LMFDB - Embedded newform 124.3.o.a.53.5

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			53.5
Character	$\chi$	$=$	124.53
Dual form			124.3.o.a.117.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.938675 - 4.41612i) q^{3} +(-0.896461 - 1.55272i) q^{5} +(3.51190 - 1.56360i) q^{7} +(-10.3991 - 4.62997i) q^{9} +O(q^{10})$	\(q+(0.938675 - 4.41612i) q^{3} +(-0.896461 - 1.55272i) q^{5} +(3.51190 - 1.56360i) q^{7} +(-10.3991 - 4.62997i) q^{9} +(-1.57591 - 0.165635i) q^{11} +(-10.8054 - 9.72918i) q^{13} +(-7.69846 + 2.50138i) q^{15} +(1.79282 - 0.188433i) q^{17} +(1.84788 + 2.05228i) q^{19} +(-3.60850 - 16.9767i) q^{21} +(20.8393 + 28.6828i) q^{23} +(10.8927 - 18.8667i) q^{25} +(-6.32435 + 8.70472i) q^{27} +(11.3809 + 3.69788i) q^{29} +(28.1367 - 13.0126i) q^{31} +(-2.21073 + 6.80392i) q^{33} +(-5.57610 - 4.05128i) q^{35} +(32.9387 + 19.0172i) q^{37} +(-53.1079 + 38.5852i) q^{39} +(20.1037 - 4.27317i) q^{41} +(-24.6510 + 22.1959i) q^{43} +(2.13334 + 20.2974i) q^{45} +(25.5097 + 78.5106i) q^{47} +(-22.8988 + 25.4317i) q^{49} +(0.850733 - 8.09418i) q^{51} +(3.08185 - 6.92196i) q^{53} +(1.15556 + 2.59542i) q^{55} +(10.7977 - 6.23403i) q^{57} +(-71.7931 - 15.2601i) q^{59} -110.408i q^{61} -43.7599 q^{63} +(-5.42008 + 25.4995i) q^{65} +(0.643629 + 1.11480i) q^{67} +(146.228 - 65.1049i) q^{69} +(40.2982 + 17.9419i) q^{71} +(11.6919 + 1.22887i) q^{73} +(-73.0930 - 65.8132i) q^{75} +(-5.79342 + 1.88240i) q^{77} +(116.095 - 12.2021i) q^{79} +(-36.0471 - 40.0343i) q^{81} +(-10.0256 - 47.1668i) q^{83} +(-1.89978 - 2.61482i) q^{85} +(27.0133 - 46.7884i) q^{87} +(-62.8547 + 86.5121i) q^{89} +(-53.1598 - 17.2727i) q^{91} +(-31.0539 - 136.469i) q^{93} +(1.53005 - 4.70902i) q^{95} +(-94.9132 - 68.9585i) q^{97} +(15.6211 + 9.01885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.938675	−	4.41612i	0.312892	−	1.47204i	−0.487796	−	0.872957i	$-0.662199\pi$
$3$	0.938675	−	4.41612i	0.312892	−	1.47204i	0.800688	−	0.599082i	$-0.204468\pi$
$4$		0			0
$5$	−0.896461	−	1.55272i	−0.179292	−	0.310543i	0.762346	−	0.647170i	$-0.224047\pi$
$5$	−0.896461	−	1.55272i	−0.179292	−	0.310543i	−0.941638	+	0.336626i	$0.890714\pi$
$6$		0			0
$7$	3.51190	−	1.56360i	0.501700	−	0.223371i	−0.140252	−	0.990116i	$-0.544791\pi$
$7$	3.51190	−	1.56360i	0.501700	−	0.223371i	0.641952	+	0.766745i	$0.278125\pi$
$8$		0			0
$9$	−10.3991	−	4.62997i	−1.15545	−	0.514441i
$10$		0			0
$11$	−1.57591	−	0.165635i	−0.143264	−	0.0150577i	0.0326248	−	0.999468i	$-0.489613\pi$
$11$	−1.57591	−	0.165635i	−0.143264	−	0.0150577i	−0.175889	+	0.984410i	$0.556280\pi$
$12$		0			0
$13$	−10.8054	−	9.72918i	−0.831181	−	0.748399i	0.139126	−	0.990275i	$-0.455571\pi$
$13$	−10.8054	−	9.72918i	−0.831181	−	0.748399i	−0.970307	+	0.241876i	$0.922237\pi$
$14$		0			0
$15$	−7.69846	+	2.50138i	−0.513231	+	0.166759i
$16$		0			0
$17$	1.79282	−	0.188433i	0.105460	−	0.0110843i	−0.0516514	−	0.998665i	$-0.516448\pi$
$17$	1.79282	−	0.188433i	0.105460	−	0.0110843i	0.157111	+	0.987581i	$0.449782\pi$
$18$		0			0
$19$	1.84788	+	2.05228i	0.0972568	+	0.108015i	0.789808	−	0.613354i	$-0.210180\pi$
$19$	1.84788	+	2.05228i	0.0972568	+	0.108015i	−0.692551	+	0.721369i	$0.743513\pi$
$20$		0			0
$21$	−3.60850	−	16.9767i	−0.171833	−	0.808413i
$22$		0			0
$23$	20.8393	+	28.6828i	0.906056	+	1.24708i	0.968496	+	0.249030i	$0.0801119\pi$
$23$	20.8393	+	28.6828i	0.906056	+	1.24708i	−0.0624396	+	0.998049i	$0.519888\pi$
$24$		0			0
$25$	10.8927	−	18.8667i	0.435709	−	0.754670i
$26$		0			0
$27$	−6.32435	+	8.70472i	−0.234235	+	0.322397i
$28$		0			0
$29$	11.3809	+	3.69788i	0.392445	+	0.127513i	0.498591	−	0.866837i	$-0.333851\pi$
$29$	11.3809	+	3.69788i	0.392445	+	0.127513i	−0.106146	+	0.994351i	$0.533851\pi$
$30$		0			0
$31$	28.1367	−	13.0126i	0.907635	−	0.419761i
$31$	28.1367	−	13.0126i	0.907635	−	0.419761i
$32$		0			0
$33$	−2.21073	+	6.80392i	−0.0669917	+	0.206179i
$34$		0			0
$35$	−5.57610	−	4.05128i	−0.159317	−	0.115751i
$36$		0			0
$37$	32.9387	+	19.0172i	0.890236	+	0.513978i	0.874020	−	0.485891i	$-0.161505\pi$
$37$	32.9387	+	19.0172i	0.890236	+	0.513978i	0.0162160	+	0.999869i	$0.494838\pi$
$38$		0			0
$39$	−53.1079	+	38.5852i	−1.36174	+	0.989363i
$40$		0			0
$41$	20.1037	−	4.27317i	0.490333	−	0.104224i	0.0438916	−	0.999036i	$-0.486024\pi$
$41$	20.1037	−	4.27317i	0.490333	−	0.104224i	0.446442	+	0.894813i	$0.352691\pi$
$42$		0			0
$43$	−24.6510	+	22.1959i	−0.573279	+	0.516183i	−0.903993	−	0.427548i	$-0.859377\pi$
$43$	−24.6510	+	22.1959i	−0.573279	+	0.516183i	0.330713	+	0.943731i	$0.392711\pi$
$44$		0			0
$45$	2.13334	+	20.2974i	0.0474076	+	0.451053i
$46$		0			0
$47$	25.5097	+	78.5106i	0.542759	+	1.67044i	0.726260	+	0.687420i	$0.241257\pi$
$47$	25.5097	+	78.5106i	0.542759	+	1.67044i	−0.183502	+	0.983019i	$0.558743\pi$
$48$		0			0
$49$	−22.8988	+	25.4317i	−0.467323	+	0.519014i
$50$		0			0
$51$	0.850733	−	8.09418i	0.0166810	−	0.158709i
$52$		0			0
$53$	3.08185	−	6.92196i	0.0581482	−	0.130603i	−0.882134	−	0.470998i	$-0.843894\pi$
$53$	3.08185	−	6.92196i	0.0581482	−	0.130603i	0.940283	+	0.340395i	$0.110561\pi$
$54$		0			0
$55$	1.15556	+	2.59542i	0.0210101	+	0.0471895i
$56$		0			0
$57$	10.7977	−	6.23403i	0.189432	−	0.109369i
$58$		0			0
$59$	−71.7931	−	15.2601i	−1.21683	−	0.258646i	−0.445619	−	0.895223i	$-0.647016\pi$
$59$	−71.7931	−	15.2601i	−1.21683	−	0.258646i	−0.771213	+	0.636577i	$0.780350\pi$
$60$		0			0
$61$		−	110.408i		−	1.80996i	−0.425454	−	0.904980i	$-0.639886\pi$
$61$		−	110.408i		−	1.80996i	0.425454	−	0.904980i	$-0.360114\pi$
$62$		0			0
$63$	−43.7599			−0.694601
$64$		0			0
$65$	−5.42008	+	25.4995i	−0.0833858	+	0.392300i
$66$		0			0
$67$	0.643629	+	1.11480i	0.00960641	+	0.0166388i	0.870789	−	0.491658i	$-0.163609\pi$
$67$	0.643629	+	1.11480i	0.00960641	+	0.0166388i	−0.861182	+	0.508296i	$0.830275\pi$
$68$		0			0
$69$	146.228	−	65.1049i	2.11925	−	0.943549i
$70$		0			0
$71$	40.2982	+	17.9419i	0.567580	+	0.252703i	0.670403	−	0.741997i	$-0.266121\pi$
$71$	40.2982	+	17.9419i	0.567580	+	0.252703i	−0.102824	+	0.994700i	$0.532788\pi$
$72$		0			0
$73$	11.6919	+	1.22887i	0.160163	+	0.0168339i	0.184271	−	0.982876i	$-0.441008\pi$
$73$	11.6919	+	1.22887i	0.160163	+	0.0168339i	−0.0241073	+	0.999709i	$0.507674\pi$
$74$		0			0
$75$	−73.0930	−	65.8132i	−0.974573	−	0.877510i
$76$		0			0
$77$	−5.79342	+	1.88240i	−0.0752392	+	0.0244467i
$78$		0			0
$79$	116.095	−	12.2021i	1.46956	−	0.154457i	0.664338	−	0.747432i	$-0.268714\pi$
$79$	116.095	−	12.2021i	1.46956	−	0.154457i	0.805220	+	0.592976i	$0.202047\pi$
$80$		0			0
$81$	−36.0471	−	40.0343i	−0.445026	−	0.494251i
$82$		0			0
$83$	−10.0256	−	47.1668i	−0.120791	−	0.568275i	−0.996365	−	0.0851911i	$-0.972850\pi$
$83$	−10.0256	−	47.1668i	−0.120791	−	0.568275i	0.875574	−	0.483084i	$-0.160483\pi$
