LMFDB - Embedded newform 980.2.g.a.391.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(391,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("980.391");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.g (of order $2$, degree $1$, 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:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			391.4
Character	$\chi$	$=$	980.391
Dual form			980.2.g.a.391.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40582 + 0.153886i) q^{2} +3.02707 q^{3} +(1.95264 - 0.432671i) q^{4} -1.00000i q^{5} +(-4.25550 + 0.465823i) q^{6} +(-2.67847 + 0.908739i) q^{8} +6.16313 q^{9} +O(q^{10})$	\(q+(-1.40582 + 0.153886i) q^{2} +3.02707 q^{3} +(1.95264 - 0.432671i) q^{4} -1.00000i q^{5} +(-4.25550 + 0.465823i) q^{6} +(-2.67847 + 0.908739i) q^{8} +6.16313 q^{9} +(0.153886 + 1.40582i) q^{10} -1.19696i q^{11} +(5.91077 - 1.30972i) q^{12} -4.83692i q^{13} -3.02707i q^{15} +(3.62559 - 1.68970i) q^{16} +2.54530i q^{17} +(-8.66423 + 0.948419i) q^{18} -1.42226 q^{19} +(-0.432671 - 1.95264i) q^{20} +(0.184195 + 1.68270i) q^{22} -5.80651i q^{23} +(-8.10790 + 2.75081i) q^{24} -1.00000 q^{25} +(0.744335 + 6.79982i) q^{26} +9.57500 q^{27} +0.774233 q^{29} +(0.465823 + 4.25550i) q^{30} +6.63865 q^{31} +(-4.83689 + 2.93333i) q^{32} -3.62326i q^{33} +(-0.391687 - 3.57823i) q^{34} +(12.0344 - 2.66661i) q^{36} +5.10930 q^{37} +(1.99944 - 0.218866i) q^{38} -14.6417i q^{39} +(0.908739 + 2.67847i) q^{40} +7.46685i q^{41} -1.38202i q^{43} +(-0.517888 - 2.33722i) q^{44} -6.16313i q^{45} +(0.893541 + 8.16289i) q^{46} +1.07086 q^{47} +(10.9749 - 5.11483i) q^{48} +(1.40582 - 0.153886i) q^{50} +7.70480i q^{51} +(-2.09280 - 9.44476i) q^{52} +3.36198 q^{53} +(-13.4607 + 1.47346i) q^{54} -1.19696 q^{55} -4.30528 q^{57} +(-1.08843 + 0.119144i) q^{58} -9.88412 q^{59} +(-1.30972 - 5.91077i) q^{60} -9.59690i q^{61} +(-9.33272 + 1.02160i) q^{62} +(6.34839 - 4.86806i) q^{64} -4.83692 q^{65} +(0.557570 + 5.09364i) q^{66} +10.5555i q^{67} +(1.10128 + 4.97006i) q^{68} -17.5767i q^{69} +16.3277i q^{71} +(-16.5077 + 5.60068i) q^{72} +0.107109i q^{73} +(-7.18274 + 0.786250i) q^{74} -3.02707 q^{75} +(-2.77716 + 0.615371i) q^{76} +(2.25315 + 20.5835i) q^{78} +10.7688i q^{79} +(-1.68970 - 3.62559i) q^{80} +10.4948 q^{81} +(-1.14904 - 10.4970i) q^{82} -15.8027 q^{83} +2.54530 q^{85} +(0.212673 + 1.94286i) q^{86} +2.34366 q^{87} +(1.08772 + 3.20601i) q^{88} +3.94128i q^{89} +(0.948419 + 8.66423i) q^{90} +(-2.51231 - 11.3380i) q^{92} +20.0956 q^{93} +(-1.50543 + 0.164790i) q^{94} +1.42226i q^{95} +(-14.6416 + 8.87940i) q^{96} -8.71387i q^{97} -7.37699i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9	$ 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9} + 28 q^{16} - 8 q^{22} - 32 q^{25} - 40 q^{29} - 4 q^{32} + 60 q^{36} - 16 q^{37} + 36 q^{44} - 4 q^{46} + 4 q^{50} + 16 q^{53} + 48 q^{57} - 4 q^{58} - 28 q^{60} + 4 q^{64} - 8 q^{65} - 8 q^{72} - 76 q^{74} + 120 q^{78} + 72 q^{81} - 56 q^{86} - 8 q^{88} - 4 q^{92} + 16 q^{93}+O(q^{100}) $ 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9 + 28 * q^16 - 8 * q^22 - 32 * q^25 - 40 * q^29 - 4 * q^32 + 60 * q^36 - 16 * q^37 + 36 * q^44 - 4 * q^46 + 4 * q^50 + 16 * q^53 + 48 * q^57 - 4 * q^58 - 28 * q^60 + 4 * q^64 - 8 * q^65 - 8 * q^72 - 76 * q^74 + 120 * q^78 + 72 * q^81 - 56 * q^86 - 8 * q^88 - 4 * q^92 + 16 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.40582	+	0.153886i	−0.994062	+	0.108814i
$2$	−1.40582	+	0.153886i	−0.994062	+	0.108814i
$3$	3.02707			1.74768			0.873839	−	0.486216i	$-0.161623\pi$
$3$	3.02707			1.74768			0.873839	+	0.486216i	$0.161623\pi$
$4$	1.95264	−	0.432671i	0.976319	−	0.216335i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−4.25550	+	0.465823i	−1.73730	+	0.190171i
$7$		0			0
$7$		0			0
$8$	−2.67847	+	0.908739i	−0.946982	+	0.321288i
$9$	6.16313			2.05438
$10$	0.153886	+	1.40582i	0.0486630	+	0.444558i
$11$		−	1.19696i		−	0.360896i	−0.983585	−	0.180448i	$-0.942245\pi$
$11$		−	1.19696i		−	0.360896i	0.983585	−	0.180448i	$-0.0577547\pi$
$12$	5.91077	−	1.30972i	1.70629	−	0.378085i
$13$		−	4.83692i		−	1.34152i	−0.741674	−	0.670760i	$-0.765968\pi$
$13$		−	4.83692i		−	1.34152i	0.741674	−	0.670760i	$-0.234032\pi$
$14$		0			0
$15$		−	3.02707i		−	0.781585i
$16$	3.62559	−	1.68970i	0.906398	−	0.422425i
$17$			2.54530i			0.617327i	0.951171	+	0.308664i	$0.0998817\pi$
$17$			2.54530i			0.617327i	−0.951171	+	0.308664i	$0.900118\pi$
$18$	−8.66423	+	0.948419i	−2.04218	+	0.223545i
$19$	−1.42226			−0.326289			−0.163144	−	0.986602i	$-0.552164\pi$
$19$	−1.42226			−0.326289			−0.163144	+	0.986602i	$0.552164\pi$
$20$	−0.432671	−	1.95264i	−0.0967481	−	0.436623i
$21$		0			0
$22$	0.184195	+	1.68270i	0.0392704	+	0.358753i
$23$		−	5.80651i		−	1.21074i	−0.795943	−	0.605371i	$-0.793025\pi$
$23$		−	5.80651i		−	1.21074i	0.795943	−	0.605371i	$-0.206975\pi$
$24$	−8.10790	+	2.75081i	−1.65502	+	0.561508i
$25$	−1.00000			−0.200000
$26$	0.744335	+	6.79982i	0.145976	+	1.33356i
$27$	9.57500			1.84271
$28$		0			0
$29$	0.774233			0.143772			0.0718858	−	0.997413i	$-0.477098\pi$
