756i	$0.525645\pi$
$464$		0			0
$465$	−114.537	−	61.1943i	−0.246316	−	0.131601i
$466$		0			0
$467$	−75.3843	+	232.009i	−0.161423	+	0.496808i	−0.998755	−	0.0498866i	$-0.984114\pi$
$467$	−75.3843	+	232.009i	−0.161423	+	0.496808i	0.837332	+	0.546694i	$0.184114\pi$
$468$		0			0
$469$	−491.872	−	357.366i	−1.04877	−	0.761975i
$470$		0			0
$471$	−116.542	−	67.2858i	−0.247436	−	0.142857i
$472$		0			0
$473$	−181.824	+	132.103i	−0.384405	+	0.279287i
$474$		0			0
$475$	−23.5646	+	5.00882i	−0.0496098	+	0.0105449i
$476$		0			0
$477$	−223.032	+	200.819i	−0.467571	+	0.421003i
$478$		0			0
$479$	42.6210	+	405.512i	0.0889791	+	0.846580i	0.944434	+	0.328702i	$0.106611\pi$
$479$	42.6210	+	405.512i	0.0889791	+	0.846580i	−0.855455	+	0.517878i	$0.826722\pi$
$480$		0			0
$481$	113.900	+	350.550i	0.236799	+	0.728793i
$482$		0			0
$483$	289.119	−	321.099i	0.598591	−	0.664802i
$484$		0			0
$485$	35.5797	−	338.518i	0.0733601	−	0.697975i
$486$		0			0
$487$	95.0888	−	213.573i	0.195254	−	0.438548i	−0.789212	−	0.614120i	$-0.789511\pi$
$487$	95.0888	−	213.573i	0.195254	−	0.438548i	0.984467	+	0.175572i	$0.0561776\pi$
$488$		0			0
$489$	53.6282	+	120.451i	0.109669	+	0.246321i
$490$		0			0
$491$	−444.512	+	256.639i	−0.905321	+	0.522687i	−0.878923	−	0.476964i	$-0.841737\pi$
$491$	−444.512	+	256.639i	−0.905321	+	0.522687i	−0.0263981	+	0.999652i	$0.508404\pi$
$492$		0			0
$493$	−220.948	−	46.9640i	−0.448171	−	0.0952616i
$494$		0			0
$495$		−	89.7094i		−	0.181231i
$496$		0			0
$497$	−203.196			−0.408844
$498$		0			0
$499$	−181.860	+	855.585i	−0.364449	+	1.71460i	0.288743	+	0.957407i	$0.406763\pi$
$499$	−181.860	+	855.585i	−0.364449	+	1.71460i	−0.653192	+	0.757192i	$0.726571\pi$
$500$		0			0
$501$	−98.5450	−	170.685i	−0.196697	−	0.340688i
$502$		0			0
$503$	896.611	−	399.197i	1.78253	−	0.793632i	0.801978	−	0.597353i	$-0.203781\pi$
$503$	896.611	−	399.197i	1.78253	−	0.793632i	0.980548	−	0.196279i	$-0.0628857\pi$
$504$		0			0
$505$	305.008	+	135.798i	0.603975	+	0.268907i
$506$		0			0
$507$	−104.492	−	10.9825i	−0.206098	−	0.0216618i
$508$		0			0
$509$	−704.729	−	634.540i	−1.38454	−	1.24664i	−0.935593	−	0.353081i	$-0.885134\pi$
$509$	−704.729	−	634.540i	−1.38454	−	1.24664i	−0.448943	−	0.893561i	$-0.648199\pi$
$510$		0			0
$511$	326.302	−	106.022i	0.638555	−	0.207479i
$512$		0			0
$513$	36.0558	−	3.78962i	0.0702842	−	0.00738717i
$514$		0			0
$515$	−217.432	−	241.483i	−0.422199	−	0.468899i
$516$		0			0
$517$	7.65720	+	36.0243i	0.0148108	+	0.0696795i
$518$		0			0
$519$	181.714	+	250.108i	0.350123	+	0.481903i
$520$		0			0
$521$	−312.009	+	540.416i	−0.598866	+	1.03727i	0.394123	+	0.919058i	$0.371049\pi$
$521$	−312.009	+	540.416i	−0.598866	+	1.03727i	−0.992989	+	0.118209i	$0.962285\pi$
$522$		0			0
$523$	20.7377	−	28.5430i	0.0396515	−	0.0545756i	−0.788731	−	0.614739i	$-0.789262\pi$
$523$	20.7377	−	28.5430i	0.0396515	−	0.0545756i	0.828382	+	0.560163i	$0.189262\pi$
$524$		0			0
$525$	162.846	+	52.9118i	0.310182	+	0.100784i
$526$		0			0
$527$	174.431	+	146.960i	0.330988	+	0.278861i
$528$		0			0
$529$	−197.469	+	607.746i	−0.373286	+	1.14886i
$530$		0			0
$531$	57.2676	+	41.6074i	0.107849	+	0.0783566i
$532$		0			0
$533$	−1011.68	−	584.093i	−1.89808	−	1.09586i
$534$		0			0
$535$	−251.573	+	182.779i	−0.470231	+	0.341643i
$536$		0			0
$537$	−160.160	+	34.0431i	−0.298250	+	0.0633950i
$538$		0			0
$539$	145.988	−	131.448i	0.270849	−	0.243874i
$540$		0			0
$541$	−74.1409	−	705.404i	−0.137044	−	1.30389i	−0.819550	−	0.573008i	$-0.805776\pi$
$541$	−74.1409	−	705.404i	−0.137044	−	1.30389i	0.682505	−	0.730881i	$-0.260890\pi$
$542$		0			0