$84$		0			0
$85$	−1.89978	−	2.61482i	−0.0223503	−	0.0307626i
$86$		0			0
$87$	27.0133	−	46.7884i	0.310497	−	0.537797i
$88$		0			0
$89$	−62.8547	+	86.5121i	−0.706233	+	0.972046i	0.293637	+	0.955917i	$0.405134\pi$
$89$	−62.8547	+	86.5121i	−0.706233	+	0.972046i	−0.999870	+	0.0161294i	$0.994866\pi$
$90$		0			0
$91$	−53.1598	−	17.2727i	−0.584174	−	0.189810i
$92$		0			0
$93$	−31.0539	−	136.469i	−0.333913	−	1.46741i
$94$		0			0
$95$	1.53005	−	4.70902i	0.0161058	−	0.0495686i
$96$		0			0
$97$	−94.9132	−	68.9585i	−0.978487	−	0.710912i	−0.0211167	−	0.999777i	$-0.506722\pi$
$97$	−94.9132	−	68.9585i	−0.978487	−	0.710912i	−0.957370	+	0.288865i	$0.906722\pi$
$98$		0			0
$99$	15.6211	+	9.01885i	0.157789	+	0.0910995i
$100$		0			0
$101$	−68.5344	+	49.7932i	−0.678559	+	0.493002i	−0.872879	−	0.487936i	$-0.837750\pi$
$101$	−68.5344	+	49.7932i	−0.678559	+	0.493002i	0.194320	+	0.980938i	$0.437750\pi$
$102$		0			0
$103$	−73.8991	+	15.7077i	−0.717467	+	0.152502i	−0.552158	−	0.833740i	$-0.686195\pi$
$103$	−73.8991	+	15.7077i	−0.717467	+	0.152502i	−0.165309	+	0.986242i	$0.552862\pi$
$104$		0			0
$105$	−23.1251	+	20.8219i	−0.220239	+	0.198304i
$106$		0			0
$107$	20.0003	+	190.290i	0.186918	+	1.77841i	0.538868	+	0.842390i	$0.318852\pi$
$107$	20.0003	+	190.290i	0.186918	+	1.77841i	−0.351950	+	0.936019i	$0.614481\pi$
$108$		0			0
$109$	−14.9721	−	46.0793i	−0.137359	−	0.422746i	0.858591	−	0.512661i	$-0.171340\pi$
$109$	−14.9721	−	46.0793i	−0.137359	−	0.422746i	−0.995949	+	0.0899152i	$0.971340\pi$
$110$		0			0
$111$	114.901	−	127.610i	1.03514	−	1.14964i
$112$		0			0
$113$	−17.2900	+	164.503i	−0.153009	+	1.45578i	0.601175	+	0.799117i	$0.294699\pi$
$113$	−17.2900	+	164.503i	−0.153009	+	1.45578i	−0.754184	+	0.656663i	$0.771967\pi$
$114$		0			0
$115$	25.8547	−	58.0705i	0.224823	−	0.504961i
$116$		0			0
$117$	67.3199	+	151.203i	0.575383	+	1.29233i
$118$		0			0
$119$	6.00157	−	3.46501i	0.0504334	−	0.0291177i
$120$		0			0
$121$	−115.900	−	24.6353i	−0.957850	−	0.203597i
$122$		0			0
$123$		−	92.7913i		−	0.754400i
$124$		0			0
$125$	−83.8826			−0.671061
$126$		0			0
$127$	−22.3913	+	105.343i	−0.176309	+	0.829469i	0.797717	+	0.603032i	$0.206041\pi$
$127$	−22.3913	+	105.343i	−0.176309	+	0.829469i	−0.974026	+	0.226437i	$0.927292\pi$
$128$		0			0
$129$	74.8803	+	129.696i	0.580467	+	1.00540i
$130$		0			0
$131$	156.180	−	69.5360i	1.19222	−	0.530809i	0.287896	−	0.957662i	$-0.407044\pi$
$131$	156.180	−	69.5360i	1.19222	−	0.530809i	0.904321	+	0.426853i	$0.140378\pi$
$132$		0			0
$133$	9.69850	+	4.31805i	0.0729210	+	0.0324665i
$134$		0			0
$135$	19.1855	+	2.01648i	0.142115	+	0.0149369i
$136$		0			0
$137$	−110.999	−	99.9443i	−0.810214	−	0.729520i	0.155862	−	0.987779i	$-0.450185\pi$
$137$	−110.999	−	99.9443i	−0.810214	−	0.729520i	−0.966076	+	0.258259i	$0.916851\pi$
$138$		0			0
$139$	199.211	−	64.7277i	1.43318	−	0.465667i	0.513413	−	0.858142i	$-0.328381\pi$
$139$	199.211	−	64.7277i	1.43318	−	0.465667i	0.919763	+	0.392475i	$0.128381\pi$
$140$		0			0
$141$	370.657	−	38.9577i	2.62878	−	0.276296i
$142$		0			0
$143$	15.4168	+	17.1220i	0.107809	+	0.119735i
$144$		0			0
$145$	−4.46078	−	20.9863i	−0.0307640	−	0.144733i
$146$		0			0
$147$	90.8149	+	124.996i	0.617788	+	0.850312i
$148$		0			0
$149$	−140.815	+	243.898i	−0.945065	+	1.63690i	−0.189444	+	0.981892i	$0.560668\pi$
$149$	−140.815	+	243.898i	−0.945065	+	1.63690i	−0.755621	+	0.655009i	$0.772665\pi$
$150$		0			0
$151$	−27.8178	+	38.2880i	−0.184224	+	0.253563i	−0.891133	−	0.453742i	$-0.850089\pi$
$151$	−27.8178	+	38.2880i	−0.184224	+	0.253563i	0.706909	+	0.707304i	$0.250089\pi$
$152$		0			0
$153$	−19.5161	−	6.34117i	−0.127556	−	0.0414455i
$154$		0			0
$155$	−45.4283	−	32.0230i	−0.293086	−	0.206600i
$156$		0			0
$157$	0.671473	−	2.06658i	0.00427690	−	0.0131629i	−0.948895	−	0.315591i	$-0.897797\pi$
$157$	0.671473	−	2.06658i	0.00427690	−	0.0131629i	0.953172	+	0.302428i	$0.0977972\pi$
$158$		0			0
$159$	−27.6753	−	20.1073i	−0.174059	−	0.126461i
$160$		0			0
$161$	118.034	+	68.1469i	0.733130	+	0.423273i
$162$		0			0
$163$	−190.945	+	138.730i	−1.17144	+	0.851104i	−0.991181	−	0.132515i	$-0.957695\pi$
$163$	−190.945	+	138.730i	−1.17144	+	0.851104i	−0.180263	+	0.983619i	$0.557695\pi$
$164$		0			0
$165$	12.5464	−	2.66682i	0.0760387	−	0.0161625i
$166$		0			0
$167$	49.7805	−	44.8226i	0.298087	−	0.268399i	−0.506492	−	0.862245i	$-0.669058\pi$
$167$	49.7805	−	44.8226i	0.298087	−	0.268399i	0.804579	+	0.593846i	$0.202391\pi$
$168$		0			0
$169$	4.43333	+	42.1803i	0.0262327	+	0.249588i
$170$		0			0
$171$	−9.71425	−	29.8974i	−0.0568085	−	0.174839i
$172$		0			0
$173$	−60.0951	+	66.7424i	−0.347371	+	0.385794i	−0.891359	−	0.453299i	$-0.850247\pi$
$173$	−60.0951	+	66.7424i	−0.347371	+	0.385794i	0.543988	+	0.839093i	$0.316914\pi$
$174$		0			0
$175$	8.75412	−	83.2899i	0.0500235	−	0.475942i
$176$		0			0
$177$	−134.781	+	302.722i	−0.761473	+	1.71030i
$178$		0			0
$179$	−36.6947	−	82.4177i	−0.204999	−	0.460434i	0.781563	−	0.623827i	$-0.214423\pi$
$179$	−36.6947	−	82.4177i	−0.204999	−	0.460434i	−0.986561	+	0.163393i	$0.947756\pi$
$180$		0			0
$181$	91.5637	−	52.8643i	0.505877	−	0.292068i	−0.225260	−	0.974299i	$-0.572323\pi$
$181$	91.5637	−	52.8643i	0.505877	−	0.292068i	0.731137	+	0.682230i	$0.238990\pi$
$182$		0			0
$183$	−487.573	−	103.637i	−2.66433	−	0.566321i
$184$		0			0
$185$		−	68.1926i		−	0.368609i
$186$		0			0
$187$	−2.85653			−0.0152756
$188$		0			0
$189$	−8.59979	+	40.4588i	−0.0455015	+	0.214068i
$190$		0			0
$191$	−31.7511	−	54.9946i	−0.166236	−	0.287930i	0.770857	−	0.637008i	$-0.219828\pi$
$191$	−31.7511	−	54.9946i	−0.166236	−	0.287930i	−0.937094	+	0.349078i	$0.886495\pi$
$192$		0			0
$193$	46.7018	−	20.7930i	0.241978	−	0.107736i	−0.282165	−	0.959366i	$-0.591052\pi$
$193$	46.7018	−	20.7930i	0.241978	−	0.107736i	0.524143	+	0.851630i	$0.324386\pi$
$194$		0			0
$195$	107.521	+	47.8714i	0.551390	+	0.245494i
$196$		0			0
$197$	195.049	+	20.5005i	0.990098	+	0.104063i	0.585707	−	0.810523i	$-0.300817\pi$
$197$	195.049	+	20.5005i	0.990098	+	0.104063i	0.404391	+	0.914586i	$0.367484\pi$
$198$		0			0
$199$	−41.6301	−	37.4839i	−0.209197	−	0.188361i	0.557871	−	0.829928i	$-0.311618\pi$
$199$	−41.6301	−	37.4839i	−0.209197	−	0.188361i	−0.767068	+	0.641566i	$0.778285\pi$
$200$		0			0
$201$	5.52724	−	1.79591i	0.0274987	−	0.00893487i
$202$		0			0
$203$	45.7506	−	4.80858i	0.225373	−	0.0236876i
$204$		0			0
$205$	−24.6572	−	27.3845i	−0.120279	−	0.133583i
$206$		0			0
$207$	−83.9088	−	394.760i	−0.405357	−	1.90705i
$208$		0			0
$209$	−2.57216	−	3.54027i	−0.0123070	−	0.0169391i
$210$		0			0
$211$	−4.40339	+	7.62689i	−0.0208691	+	0.0361464i	−0.876271	−	0.481818i	$-0.839977\pi$