$29$	0.774233			0.143772			0.0718858	+	0.997413i	$0.477098\pi$
$30$	0.465823	+	4.25550i	0.0850473	+	0.776944i
$31$	6.63865			1.19234			0.596169	−	0.802859i	$-0.296689\pi$
$31$	6.63865			1.19234			0.596169	+	0.802859i	$0.296689\pi$
$32$	−4.83689	+	2.93333i	−0.855050	+	0.518545i
$33$		−	3.62326i		−	0.630729i
$34$	−0.391687	−	3.57823i	−0.0671737	−	0.613661i
$35$		0			0
$36$	12.0344	−	2.66661i	2.00573	−	0.444434i
$37$	5.10930			0.839964			0.419982	−	0.907532i	$-0.362036\pi$
$37$	5.10930			0.839964			0.419982	+	0.907532i	$0.362036\pi$
$38$	1.99944	−	0.218866i	0.324352	−	0.0355047i
$39$		−	14.6417i		−	2.34455i
$40$	0.908739	+	2.67847i	0.143684	+	0.423503i
$41$			7.46685i			1.16613i	0.812427	+	0.583063i	$0.198146\pi$
$41$			7.46685i			1.16613i	−0.812427	+	0.583063i	$0.801854\pi$
$42$		0			0
$43$		−	1.38202i		−	0.210756i	−0.994432	−	0.105378i	$-0.966395\pi$
$43$		−	1.38202i		−	0.210756i	0.994432	−	0.105378i	$-0.0336052\pi$
$44$	−0.517888	−	2.33722i	−0.0780745	−	0.352349i
$45$		−	6.16313i		−	0.918745i
$46$	0.893541	+	8.16289i	0.131745	+	1.20355i
$47$	1.07086			0.156200			0.0781002	−	0.996946i	$-0.475115\pi$
$47$	1.07086			0.156200			0.0781002	+	0.996946i	$0.475115\pi$
$48$	10.9749	−	5.11483i	1.58409	−	0.738262i
$49$		0			0
$50$	1.40582	−	0.153886i	0.198812	−	0.0217628i
$51$			7.70480i			1.07889i
$52$	−2.09280	−	9.44476i	−0.290218	−	1.30975i
$53$	3.36198			0.461804			0.230902	−	0.972977i	$-0.425832\pi$
$53$	3.36198			0.461804			0.230902	+	0.972977i	$0.425832\pi$
$54$	−13.4607	+	1.47346i	−1.83177	+	0.200512i
$55$	−1.19696			−0.161398
$56$		0			0
$57$	−4.30528			−0.570248
$58$	−1.08843	+	0.119144i	−0.142918	+	0.0156443i
$59$	−9.88412			−1.28680			−0.643402	−	0.765529i	$-0.722477\pi$
$59$	−9.88412			−1.28680			−0.643402	+	0.765529i	$0.722477\pi$
$60$	−1.30972	−	5.91077i	−0.169085	−	0.763076i
$61$		−	9.59690i		−	1.22876i	−0.789012	−	0.614378i	$-0.789407\pi$
$61$		−	9.59690i		−	1.22876i	0.789012	−	0.614378i	$-0.210593\pi$
$62$	−9.33272	+	1.02160i	−1.18526	+	0.129743i
$63$		0			0
$64$	6.34839	−	4.86806i	0.793548	−	0.608507i
$65$	−4.83692			−0.599946
$66$	0.557570	+	5.09364i	0.0686321	+	0.626984i
$67$			10.5555i			1.28956i	0.764367	+	0.644781i	$0.223051\pi$
$67$			10.5555i			1.28956i	−0.764367	+	0.644781i	$0.776949\pi$
$68$	1.10128	+	4.97006i	0.133550	+	0.602708i
$69$		−	17.5767i		−	2.11599i
$70$		0			0
$71$			16.3277i			1.93775i	0.247558	+	0.968873i	$0.420372\pi$
$71$			16.3277i			1.93775i	−0.247558	+	0.968873i	$0.579628\pi$
$72$	−16.5077	+	5.60068i	−1.94546	+	0.660046i
$73$			0.107109i			0.0125362i	0.999980	+	0.00626810i	$0.00199521\pi$
$73$			0.107109i			0.0125362i	−0.999980	+	0.00626810i	$0.998005\pi$
$74$	−7.18274	+	0.786250i	−0.834977	+	0.0913997i
$75$	−3.02707			−0.349535
$76$	−2.77716	+	0.615371i	−0.318562	+	0.0705879i
$77$		0			0
$78$	2.25315	+	20.5835i	0.255119	+	2.33062i
$79$			10.7688i			1.21159i	0.795621	+	0.605795i	$0.207145\pi$
$79$			10.7688i			1.21159i	−0.795621	+	0.605795i	$0.792855\pi$
$80$	−1.68970	−	3.62559i	−0.188914	−	0.405354i
$81$	10.4948			1.16609
$82$	−1.14904	−	10.4970i	−0.126891	−	1.15920i
$83$	−15.8027			−1.73457			−0.867287	−	0.497808i	$-0.834138\pi$
$83$	−15.8027			−1.73457			−0.867287	+	0.497808i	$0.834138\pi$
$84$		0			0
$85$	2.54530			0.276077
$86$	0.212673	+	1.94286i	0.0229331	+	0.209504i
$87$	2.34366			0.251266
$88$	1.08772	+	3.20601i	0.115951	+	0.341762i
$89$			3.94128i			0.417775i	0.977940	+	0.208887i	$0.0669842\pi$
$89$			3.94128i			0.417775i	−0.977940	+	0.208887i	$0.933016\pi$
$90$	0.948419	+	8.66423i	0.0999722	+	0.913290i
$91$		0			0
$92$	−2.51231	−	11.3380i	−0.261926	−	1.18207i
$93$	20.0956			2.08382
$94$	−1.50543	+	0.164790i	−0.155273	+	0.0169968i
$95$			1.42226i			0.145921i
$96$	−14.6416	+	8.87940i	−1.49435	+	0.906250i
$97$		−	8.71387i		−	0.884760i	−0.896828	−	0.442380i	$-0.854134\pi$
$97$		−	8.71387i		−	0.884760i	0.896828	−	0.442380i	$-0.145866\pi$
$98$		0			0
$99$		−	7.37699i		−	0.741416i
$100$	−1.95264	+	0.432671i	−0.195264	+	0.0432671i
$101$		−	3.00544i		−	0.299052i	−0.988758	−	0.149526i	$-0.952225\pi$
$101$		−	3.00544i		−	0.299052i	0.988758	−	0.149526i	$-0.0477748\pi$
$102$	−1.18566	−	10.8315i	−0.117398	−	1.07248i
$103$	−0.382749			−0.0377133			−0.0188567	−	0.999822i	$-0.506003\pi$
$103$	−0.382749			−0.0377133			−0.0188567	+	0.999822i	$0.506003\pi$
$104$	4.39550	+	12.9555i	0.431014	+	1.27040i
$105$		0			0
$106$	−4.72633	+	0.517362i	−0.459062	+	0.0502507i
$107$		−	0.842470i		−	0.0814446i	−0.999171	−	0.0407223i	$-0.987034\pi$
$107$		−	0.842470i		−	0.0814446i	0.999171	−	0.0407223i	$-0.0129659\pi$
$108$	18.6965	−	4.14282i	1.79907	−	0.398643i
$109$	3.95068			0.378407			0.189203	−	0.981938i	$-0.439409\pi$
$109$	3.95068			0.378407			0.189203	+	0.981938i	$0.439409\pi$
$110$	1.68270	−	0.184195i	0.160439	−	0.0175623i
$111$	15.4662			1.46799
$112$		0			0
$113$	2.68201			0.252302			0.126151	−	0.992011i	$-0.459738\pi$
$113$	2.68201			0.252302			0.126151	+	0.992011i	$0.459738\pi$
$114$	6.05243	−	0.662522i	0.566862	−	0.0620508i
$115$	−5.80651			−0.541460
$116$	1.51180	−	0.334988i	0.140367	−	0.0311029i
$117$		−	29.8106i		−	2.75599i