$543$	−57.9514	−	178.356i	−0.106725	−	0.328464i
$544$		0			0
$545$	−142.431	+	158.186i	−0.261342	+	0.290249i
$546$		0			0
$547$	15.3427	−	145.976i	0.0280488	−	0.266867i	−0.971506	−	0.237017i	$-0.923830\pi$
$547$	15.3427	−	145.976i	0.0280488	−	0.266867i	0.999554	−	0.0298499i	$-0.00950293\pi$
$548$		0			0
$549$	−223.457	+	501.892i	−0.407025	+	0.914194i
$550$		0			0
$551$	−22.2121	−	49.8892i	−0.0403124	−	0.0905430i
$552$		0			0
$553$	−130.970	+	75.6156i	−0.236836	+	0.136737i
$554$		0			0
$555$	94.7833	+	20.1468i	0.170781	+	0.0363006i
$556$		0			0
$557$		−	908.998i		−	1.63195i	−0.578085	−	0.815977i	$-0.696200\pi$
$557$		−	908.998i		−	1.63195i	0.578085	−	0.815977i	$-0.303800\pi$
$558$		0			0
$559$	−1009.09			−1.80518
$560$		0			0
$561$	6.71874	−	31.6092i	0.0119764	−	0.0563444i
$562$		0			0
$563$	366.439	+	634.691i	0.650868	+	1.12734i	0.982913	+	0.184073i	$0.0589283\pi$
$563$	366.439	+	634.691i	0.650868	+	1.12734i	−0.332044	+	0.943264i	$0.607738\pi$
$564$		0			0
$565$	−596.454	+	265.558i	−1.05567	+	0.470015i
$566$		0			0
$567$	391.867	+	174.470i	0.691123	+	0.307708i
$568$		0			0
$569$	−0.137218	−	0.0144222i	−0.000241156	−	2.53465e-5i	0.104408	−	0.994535i	$-0.466705\pi$
$569$	−0.137218	−	0.0144222i	−0.000241156	−	2.53465e-5i	−0.104649	+	0.994509i	$0.533372\pi$
$570$		0			0
$571$	298.853	+	269.089i	0.523385	+	0.471258i	0.887963	−	0.459915i	$-0.152120\pi$
$571$	298.853	+	269.089i	0.523385	+	0.471258i	−0.364578	+	0.931173i	$0.618787\pi$
$572$		0			0
$573$	−433.831	+	140.960i	−0.757122	+	0.246004i
$574$		0			0
$575$	−460.330	+	48.3826i	−0.800573	+	0.0841436i
$576$		0			0
$577$	−97.6158	−	108.413i	−0.169178	−	0.187891i	0.652594	−	0.757708i	$-0.273681\pi$
$577$	−97.6158	−	108.413i	−0.169178	−	0.187891i	−0.821772	+	0.569817i	$0.807014\pi$
$578$		0			0
$579$	51.8988	+	244.165i	0.0896352	+	0.421700i
$580$		0			0
$581$	−619.121	−	852.147i	−1.06561	−	1.46669i
$582$		0			0
$583$	−71.3063	+	123.506i	−0.122309	+	0.211846i
$584$		0			0
$585$	236.753	−	325.863i	0.404706	−	0.557030i
$586$		0			0
$587$	−205.582	−	66.7975i	−0.350224	−	0.113795i	0.128622	−	0.991694i	$-0.458945\pi$
$587$	−205.582	−	66.7975i	−0.350224	−	0.113795i	−0.478846	+	0.877899i	$0.658945\pi$
$588$		0			0
$589$	−3.95649	+	55.0007i	−0.00671730	+	0.0933798i
$590$		0			0
$591$	−106.057	+	326.411i	−0.179454	+	0.552302i
$592$		0			0
$593$	699.634	+	508.314i	1.17982	+	0.857190i	0.992151	−	0.125042i	$-0.0399065\pi$
$593$	699.634	+	508.314i	1.17982	+	0.857190i	0.187670	+	0.982232i	$0.439906\pi$
$594$		0			0
$595$	220.318	+	127.201i	0.370283	+	0.213783i
$596$		0			0
$597$	262.529	−	190.739i	0.439747	−	0.319495i
$598$		0			0
$599$	871.864	−	185.320i	1.45553	−	0.309383i	0.588849	−	0.808243i	$-0.299581\pi$
$599$	871.864	−	185.320i	1.45553	−	0.309383i	0.866683	+	0.498860i	$0.166248\pi$
$600$		0			0
$601$	39.8610	−	35.8910i	0.0663245	−	0.0597189i	−0.635302	−	0.772264i	$-0.719124\pi$
$601$	39.8610	−	35.8910i	0.0663245	−	0.0597189i	0.701626	+	0.712545i	$0.252458\pi$
$602$		0			0
$603$	−46.4618	−	442.054i	−0.0770511	−	0.733092i
$604$		0			0
$605$	113.386	+	348.968i	0.187416	+	0.576806i
$606$		0			0
$607$	444.323	−	493.471i	0.731999	−	0.812967i	−0.256122	−	0.966644i	$-0.582445\pi$
$607$	444.323	−	493.471i	0.731999	−	0.812967i	0.988121	+	0.153677i	$0.0491116\pi$
$608$		0			0
$609$	−40.5718	+	386.015i	−0.0666204	+	0.633851i
$610$		0			0
$611$	−67.2580	+	151.064i	−0.110079	+	0.247240i
$612$		0			0
$613$	65.7479	+	147.672i	0.107256	+	0.240901i	0.959198	−	0.282735i	$-0.0912418\pi$
$613$	65.7479	+	147.672i	0.107256	+	0.240901i	−0.851942	+	0.523636i	$0.824575\pi$
$614$		0			0