$211$	−4.40339	+	7.62689i	−0.0208691	+	0.0361464i	0.855402	+	0.517964i	$0.173310\pi$
$212$		0			0
$213$	117.060	−	161.120i	0.549579	−	0.756431i
$214$		0			0
$215$	56.5625	+	18.3783i	0.263082	+	0.0854804i
$216$		0			0
$217$	78.4667	−	89.6933i	0.361598	−	0.413333i
$218$		0			0
$219$	16.4018	−	50.4794i	0.0748939	−	0.230500i
$220$		0			0
$221$	−21.2054	−	15.4066i	−0.0959518	−	0.0697131i
$222$		0			0
$223$	−162.446	−	93.7883i	−0.728458	−	0.420575i	0.0894001	−	0.995996i	$-0.471505\pi$
$223$	−162.446	−	93.7883i	−0.728458	−	0.420575i	−0.817858	+	0.575421i	$0.804838\pi$
$224$		0			0
$225$	−200.626	+	145.764i	−0.891673	+	0.647839i
$226$		0			0
$227$	329.954	−	70.1338i	1.45354	−	0.308960i	0.587619	−	0.809138i	$-0.300066\pi$
$227$	329.954	−	70.1338i	1.45354	−	0.308960i	0.865922	+	0.500178i	$0.166732\pi$
$228$		0			0
$229$	41.8535	−	37.6850i	0.182766	−	0.164563i	−0.572669	−	0.819787i	$-0.694092\pi$
$229$	41.8535	−	37.6850i	0.182766	−	0.164563i	0.755435	+	0.655223i	$0.227425\pi$
$230$		0			0
$231$	2.87474	+	27.3514i	0.0124448	+	0.118404i
$232$		0			0
$233$	−84.3846	−	259.709i	−0.362166	−	1.11463i	−0.951737	−	0.306915i	$-0.900703\pi$
$233$	−84.3846	−	259.709i	−0.362166	−	1.11463i	0.589571	−	0.807717i	$-0.299297\pi$
$234$		0			0
$235$	99.0363	−	109.991i	0.421431	−	0.468047i
$236$		0			0
$237$	55.0897	−	524.143i	0.232446	−	2.21158i
$238$		0			0
$239$	42.2833	−	94.9698i	0.176918	−	0.397363i	−0.803220	−	0.595683i	$-0.796882\pi$
$239$	42.2833	−	94.9698i	0.176918	−	0.397363i	0.980137	+	0.198319i	$0.0635483\pi$
$240$		0			0
$241$	141.212	+	317.167i	0.585941	+	1.31605i	0.926667	+	0.375883i	$0.122661\pi$
$241$	141.212	+	317.167i	0.585941	+	1.31605i	−0.340726	+	0.940163i	$0.610673\pi$
$242$		0			0
$243$	−294.496	+	170.027i	−1.21192	+	0.699701i
$244$		0			0
$245$	60.0161	+	12.7568i	0.244964	+	0.0520686i
$246$		0			0
$247$		−	40.1539i		−	0.162566i
$248$		0			0
$249$	−217.705			−0.874318
$250$		0			0
$251$	−36.2258	+	170.429i	−0.144326	+	0.679000i	0.845177	+	0.534487i	$0.179495\pi$
$251$	−36.2258	+	170.429i	−0.144326	+	0.679000i	−0.989503	+	0.144513i	$0.953838\pi$
$252$		0			0
$253$	−28.0899	−	48.6532i	−0.111027	−	0.192305i
$254$		0			0
$255$	−13.3306	+	5.93517i	−0.0522769	+	0.0232752i
$256$		0			0
$257$	−238.549	−	106.209i	−0.928205	−	0.413264i	−0.113763	−	0.993508i	$-0.536290\pi$
$257$	−238.549	−	106.209i	−0.928205	−	0.413264i	−0.814443	+	0.580244i	$0.802957\pi$
$258$		0			0
$259$	145.413	+	15.2835i	0.561439	+	0.0590096i
$260$		0			0
$261$	−101.230	−	91.1478i	−0.387854	−	0.349225i
$262$		0			0
$263$	3.97780	−	1.29246i	0.0151247	−	0.00491431i	−0.301445	−	0.953484i	$-0.597469\pi$
$263$	3.97780	−	1.29246i	0.0151247	−	0.00491431i	0.316570	+	0.948569i	$0.397469\pi$
$264$		0			0
$265$	−13.5106	+	1.42002i	−0.0509834	+	0.00535857i
$266$		0			0
$267$	323.048	+	358.781i	1.20992	+	1.34375i
$268$		0			0
$269$	−57.2001	−	269.105i	−0.212640	−	1.00039i	−0.946901	−	0.321525i	$-0.895805\pi$
$269$	−57.2001	−	269.105i	−0.212640	−	1.00039i	0.734261	−	0.678867i	$-0.237529\pi$
$270$		0			0
$271$	275.952	+	379.815i	1.01827	+	1.40153i	0.913408	+	0.407046i	$0.133441\pi$
$271$	275.952	+	379.815i	1.01827	+	1.40153i	0.104865	+	0.994486i	$0.466559\pi$
$272$		0			0
$273$	−126.178	+	218.547i	−0.462190	+	0.800537i
$274$		0			0
$275$	−20.2909	+	27.9280i	−0.0737851	+	0.101557i
$276$		0			0
$277$	369.300	+	119.993i	1.33321	+	0.433187i	0.887012	−	0.461746i	$-0.152777\pi$
$277$	369.300	+	119.993i	1.33321	+	0.433187i	0.446201	+	0.894933i	$0.352777\pi$
$278$		0			0
$279$	−352.843	+	5.04695i	−1.26467	+	0.0180894i
$280$		0			0
$281$	−101.965	+	313.814i	−0.362863	+	1.11678i	0.588445	+	0.808537i	$0.299740\pi$
$281$	−101.965	+	313.814i	−0.362863	+	1.11678i	−0.951308	+	0.308241i	$0.900260\pi$
$282$		0			0
$283$	−105.513	−	76.6596i	−0.372837	−	0.270882i	0.385549	−	0.922687i	$-0.374012\pi$
$283$	−105.513	−	76.6596i	−0.372837	−	0.270882i	−0.758386	+	0.651805i	$0.774012\pi$
$284$		0			0
$285$	−19.3593	−	11.1771i	−0.0679275	−	0.0392180i
$286$		0			0
$287$	63.9205	−	46.4410i	0.222720	−	0.161815i
$288$		0			0
$289$	−279.506	+	59.4108i	−0.967149	+	0.205574i
$290$		0			0
$291$	−393.621	+	354.418i	−1.35265	+	1.21793i
$292$		0			0
$293$	−20.7058	−	197.003i	−0.0706683	−	0.672364i	−0.971313	−	0.237806i	$-0.923572\pi$
$293$	−20.7058	−	197.003i	−0.0706683	−	0.672364i	0.900644	−	0.434557i	$-0.143095\pi$
$294$		0			0
$295$	40.6651	+	125.154i	0.137848	+	0.424252i
$296$		0			0
$297$	11.4084	−	12.6703i	0.0384121	−	0.0426610i
$298$		0			0
$299$	53.8845	−	512.677i	0.180216	−	1.71464i
$300$		0			0
$301$	−51.8664	+	116.494i	−0.172314	+	0.387023i
$302$		0			0
$303$	155.561	+	349.396i	0.513403	+	1.15312i
$304$		0			0
$305$	−171.432	+	98.9761i	−0.562071	+	0.324512i
$306$		0			0
$307$	108.797	+	23.1255i	0.354388	+	0.0753275i	0.381666	−	0.924300i	$-0.375351\pi$
$307$	108.797	+	23.1255i	0.354388	+	0.0753275i	−0.0272778	+	0.999628i	$0.508684\pi$
$308$		0			0
$309$			341.092i			1.10386i
$310$		0			0
$311$	473.680			1.52309			0.761543	−	0.648115i	$-0.224442\pi$
$311$	473.680			1.52309			0.761543	+	0.648115i	$0.224442\pi$
$312$		0			0
$313$	18.2450	−	85.8360i	0.0582907	−	0.274236i	−0.939344	−	0.342977i	$-0.888565\pi$
$313$	18.2450	−	85.8360i	0.0582907	−	0.274236i	0.997635	+	0.0687406i	$0.0218981\pi$
$314$		0			0
$315$	39.2290	+	67.9467i	0.124537	+	0.215704i
$316$		0			0
$317$	211.159	−	94.0138i	0.666115	−	0.296574i	−0.0456846	−	0.998956i	$-0.514547\pi$
$317$	211.159	−	94.0138i	0.666115	−	0.296574i	0.711800	+	0.702382i	$0.247880\pi$
$318$		0			0
$319$	−17.3228	−	7.71260i	−0.0543034	−	0.0241774i
$320$		0			0
$321$	859.116	+	90.2967i	2.67637	+	0.281298i
$322$		0			0
$323$	3.69963	+	3.33116i	0.0114540	+	0.0103132i
$324$		0			0
$325$	−301.258	+	97.8845i	−0.926946	+	0.301183i
$326$		0			0
$327$	−217.546	+	22.8650i	−0.665277	+	0.0699235i
$328$		0			0
$329$	212.346	+	235.835i	0.645430	+	0.716822i
$330$		0			0
$331$	46.3359	+	217.993i	0.139988	+	0.658589i	0.991046	+	0.133519i	$0.0426277\pi$
$331$	46.3359	+	217.993i	0.139988	+	0.658589i	−0.851059	+	0.525070i	$0.824039\pi$
$332$		0			0
$333$	−254.483	−	350.266i	−0.764214	−	1.05185i
$334$		0			0
$335$	1.15398	−	1.99875i	0.00344471	−	0.00596641i
$336$		0			0
$337$	255.249	−	351.320i	0.757416	−	1.04249i	−0.240009	−	0.970771i	$-0.577150\pi$
$337$	255.249	−	351.320i	0.757416	−	1.04249i	0.997425	−	0.0717225i	$-0.0228496\pi$
$338$		0			0
$339$	710.236	+	230.770i	2.09509	+	0.680736i
$340$		0			0
$341$	−46.4962	+	15.8462i	−0.136352	+	0.0464699i
$342$		0			0
$343$	−98.8623	+	304.267i	−0.288228	+	0.887076i
$344$		0			0
$345$	−232.177	−	168.687i	−0.672977	−	0.488946i
$346$		0			0
$347$	−540.454	−	312.031i	−1.55750	−	0.899226i	−0.997495	−	0.0707398i	$-0.977464\pi$