$118$	13.8953	−	1.52103i	1.27916	−	0.140022i
$119$		0			0
$120$	2.75081	+	8.10790i	0.251114	+	0.740147i
$121$	9.56730			0.869754
$122$	1.47683	+	13.4915i	0.133706	+	1.22146i
$123$			22.6027i			2.03801i
$124$	12.9629	−	2.87235i	1.16410	−	0.257945i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$			2.14034i			0.189925i	0.995481	+	0.0949624i	$0.0302731\pi$
$127$			2.14034i			0.189925i	−0.995481	+	0.0949624i	$0.969727\pi$
$128$	−8.17554	+	7.82052i	−0.722622	+	0.691243i
$129$		−	4.18346i		−	0.368333i
$130$	6.79982	−	0.744335i	0.596384	−	0.0652825i
$131$	9.66575			0.844500			0.422250	−	0.906479i	$-0.361240\pi$
$131$	9.66575			0.844500			0.422250	+	0.906479i	$0.361240\pi$
$132$	−1.56768	−	7.07493i	−0.136449	−	0.615793i
$133$		0			0
$134$	−1.62435	−	14.8391i	−0.140322	−	1.28190i
$135$		−	9.57500i		−	0.824085i
$136$	−2.31302	−	6.81752i	−0.198340	−	0.584597i
$137$	4.27568			0.365296			0.182648	−	0.983178i	$-0.441533\pi$
$137$	4.27568			0.365296			0.182648	+	0.983178i	$0.441533\pi$
$138$	2.70481	+	24.7096i	0.230249	+	2.10342i
$139$	−7.53742			−0.639316			−0.319658	−	0.947533i	$-0.603568\pi$
$139$	−7.53742			−0.639316			−0.319658	+	0.947533i	$0.603568\pi$
$140$		0			0
$141$	3.24155			0.272988
$142$	−2.51261	−	22.9538i	−0.210854	−	1.92624i
$143$	−5.78958			−0.484149
$144$	22.3450	−	10.4138i	1.86208	−	0.867820i
$145$		−	0.774233i		−	0.0642966i
$146$	−0.0164826	−	0.150576i	−0.00136411	−	0.0124618i
$147$		0			0
$148$	9.97662	−	2.21065i	0.820073	−	0.181714i
$149$	−2.85765			−0.234108			−0.117054	−	0.993126i	$-0.537345\pi$
$149$	−2.85765			−0.234108			−0.117054	+	0.993126i	$0.537345\pi$
$150$	4.25550	−	0.465823i	0.347460	−	0.0380343i
$151$			6.60903i			0.537835i	0.963163	+	0.268918i	$0.0866659\pi$
$151$			6.60903i			0.537835i	−0.963163	+	0.268918i	$0.913334\pi$
$152$	3.80948	−	1.29246i	0.308990	−	0.104833i
$153$			15.6870i			1.26822i
$154$		0			0
$155$		−	6.63865i		−	0.533229i
$156$	−6.33503	−	28.5899i	−0.507208	−	2.28902i
$157$		−	15.5831i		−	1.24367i	−0.783149	−	0.621834i	$-0.786388\pi$
$157$		−	15.5831i		−	1.24367i	0.783149	−	0.621834i	$-0.213612\pi$
$158$	−1.65717	−	15.1390i	−0.131838	−	1.20440i
$159$	10.1769			0.807085
$160$	2.93333	+	4.83689i	0.231900	+	0.382390i
$161$		0			0
$162$	−14.7537	+	1.61500i	−1.15916	+	0.126886i
$163$		−	9.64030i		−	0.755086i	−0.925992	−	0.377543i	$-0.876769\pi$
$163$		−	9.64030i		−	0.755086i	0.925992	−	0.377543i	$-0.123231\pi$
$164$	3.23069	+	14.5801i	0.252274	+	1.13851i
$165$	−3.62326			−0.282071
$166$	22.2157	−	2.43182i	1.72427	−	0.188746i
$167$	−4.94876			−0.382947			−0.191473	−	0.981498i	$-0.561327\pi$
$167$	−4.94876			−0.382947			−0.191473	+	0.981498i	$0.561327\pi$
$168$		0			0
$169$	−10.3958			−0.799678
$170$	−3.57823	+	0.391687i	−0.274438	+	0.0300410i
$171$	−8.76558			−0.670320
$172$	−0.597958	−	2.69858i	−0.0455939	−	0.205765i
$173$			6.93069i			0.526931i	0.964669	+	0.263465i	$0.0848655\pi$
$173$			6.93069i			0.526931i	−0.964669	+	0.263465i	$0.915135\pi$
$174$	−3.29475	+	0.360656i	−0.249774	+	0.0273412i
$175$		0			0
$176$	−2.02250	−	4.33967i	−0.152451	−	0.327115i
$177$	−29.9199			−2.24892
$178$	−0.606507	−	5.54071i	−0.0454596	−	0.415294i
$179$			21.1123i			1.57801i	0.614389	+	0.789003i	$0.289403\pi$
$179$			21.1123i			1.57801i	−0.614389	+	0.789003i	$0.710597\pi$
$180$	−2.66661	−	12.0344i	−0.198757	−	0.896988i
$181$			6.10438i			0.453735i	0.973926	+	0.226868i	$0.0728485\pi$
$181$			6.10438i			0.453735i	−0.973926	+	0.226868i	$0.927152\pi$
$182$		0			0
$183$		−	29.0504i		−	2.14747i
$184$	5.27661	+	15.5526i	0.388997	+	1.14655i
$185$		−	5.10930i		−	0.375644i
$186$	−28.2508	+	3.09244i	−2.07145	+	0.226748i
$187$	3.04662			0.222791
$188$	2.09099	−	0.463328i	0.152501	−	0.0337917i
$189$		0			0
$190$	−0.218866	−	1.99944i	−0.0158782	−	0.145054i
$191$			3.71319i			0.268677i	0.990936	+	0.134339i	$0.0428909\pi$
$191$			3.71319i			0.268677i	−0.990936	+	0.134339i	$0.957109\pi$
$192$	19.2170	−	14.7359i	1.38687	−	1.06347i
$193$	15.3309			1.10354			0.551771	−	0.833996i	$-0.313952\pi$
$193$	15.3309			1.10354			0.551771	+	0.833996i	$0.313952\pi$
$194$	1.34094	+	12.2501i	0.0962741	+	0.879506i
$195$	−14.6417			−1.04851
$196$		0			0
$197$	−24.4602			−1.74272			−0.871360	−	0.490644i	$-0.836761\pi$
$197$	−24.4602			−1.74272			−0.871360	+	0.490644i	$0.836761\pi$
$198$	1.13522	+	10.3707i	0.0806763	+	0.737013i
$199$	12.8662			0.912062			0.456031	−	0.889964i	$-0.349271\pi$
$199$	12.8662			0.912062			0.456031	+	0.889964i	$0.349271\pi$
$200$	2.67847	−	0.908739i	0.189396	−	0.0642576i
$201$			31.9523i			2.25374i
$202$	0.462495	+	4.22510i	0.0325410	+	0.297277i
$203$		0			0
$204$	3.33364	+	15.0447i	0.233402	+	1.05334i
$205$	7.46685			0.521508
$206$	0.538074	−	0.0588997i	0.0374894	−	0.00410373i
$207$		−	35.7863i		−	2.48732i
$208$	−8.17294	−	17.5367i	−0.566692	−	1.21595i
$209$			1.70238i			0.117756i
$210$		0			0
$211$			16.9384i			1.16609i	0.812441	+	0.583044i	$0.198138\pi$
$211$			16.9384i			1.16609i	−0.812441	+	0.583044i	$0.801862\pi$
$212$	6.56474	−	1.45463i	0.450868	−	0.0999046i
$213$			49.4252i			3.38656i
$214$	0.129644	+	1.18436i	0.00886230	+	0.0809610i
$215$	−1.38202			−0.0942528