$615$	−265.967	+	153.556i	−0.432466	+	0.249684i
$616$		0			0
$617$	−797.085	−	169.426i	−1.29187	−	0.274596i	−0.489806	−	0.871831i	$-0.662933\pi$
$617$	−797.085	−	169.426i	−1.29187	−	0.274596i	−0.802066	+	0.597235i	$0.796266\pi$
$618$		0			0
$619$		−	493.904i		−	0.797906i	−0.916971	−	0.398953i	$-0.869374\pi$
$619$		−	493.904i		−	0.797906i	0.916971	−	0.398953i	$-0.130626\pi$
$620$		0			0
$621$	696.561			1.12168
$622$		0			0
$623$	−119.094	+	560.292i	−0.191162	+	0.899346i
$624$		0			0
$625$	51.4945	+	89.1911i	0.0823912	+	0.142706i
$626$		0			0
$627$	7.13723	−	3.17770i	0.0113831	−	0.00506810i
$628$		0			0
$629$	−155.483	−	69.2255i	−0.247191	−	0.110056i
$630$		0			0
$631$	−336.628	−	35.3810i	−0.533484	−	0.0560714i	−0.166043	−	0.986118i	$-0.553099\pi$
$631$	−336.628	−	35.3810i	−0.533484	−	0.0560714i	−0.367440	+	0.930047i	$0.619766\pi$
$632$		0			0
$633$	−205.128	−	184.698i	−0.324057	−	0.291782i
$634$		0			0
$635$	559.295	−	181.726i	0.880780	−	0.286183i
$636$		0			0
$637$	877.197	−	92.1971i	1.37707	−	0.144736i
$638$		0			0
$639$	−99.4012	−	110.396i	−0.155558	−	0.172764i
$640$		0			0
$641$	−161.442	−	759.525i	−0.251860	−	1.18491i	−0.904243	−	0.427018i	$-0.859564\pi$
$641$	−161.442	−	759.525i	−0.251860	−	1.18491i	0.652384	−	0.757889i	$-0.273769\pi$
$642$		0			0
$643$	458.042	+	630.440i	0.712351	+	0.980467i	0.999743	+	0.0226542i	$0.00721167\pi$
$643$	458.042	+	630.440i	0.712351	+	0.980467i	−0.287392	+	0.957813i	$0.592788\pi$
$644$		0			0
$645$	−132.644	+	229.745i	−0.205649	+	0.356194i
$646$		0			0
$647$	−52.2694	+	71.9426i	−0.0807873	+	0.111194i	−0.847498	−	0.530799i	$-0.821892\pi$
$647$	−52.2694	+	71.9426i	−0.0807873	+	0.111194i	0.766711	+	0.641993i	$0.221892\pi$
$648$		0			0
$649$	31.9906	+	10.3944i	0.0492922	+	0.0160160i
$650$		0			0
$651$	219.810	−	324.481i	0.337650	−	0.498435i
$652$		0			0
$653$	344.961	−	1061.68i	0.528271	−	1.62585i	−0.229484	−	0.973312i	$-0.573704\pi$
$653$	344.961	−	1061.68i	0.528271	−	1.62585i	0.757755	−	0.652539i	$-0.226296\pi$
$654$		0			0
$655$	301.905	+	219.347i	0.460924	+	0.334881i
$656$		0			0
$657$	217.225	+	125.415i	0.330632	+	0.190890i
$658$		0			0
$659$	122.973	−	89.3448i	0.186605	−	0.135576i	−0.490561	−	0.871407i	$-0.663208\pi$
$659$	122.973	−	89.3448i	0.186605	−	0.135576i	0.677166	+	0.735831i	$0.263208\pi$
$660$		0			0
$661$	155.392	−	33.0295i	0.235086	−	0.0499690i	−0.0888621	−	0.996044i	$-0.528323\pi$
$661$	155.392	−	33.0295i	0.235086	−	0.0499690i	0.323948	+	0.946075i	$0.394990\pi$
$662$		0			0
$663$	107.826	−	97.0866i	0.162633	−	0.146435i
$664$		0			0
$665$	6.42903	+	61.1681i	0.00966771	+	0.0919821i
$666$		0			0
$667$	−324.233	−	997.886i	−0.486106	−	1.49608i
$668$		0			0
$669$	−43.6167	+	48.4412i	−0.0651968	+	0.0724084i
$670$		0			0
$671$	−27.2885	+	259.633i	−0.0406684	+	0.386934i
$672$		0			0
$673$	−181.791	+	408.309i	−0.270120	+	0.606700i	−0.996770	−	0.0803083i	$-0.974410\pi$
$673$	−181.791	+	408.309i	−0.270120	+	0.606700i	0.726650	+	0.687008i	$0.241076\pi$
$674$		0			0
$675$	112.273	+	252.170i	0.166331	+	0.373585i
$676$		0			0
$677$	379.848	−	219.306i	0.561076	−	0.323937i	−0.192501	−	0.981297i	$-0.561660\pi$
$677$	379.848	−	219.306i	0.561076	−	0.323937i	0.753577	+	0.657359i	$0.228327\pi$
$678$		0			0
$679$	1004.85	+	213.587i	1.47990	+	0.314561i
$680$		0			0
$681$			323.066i			0.474400i
$682$		0			0
$683$	−347.493			−0.508775			−0.254387	−	0.967102i	$-0.581874\pi$
$683$	−347.493			−0.508775			−0.254387	+	0.967102i	$0.581874\pi$
$684$		0			0
$685$	−88.1743	+	414.827i	−0.128722	+	0.605588i
$686$		0			0
$687$	178.637	+	309.408i	0.260024	+	0.450375i