$347$	−540.454	−	312.031i	−1.55750	−	0.899226i	−0.560010	−	0.828486i	$-0.689203\pi$
$348$		0			0
$349$	285.404	−	207.358i	0.817777	−	0.594150i	−0.0982978	−	0.995157i	$-0.531340\pi$
$349$	285.404	−	207.358i	0.817777	−	0.594150i	0.916075	+	0.401007i	$0.131340\pi$
$350$		0			0
$351$	153.027	−	32.5268i	0.435973	−	0.0926690i
$352$		0			0
$353$	28.5383	−	25.6960i	0.0808449	−	0.0727931i	−0.627718	−	0.778441i	$-0.716011\pi$
$353$	28.5383	−	25.6960i	0.0808449	−	0.0727931i	0.708562	+	0.705648i	$0.249344\pi$
$354$		0			0
$355$	−8.26706	−	78.6558i	−0.0232875	−	0.221566i
$356$		0			0
$357$	−9.66836	−	29.7562i	−0.0270822	−	0.0833506i
$358$		0			0
$359$	317.091	−	352.166i	0.883263	−	0.980963i	−0.116662	−	0.993172i	$-0.537220\pi$
$359$	317.091	−	352.166i	0.883263	−	0.980963i	0.999925	+	0.0122085i	$0.00388617\pi$
$360$		0			0
$361$	36.9376	−	351.438i	0.102320	−	0.973512i
$362$		0			0
$363$	−217.584	+	488.703i	−0.599406	+	1.34629i
$364$		0			0
$365$	−8.57327	−	19.2559i	−0.0234884	−	0.0527558i
$366$		0			0
$367$	−535.433	+	309.133i	−1.45895	+	0.842323i	−0.998960	−	0.0456022i	$-0.985479\pi$
$367$	−535.433	+	309.133i	−1.45895	+	0.842323i	−0.459987	+	0.887926i	$0.652146\pi$
$368$		0			0
$369$	−228.844	−	48.6423i	−0.620174	−	0.131822i
$370$		0			0
$371$		−	29.1280i		−	0.0785121i
$372$		0			0
$373$	140.775			0.377413			0.188706	−	0.982034i	$-0.439571\pi$
$373$	140.775			0.377413			0.188706	+	0.982034i	$0.439571\pi$
$374$		0			0
$375$	−78.7385	+	370.435i	−0.209969	+	0.987828i
$376$		0			0
$377$	−86.9974	−	150.684i	−0.230762	−	0.399692i
$378$		0			0
$379$	−402.453	+	179.184i	−1.06188	+	0.472781i	−0.861931	−	0.507025i	$-0.830745\pi$
$379$	−402.453	+	179.184i	−1.06188	+	0.472781i	−0.199951	+	0.979806i	$0.564078\pi$
$380$		0			0
$381$	444.187	+	197.765i	1.16585	+	0.519068i
$382$		0			0
$383$	67.3408	+	7.07780i	0.175825	+	0.0184799i	0.192032	−	0.981389i	$-0.438492\pi$
$383$	67.3408	+	7.07780i	0.175825	+	0.0184799i	−0.0162070	+	0.999869i	$0.505159\pi$
$384$		0			0
$385$	8.11640	+	7.30804i	0.0210815	+	0.0189819i
$386$		0			0
$387$	359.114	−	116.683i	0.927943	−	0.301507i
$388$		0			0
$389$	−358.451	+	37.6747i	−0.921468	+	0.0968502i	−0.553369	−	0.832936i	$-0.686658\pi$
$389$	−358.451	+	37.6747i	−0.921468	+	0.0968502i	−0.368099	+	0.929787i	$0.619991\pi$
$390$		0			0
$391$	42.7659	+	47.4963i	0.109376	+	0.121474i
$392$		0			0
$393$	−160.477	−	754.983i	−0.408337	−	1.92108i
$394$		0			0
$395$	−123.021	−	169.324i	−0.311446	−	0.428668i
$396$		0			0
$397$	−315.817	+	547.012i	−0.795510	+	1.37786i	0.127005	+	0.991902i	$0.459464\pi$
$397$	−315.817	+	547.012i	−0.795510	+	1.37786i	−0.922515	+	0.385962i	$0.873870\pi$
$398$		0			0
$399$	28.1727	−	38.7765i	0.0706084	−	0.0971841i
$400$		0			0
$401$	273.784	+	88.9579i	0.682754	+	0.221840i	0.629801	−	0.776757i	$-0.283137\pi$
$401$	273.784	+	88.9579i	0.682754	+	0.221840i	0.0529533	+	0.998597i	$0.483137\pi$
$402$		0			0
$403$	−430.629	−	133.141i	−1.06856	−	0.330376i
$404$		0			0
$405$	−29.8472	+	91.8601i	−0.0736967	+	0.226815i
$406$		0			0
$407$	−48.7585	−	35.4251i	−0.119800	−	0.0870396i
$408$		0			0
$409$	233.769	+	134.967i	0.571563	+	0.329992i	0.757773	−	0.652518i	$-0.226287\pi$
$409$	233.769	+	134.967i	0.571563	+	0.329992i	−0.186210	+	0.982510i	$0.559621\pi$
$410$		0			0
$411$	−545.558	+	396.371i	−1.32739	+	0.964406i
$412$		0			0
$413$	−275.991	+	58.6636i	−0.668258	+	0.142043i
$414$		0			0
$415$	−64.2491	+	57.8502i	−0.154817	+	0.139398i
$416$		0			0
$417$	−98.8504	−	940.499i	−0.237051	−	2.25539i
$418$		0			0
$419$	−201.948	−	621.533i	−0.481977	−	1.48337i	−0.836312	−	0.548254i	$-0.815293\pi$
$419$	−201.948	−	621.533i	−0.481977	−	1.48337i	0.354335	−	0.935119i	$-0.384707\pi$
$420$		0			0
$421$	38.7094	−	42.9911i	0.0919463	−	0.102117i	−0.695416	−	0.718608i	$-0.744780\pi$
$421$	38.7094	−	42.9911i	0.0919463	−	0.102117i	0.787362	+	0.616491i	$0.211446\pi$
$422$		0			0
$423$	98.2248	−	934.547i	0.232210	−	2.20933i
$424$		0			0
$425$	15.9736	−	35.8772i	0.0375849	−	0.0844170i
$426$		0			0
$427$	−172.633	−	387.740i	−0.404293	−	0.908057i
$428$		0			0
$429$	90.0843	−	52.0102i	0.209987	−	0.121236i
$430$		0			0
$431$	−156.805	−	33.3299i	−0.363816	−	0.0773314i	0.0223768	−	0.999750i	$-0.492877\pi$
$431$	−156.805	−	33.3299i	−0.363816	−	0.0773314i	−0.386193	+	0.922418i	$0.626210\pi$
$432$		0			0
$433$			671.573i			1.55098i	0.631362	+	0.775489i	$0.282496\pi$
$433$			671.573i			1.55098i	−0.631362	+	0.775489i	$0.717504\pi$
$434$		0			0
$435$	−96.8653			−0.222679
$436$		0			0
$437$	−20.3566	+	95.7704i	−0.0465826	+	0.219154i
$438$		0			0
$439$	−239.705	−	415.181i	−0.546025	−	0.945742i	−0.998542	−	0.0539865i	$-0.982807\pi$
$439$	−239.705	−	415.181i	−0.546025	−	0.945742i	0.452517	−	0.891756i	$-0.350526\pi$
$440$		0			0
$441$	355.874	−	158.445i	0.806971	−	0.359287i
$442$		0			0
$443$	−380.302	−	169.321i	−0.858469	−	0.382215i	−0.0701906	−	0.997534i	$-0.522361\pi$
$443$	−380.302	−	169.321i	−0.858469	−	0.382215i	−0.788279	+	0.615319i	$0.789027\pi$
$444$		0			0
$445$	190.676	+	20.0408i	0.428484	+	0.0450355i
$446$		0			0
$447$	944.904	+	850.795i	2.11388	+	1.90334i
$448$		0			0
$449$	693.102	−	225.202i	1.54366	−	0.501564i	0.591274	−	0.806471i	$-0.298625\pi$
$449$	693.102	−	225.202i	1.54366	−	0.501564i	0.952382	+	0.304906i	$0.0986252\pi$
$450$		0			0
$451$	−32.3893	+	3.40425i	−0.0718167	+	0.00754824i
$452$		0			0
$453$	142.972	+	158.787i	0.315612	+	0.350523i
$454$		0			0
$455$	20.8361	+	98.0264i	0.0457937	+	0.215443i
$456$		0			0
$457$	−339.220	−	466.896i	−0.742275	−	1.02165i	−0.998485	−	0.0550331i	$-0.982474\pi$
$457$	−339.220	−	466.896i	−0.742275	−	1.02165i	0.256209	−	0.966621i	$-0.417526\pi$
$458$		0			0
$459$	−9.69817	+	16.7977i	−0.0211289	+	0.0365963i
$460$		0			0
$461$	72.9788	−	100.447i	0.158305	−	0.217889i	−0.722495	−	0.691376i	$-0.757005\pi$
$461$	72.9788	−	100.447i	0.158305	−	0.217889i	0.880801	+	0.473487i	$0.157005\pi$
$462$		0			0
$463$	645.157	+	209.624i	1.39343	+	0.452752i	0.907060	−	0.421002i	$-0.138322\pi$
$463$	645.157	+	209.624i	1.39343	+	0.452752i	0.486368	+	0.873754i	$0.338322\pi$
$464$		0			0
$465$	−184.060	+	170.557i	−0.395827	+	0.366790i
$466$		0			0
$467$	177.835	−	547.320i	0.380803	−	1.17199i	−0.558677	−	0.829386i	$-0.688691\pi$
$467$	177.835	−	547.320i	0.380803	−	1.17199i	0.939479	−	0.342605i	$-0.111309\pi$
$468$		0			0
$469$	4.00346	+	2.90868i	0.00853616	+	0.00620188i
$470$		0			0
$471$	−8.49597	−	4.90515i	−0.0180382	−	0.0104143i
$472$		0			0
$473$	42.5241	−	30.8956i	0.0899031	−	0.0653184i
$474$		0			0
$475$	58.8482	−	12.5086i	0.123891	−	0.0263338i
$476$		0			0
$477$	−64.0969	+	57.7131i	−0.134375	+	0.120992i
$478$		0			0
$479$	−5.05566	−	48.1014i	−0.0105546	−	0.100420i	0.987976	−	0.154605i	$-0.0494106\pi$