$216$	−25.6463	+	8.70118i	−1.74501	+	0.592040i
$217$		0			0
$218$	−5.55393	+	0.607955i	−0.376160	+	0.0411759i
$219$			0.324227i			0.0219092i
$220$	−2.33722	+	0.517888i	−0.157575	+	0.0349160i
$221$	12.3114			0.828157
$222$	−21.7426	+	2.38003i	−1.45927	+	0.159737i
$223$	−18.9687			−1.27024			−0.635119	−	0.772414i	$-0.719049\pi$
$223$	−18.9687			−1.27024			−0.635119	+	0.772414i	$0.719049\pi$
$224$		0			0
$225$	−6.16313			−0.410875
$226$	−3.77042	+	0.412724i	−0.250804	+	0.0274540i
$227$	0.934456			0.0620220			0.0310110	−	0.999519i	$-0.490127\pi$
$227$	0.934456			0.0620220			0.0310110	+	0.999519i	$0.490127\pi$
$228$	−8.40665	+	1.86277i	−0.556744	+	0.123365i
$229$			13.0808i			0.864401i	0.901777	+	0.432201i	$0.142263\pi$
$229$			13.0808i			0.864401i	−0.901777	+	0.432201i	$0.857737\pi$
$230$	8.16289	−	0.893541i	0.538245	−	0.0589184i
$231$		0			0
$232$	−2.07376	+	0.703576i	−0.136149	+	0.0461920i
$233$	−15.6016			−1.02209			−0.511047	−	0.859553i	$-0.670742\pi$
$233$	−15.6016			−1.02209			−0.511047	+	0.859553i	$0.670742\pi$
$234$	4.58743	+	41.9082i	0.299890	+	2.73962i
$235$		−	1.07086i		−	0.0698550i
$236$	−19.3001	+	4.27657i	−1.25633	+	0.278381i
$237$			32.5980i			2.11747i
$238$		0			0
$239$			14.1327i			0.914167i	0.889424	+	0.457084i	$0.151106\pi$
$239$			14.1327i			0.914167i	−0.889424	+	0.457084i	$0.848894\pi$
$240$	−5.11483	−	10.9749i	−0.330161	−	0.708427i
$241$			21.5832i			1.39029i	0.718868	+	0.695146i	$0.244661\pi$
$241$			21.5832i			1.39029i	−0.718868	+	0.695146i	$0.755339\pi$
$242$	−13.4499	+	1.47227i	−0.864590	+	0.0946413i
$243$	3.04338			0.195233
$244$	−4.15230	−	18.7393i	−0.265824	−	1.19966i
$245$		0			0
$246$	−3.47823	−	31.7752i	−0.221764	−	2.02591i
$247$			6.87936i			0.437723i
$248$	−17.7814	+	6.03280i	−1.12912	+	0.383083i
$249$	−47.8359			−3.03148
$250$	−0.153886	−	1.40582i	−0.00973260	−	0.0889116i
$251$	1.04460			0.0659345			0.0329673	−	0.999456i	$-0.489504\pi$
$251$	1.04460			0.0659345			0.0329673	+	0.999456i	$0.489504\pi$
$252$		0			0
$253$	−6.95014			−0.436952
$254$	−0.329369	−	3.00893i	−0.0206665	−	0.188797i
$255$	7.70480			0.482494
$256$	10.2898	−	12.2523i	0.643115	−	0.765770i
$257$		−	4.90387i		−	0.305895i	−0.988234	−	0.152948i	$-0.951123\pi$
$257$		−	4.90387i		−	0.305895i	0.988234	−	0.152948i	$-0.0488766\pi$
$258$	0.643775	+	5.88117i	0.0400797	+	0.366146i
$259$		0			0
$260$	−9.44476	+	2.09280i	−0.585739	+	0.129790i
$261$	4.77170			0.295361
$262$	−13.5883	+	1.48742i	−0.839486	+	0.0918933i
$263$		−	7.79637i		−	0.480745i	−0.970681	−	0.240373i	$-0.922730\pi$
$263$		−	7.79637i		−	0.480745i	0.970681	−	0.240373i	$-0.0772696\pi$
$264$	3.29260	+	9.70480i	0.202646	+	0.597289i
$265$		−	3.36198i		−	0.206525i
$266$		0			0
$267$			11.9305i			0.730135i
$268$	4.56707	+	20.6111i	0.278978	+	1.25902i
$269$		−	21.1124i		−	1.28724i	−0.765344	−	0.643622i	$-0.777431\pi$
$269$		−	21.1124i		−	1.28724i	0.765344	−	0.643622i	$-0.222569\pi$
$270$	1.47346	+	13.4607i	0.0896718	+	0.819192i
$271$	−21.5208			−1.30729			−0.653647	−	0.756799i	$-0.726762\pi$
$271$	−21.5208			−1.30729			−0.653647	+	0.756799i	$0.726762\pi$
$272$	4.30080	+	9.22824i	0.260774	+	0.559544i
$273$		0			0
$274$	−6.01082	+	0.657967i	−0.363127	+	0.0397492i
$275$			1.19696i			0.0721792i
$276$	−7.60493	−	34.3209i	−0.457763	−	2.06588i
$277$	−5.16743			−0.310481			−0.155241	−	0.987877i	$-0.549615\pi$
$277$	−5.16743			−0.310481			−0.155241	+	0.987877i	$0.549615\pi$
$278$	10.5962	−	1.15990i	0.635519	−	0.0695664i
$279$	40.9149			2.44951
$280$		0			0
$281$	15.6322			0.932539			0.466270	−	0.884643i	$-0.345598\pi$
$281$	15.6322			0.932539			0.466270	+	0.884643i	$0.345598\pi$
$282$	−4.55703	+	0.498830i	−0.271367	+	0.0297049i
$283$	−28.5700			−1.69831			−0.849156	−	0.528142i	$-0.822889\pi$
$283$	−28.5700			−1.69831			−0.849156	+	0.528142i	$0.822889\pi$
$284$	7.06454	+	31.8822i	0.419203	+	1.89186i
$285$			4.30528i			0.255023i
$286$	8.13909	−	0.890936i	0.481274	−	0.0526821i
$287$		0			0
$288$	−29.8104	+	18.0785i	−1.75660	+	1.06529i
$289$	10.5214			0.618907
$290$	0.119144	+	1.08843i	0.00699636	+	0.0639148i
$291$		−	26.3775i		−	1.54627i
$292$	0.0463431	+	0.209146i	0.00271202	+	0.0122393i
$293$		−	0.657174i		−	0.0383925i	−0.999816	−	0.0191963i	$-0.993889\pi$
$293$		−	0.657174i		−	0.0383925i	0.999816	−	0.0191963i	$-0.00611074\pi$
$294$		0			0
$295$			9.88412i			0.575476i
$296$	−13.6851	+	4.64303i	−0.795431	+	0.269870i
$297$		−	11.4609i		−	0.665026i
$298$	4.01733	−	0.439752i	0.232717	−	0.0254741i
$299$	−28.0857			−1.62424
$300$	−5.91077	+	1.30972i	−0.341258	+	0.0756169i
$301$		0			0
$302$	−1.01704	−	9.29108i	−0.0585239	−	0.534642i
$303$		−	9.09766i		−	0.522647i
$304$	−5.15654	+	2.40319i	−0.295748	+	0.137833i
$305$	−9.59690			−0.549517
$306$	−2.41402	−	22.0531i	−0.138000	−	1.26069i
$307$	−4.88042			−0.278540			−0.139270	−	0.990254i	$-0.544476\pi$
$307$	−4.88042			−0.278540			−0.139270	+	0.990254i	$0.544476\pi$
$308$		0			0
$309$	−1.15861			−0.0659108
$310$	1.02160	+	9.33272i	0.0580227	+	0.530063i
$311$	11.8968			0.674606			0.337303	−	0.941396i	$-0.390485\pi$
$311$	11.8968			0.674606			0.337303	+	0.941396i	$0.390485\pi$