$688$		0			0
$689$	−584.962	+	260.442i	−0.849001	+	0.378000i
$690$		0			0
$691$	−341.634	−	152.105i	−0.494405	−	0.220123i	0.144360	−	0.989525i	$-0.453888\pi$
$691$	−341.634	−	152.105i	−0.494405	−	0.220123i	−0.638765	+	0.769402i	$0.720554\pi$
$692$		0			0
$693$	269.266	+	28.3010i	0.388551	+	0.0408384i
$694$		0			0
$695$	3.41058	+	3.07090i	0.00490731	+	0.00441857i
$696$		0			0
$697$	513.013	−	166.688i	0.736030	−	0.239151i
$698$		0			0
$699$	492.460	−	51.7596i	0.704521	−	0.0740481i
$700$		0			0
$701$	687.391	+	763.425i	0.980587	+	1.08905i	0.996016	+	0.0891710i	$0.0284217\pi$
$701$	687.391	+	763.425i	0.980587	+	1.08905i	−0.0154296	+	0.999881i	$0.504912\pi$
$702$		0			0
$703$	−8.55504	−	40.2483i	−0.0121693	−	0.0572522i
$704$		0			0
$705$	25.5525	+	35.1700i	0.0362447	+	0.0498865i
$706$		0			0
$707$	−503.825	+	872.650i	−0.712624	+	1.23430i
$708$		0			0
$709$	296.394	−	407.952i	0.418045	−	0.575390i	−0.547112	−	0.837059i	$-0.684273\pi$
$709$	296.394	−	407.952i	0.418045	−	0.575390i	0.965158	+	0.261669i	$0.0842729\pi$
$710$		0			0
$711$	−105.151	−	34.1657i	−0.147892	−	0.0480530i
$712$		0			0
$713$	−186.059	+	1043.00i	−0.260952	+	1.46283i
$714$		0			0
$715$	59.1459	−	182.032i	0.0827215	−	0.254591i
$716$		0			0
$717$	37.2650	+	27.0746i	0.0519735	+	0.0377610i
$718$		0			0
$719$	−341.912	−	197.403i	−0.475539	−	0.274552i	0.243017	−	0.970022i	$-0.421863\pi$
$719$	−341.912	−	197.403i	−0.475539	−	0.274552i	−0.718555	+	0.695470i	$0.755196\pi$
$720$		0			0
$721$	793.415	−	576.450i	1.10044	−	0.799514i
$722$		0			0
$723$	−419.402	+	89.1466i	−0.580086	+	0.123301i
$724$		0			0
$725$	308.995	−	278.221i	0.426200	−	0.383752i
$726$		0			0
$727$	101.505	+	965.758i	0.139622	+	1.32842i	0.810015	+	0.586409i	$0.199459\pi$
$727$	101.505	+	965.758i	0.139622	+	1.32842i	−0.670393	+	0.742006i	$0.733874\pi$
$728$		0			0
$729$	26.7550	+	82.3435i	0.0367010	+	0.112954i
$730$		0			0
$731$	311.783	−	346.270i	0.426516	−	0.473694i
$732$		0			0
$733$	−1.40874	+	13.4033i	−0.00192188	+	0.0182855i	−0.995441	−	0.0953813i	$-0.969593\pi$
$733$	−1.40874	+	13.4033i	−0.00192188	+	0.0182855i	0.993519	+	0.113667i	$0.0362596\pi$
$734$		0			0
$735$	94.3149	−	211.835i	0.128320	−	0.288210i
$736$		0			0
$737$	−85.9092	−	192.955i	−0.116566	−	0.261812i
$738$		0			0
$739$	1107.70	−	639.530i	1.49891	−	0.865399i	0.498916	−	0.866651i	$-0.333732\pi$
$739$	1107.70	−	639.530i	1.49891	−	0.865399i	0.999999	+	0.00125164i	$0.000398411\pi$
$740$		0			0
$741$	34.3118	+	7.29320i	0.0463047	+	0.00984237i
$742$		0			0
$743$			974.374i			1.31140i	0.755019	+	0.655702i	$0.227627\pi$
$743$			974.374i			1.31140i	−0.755019	+	0.655702i	$0.772373\pi$
$744$		0			0
$745$	690.313			0.926594
$746$		0			0
$747$	160.104	−	753.230i	0.214329	−	1.00834i
$748$		0			0
$749$	−469.252	−	812.769i	−0.626505	−	1.08514i
$750$		0			0
$751$	−329.273	+	146.602i	−0.438446	+	0.195209i	−0.614075	−	0.789248i	$-0.710471\pi$
$751$	−329.273	+	146.602i	−0.438446	+	0.195209i	0.175629	+	0.984456i	$0.443804\pi$
$752$		0			0
$753$	−155.439	−	69.2059i	−0.206426	−	0.0919069i
$754$		0			0
$755$	−872.132	−	91.6648i	−1.15514	−	0.121410i
$756$		0			0
$757$	−292.483	−	263.353i	−0.386371	−	0.347890i	0.452941	−	0.891541i	$-0.350375\pi$
$757$	−292.483	−	263.353i	−0.386371	−	0.347890i	−0.839311	+	0.543651i	$0.817042\pi$
$758$		0			0
$759$	142.759	−	46.3853i	0.188089	−	0.0611137i
$760$		0			0
$761$	−625.006	+	65.6908i	−0.821296	+	0.0863217i	−0.505850	−	0.862622i	$-0.668821\pi$
$761$	−625.006	+	65.6908i	−0.821296	+	0.0863217i	−0.315446	+	0.948943i	$0.602154\pi$
$762$		0			0
$763$	−429.867	−	477.416i	−0.563391	−	0.625709i