$479$	−5.05566	−	48.1014i	−0.0105546	−	0.100420i	−0.998531	+	0.0541850i	$0.982744\pi$
$480$		0			0
$481$	−170.893	−	525.954i	−0.355287	−	1.09346i
$482$		0			0
$483$	411.740	−	457.284i	0.852464	−	0.946757i
$484$		0			0
$485$	−21.9869	+	209.192i	−0.0453339	+	0.431323i
$486$		0			0
$487$	−341.879	+	767.873i	−0.702010	+	1.57674i	0.110555	+	0.993870i	$0.464737\pi$
$487$	−341.879	+	767.873i	−0.702010	+	1.57674i	−0.812565	+	0.582871i	$0.801929\pi$
$488$		0			0
$489$	433.412	+	973.459i	0.886323	+	1.99071i
$490$		0			0
$491$	−73.7431	+	42.5756i	−0.150190	+	0.0867120i	−0.573212	−	0.819407i	$-0.694303\pi$
$491$	−73.7431	+	42.5756i	−0.150190	+	0.0867120i	0.423022	+	0.906119i	$0.360969\pi$
$492$		0			0
$493$	21.1007	+	4.48510i	0.0428007	+	0.00909757i
$494$		0			0
$495$		−	32.3402i		−	0.0653337i
$496$		0			0
$497$	169.577			0.341201
$498$		0			0
$499$	64.3321	−	302.659i	0.128922	−	0.606531i	−0.865487	−	0.500932i	$-0.832991\pi$
$499$	64.3321	−	302.659i	0.128922	−	0.606531i	0.994409	−	0.105599i	$-0.0336759\pi$
$500$		0			0
$501$	−151.214	−	261.910i	−0.301825	−	0.522775i
$502$		0			0
$503$	−641.732	+	285.717i	−1.27581	+	0.568026i	−0.929059	−	0.369931i	$-0.879381\pi$
$503$	−641.732	+	285.717i	−1.27581	+	0.568026i	−0.346749	+	0.937958i	$0.612715\pi$
$504$		0			0
$505$	138.753	+	61.7769i	0.274759	+	0.122330i
$506$		0			0
$507$	190.435	+	20.0155i	0.375611	+	0.0394783i
$508$		0			0
$509$	−427.604	−	385.016i	−0.840086	−	0.756417i	0.131948	−	0.991257i	$-0.457877\pi$
$509$	−427.604	−	385.016i	−0.840086	−	0.756417i	−0.972034	+	0.234839i	$0.924544\pi$
$510$		0			0
$511$	42.9823	−	13.9658i	0.0841142	−	0.0273304i
$512$		0			0
$513$	−29.5511	+	3.10595i	−0.0576045	+	0.00605448i
$514$		0			0
$515$	90.6373	+	100.663i	0.175995	+	0.195462i
$516$		0			0
$517$	−27.1968	−	127.951i	−0.0526050	−	0.247487i
$518$		0			0
$519$	238.332	+	328.036i	0.459215	+	0.632055i
$520$		0			0
$521$	−483.268	+	837.044i	−0.927577	+	1.60661i	−0.140215	+	0.990121i	$0.544779\pi$
$521$	−483.268	+	837.044i	−0.927577	+	1.60661i	−0.787363	+	0.616490i	$0.788554\pi$
$522$		0			0
$523$	−285.557	+	393.036i	−0.545998	+	0.751502i	−0.989462	−	0.144790i	$-0.953749\pi$
$523$	−285.557	+	393.036i	−0.545998	+	0.751502i	0.443464	+	0.896292i	$0.353749\pi$
$524$		0			0
$525$	−359.601	−	116.841i	−0.684954	−	0.222555i
$526$		0			0
$527$	47.9920	−	28.6311i	0.0910664	−	0.0543285i
$528$		0			0
$529$	−224.958	+	692.350i	−0.425252	+	1.30879i
$530$		0			0
$531$	675.928	+	491.090i	1.27293	+	0.924840i
$532$		0			0
$533$	−258.802	−	149.419i	−0.485556	−	0.280336i
$534$		0			0
$535$	277.536	−	201.642i	0.518760	−	0.376901i
$536$		0			0
$537$	−398.411	+	84.6848i	−0.741920	+	0.157700i
$538$		0			0
$539$	40.2988	−	36.2852i	0.0747659	−	0.0673195i
$540$		0			0
$541$	35.3181	+	336.029i	0.0652830	+	0.621126i	0.977430	+	0.211262i	$0.0677573\pi$
$541$	35.3181	+	336.029i	0.0652830	+	0.621126i	−0.912147	+	0.409864i	$0.865576\pi$
$542$		0			0
$543$	−147.507	−	453.979i	−0.271651	−	0.836056i
$544$		0			0
$545$	−58.1262	+	64.5557i	−0.106654	+	0.118451i
$546$		0			0
$547$	0.336489	−	3.20148i	0.000615154	−	0.00585280i	−0.994210	−	0.107454i	$-0.965730\pi$
$547$	0.336489	−	3.20148i	0.000615154	−	0.00585280i	0.994825	+	0.101602i	$0.0323967\pi$
$548$		0			0
$549$	−511.183	+	1148.14i	−0.931117	+	2.09132i
$550$		0			0
$551$	13.4415	+	30.1900i	0.0243947	+	0.0547913i
$552$		0			0
$553$	388.635	−	224.379i	0.702776	−	0.405748i
$554$		0			0
$555$	−301.147	−	64.0107i	−0.542606	−	0.115335i
$556$		0			0
$557$			962.735i			1.72843i	0.503123	+	0.864215i	$0.332184\pi$
$557$			962.735i			1.72843i	−0.503123	+	0.864215i	$0.667816\pi$
$558$		0			0
$559$	482.311			0.862810
$560$		0			0
$561$	−2.68135	+	12.6148i	−0.00477960	+	0.0224862i
$562$		0			0
$563$	359.909	+	623.381i	0.639270	+	1.10725i	0.985593	+	0.169133i	$0.0540968\pi$
$563$	359.909	+	623.381i	0.639270	+	1.10725i	−0.346323	+	0.938115i	$0.612570\pi$
$564$		0			0
$565$	270.926	−	120.624i	0.479516	−	0.213494i
$566$		0			0
$567$	−189.191	−	84.2334i	−0.333671	−	0.148560i
$568$		0			0
$569$	95.0192	+	9.98692i	0.166993	+	0.0175517i	0.187656	−	0.982235i	$-0.439911\pi$
$569$	95.0192	+	9.98692i	0.166993	+	0.0175517i	−0.0206628	+	0.999787i	$0.506578\pi$
$570$		0			0
$571$	−382.399	−	344.314i	−0.669701	−	0.603002i	0.262504	−	0.964931i	$-0.415452\pi$
$571$	−382.399	−	344.314i	−0.669701	−	0.603002i	−0.932206	+	0.361929i	$0.882118\pi$
$572$		0			0
$573$	−272.666	+	88.5947i	−0.475858	+	0.154616i
$574$		0			0
$575$	768.148	−	80.7356i	1.33591	−	0.140410i
$576$		0			0
$577$	296.180	+	328.942i	0.513311	+	0.570090i	0.942960	−	0.332906i	$-0.108029\pi$
$577$	296.180	+	328.942i	0.513311	+	0.570090i	−0.429649	+	0.902996i	$0.641363\pi$
$578$		0			0
$579$	−47.9865	−	225.759i	−0.0828782	−	0.389911i
$580$		0			0
$581$	−108.959	−	149.969i	−0.187537	−	0.258122i
$582$		0			0
$583$	−6.00324	+	10.3979i	−0.0102971	+	0.0178352i
$584$		0			0
$585$	174.425	−	240.076i	0.298163	−	0.410386i
$586$		0			0
$587$	552.735	+	179.595i	0.941627	+	0.305953i	0.739309	−	0.673367i	$-0.235152\pi$
$587$	552.735	+	179.595i	0.941627	+	0.305953i	0.202318	+	0.979320i	$0.435152\pi$
$588$		0			0
$589$	78.6986	+	33.6986i	0.133614	+	0.0572132i
$590$		0			0
$591$	273.620	−	842.117i	0.462979	−	1.42490i
$592$		0			0
$593$	9.29933	+	6.75636i	0.0156818	+	0.0113935i	0.595599	−	0.803282i	$-0.296915\pi$
$593$	9.29933	+	6.75636i	0.0156818	+	0.0113935i	−0.579917	+	0.814676i	$0.696915\pi$
$594$		0			0
$595$	−10.7603	−	6.21249i	−0.0180846	−	0.0104412i
$596$		0			0
$597$	−204.611	+	148.658i	−0.342731	+	0.249009i
$598$		0			0
$599$	−155.257	+	33.0010i	−0.259194	+	0.0550934i	−0.335676	−	0.941978i	$-0.608965\pi$
$599$	−155.257	+	33.0010i	−0.259194	+	0.0550934i	0.0764817	+	0.997071i	$0.475631\pi$
$600$		0			0
$601$	−160.439	+	144.460i	−0.266953	+	0.240366i	−0.791726	−	0.610877i	$-0.790817\pi$
$601$	−160.439	+	144.460i	−0.266953	+	0.240366i	0.524773	+	0.851242i	$0.324150\pi$
$602$		0			0
$603$	−1.53167	−	14.5729i	−0.00254008	−	0.0241673i
$604$		0			0
$605$	65.6481	+	202.044i	0.108509	+	0.333957i
$606$		0			0
$607$	570.711	−	633.839i	0.940216	−	1.04422i	−0.0587278	−	0.998274i	$-0.518704\pi$
$607$	570.711	−	633.839i	0.940216	−	1.04422i	0.998944	−	0.0459420i	$-0.0146289\pi$
$608$		0			0
$609$	21.7097	−	206.554i	0.0356481	−	0.339169i
$610$		0			0
$611$	488.204	−	1096.52i	0.799024	−	1.79464i
$612$		0			0
$613$	−194.160	−	436.091i	−0.316738	−	0.711405i	0.683083	−	0.730341i	$-0.260639\pi$
$613$	−194.160	−	436.091i	−0.316738	−	0.711405i	−0.999821	+	0.0189361i	$0.993972\pi$
$614$		0			0
$615$	−144.078	+	83.1837i	−0.234274	+	0.135258i
$616$		0			0
$617$	393.119	+	83.5599i	0.637145	+	0.135429i	0.515148	−	0.857101i	$-0.327737\pi$