$312$	13.3055	+	39.2173i	0.753274	+	2.22024i
$313$		−	26.6074i		−	1.50394i	−0.659197	−	0.751970i	$-0.729104\pi$
$313$		−	26.6074i		−	1.50394i	0.659197	−	0.751970i	$-0.270896\pi$
$314$	2.39802	+	21.9070i	0.135328	+	1.23628i
$315$		0			0
$316$	4.65936	+	21.0277i	0.262110	+	1.18290i
$317$	−26.4557			−1.48590			−0.742950	−	0.669347i	$-0.766574\pi$
$317$	−26.4557			−1.48590			−0.742950	+	0.669347i	$0.766574\pi$
$318$	−14.3069	+	1.56609i	−0.802292	+	0.0878220i
$319$		−	0.926723i		−	0.0518865i
$320$	−4.86806	−	6.34839i	−0.272133	−	0.354886i
$321$		−	2.55021i		−	0.142339i
$322$		0			0
$323$		−	3.62009i		−	0.201427i
$324$	20.4925	−	4.54078i	1.13847	−	0.252266i
$325$			4.83692i			0.268304i
$326$	1.48351	+	13.5525i	0.0821638	+	0.750603i
$327$	11.9590			0.661333
$328$	−6.78542	−	19.9997i	−0.374662	−	1.10430i
$329$		0			0
$330$	5.09364	−	0.557570i	0.280396	−	0.0306932i
$331$			24.2827i			1.33470i	0.744745	+	0.667349i	$0.232571\pi$
$331$			24.2827i			1.33470i	−0.744745	+	0.667349i	$0.767429\pi$
$332$	−30.8570	+	6.83738i	−1.69350	+	0.375250i
$333$	31.4893			1.72560
$334$	6.95705	−	0.761545i	0.380673	−	0.0416699i
$335$	10.5555			0.576710
$336$		0			0
$337$	19.7077			1.07355			0.536774	−	0.843726i	$-0.319643\pi$
$337$	19.7077			1.07355			0.536774	+	0.843726i	$0.319643\pi$
$338$	14.6146	−	1.59977i	0.794930	−	0.0870161i
$339$	8.11863			0.440943
$340$	4.97006	−	1.10128i	0.269539	−	0.0597252i
$341$		−	7.94617i		−	0.430309i
$342$	12.3228	−	1.34890i	0.666340	−	0.0729401i
$343$		0			0
$344$	1.25589	+	3.70169i	0.0677132	+	0.199582i
$345$	−17.5767			−0.946298
$346$	−1.06654	−	9.74328i	−0.0573374	−	0.523802i
$347$			8.43701i			0.452923i	0.974020	+	0.226461i	$0.0727157\pi$
$347$			8.43701i			0.452923i	−0.974020	+	0.226461i	$0.927284\pi$
$348$	4.57631	−	1.01403i	0.245316	−	0.0543578i
$349$		−	23.5784i		−	1.26212i	−0.775732	−	0.631062i	$-0.782619\pi$
$349$		−	23.5784i		−	1.26212i	0.775732	−	0.631062i	$-0.217381\pi$
$350$		0			0
$351$		−	46.3135i		−	2.47203i
$352$	3.51107	+	5.78955i	0.187141	+	0.308584i
$353$		−	20.6724i		−	1.10028i	−0.835072	−	0.550141i	$-0.814574\pi$
$353$		−	20.6724i		−	1.10028i	0.835072	−	0.550141i	$-0.185426\pi$
$354$	42.0619	−	4.60425i	2.23556	−	0.244713i
$355$	16.3277			0.866587
$356$	1.70528	+	7.69589i	0.0903794	+	0.407881i
$357$		0			0
$358$	−3.24889	−	29.6800i	−0.171709	−	1.56864i
$359$		−	27.4519i		−	1.44886i	−0.689349	−	0.724429i	$-0.742104\pi$
$359$		−	27.4519i		−	1.44886i	0.689349	−	0.724429i	$-0.257896\pi$
$360$	5.60068	+	16.5077i	0.295182	+	0.870035i
$361$	−16.9772			−0.893536
$362$	−0.939379	−	8.58164i	−0.0493727	−	0.451041i
$363$	28.9608			1.52005
$364$		0			0
$365$	0.107109			0.00560636
$366$	4.47045	+	40.8396i	0.233674	+	2.13472i
$367$	20.0426			1.04622			0.523109	−	0.852266i	$-0.324772\pi$
$367$	20.0426			1.04622			0.523109	+	0.852266i	$0.324772\pi$
$368$	−9.81126	−	21.0521i	−0.511447	−	1.09741i
$369$			46.0192i			2.39566i
$370$	0.786250	+	7.18274i	0.0408752	+	0.373413i
$371$		0			0
$372$	39.2395	−	8.69480i	2.03447	−	0.450804i
$373$	20.5912			1.06617			0.533085	−	0.846062i	$-0.321033\pi$
$373$	20.5912			1.06617			0.533085	+	0.846062i	$0.321033\pi$
$374$	−4.28298	+	0.468832i	−0.221468	+	0.0242427i
$375$			3.02707i			0.156317i
$376$	−2.86825	+	0.973129i	−0.147919	+	0.0501853i
$377$		−	3.74491i		−	0.192873i
$378$		0			0
$379$			3.26339i			0.167629i	0.996481	+	0.0838145i	$0.0267103\pi$
$379$			3.26339i			0.167629i	−0.996481	+	0.0838145i	$0.973290\pi$
$380$	0.615371	+	2.77716i	0.0315678	+	0.142465i
$381$			6.47897i			0.331927i
$382$	−0.571408	−	5.22006i	−0.0292358	−	0.267082i
$383$	−33.7511			−1.72460			−0.862300	−	0.506398i	$-0.830977\pi$
$383$	−33.7511			−1.72460			−0.862300	+	0.506398i	$0.830977\pi$
$384$	−24.7479	+	23.6732i	−1.26291	+	1.20807i
$385$		0			0
$386$	−21.5524	+	2.35921i	−1.09699	+	0.120081i
$387$		−	8.51755i		−	0.432971i
$388$	−3.77024	−	17.0150i	−0.191405	−	0.863808i
$389$	−3.61209			−0.183140			−0.0915701	−	0.995799i	$-0.529189\pi$
$389$	−3.61209			−0.183140			−0.0915701	+	0.995799i	$0.529189\pi$
$390$	20.5835	−	2.25315i	1.04229	−	0.114093i
$391$	14.7793			0.747424
$392$		0			0
$393$	29.2589			1.47591
$394$	34.3866	−	3.76409i	1.73237	−	0.189632i
$395$	10.7688			0.541839
$396$	−3.19181	−	14.4046i	−0.160394	−	0.723858i
$397$			7.47724i			0.375272i	0.982239	+	0.187636i	$0.0600826\pi$
$397$			7.47724i			0.375272i	−0.982239	+	0.187636i	$0.939917\pi$
$398$	−18.0875	+	1.97993i	−0.906646	+	0.0992449i
$399$		0			0
$400$	−3.62559	+	1.68970i	−0.181280	+	0.0844850i
$401$	−9.54674			−0.476742			−0.238371	−	0.971174i	$-0.576613\pi$
$401$	−9.54674			−0.476742			−0.238371	+	0.971174i	$0.576613\pi$
$402$	−4.91700	−	44.9190i	−0.245238	−	2.24036i
$403$		−	32.1106i		−	1.59955i
$404$	−1.30037	−	5.86854i	−0.0646956	−	0.291971i
$405$		−	10.4948i		−	0.521490i
$406$		0			0
$407$		−	6.11561i		−	0.303140i
$408$	−7.00166	−	20.6371i	−0.346634	−	1.02169i
$409$			21.6716i			1.07159i	0.844347	+	0.535796i	$0.179988\pi$
$409$			21.6716i			1.07159i	−0.844347	+	0.535796i	$0.820012\pi$
$410$	−10.4970	+	1.14904i	−0.518411	+	0.0567472i
$411$	12.9428			0.638419