$764$		0			0
$765$	38.6692	+	181.924i	0.0505480	+	0.237810i
$766$		0			0
$767$	88.7717	+	122.184i	0.115739	+	0.159301i
$768$		0			0
$769$	366.464	−	634.734i	0.476546	−	0.825402i	−0.523093	−	0.852276i	$-0.675222\pi$
$769$	366.464	−	634.734i	0.476546	−	0.825402i	0.999639	+	0.0268737i	$0.00855519\pi$
$770$		0			0
$771$	−47.9900	+	66.0526i	−0.0622439	+	0.0856714i
$772$		0			0
$773$	−1153.40	−	374.762i	−1.49211	−	0.484815i	−0.554404	−	0.832248i	$-0.687054\pi$
$773$	−1153.40	−	374.762i	−1.49211	−	0.484815i	−0.937705	+	0.347433i	$0.887054\pi$
$774$		0			0
$775$	−407.578	+	100.756i	−0.525907	+	0.130008i
$776$		0			0
$777$	−90.3730	+	278.140i	−0.116310	+	0.357966i
$778$		0			0
$779$	105.504	+	76.6533i	0.135435	+	0.0983996i
$780$		0			0
$781$	−61.1331	−	35.2952i	−0.0782755	−	0.0451924i
$782$		0			0
$783$	−506.221	+	367.791i	−0.646515	+	0.469721i
$784$		0			0
$785$	359.998	−	76.5200i	0.458596	−	0.0974777i
$786$		0			0
$787$	−135.601	+	122.096i	−0.172302	+	0.155141i	−0.750770	−	0.660564i	$-0.770317\pi$
$787$	−135.601	+	122.096i	−0.172302	+	0.155141i	0.578468	+	0.815705i	$0.303651\pi$
$788$		0			0
$789$	28.8811	+	274.786i	0.0366047	+	0.348271i
$790$		0			0
$791$	−608.917	−	1874.05i	−0.769806	−	2.36922i
$792$		0			0
$793$	−784.324	+	871.080i	−0.989060	+	1.09846i
$794$		0			0
$795$	−17.5961	+	167.416i	−0.0221334	+	0.210586i
$796$		0			0
$797$	266.004	−	597.455i	0.333757	−	0.749630i	−0.666236	−	0.745741i	$-0.732096\pi$
$797$	266.004	−	597.455i	0.333757	−	0.749630i	0.999992	−	0.00388860i	$-0.00123778\pi$
$798$		0			0
$799$	−31.0566	−	69.7542i	−0.0388693	−	0.0873019i
$800$		0			0
$801$	−362.667	+	209.386i	−0.452767	+	0.261405i
$802$		0			0
$803$	116.587	+	24.7813i	0.145189	+	0.0308609i
$804$		0			0
$805$			1181.70i			1.46796i
$806$		0			0
$807$	−121.171			−0.150149
$808$		0			0
$809$	114.164	−	537.098i	0.141117	−	0.663903i	−0.849540	−	0.527525i	$-0.823120\pi$
$809$	114.164	−	537.098i	0.141117	−	0.663903i	0.990657	−	0.136379i	$-0.0435464\pi$
$810$		0			0
$811$	−119.793	−	207.487i	−0.147710	−	0.255841i	0.782671	−	0.622436i	$-0.213857\pi$
$811$	−119.793	−	207.487i	−0.147710	−	0.255841i	−0.930381	+	0.366595i	$0.880523\pi$
$812$		0			0
$813$	−145.477	+	64.7705i	−0.178938	+	0.0796685i
$814$		0			0
$815$	−329.422	−	146.668i	−0.404198	−	0.179961i
$816$		0			0
$817$	112.033	+	11.7752i	0.137127	+	0.0144127i
$818$		0			0
$819$	903.399	+	813.424i	1.10305	+	0.993192i
$820$		0			0
$821$	−813.661	+	264.374i	−0.991060	+	0.322015i	−0.759288	−	0.650755i	$-0.774453\pi$
$821$	−813.661	+	264.374i	−0.991060	+	0.322015i	−0.231773	+	0.972770i	$0.574453\pi$
$822$		0			0
$823$	−178.627	+	18.7744i	−0.217043	+	0.0228122i	−0.212426	−	0.977177i	$-0.568136\pi$
$823$	−178.627	+	18.7744i	−0.217043	+	0.0228122i	−0.00461733	+	0.999989i	$0.501470\pi$
$824$		0			0
$825$	39.8027	+	44.2054i	0.0482457	+	0.0535823i
$826$		0			0
$827$	106.636	+	501.682i	0.128943	+	0.606629i	0.994403	+	0.105651i	$0.0336928\pi$
$827$	106.636	+	501.682i	0.128943	+	0.606629i	−0.865460	+	0.500978i	$0.832974\pi$
$828$		0			0
$829$	−521.354	−	717.583i	−0.628896	−	0.865601i	0.369067	−	0.929403i	$-0.379677\pi$
$829$	−521.354	−	717.583i	−0.628896	−	0.865601i	−0.997963	+	0.0638023i	$0.979677\pi$
$830$		0			0
$831$	63.0279	−	109.168i	0.0758459	−	0.131369i
$832$		0			0
$833$	−239.393	+	329.496i	−0.287386	+	0.395553i
$834$		0			0
$835$	512.641	+	166.567i	0.613942	+	0.199482i
$836$		0			0
$837$	625.849	−	86.6822i	0.747728	−	0.103563i
$838$		0			0
$839$	−9.14114	+	28.1335i	−0.0108953	+	0.0335322i	−0.956356	−	0.292203i	$-0.905612\pi$