$617$	393.119	+	83.5599i	0.637145	+	0.135429i	0.121997	+	0.992530i	$0.461070\pi$
$618$		0			0
$619$		−	384.744i		−	0.621557i	−0.950482	−	0.310779i	$-0.899410\pi$
$619$		−	384.744i		−	0.621557i	0.950482	−	0.310779i	$-0.100590\pi$
$620$		0			0
$621$	−381.471			−0.614285
$622$		0			0
$623$	−85.4693	+	402.101i	−0.137190	+	0.645428i
$624$		0			0
$625$	−197.120	−	341.423i	−0.315393	−	0.546276i
$626$		0			0
$627$	−18.0487	+	8.03579i	−0.0287858	+	0.0128163i
$628$		0			0
$629$	62.6367	+	27.8876i	0.0995813	+	0.0443365i
$630$		0			0
$631$	−432.274	−	45.4338i	−0.685062	−	0.0720029i	−0.244398	−	0.969675i	$-0.578590\pi$
$631$	−432.274	−	45.4338i	−0.685062	−	0.0720029i	−0.440664	+	0.897672i	$0.645257\pi$
$632$		0			0
$633$	29.5479	+	26.6051i	0.0466792	+	0.0420301i
$634$		0			0
$635$	183.640	−	59.6682i	0.289197	−	0.0939657i
$636$		0			0
$637$	494.859	−	52.0118i	0.776859	−	0.0816512i
$638$		0			0
$639$	−335.993	−	373.158i	−0.525811	−	0.583972i
$640$		0			0
$641$	−58.5262	−	275.344i	−0.0913045	−	0.429554i	−0.999929	−	0.0119392i	$-0.996200\pi$
$641$	−58.5262	−	275.344i	−0.0913045	−	0.429554i	0.908624	−	0.417615i	$-0.137134\pi$
$642$		0			0
$643$	323.886	+	445.791i	0.503711	+	0.693299i	0.982843	−	0.184444i	$-0.0590484\pi$
$643$	323.886	+	445.791i	0.503711	+	0.693299i	−0.479132	+	0.877743i	$0.659048\pi$
$644$		0			0
$645$	134.254	−	232.536i	0.208146	−	0.360520i
$646$		0			0
$647$	−99.3074	+	136.685i	−0.153489	+	0.211259i	−0.878836	−	0.477124i	$-0.841679\pi$
$647$	−99.3074	+	136.685i	−0.153489	+	0.211259i	0.725347	+	0.688383i	$0.241679\pi$
$648$		0			0
$649$	110.612	+	35.9399i	0.170434	+	0.0553774i
$650$		0			0
$651$	−322.442	−	430.711i	−0.495302	−	0.661615i
$652$		0			0
$653$	−255.428	+	786.126i	−0.391161	+	1.20387i	0.540751	+	0.841183i	$0.318140\pi$
$653$	−255.428	+	786.126i	−0.391161	+	1.20387i	−0.931911	+	0.362686i	$0.881860\pi$
$654$		0			0
$655$	−247.979	−	180.167i	−0.378594	−	0.275065i
$656$		0			0
$657$	−115.896	−	66.9124i	−0.176401	−	0.101845i
$658$		0			0
$659$	109.224	−	79.3557i	0.165742	−	0.120418i	−0.501823	−	0.864971i	$-0.667337\pi$
$659$	109.224	−	79.3557i	0.165742	−	0.120418i	0.667564	+	0.744552i	$0.267337\pi$
$660$		0			0
$661$	−29.3158	+	6.23126i	−0.0443507	+	0.00942702i	−0.230034	−	0.973183i	$-0.573884\pi$
$661$	−29.3158	+	6.23126i	−0.0443507	+	0.00942702i	0.185683	+	0.982610i	$0.440550\pi$
$662$		0			0
$663$	−87.9423	+	79.1836i	−0.132643	+	0.119432i
$664$		0			0
$665$	−1.98962	−	18.9300i	−0.00299191	−	0.0284661i
$666$		0			0
$667$	131.104	+	403.498i	0.196558	+	0.604945i
$668$		0			0
$669$	−566.664	+	629.344i	−0.847031	+	0.940724i
$670$		0			0
$671$	−18.2873	+	173.992i	−0.0272538	+	0.259303i
$672$		0			0
$673$	471.449	−	1058.89i	0.700519	−	1.57339i	−0.114150	−	0.993464i	$-0.536414\pi$
$673$	471.449	−	1058.89i	0.700519	−	1.57339i	0.814668	−	0.579927i	$-0.196919\pi$
$674$		0			0
$675$	95.3403	+	214.138i	0.141245	+	0.317241i
$676$		0			0
$677$	−333.817	+	192.729i	−0.493082	+	0.284681i	−0.725852	−	0.687851i	$-0.758554\pi$
$677$	−333.817	+	192.729i	−0.493082	+	0.284681i	0.232770	+	0.972532i	$0.425221\pi$
$678$		0			0
$679$	−441.149	−	93.7691i	−0.649704	−	0.138099i
$680$		0			0
$681$		−	1522.95i		−	2.23634i
$682$		0			0
$683$	−741.400			−1.08550			−0.542752	−	0.839893i	$-0.682618\pi$
$683$	−741.400			−1.08550			−0.542752	+	0.839893i	$0.682618\pi$
$684$		0			0
$685$	−55.6785	+	261.947i	−0.0812824	+	0.382404i
$686$		0			0
$687$	−127.135	−	220.204i	−0.185058	−	0.320530i
$688$		0			0
$689$	−100.646	+	44.8103i	−0.146075	+	0.0650367i
$690$		0			0
$691$	−77.9220	−	34.6931i	−0.112767	−	0.0502071i	0.349578	−	0.936907i	$-0.386325\pi$
$691$	−77.9220	−	34.6931i	−0.112767	−	0.0502071i	−0.462345	+	0.886700i	$0.652992\pi$
$692$		0			0
$693$	68.9616	+	7.24816i	0.0995117	+	0.0104591i
$694$		0			0
$695$	−279.089	−	251.293i	−0.401567	−	0.361572i
$696$		0			0
$697$	35.2371	−	11.4492i	0.0505553	−	0.0164264i
$698$		0			0
$699$	−1226.12	+	128.870i	−1.75410	+	0.184363i
$700$		0			0
$701$	−297.985	−	330.946i	−0.425086	−	0.472106i	0.492115	−	0.870530i	$-0.336224\pi$
$701$	−297.985	−	330.946i	−0.425086	−	0.472106i	−0.917201	+	0.398424i	$0.869557\pi$
$702$		0			0
$703$	21.8382	+	102.741i	0.0310643	+	0.146146i
$704$		0			0
$705$	−392.770	−	540.602i	−0.557121	−	0.766811i
$706$		0			0
$707$	−162.829	+	282.029i	−0.230310	+	0.398909i
$708$		0			0
$709$	478.992	−	659.275i	0.675588	−	0.929866i	−0.324283	−	0.945960i	$-0.605123\pi$
$709$	478.992	−	659.275i	0.675588	−	0.929866i	0.999870	+	0.0160936i	$0.00512299\pi$
$710$		0			0
$711$	−1263.78	−	410.626i	−1.77746	−	0.577533i
$712$		0			0
$713$	959.586	+	535.866i	1.34584	+	0.751566i
$714$		0			0
$715$	12.7651	−	39.2871i	0.0178534	−	0.0549470i
$716$		0			0
$717$	−379.708	−	275.874i	−0.529578	−	0.384761i
$718$		0			0
$719$	−0.652314	−	0.376614i	−0.000907252	−	0.000523802i	0.499546	−	0.866287i	$-0.333500\pi$
$719$	−0.652314	−	0.376614i	−0.000907252	−	0.000523802i	−0.500454	+	0.865763i	$0.666833\pi$
$720$		0			0
$721$	−234.966	+	170.712i	−0.325888	+	0.236772i
$722$		0			0
$723$	1533.20	−	325.891i	2.12061	−	0.450749i
$724$		0			0
$725$	193.736	−	174.441i	0.267222	−	0.240608i
$726$		0			0
$727$	52.8691	+	503.016i	0.0727223	+	0.691907i	0.968772	+	0.247953i	$0.0797578\pi$
$727$	52.8691	+	503.016i	0.0727223	+	0.691907i	−0.896050	+	0.443954i	$0.853575\pi$
$728$		0			0
$729$	324.600	+	999.015i	0.445267	+	1.37039i
$730$		0			0
$731$	−40.0124	+	44.4383i	−0.0547365	+	0.0607911i
$732$		0			0
$733$	−57.8687	+	550.584i	−0.0789478	+	0.751138i	0.881407	+	0.472357i	$0.156597\pi$
$733$	−57.8687	+	550.584i	−0.0789478	+	0.751138i	−0.960355	+	0.278780i	$0.910070\pi$
$734$		0			0
$735$	112.671	−	253.064i	0.153294	−	0.344304i
$736$		0			0
$737$	−0.829652	−	1.86343i	−0.00112571	−	0.00252840i
$738$		0			0
$739$	−340.930	+	196.836i	−0.461339	+	0.266354i	−0.712607	−	0.701563i	$-0.752486\pi$
$739$	−340.930	+	196.836i	−0.461339	+	0.266354i	0.251268	+	0.967918i	$0.419152\pi$
$740$		0			0
$741$	−177.324	−	37.6915i	−0.239304	−	0.0508657i
$742$		0			0
$743$		−	1166.94i		−	1.57058i	−0.619125	−	0.785292i	$-0.712513\pi$
$743$		−	1166.94i		−	1.57058i	0.619125	−	0.785292i	$-0.287487\pi$
$744$		0			0
$745$	504.939			0.677771
$746$		0			0
$747$	−114.124	+	536.910i	−0.152776	+	0.718755i
$748$		0			0
$749$	367.776	+	637.006i	0.491022	+	0.850475i
$750$		0			0
$751$	464.749	−	206.919i	0.618840	−	0.275525i	−0.0732761	−	0.997312i	$-0.523345\pi$
$751$	464.749	−	206.919i	0.618840	−	0.275525i	0.692116	+	0.721787i	$0.256679\pi$
$752$		0			0
$753$	718.630	+	319.955i	0.954356	+	0.424907i
$754$		0			0
$755$	84.3879	+	8.86953i	0.111772	+	0.0117477i
$756$		0			0
$757$	−735.851	−	662.563i	−0.972062	−	0.875249i	0.0201515	−	0.999797i	$-0.493585\pi$