$412$	−0.747370	+	0.165604i	−0.0368203	+	0.00815873i
$413$		0			0
$414$	5.50701	+	50.3090i	0.270655	+	2.47255i
$415$			15.8027i			0.775725i
$416$	14.1883	+	23.3957i	0.695639	+	1.14707i
$417$	−22.8163			−1.11732
$418$	−0.261973	−	2.39324i	−0.0128135	−	0.117057i
$419$	−13.0327			−0.636690			−0.318345	−	0.947975i	$-0.603127\pi$
$419$	−13.0327			−0.636690			−0.318345	+	0.947975i	$0.603127\pi$
$420$		0			0
$421$	−34.2800			−1.67070			−0.835352	−	0.549715i	$-0.814736\pi$
$421$	−34.2800			−1.67070			−0.835352	+	0.549715i	$0.814736\pi$
$422$	−2.60658	−	23.8123i	−0.126886	−	1.15916i
$423$	6.59983			0.320895
$424$	−9.00497	+	3.05517i	−0.437320	+	0.148372i
$425$		−	2.54530i		−	0.123465i
$426$	−7.60584	−	69.4827i	−0.368504	−	3.36645i
$427$		0			0
$428$	−0.364512	−	1.64504i	−0.0176194	−	0.0795159i
$429$	−17.5255			−0.846137
$430$	1.94286	−	0.212673i	0.0936931	−	0.0102560i
$431$		−	2.85250i		−	0.137400i	−0.997637	−	0.0687001i	$-0.978115\pi$
$431$		−	2.85250i		−	0.137400i	0.997637	−	0.0687001i	$-0.0218852\pi$
$432$	34.7151	−	16.1789i	1.67023	−	0.778406i
$433$			34.6179i			1.66363i	0.555053	+	0.831815i	$0.312698\pi$
$433$			34.6179i			1.66363i	−0.555053	+	0.831815i	$0.687302\pi$
$434$		0			0
$435$		−	2.34366i		−	0.112370i
$436$	7.71426	−	1.70935i	0.369446	−	0.0818628i
$437$			8.25838i			0.395052i
$438$	−0.0498940	−	0.455804i	−0.00238403	−	0.0217791i
$439$	−10.9381			−0.522047			−0.261023	−	0.965332i	$-0.584060\pi$
$439$	−10.9381			−0.522047			−0.261023	+	0.965332i	$0.584060\pi$
$440$	3.20601	−	1.08772i	0.152840	−	0.0518551i
$441$		0			0
$442$	−17.3076	+	1.89456i	−0.823240	+	0.0901149i
$443$			35.3941i			1.68163i	0.541325	+	0.840813i	$0.317923\pi$
$443$			35.3941i			1.68163i	−0.541325	+	0.840813i	$0.682077\pi$
$444$	30.1999	−	6.69177i	1.43322	−	0.317578i
$445$	3.94128			0.186834
$446$	26.6665	−	2.91902i	1.26270	−	0.138219i
$447$	−8.65029			−0.409145
$448$		0			0
$449$	28.0029			1.32154			0.660768	−	0.750590i	$-0.270231\pi$
$449$	28.0029			1.32154			0.660768	+	0.750590i	$0.270231\pi$
$450$	8.66423	−	0.948419i	0.408436	−	0.0447089i
$451$	8.93750			0.420850
$452$	5.23700	−	1.16043i	0.246328	−	0.0545820i
$453$			20.0060i			0.939962i
$454$	−1.31367	+	0.143800i	−0.0616537	+	0.00674885i
$455$		0			0
$456$	11.5315	−	3.91237i	0.540014	−	0.183214i
$457$	20.1898			0.944439			0.472220	−	0.881481i	$-0.343453\pi$
$457$	20.1898			0.944439			0.472220	+	0.881481i	$0.343453\pi$
$458$	−2.01295	−	18.3892i	−0.0940588	−	0.859269i
$459$			24.3713i			1.13755i
$460$	−11.3380	+	2.51231i	−0.528638	+	0.117137i
$461$			0.127845i			0.00595433i	0.999996	+	0.00297717i	$0.000947663\pi$
$461$			0.127845i			0.00595433i	−0.999996	+	0.00297717i	$0.999052\pi$
$462$		0			0
$463$			17.8655i			0.830282i	0.909757	+	0.415141i	$0.136268\pi$
$463$			17.8655i			0.830282i	−0.909757	+	0.415141i	$0.863732\pi$
$464$	2.80705	−	1.30822i	0.130314	−	0.0607327i
$465$		−	20.0956i		−	0.931913i
$466$	21.9330	−	2.40087i	1.01603	−	0.111218i
$467$	14.6695			0.678826			0.339413	−	0.940638i	$-0.389772\pi$
$467$	14.6695			0.678826			0.339413	+	0.940638i	$0.389772\pi$
$468$	−12.8982	−	58.2093i	−0.596218	−	2.69072i
$469$		0			0
$470$	0.164790	+	1.50543i	0.00760119	+	0.0694402i
$471$		−	47.1711i		−	2.17353i
$472$	26.4743	−	8.98209i	1.21858	−	0.413434i
$473$	−1.65421			−0.0760608
$474$	−5.01638	−	45.8268i	−0.230410	−	2.10489i
$475$	1.42226			0.0652578
$476$		0			0
$477$	20.7203			0.948719
$478$	−2.17482	−	19.8680i	−0.0994740	−	0.908739i
$479$	26.1514			1.19489			0.597444	−	0.801911i	$-0.296183\pi$
$479$	26.1514			1.19489			0.597444	+	0.801911i	$0.296183\pi$
$480$	8.87940	+	14.6416i	0.405287	+	0.668295i
$481$		−	24.7133i		−	1.12683i
$482$	−3.32134	−	30.3419i	−0.151283	−	1.38204i
$483$		0			0
$484$	18.6815	−	4.13949i	0.849158	−	0.188159i
$485$	−8.71387			−0.395677
$486$	−4.27843	+	0.468333i	−0.194073	+	0.0212440i
$487$			16.6245i			0.753330i	0.926350	+	0.376665i	$0.122929\pi$
$487$			16.6245i			0.753330i	−0.926350	+	0.376665i	$0.877071\pi$
$488$	8.72108	+	25.7050i	0.394785	+	1.16361i
$489$		−	29.1818i		−	1.31965i
$490$		0			0
$491$			21.9094i			0.988758i	0.869246	+	0.494379i	$0.164605\pi$
$491$			21.9094i			0.988758i	−0.869246	+	0.494379i	$0.835395\pi$
$492$	9.77951	+	44.1348i	0.440894	+	1.98975i
$493$			1.97066i			0.0887540i
$494$	−1.05864	−	9.67112i	−0.0476304	−	0.435124i
$495$	−7.37699			−0.331571
$496$	24.0690	−	11.2173i	1.08073	−	0.503673i
$497$		0			0
$498$	67.2485	−	7.36127i	3.01348	−	0.329867i
$499$		−	40.6890i		−	1.82149i	−0.412970	−	0.910745i	$-0.635508\pi$
$499$		−	40.6890i		−	1.82149i	0.412970	−	0.910745i	$-0.364492\pi$
$500$	0.432671	+	1.95264i	0.0193496	+	0.0873246i
$501$	−14.9802			−0.669267
$502$	−1.46851	+	0.160749i	−0.0655430	+	0.00717459i
$503$	−7.19624			−0.320864			−0.160432	−	0.987047i	$-0.551289\pi$
$503$	−7.19624			−0.320864			−0.160432	+	0.987047i	$0.551289\pi$
$504$		0			0
$505$	−3.00544			−0.133740
$506$	9.77062	−	1.06953i	0.434357	−	0.0475464i
$507$	−31.4688			−1.39758
$508$	0.926065	+	4.17932i	0.0410875	+	0.185427i
$509$		−	5.14254i		−	0.227939i	−0.993484	−	0.113970i	$-0.963643\pi$