$839$	−9.14114	+	28.1335i	−0.0108953	+	0.0335322i	0.945461	+	0.325735i	$0.105612\pi$
$840$		0			0
$841$	82.1451	+	59.6819i	0.0976755	+	0.0709654i
$842$		0			0
$843$	−108.992	−	62.9268i	−0.129291	−	0.0746462i
$844$		0			0
$845$	232.470	−	168.900i	0.275113	−	0.199881i
$846$		0			0
$847$	−1083.21	+	230.243i	−1.27888	+	0.271834i
$848$		0			0
$849$	399.094	−	359.345i	0.470075	−	0.423257i
$850$		0			0
$851$	−82.6373	−	786.241i	−0.0971061	−	0.923902i
$852$		0			0
$853$	447.256	+	1376.51i	0.524333	+	1.61373i	0.765630	+	0.643281i	$0.222427\pi$
$853$	447.256	+	1376.51i	0.524333	+	1.61373i	−0.241297	+	0.970451i	$0.577573\pi$
$854$		0			0
$855$	−30.0876	+	33.4157i	−0.0351902	+	0.0390827i
$856$		0			0
$857$	−56.0606	+	533.381i	−0.0654149	+	0.622381i	0.911874	+	0.410470i	$0.134635\pi$
$857$	−56.0606	+	533.381i	−0.0654149	+	0.622381i	−0.977289	+	0.211911i	$0.932031\pi$
$858$		0			0
$859$	−125.626	+	282.160i	−0.146247	+	0.328475i	−0.971784	−	0.235872i	$-0.924205\pi$
$859$	−125.626	+	282.160i	−0.146247	+	0.328475i	0.825538	+	0.564347i	$0.190872\pi$
$860$		0			0
$861$	−376.998	−	846.751i	−0.437860	−	0.983451i
$862$		0			0
$863$	−657.488	+	379.601i	−0.761863	+	0.439862i	−0.829964	−	0.557817i	$-0.811639\pi$
$863$	−657.488	+	379.601i	−0.761863	+	0.439862i	0.0681011	+	0.997678i	$0.478306\pi$
$864$		0			0
$865$	−827.020	−	175.789i	−0.956093	−	0.203224i
$866$		0			0
$867$		−	290.672i		−	0.335262i
$868$		0			0
$869$	−52.5380			−0.0604579
$870$		0			0
$871$	197.172	−	927.620i	0.226374	−	1.06501i
$872$		0			0
$873$	375.520	+	650.419i	0.430149	+	0.745040i
$874$		0			0
$875$	−1217.49	+	542.060i	−1.39141	+	0.619497i
$876$		0			0
$877$	525.119	+	233.798i	0.598768	+	0.266589i	0.683659	−	0.729802i	$-0.260388\pi$
$877$	525.119	+	233.798i	0.598768	+	0.266589i	−0.0848913	+	0.996390i	$0.527054\pi$
$878$		0			0
$879$	−141.453	−	14.8673i	−0.160924	−	0.0169138i
$880$		0			0
$881$	222.482	+	200.324i	0.252533	+	0.227382i	0.785668	−	0.618648i	$-0.212319\pi$
$881$	222.482	+	200.324i	0.252533	+	0.227382i	−0.533135	+	0.846030i	$0.678986\pi$
$882$		0			0
$883$	−1398.89	+	454.528i	−1.58425	+	0.514754i	−0.963147	−	0.268974i	$-0.913315\pi$
$883$	−1398.89	+	454.528i	−1.58425	+	0.514754i	−0.621103	+	0.783729i	$0.713315\pi$
$884$		0			0
$885$	39.4870	−	4.15025i	0.0446181	−	0.00468955i
$886$		0			0
$887$	−700.853	−	778.376i	−0.790139	−	0.877538i	0.204719	−	0.978821i	$-0.434372\pi$
$887$	−700.853	−	778.376i	−0.790139	−	0.877538i	−0.994858	+	0.101283i	$0.967705\pi$
$888$		0			0
$889$	369.014	+	1736.07i	0.415089	+	1.95284i
$890$		0			0
$891$	87.5909	+	120.558i	0.0983063	+	0.135307i
$892$		0			0
$893$	9.22998	−	15.9868i	0.0103359	−	0.0179023i
$894$		0			0
$895$	263.216	−	362.285i	0.294096	−	0.404788i
$896$		0			0
$897$	640.978	+	208.267i	0.714580	+	0.232181i
$898$		0			0
$899$	−415.498	−	856.236i	−0.462178	−	0.952431i
$900$		0			0
$901$	91.3670	−	281.199i	0.101406	−	0.312096i
$902$		0			0
$903$	−647.743	−	470.613i	−0.717324	−	0.521166i
$904$		0			0
$905$	444.176	+	256.445i	0.490802	+	0.283365i
$906$		0			0
$907$	243.229	−	176.716i	0.268169	−	0.194836i	−0.445572	−	0.895246i	$-0.647000\pi$
$907$	243.229	−	176.716i	0.268169	−	0.194836i	0.713741	+	0.700410i	$0.247000\pi$
$908$		0			0
$909$	−720.577	+	153.163i	−0.792714	+	0.168497i
$910$		0			0
$911$	386.443	−	347.955i	0.424196	−	0.381948i	−0.429201	−	0.903209i	$-0.641205\pi$
$911$	386.443	−	347.955i	0.424196	−	0.381948i	0.853397	+	0.521261i	$0.174538\pi$
$912$		0			0
$913$	−38.2493	−	363.917i	−0.0418940	−	0.398595i
$914$		0			0
$915$	95.2251	+	293.073i	0.104071	+	0.320298i
$916$		0			0
$917$	−753.621	+	836.981i	−0.821834	+	0.912739i