$757$	−735.851	−	662.563i	−0.972062	−	0.875249i	−0.992214	+	0.124548i	$0.960252\pi$
$758$		0			0
$759$	−241.226	+	78.3790i	−0.317820	+	0.103266i
$760$		0			0
$761$	913.844	−	96.0489i	1.20085	−	0.126214i	0.517094	−	0.855929i	$-0.327014\pi$
$761$	913.844	−	96.0489i	1.20085	−	0.126214i	0.683752	+	0.729715i	$0.260347\pi$
$762$		0			0
$763$	−124.630	−	138.416i	−0.163342	−	0.181410i
$764$		0			0
$765$	7.64940	+	35.9876i	0.00999921	+	0.0470426i
$766$		0			0
$767$	627.281	+	863.379i	0.817837	+	1.12566i
$768$		0			0
$769$	653.102	−	1131.21i	0.849287	−	1.47101i	−0.0325590	−	0.999470i	$-0.510366\pi$
$769$	653.102	−	1131.21i	0.849287	−	1.47101i	0.881846	−	0.471538i	$-0.156301\pi$
$770$		0			0
$771$	−692.950	+	953.764i	−0.898768	+	1.23705i
$772$		0			0
$773$	−71.2663	−	23.1558i	−0.0921944	−	0.0299558i	0.262557	−	0.964917i	$-0.415434\pi$
$773$	−71.2663	−	23.1558i	−0.0921944	−	0.0299558i	−0.354751	+	0.934961i	$0.615434\pi$
$774$		0			0
$775$	60.9799	−	672.590i	0.0786837	−	0.867858i
$776$		0			0
$777$	203.989	−	627.813i	0.262534	−	0.807996i
$778$		0			0
$779$	45.9188	+	33.3620i	0.0589459	+	0.0428267i
$780$		0			0
$781$	−60.5344	−	34.9496i	−0.0775089	−	0.0447498i
$782$		0			0
$783$	−104.166	+	75.6810i	−0.133034	+	0.0966552i
$784$		0			0
$785$	−3.81076	+	0.810002i	−0.00485447	+	0.00103185i
$786$		0			0
$787$	600.198	−	540.421i	0.762640	−	0.686684i	−0.193007	−	0.981197i	$-0.561824\pi$
$787$	600.198	−	540.421i	0.762640	−	0.686684i	0.955647	+	0.294513i	$0.0951574\pi$
$788$		0			0
$789$	−1.97382	−	18.7796i	−0.00250167	−	0.0238018i
$790$		0			0
$791$	196.496	+	604.753i	0.248415	+	0.764543i
$792$		0			0
$793$	−1074.18	+	1192.99i	−1.35457	+	1.50440i
$794$		0			0
$795$	−6.41108	+	60.9973i	−0.00806425	+	0.0767262i
$796$		0			0
$797$	−506.822	+	1138.34i	−0.635913	+	1.42828i	0.251752	+	0.967792i	$0.418993\pi$
$797$	−506.822	+	1138.34i	−0.635913	+	1.42828i	−0.887664	+	0.460491i	$0.847673\pi$
$798$		0			0
$799$	60.5282	+	135.949i	0.0757550	+	0.170148i
$800$		0			0
$801$	1054.18	−	608.631i	1.31608	−	0.759839i
$802$		0			0
$803$	−18.2219	−	3.87318i	−0.0226922	−	0.00482339i
$804$		0			0
$805$		−	244.364i		−	0.303558i
$806$		0			0
$807$	−1242.09			−1.53915
$808$		0			0
$809$	106.566	−	501.353i	0.131725	−	0.619719i	−0.861909	−	0.507063i	$-0.830731\pi$
$809$	106.566	−	501.353i	0.131725	−	0.619719i	0.993634	−	0.112656i	$-0.0359357\pi$
$810$		0			0
$811$	115.872	+	200.697i	0.142876	+	0.247468i	0.928578	−	0.371136i	$-0.121032\pi$
$811$	115.872	+	200.697i	0.142876	+	0.247468i	−0.785703	+	0.618604i	$0.787698\pi$
$812$		0			0
$813$	1936.34	−	862.113i	2.38172	−	1.06041i
$814$		0			0
$815$	386.583	+	172.118i	0.474335	+	0.211188i
$816$		0			0
$817$	−91.1041	−	9.57543i	−0.111511	−	0.0117202i
$818$		0			0
$819$	472.841	+	425.748i	0.577340	+	0.519839i
$820$		0			0
$821$	−1226.99	+	398.674i	−1.49451	+	0.485596i	−0.938411	−	0.345521i	$-0.887702\pi$
$821$	−1226.99	+	398.674i	−1.49451	+	0.485596i	−0.556099	+	0.831116i	$0.687702\pi$
$822$		0			0
$823$	−289.921	+	30.4719i	−0.352273	+	0.0370254i	−0.279013	−	0.960287i	$-0.590007\pi$
$823$	−289.921	+	30.4719i	−0.352273	+	0.0370254i	−0.0732606	+	0.997313i	$0.523340\pi$
$824$		0			0
$825$	104.287	+	115.822i	0.126408	+	0.140391i
$826$		0			0
$827$	244.116	+	1148.48i	0.295183	+	1.38873i	0.836527	+	0.547925i	$0.184582\pi$
$827$	244.116	+	1148.48i	0.295183	+	1.38873i	−0.541345	+	0.840801i	$0.682085\pi$
$828$		0			0
$829$	363.500	+	500.314i	0.438480	+	0.603515i	0.969873	−	0.243610i	$-0.0783315\pi$
$829$	363.500	+	500.314i	0.438480	+	0.603515i	−0.531394	+	0.847125i	$0.678332\pi$
$830$		0			0
$831$	876.555	−	1518.24i	1.05482	−	1.82700i
$832$		0			0
$833$	−36.2613	+	49.9094i	−0.0435309	+	0.0599152i
$834$		0			0
$835$	−114.223	−	37.1133i	−0.136794	−	0.0444471i
$836$		0			0
$837$	−64.6753	+	327.218i	−0.0772704	+	0.390942i
$838$		0			0
$839$	−334.101	+	1028.26i	−0.398213	+	1.22557i	0.528218	+	0.849109i	$0.322860\pi$
$839$	−334.101	+	1028.26i	−0.398213	+	1.22557i	−0.926431	+	0.376464i	$0.877140\pi$
$840$		0			0
$841$	−564.532	−	410.157i	−0.671263	−	0.487701i
$842$		0			0
$843$	1290.13	+	744.857i	1.53040	+	0.883579i
$844$		0			0
$845$	61.5197	−	44.6967i	0.0728044	−	0.0528955i
$846$		0			0
$847$	−445.548	+	94.7041i	−0.526031	+	0.111811i
$848$		0			0
$849$	−437.580	+	393.999i	−0.515407	+	0.464074i
$850$		0			0
$851$	140.953	+	1341.08i	0.165632	+	1.57589i
$852$		0			0
$853$	139.701	+	429.957i	0.163777	+	0.504053i	0.998944	−	0.0459431i	$-0.0146293\pi$
$853$	139.701	+	429.957i	0.163777	+	0.504053i	−0.835167	+	0.549996i	$0.814629\pi$
$854$		0			0
$855$	−37.7137	+	41.8853i	−0.0441096	+	0.0489887i
$856$		0			0
$857$	−119.188	+	1134.00i	−0.139076	+	1.32322i	0.672989	+	0.739652i	$0.265010\pi$
$857$	−119.188	+	1134.00i	−0.139076	+	1.32322i	−0.812065	+	0.583567i	$0.801657\pi$
$858$		0			0
$859$	646.891	−	1452.94i	0.753074	−	1.69143i	0.0310963	−	0.999516i	$-0.490100\pi$
$859$	646.891	−	1452.94i	0.753074	−	1.69143i	0.721978	−	0.691916i	$-0.243233\pi$
$860$		0			0
$861$	−145.088	−	325.873i	−0.168511	−	0.378483i
$862$		0			0
$863$	−561.283	+	324.057i	−0.650386	+	0.375500i	−0.788604	−	0.614901i	$-0.789196\pi$
$863$	−561.283	+	324.057i	−0.650386	+	0.375500i	0.138218	+	0.990402i	$0.455862\pi$
$864$		0			0
$865$	157.505	+	33.4787i	0.182087	+	0.0387037i
$866$		0			0
$867$			1290.10i			1.48800i
$868$		0			0
$869$	−184.976			−0.212861
$870$		0			0
$871$	3.89144	−	18.3078i	0.00446778	−	0.0210193i
$872$		0			0
$873$	667.734	+	1156.55i	0.764873	+	1.32480i
$874$		0			0
$875$	−294.587	+	131.159i	−0.336671	+	0.149896i
$876$		0			0
$877$	−1421.46	−	632.874i	−1.62082	−	0.721635i	−0.622672	−	0.782483i	$-0.713953\pi$
$877$	−1421.46	−	632.874i	−1.62082	−	0.721635i	−0.998147	+	0.0608473i	$0.980620\pi$
$878$		0			0
$879$	−889.422	−	93.4820i	−1.01186	−	0.106350i
$880$		0			0
$881$	−753.579	−	678.526i	−0.855368	−	0.770177i	0.119529	−	0.992831i	$-0.461861\pi$
$881$	−753.579	−	678.526i	−0.855368	−	0.770177i	−0.974898	+	0.222654i	$0.928528\pi$
$882$		0			0
$883$	130.460	−	42.3890i	0.147746	−	0.0480057i	−0.234210	−	0.972186i	$-0.575250\pi$
$883$	130.460	−	42.3890i	0.147746	−	0.0480057i	0.381957	+	0.924180i	$0.375250\pi$
$884$		0			0
$885$	590.867	−	62.1027i	0.667647	−	0.0701725i
$886$		0			0
$887$	−300.710	−	333.972i	−0.339019	−	0.376519i	0.549394	−	0.835563i	$-0.314859\pi$
$887$	−300.710	−	333.972i	−0.339019	−	0.376519i	−0.888413	+	0.459044i	$0.848192\pi$
$888$		0			0
$889$	86.0776	+	404.963i	0.0968252	+	0.455527i
$890$		0			0
$891$	50.1758	+	69.0611i	0.0563141	+	0.0775097i
$892$		0			0
$893$	−113.987	+	197.431i	−0.127645	+	0.221087i
$894$		0			0
$895$	−95.0759	+	130.861i	−0.106230	+	0.146213i
$896$		0			0
$897$	−2213.46	−	719.198i	−2.46763	−	0.801781i