$509$		−	5.14254i		−	0.227939i	0.993484	−	0.113970i	$-0.0363567\pi$
$510$	−10.8315	+	1.18566i	−0.479629	+	0.0525020i
$511$		0			0
$512$	−12.5802	+	18.8080i	−0.555970	+	0.831203i
$513$	−13.6181			−0.601256
$514$	0.754638	+	6.89395i	0.0332856	+	0.304079i
$515$			0.382749i			0.0168659i
$516$	−1.81006	−	8.16878i	−0.0796834	−	0.359610i
$517$		−	1.28177i		−	0.0563721i
$518$		0			0
$519$			20.9797i			0.920905i
$520$	12.9555	−	4.39550i	0.568138	−	0.192755i
$521$			9.06489i			0.397140i	0.980087	+	0.198570i	$0.0636298\pi$
$521$			9.06489i			0.397140i	−0.980087	+	0.198570i	$0.936370\pi$
$522$	−6.70813	+	0.734298i	−0.293607	+	0.0321393i
$523$	17.6074			0.769918			0.384959	−	0.922934i	$-0.374216\pi$
$523$	17.6074			0.769918			0.384959	+	0.922934i	$0.374216\pi$
$524$	18.8737	−	4.18209i	0.824502	−	0.182695i
$525$		0			0
$526$	1.19975	+	10.9603i	0.0523117	+	0.477890i
$527$			16.8974i			0.736062i
$528$	−6.12223	−	13.1365i	−0.266436	−	0.571692i
$529$	−10.7156			−0.465896
$530$	0.517362	+	4.72633i	0.0224728	+	0.205299i
$531$	−60.9171			−2.64358
$532$		0			0
$533$	36.1166			1.56438
$534$	−1.83594	−	16.7721i	−0.0794488	−	0.725800i
$535$	−0.842470			−0.0364231
$536$	−9.59222	−	28.2726i	−0.414321	−	1.22119i
$537$			63.9083i			2.75785i
$538$	3.24890	+	29.6801i	0.140070	+	1.27960i
$539$		0			0
$540$	−4.14282	−	18.6965i	−0.178279	−	0.804570i
$541$	−27.9622			−1.20219			−0.601094	−	0.799178i	$-0.705268\pi$
$541$	−27.9622			−1.20219			−0.601094	+	0.799178i	$0.705268\pi$
$542$	30.2543	−	3.31175i	1.29953	−	0.142252i
$543$			18.4784i			0.792983i
$544$	−7.46623	−	12.3114i	−0.320112	−	0.527846i
$545$		−	3.95068i		−	0.169229i
$546$		0			0
$547$		−	29.6385i		−	1.26725i	−0.773640	−	0.633626i	$-0.781566\pi$
$547$		−	29.6385i		−	1.26725i	0.773640	−	0.633626i	$-0.218434\pi$
$548$	8.34885	−	1.84996i	0.356645	−	0.0790264i
$549$		−	59.1469i		−	2.52433i
$550$	−0.184195	−	1.68270i	−0.00785409	−	0.0717506i
$551$	−1.10116			−0.0469111
$552$	15.9726	+	47.0786i	0.679841	+	2.00380i
$553$		0			0
$554$	7.26446	−	0.795196i	0.308637	−	0.0337846i
$555$		−	15.4662i		−	0.656504i
$556$	−14.7179	+	3.26122i	−0.624176	+	0.138307i
$557$	35.7334			1.51407			0.757037	−	0.653372i	$-0.226646\pi$
$557$	35.7334			1.51407			0.757037	+	0.653372i	$0.226646\pi$
$558$	−57.5188	+	6.29622i	−2.43496	+	0.266540i
$559$	−6.68471			−0.282733
$560$		0			0
$561$	9.22231			0.389366
$562$	−21.9760	+	2.40558i	−0.927002	+	0.101473i
$563$	23.0047			0.969532			0.484766	−	0.874644i	$-0.338905\pi$
$563$	23.0047			0.969532			0.484766	+	0.874644i	$0.338905\pi$
$564$	6.32958	−	1.40253i	0.266523	−	0.0590570i
$565$		−	2.68201i		−	0.112833i
$566$	40.1642	−	4.39653i	1.68823	−	0.184800i
$567$		0			0
$568$	−14.8377	−	43.7333i	−0.622574	−	1.83501i
$569$	−18.8787			−0.791438			−0.395719	−	0.918372i	$-0.629505\pi$
$569$	−18.8787			−0.791438			−0.395719	+	0.918372i	$0.629505\pi$
$570$	−0.662522	−	6.05243i	−0.0277500	−	0.253508i
$571$			23.9624i			1.00279i	0.865217	+	0.501397i	$0.167180\pi$
$571$			23.9624i			1.00279i	−0.865217	+	0.501397i	$0.832820\pi$
$572$	−11.3050	+	2.50498i	−0.472684	+	0.104739i
$573$			11.2401i			0.469561i
$574$		0			0
$575$			5.80651i			0.242148i
$576$	39.1259	−	30.0025i	1.63025	−	1.25010i
$577$			10.6311i			0.442580i	0.975208	+	0.221290i	$0.0710268\pi$
$577$			10.6311i			0.442580i	−0.975208	+	0.221290i	$0.928973\pi$
$578$	−14.7912	+	1.61910i	−0.615232	+	0.0673457i
$579$	46.4076			1.92864
$580$	−0.334988	−	1.51180i	−0.0139096	−	0.0627740i
$581$		0			0
$582$	4.05912	+	37.0819i	0.168256	+	1.53709i
$583$		−	4.02415i		−	0.166663i
$584$	−0.0973345	−	0.286889i	−0.00402773	−	0.0118716i
$585$	−29.8106			−1.23252
$586$	0.101130	+	0.923866i	0.00417764	+	0.0381646i
$587$	−0.240690			−0.00993436			−0.00496718	−	0.999988i	$-0.501581\pi$
$587$	−0.240690			−0.00993436			−0.00496718	+	0.999988i	$0.501581\pi$
$588$		0			0
$589$	−9.44189			−0.389046
$590$	−1.52103	−	13.8953i	−0.0626197	−	0.572059i
$591$	−74.0428			−3.04571
$592$	18.5243	−	8.63319i	0.761342	−	0.354822i
$593$			30.9254i			1.26995i	0.772531	+	0.634977i	$0.218990\pi$
$593$			30.9254i			1.26995i	−0.772531	+	0.634977i	$0.781010\pi$
$594$	1.76366	+	16.1119i	0.0723640	+	0.661077i
$595$		0			0
$596$	−5.57995	+	1.23642i	−0.228564	+	0.0506458i
$597$	38.9469			1.59399
$598$	39.4833	−	4.32199i	1.61459	−	0.176739i
$599$		−	29.9488i		−	1.22368i	−0.790983	−	0.611838i	$-0.790430\pi$
$599$		−	29.9488i		−	1.22368i	0.790983	−	0.611838i	$-0.209570\pi$
$600$	8.10790	−	2.75081i	0.331004	−	0.112302i
$601$		−	23.0748i		−	0.941241i	−0.882336	−	0.470621i	$-0.844030\pi$
$601$		−	23.0748i		−	0.941241i	0.882336	−	0.470621i	$-0.155970\pi$
$602$		0			0
$603$			65.0550i			2.64925i
$604$	2.85953	+	12.9050i	0.116353	+	0.525099i
$605$		−	9.56730i		−	0.388966i
$606$	1.40000	+	12.7896i	0.0568712	+	0.519544i
$607$	−17.8801			−0.725730			−0.362865	−	0.931842i	$-0.618201\pi$
$607$	−17.8801			−0.725730			−0.362865	+	0.931842i	$0.618201\pi$
$608$	6.87932	−	4.17197i	0.278993	−	0.169196i
$609$		0			0
$610$	13.4915	−	1.47683i	0.546254	−	0.0597950i
$611$		−	5.17965i		−	0.209546i
$612$	6.78732	+	30.6311i	0.274361	+	1.23819i