$918$		0			0
$919$	142.101	−	1352.00i	0.154626	−	1.47117i	−0.592009	−	0.805931i	$-0.701665\pi$
$919$	142.101	−	1352.00i	0.154626	−	1.47117i	0.746635	−	0.665234i	$-0.231668\pi$
$920$		0			0
$921$	286.519	−	643.533i	0.311096	−	0.698733i
$922$		0			0
$923$	−128.914	−	289.545i	−0.139668	−	0.313700i
$924$		0			0
$925$	271.316	−	156.644i	0.293315	−	0.169345i
$926$		0			0
$927$	701.316	+	149.069i	0.756543	+	0.160808i
$928$		0			0
$929$		−	440.110i		−	0.473746i	−0.971541	−	0.236873i	$-0.923877\pi$
$929$		−	440.110i		−	0.473746i	0.971541	−	0.236873i	$-0.0761225\pi$
$930$		0			0
$931$	−98.4652			−0.105763
$932$		0			0
$933$	77.8376	−	366.197i	0.0834272	−	0.392494i
$934$		0			0
$935$	44.1898	+	76.5389i	0.0472618	+	0.0818598i
$936$		0			0
$937$	975.822	−	434.464i	1.04143	−	0.463675i	0.186521	−	0.982451i	$-0.440279\pi$
$937$	975.822	−	434.464i	1.04143	−	0.463675i	0.854910	+	0.518776i	$0.173612\pi$
$938$		0			0
$939$	257.963	+	114.853i	0.274721	+	0.122314i
$940$		0			0
$941$	1015.32	+	106.714i	1.07898	+	0.113405i	0.627301	−	0.778777i	$-0.284159\pi$
$941$	1015.32	+	106.714i	1.07898	+	0.113405i	0.451677	+	0.892182i	$0.350826\pi$
$942$		0			0
$943$	1862.02	+	1676.57i	1.97457	+	1.77791i
$944$		0			0
$945$	670.229	−	217.771i	0.709237	−	0.230445i
$946$		0			0
$947$	−1305.31	+	137.193i	−1.37836	+	0.144872i	−0.764542	−	0.644574i	$-0.777035\pi$
$947$	−1305.31	+	137.193i	−1.37836	+	0.144872i	−0.613820	+	0.789446i	$0.710368\pi$
$948$		0			0
$949$	358.092	+	397.702i	0.377336	+	0.419075i
$950$		0			0
$951$	127.571	+	600.174i	0.134144	+	0.631097i
$952$		0			0
$953$	35.7778	+	49.2440i	0.0375423	+	0.0516726i	0.827376	−	0.561649i	$-0.189833\pi$
$953$	35.7778	+	49.2440i	0.0375423	+	0.0516726i	−0.789833	+	0.613322i	$0.789833\pi$
$954$		0			0
$955$	623.773	−	1080.41i	0.653166	−	1.13132i
$956$		0			0
$957$	−79.2575	+	109.089i	−0.0828187	+	0.113990i
$958$		0			0
$959$	−1217.30	−	395.526i	−1.26935	−	0.412436i
$960$		0			0
$961$	−37.3767	+	960.273i	−0.0388936	+	0.999243i
$962$		0			0
$963$	212.024	−	652.543i	0.220170	−	0.677615i
$964$		0			0
$965$	−552.304	−	401.273i	−0.572336	−	0.415827i
$966$		0			0
$967$	614.594	+	354.836i	0.635567	+	0.366945i	0.782905	−	0.622141i	$-0.213737\pi$
$967$	614.594	+	354.836i	0.635567	+	0.366945i	−0.147338	+	0.989086i	$0.547070\pi$
$968$		0			0
$969$	−13.1041	+	9.52067i	−0.0135233	+	0.00982525i
$970$		0			0
$971$	1266.09	−	269.117i	1.30391	−	0.277154i	0.496958	−	0.867774i	$-0.334450\pi$
$971$	1266.09	−	269.117i	1.30391	−	0.277154i	0.806950	+	0.590620i	$0.201117\pi$
$972$		0			0
$973$	−10.2934	+	9.26820i	−0.0105790	+	0.00952538i
$974$		0			0
$975$	27.9174	+	265.617i	0.0286333	+	0.272427i
$976$		0			0
$977$	359.101	+	1105.20i	0.367554	+	1.13122i	0.948366	+	0.317178i	$0.102735\pi$
$977$	359.101	+	1105.20i	0.367554	+	1.13122i	−0.580812	+	0.814038i	$0.697265\pi$
$978$		0			0
$979$	−133.154	+	147.882i	−0.136010	+	0.151054i
$980$		0			0
$981$	49.0936	−	467.094i	0.0500444	−	0.476141i
$982$		0			0
$983$	583.983	−	1311.65i	0.594082	−	1.33433i	−0.327023	−	0.945016i	$-0.606045\pi$
$983$	583.983	−	1311.65i	0.594082	−	1.33433i	0.921105	−	0.389314i	$-0.127288\pi$
$984$		0			0
$985$	−381.780	−	857.493i	−0.387594	−	0.870551i
$986$		0			0
$987$	−113.625	+	65.6015i	−0.115122	+	0.0664656i
$988$		0			0
$989$	2117.07	+	449.996i	2.14061	+	0.455001i
$990$		0			0
$991$			898.574i			0.906735i	0.891324	+	0.453367i	$0.149777\pi$
$991$			898.574i			0.906735i	−0.891324	+	0.453367i	$0.850223\pi$
$992$		0			0
$993$	667.360			0.672065
$994$		0			0
$995$	−184.519	+	868.095i	−0.185446	+	0.872457i
$996$		0			0