$898$		0			0
$899$	368.340	−	44.0490i	0.409722	−	0.0489977i
$900$		0			0
$901$	4.22089	−	12.9906i	0.00468467	−	0.0144179i
$902$		0			0
$903$	465.765	+	338.398i	0.515797	+	0.374749i
$904$		0			0
$905$	−164.167	−	94.7816i	−0.181400	−	0.104731i
$906$		0			0
$907$	−590.671	+	429.148i	−0.651236	+	0.473151i	−0.863692	−	0.504020i	$-0.831854\pi$
$907$	−590.671	+	429.148i	−0.651236	+	0.473151i	0.212456	+	0.977171i	$0.431854\pi$
$908$		0			0
$909$	943.235	−	200.491i	1.03766	−	0.220562i
$910$		0			0
$911$	−127.685	+	114.969i	−0.140160	+	0.126200i	−0.736229	−	0.676733i	$-0.763395\pi$
$911$	−127.685	+	114.969i	−0.140160	+	0.126200i	0.596069	+	0.802933i	$0.296729\pi$
$912$		0			0
$913$	7.98700	+	75.9912i	0.00874808	+	0.0832324i
$914$		0			0
$915$	276.171	+	849.968i	0.301827	+	0.928927i
$916$		0			0
$917$	439.763	−	488.407i	0.479567	−	0.532614i
$918$		0			0
$919$	−145.811	+	1387.30i	−0.158663	+	1.50958i	0.568256	+	0.822852i	$0.307618\pi$
$919$	−145.811	+	1387.30i	−0.158663	+	1.50958i	−0.726919	+	0.686723i	$0.759048\pi$
$920$		0			0
$921$	204.250	−	458.754i	0.221770	−	0.498104i
$922$		0			0
$923$	−260.876	−	585.937i	−0.282639	−	0.634818i
$924$		0			0
$925$	717.584	−	414.297i	0.775767	−	0.447889i
$926$		0			0
$927$	841.208	+	178.804i	0.907452	+	0.192885i
$928$		0			0
$929$		−	1599.86i		−	1.72213i	−0.508498	−	0.861063i	$-0.669799\pi$
$929$		−	1599.86i		−	1.72213i	0.508498	−	0.861063i	$-0.330201\pi$
$930$		0			0
$931$	−94.5071			−0.101511
$932$		0			0
$933$	444.631	−	2091.82i	0.476561	−	2.24204i
$934$		0			0
$935$	2.56077	+	4.43538i	0.00273879	+	0.00474372i
$936$		0			0
$937$	−787.912	+	350.801i	−0.840888	+	0.374387i	−0.781544	−	0.623850i	$-0.785568\pi$
$937$	−787.912	+	350.801i	−0.840888	+	0.374387i	−0.0593440	+	0.998238i	$0.518901\pi$
$938$		0			0
$939$	−361.936	−	161.144i	−0.385448	−	0.171612i
$940$		0			0
$941$	−1251.68	−	131.557i	−1.33016	−	0.139805i	−0.587362	−	0.809324i	$-0.699833\pi$
$941$	−1251.68	−	131.557i	−1.33016	−	0.139805i	−0.742795	+	0.669519i	$0.766500\pi$
$942$		0			0
$943$	541.513	+	487.580i	0.574244	+	0.517052i
$944$		0			0
$945$	70.5304	−	22.9167i	0.0746354	−	0.0242505i
$946$		0			0
$947$	1149.90	−	120.859i	1.21425	−	0.127623i	0.524336	−	0.851511i	$-0.324313\pi$
$947$	1149.90	−	120.859i	1.21425	−	0.127623i	0.689918	+	0.723888i	$0.257647\pi$
$948$		0			0
$949$	−114.380	−	127.031i	−0.120526	−	0.133858i
$950$		0			0
$951$	−216.967	−	1020.75i	−0.228146	−	1.07334i
$952$		0			0
$953$	642.003	+	883.641i	0.673665	+	0.927221i	0.999836	−	0.0180901i	$-0.00575857\pi$
$953$	642.003	+	883.641i	0.673665	+	0.927221i	−0.326171	+	0.945311i	$0.605759\pi$
$954$		0			0
$955$	−56.9273	+	98.6010i	−0.0596097	+	0.103247i
$956$		0			0
$957$	−50.3202	+	69.2598i	−0.0525812	+	0.0723718i
$958$		0			0
$959$	−546.091	−	177.436i	−0.569438	−	0.185022i
$960$		0			0
$961$	622.345	−	732.262i	0.647602	−	0.761979i
$962$		0			0
$963$	673.051	−	2071.44i	0.698911	−	2.15103i
$964$		0			0
$965$	−74.1520	−	53.8746i	−0.0768414	−	0.0558286i
$966$		0			0
$967$	1045.67	+	603.718i	1.08135	+	0.624320i	0.931261	−	0.364352i	$-0.118709\pi$
$967$	1045.67	+	603.718i	1.08135	+	0.624320i	0.150093	+	0.988672i	$0.452043\pi$
$968$		0			0
$969$	18.1836	−	13.2111i	0.0187653	−	0.0136338i
$970$		0			0
$971$	−929.310	+	197.531i	−0.957065	+	0.203430i	−0.659864	−	0.751385i	$-0.729386\pi$
$971$	−929.310	+	197.531i	−0.957065	+	0.203430i	−0.297200	+	0.954815i	$0.596053\pi$
$972$		0			0
$973$	598.402	−	538.804i	0.615007	−	0.553755i
$974$		0			0
$975$	149.487	+	1422.27i	0.153320	+	1.45874i
$976$		0			0
$977$	−367.336	−	1130.54i	−0.375983	−	1.15716i	−0.942813	−	0.333322i	$-0.891830\pi$
$977$	−367.336	−	1130.54i	−0.375983	−	1.15716i	0.566830	−	0.823835i	$-0.308170\pi$
$978$		0			0
$979$	113.383	−	125.924i	0.115815	−	0.128625i
$980$		0			0
$981$	−57.6499	+	548.503i	−0.0587665	+	0.559126i
$982$		0			0
$983$	460.819	−	1035.02i	0.468789	−	1.05292i	−0.512202	−	0.858865i	$-0.671170\pi$
$983$	460.819	−	1035.02i	0.468789	−	1.05292i	0.980991	−	0.194052i	$-0.0621631\pi$
$984$		0			0
$985$	−143.023	−	321.234i	−0.145201	−	0.326126i
$986$		0			0
$987$	1240.80	−	716.375i	1.25714	−	0.725810i
$988$		0			0
$989$	−1150.35	−	244.514i	−1.16314	−	0.247234i
$990$		0			0
$991$			282.357i			0.284921i	0.989800	+	0.142461i	$0.0455014\pi$
$991$			282.357i			0.284921i	−0.989800	+	0.142461i	$0.954499\pi$
$992$		0			0
$993$	1006.18			1.01327
$994$		0			0
$995$	−20.8821	+	98.2426i	−0.0209871	+	0.0987363i
$996$		0			0
$997$	−456.044	−	789.891i	−0.457416	−	0.792267i	0.541408	−	0.840760i	$-0.317892\pi$
$997$	−456.044	−	789.891i	−0.457416	−	0.792267i	−0.998824	+	0.0484927i	$0.984558\pi$
$998$		0			0
$999$	−373.855	+	166.451i	−0.374229	+	0.166618i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.3.o.a.53.5	✓	40
31.24	odd	30	inner	124.3.o.a.117.5	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.3.o.a.53.5	✓	40	1.1	even	1	trivial
124.3.o.a.117.5	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)

\(f(q)\)	\(=\)	\(q+(0.938675 - 4.41612i) q^{3} +(-0.896461 - 1.55272i) q^{5} +(3.51190 - 1.56360i) q^{7} +(-10.3991 - 4.62997i) q^{9} +O(q^{10})\)	\(q+(0.938675 - 4.41612i) q^{3} +(-0.896461 - 1.55272i) q^{5} +(3.51190 - 1.56360i) q^{7} +(-10.3991 - 4.62997i) q^{9} +(-1.57591 - 0.165635i) q^{11} +(-10.8054 - 9.72918i) q^{13} +(-7.69846 + 2.50138i) q^{15} +(1.79282 - 0.188433i) q^{17} +(1.84788 + 2.05228i) q^{19} +(-3.60850 - 16.9767i) q^{21} +(20.8393 + 28.6828i) q^{23} +(10.8927 - 18.8667i) q^{25} +(-6.32435 + 8.70472i) q^{27} +(11.3809 + 3.69788i) q^{29} +(28.1367 - 13.0126i) q^{31} +(-2.21073 + 6.80392i) q^{33} +(-5.57610 - 4.05128i) q^{35} +(32.9387 + 19.0172i) q^{37} +(-53.1079 + 38.5852i) q^{39} +(20.1037 - 4.27317i) q^{41} +(-24.6510 + 22.1959i) q^{43} +(2.13334 + 20.2974i) q^{45} +(25.5097 + 78.5106i) q^{47} +(-22.8988 + 25.4317i) q^{49} +(0.850733 - 8.09418i) q^{51} +(3.08185 - 6.92196i) q^{53} +(1.15556 + 2.59542i) q^{55} +(10.7977 - 6.23403i) q^{57} +(-71.7931 - 15.2601i) q^{59} -110.408i q^{61} -43.7599 q^{63} +(-5.42008 + 25.4995i) q^{65} +(0.643629 + 1.11480i) q^{67} +(146.228 - 65.1049i) q^{69} +(40.2982 + 17.9419i) q^{71} +(11.6919 + 1.22887i) q^{73} +(-73.0930 - 65.8132i) q^{75} +(-5.79342 + 1.88240i) q^{77} +(116.095 - 12.2021i) q^{79} +(-36.0471 - 40.0343i) q^{81} +(-10.0256 - 47.1668i) q^{83} +(-1.89978 - 2.61482i) q^{85} +(27.0133 - 46.7884i) q^{87} +(-62.8547 + 86.5121i) q^{89} +(-53.1598 - 17.2727i) q^{91} +(-31.0539 - 136.469i) q^{93} +(1.53005 - 4.70902i) q^{95} +(-94.9132 - 68.9585i) q^{97} +(15.6211 + 9.01885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{3} - 3 q^{5} + 19 q^{7} - 2 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more