$997$	−77.0880	−	133.520i	−0.0773199	−	0.133922i	0.824773	−	0.565464i	$-0.191303\pi$
$997$	−77.0880	−	133.520i	−0.0773199	−	0.133922i	−0.902093	+	0.431542i	$0.857970\pi$
$998$		0			0
$999$	−430.705	+	191.762i	−0.431136	+	0.191954i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.3.o.a.53.3	✓	40
31.24	odd	30	inner	124.3.o.a.117.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.3.o.a.53.3	✓	40	1.1	even	1	trivial
124.3.o.a.117.3	yes	40	31.24	odd	30	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	124.o (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.257314 + 1.21057i) q^{3} +(-1.69238 - 2.93128i) q^{5} +(9.33225 - 4.15499i) q^{7} +(6.82265 + 3.03764i) q^{9} +O(q^{10})\)	\(q+(-0.257314 + 1.21057i) q^{3} +(-1.69238 - 2.93128i) q^{5} +(9.33225 - 4.15499i) q^{7} +(6.82265 + 3.03764i) q^{9} +(3.52941 + 0.370956i) q^{11} +(11.8413 + 10.6620i) q^{13} +(3.98399 - 1.29448i) q^{15} +(-7.31731 + 0.769080i) q^{17} +(-1.19025 - 1.32191i) q^{19} +(2.62857 + 12.3665i) q^{21} +(-20.0883 - 27.6492i) q^{23} +(6.77172 - 11.7290i) q^{25} +(-11.9799 + 16.4889i) q^{27} +(29.1982 + 9.48706i) q^{29} +(-21.4898 - 22.3425i) q^{31} +(-1.35723 + 4.17714i) q^{33} +(-27.9731 - 20.3237i) q^{35} +(20.0330 + 11.5661i) q^{37} +(-15.9540 + 11.5913i) q^{39} +(-71.7116 + 15.2428i) q^{41} +(-47.0628 + 42.3756i) q^{43} +(-2.64231 - 25.1399i) q^{45} +(3.20690 + 9.86983i) q^{47} +(37.0396 - 41.1366i) q^{49} +(0.951822 - 9.05598i) q^{51} +(-16.3449 + 36.7113i) q^{53} +(-4.88572 - 10.9735i) q^{55} +(1.90652 - 1.10073i) q^{57} +(9.27114 + 1.97064i) q^{59} +73.5627i q^{61} +76.2920 q^{63} +(11.2133 - 52.7544i) q^{65} +(-29.7583 - 51.5429i) q^{67} +(38.6403 - 17.2038i) q^{69} +(-18.1714 - 8.09043i) q^{71} +(33.4019 + 3.51068i) q^{73} +(12.4562 + 11.2156i) q^{75} +(34.4787 - 11.2028i) q^{77} +(-14.7231 + 1.54746i) q^{79} +(28.0972 + 31.2051i) q^{81} +(-21.4378 - 100.857i) q^{83} +(14.6380 + 20.1475i) q^{85} +(-18.9978 + 32.9052i) q^{87} +(-32.9589 + 45.3640i) q^{89} +(154.807 + 50.2997i) q^{91} +(32.5767 - 20.2658i) q^{93} +(-1.86053 + 5.72612i) q^{95} +(81.3575 + 59.1097i) q^{97} +(22.9531 + 13.2520i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{3} - 3 q^{5} + 19 q^{7} - 2 q^{9}+O(q^{10}) \) 40 * q - 3 * q^3 - 3 * q^5 + 19 * q^7 - 2 * q^9	\( 40 q - 3 q^{3} - 3 q^{5} + 19 q^{7} - 2 q^{9} + 2 q^{11} - 18 q^{13} + 35 q^{15} + 25 q^{17} - 11 q^{19} + 54 q^{21} + 25 q^{23} - 75 q^{25} + 225 q^{27} + 20 q^{29} + 59 q^{31} - 303 q^{33} - 66 q^{35} - 222 q^{37} - 169 q^{39} + q^{41} + 122 q^{43} + 54 q^{45} - 120 q^{47} - 118 q^{49} - 515 q^{51} + 61 q^{53} - 121 q^{55} - 201 q^{57} - 257 q^{59} - 158 q^{63} + 182 q^{65} - q^{67} + 510 q^{69} + 459 q^{71} + 253 q^{73} + 651 q^{75} + 670 q^{77} + 385 q^{79} + 974 q^{81} + 375 q^{83} - 370 q^{85} - 344 q^{87} + 245 q^{89} + 960 q^{91} - 212 q^{93} - 851 q^{95} - 797 q^{97} - 21 q^{99}+O(q^{100}) \) 40 * q - 3 * q^3 - 3 * q^5 + 19 * q^7 - 2 * q^9 + 2 * q^11 - 18 * q^13 + 35 * q^15 + 25 * q^17 - 11 * q^19 + 54 * q^21 + 25 * q^23 - 75 * q^25 + 225 * q^27 + 20 * q^29 + 59 * q^31 - 303 * q^33 - 66 * q^35 - 222 * q^37 - 169 * q^39 + q^41 + 122 * q^43 + 54 * q^45 - 120 * q^47 - 118 * q^49 - 515 * q^51 + 61 * q^53 - 121 * q^55 - 201 * q^57 - 257 * q^59 - 158 * q^63 + 182 * q^65 - q^67 + 510 * q^69 + 459 * q^71 + 253 * q^73 + 651 * q^75 + 670 * q^77 + 385 * q^79 + 974 * q^81 + 375 * q^83 - 370 * q^85 - 344 * q^87 + 245 * q^89 + 960 * q^91 - 212 * q^93 - 851 * q^95 - 797 * q^97 - 21 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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