$613$	−8.37011			−0.338065			−0.169033	−	0.985610i	$-0.554064\pi$
$613$	−8.37011			−0.338065			−0.169033	+	0.985610i	$0.554064\pi$
$614$	6.86097	−	0.751028i	0.276886	−	0.0303090i
$615$	22.6027			0.911427
$616$		0			0
$617$	33.7886			1.36028			0.680139	−	0.733084i	$-0.261920\pi$
$617$	33.7886			1.36028			0.680139	+	0.733084i	$0.261920\pi$
$618$	1.62879	−	0.178293i	0.0655194	−	0.00717200i
$619$	−33.2883			−1.33797			−0.668986	−	0.743275i	$-0.733271\pi$
$619$	−33.2883			−1.33797			−0.668986	+	0.743275i	$0.733271\pi$
$620$	−2.87235	−	12.9629i	−0.115356	−	0.520602i
$621$		−	55.5974i		−	2.23105i
$622$	−16.7247	+	1.83075i	−0.670600	+	0.0734065i
$623$		0			0
$624$	−24.7400	−	53.0848i	−0.990394	−	2.12509i
$625$	1.00000			0.0400000
$626$	4.09451	+	37.4051i	0.163649	+	1.49501i
$627$			5.15323i			0.205800i
$628$	−6.74236	−	30.4282i	−0.269049	−	1.21422i
$629$			13.0047i			0.518533i
$630$		0			0
$631$		−	43.1690i		−	1.71853i	−0.511528	−	0.859266i	$-0.670921\pi$
$631$		−	43.1690i		−	1.71853i	0.511528	−	0.859266i	$-0.329079\pi$
$632$	−9.78607	−	28.8440i	−0.389269	−	1.14735i
$633$			51.2737i			2.03794i
$634$	37.1918	−	4.07116i	1.47708	−	0.161686i
$635$	2.14034			0.0849370
$636$	19.8719	−	4.40327i	0.787972	−	0.174601i
$637$		0			0
$638$	0.142610	+	1.30280i	0.00564597	+	0.0515784i
$639$			100.630i			3.98086i
$640$	7.82052	+	8.17554i	0.309133	+	0.323166i
$641$	32.0262			1.26496			0.632479	−	0.774578i	$-0.282038\pi$
$641$	32.0262			1.26496			0.632479	+	0.774578i	$0.282038\pi$
$642$	0.392442	+	3.58513i	0.0154884	+	0.141494i
$643$	37.9515			1.49666			0.748331	−	0.663326i	$-0.230856\pi$
$643$	37.9515			1.49666			0.748331	+	0.663326i	$0.230856\pi$
$644$		0			0
$645$	−4.18346			−0.164723
$646$	0.557081	+	5.08918i	0.0219180	+	0.200231i
$647$	−8.98771			−0.353344			−0.176672	−	0.984270i	$-0.556533\pi$
$647$	−8.98771			−0.353344			−0.176672	+	0.984270i	$0.556533\pi$
$648$	−28.1099	+	9.53702i	−1.10426	+	0.374649i
$649$			11.8309i			0.464402i
$650$	−0.744335	−	6.79982i	−0.0291952	−	0.266711i
$651$		0			0
$652$	−4.17108	−	18.8240i	−0.163352	−	0.737205i
$653$	18.2791			0.715317			0.357658	−	0.933852i	$-0.383575\pi$
$653$	18.2791			0.715317			0.357658	+	0.933852i	$0.383575\pi$
$654$	−16.8121	+	1.84032i	−0.657406	+	0.0719622i
$655$		−	9.66575i		−	0.377672i
$656$	12.6167	+	27.0718i	0.492601	+	1.05697i
$657$			0.660129i			0.0257541i
$658$		0			0
$659$		−	36.9643i		−	1.43992i	−0.694014	−	0.719962i	$-0.744159\pi$
$659$		−	36.9643i		−	1.43992i	0.694014	−	0.719962i	$-0.255841\pi$
$660$	−7.07493	+	1.56768i	−0.275391	+	0.0610219i
$661$		−	23.0087i		−	0.894933i	−0.894301	−	0.447466i	$-0.852326\pi$
$661$		−	23.0087i		−	0.894933i	0.894301	−	0.447466i	$-0.147674\pi$
$662$	−3.73677	−	34.1370i	−0.145234	−	1.32677i
$663$	37.2675			1.44735
$664$	42.3271	−	14.3606i	1.64261	−	0.557298i
$665$		0			0
$666$	−44.2682	+	4.84576i	−1.71536	+	0.187769i
$667$		−	4.49560i		−	0.174070i
$668$	−9.66314	+	2.14118i	−0.373878	+	0.0828449i
$669$	−57.4195			−2.21997
$670$	−14.8391	+	1.62435i	−0.573285	+	0.0627540i
$671$	−11.4871			−0.443453
$672$		0			0
$673$	−42.0925			−1.62255			−0.811273	−	0.584668i	$-0.801225\pi$
$673$	−42.0925			−1.62255			−0.811273	+	0.584668i	$0.801225\pi$
$674$	−27.7054	+	3.03274i	−1.06717	+	0.116817i
$675$	−9.57500			−0.368542
$676$	−20.2993	+	4.49797i	−0.780741	+	0.172999i
$677$		−	24.3252i		−	0.934894i	−0.884021	−	0.467447i	$-0.845174\pi$
$677$		−	24.3252i		−	0.934894i	0.884021	−	0.467447i	$-0.154826\pi$
$678$	−11.4133	+	1.24934i	−0.438325	+	0.0479807i
$679$		0			0
$680$	−6.81752	+	2.31302i	−0.261440	+	0.0887002i
$681$	2.82866			0.108394
$682$	1.22280	+	11.1709i	0.0468236	+	0.427754i
$683$		−	19.1971i		−	0.734555i	−0.930111	−	0.367278i	$-0.880290\pi$
$683$		−	19.1971i		−	0.734555i	0.930111	−	0.367278i	$-0.119710\pi$
$684$	−17.1160	+	3.79261i	−0.654447	+	0.145014i
$685$		−	4.27568i		−	0.163365i
$686$		0			0
$687$			39.5963i			1.51069i
$688$	−2.33519	−	5.01063i	−0.0890284	−	0.191028i
$689$		−	16.2617i		−	0.619520i
$690$	24.7096	−	2.70481i	0.940679	−	0.102970i
$691$	14.0055			0.532794			0.266397	−	0.963863i	$-0.414167\pi$
$691$	14.0055			0.532794			0.266397	+	0.963863i	$0.414167\pi$
$692$	2.99871	+	13.5331i	0.113994	+	0.514453i
$693$		0			0
$694$	−1.29834	−	11.8609i	−0.0492842	−	0.450233i
$695$			7.53742i			0.285911i
$696$	−6.27741	+	2.12977i	−0.237945	+	0.0807288i
$697$	−19.0054			−0.719882
$698$	3.62839	+	33.1469i	0.137337	+	1.25463i
$699$	−47.2271			−1.78629
$700$		0			0
$701$	11.9124			0.449923			0.224962	−	0.974368i	$-0.427774\pi$
$701$	11.9124			0.449923			0.224962	+	0.974368i	$0.427774\pi$
$702$	7.12700	+	65.1083i	0.268991	+	2.45736i
$703$	−7.26676			−0.274071
$704$	−5.82685	−	7.59874i	−0.219608	−	0.286388i
$705$		−	3.24155i		−	0.122084i
$706$	3.18120	+	29.0616i	0.119726	+	1.09375i
$707$		0			0
$708$	−58.4227	+	12.9455i	−2.19566	+	0.486520i
$709$	47.2981			1.77632			0.888158	−	0.459538i	$-0.151985\pi$
$709$	47.2981			1.77632			0.888158	+	0.459538i	$0.151985\pi$
$710$	−22.9538	+	2.51261i	−0.861441	+	0.0942966i
$711$			66.3698i			2.48906i
$712$	−3.58159	−	10.5566i	−0.134226	−	0.395625i
$713$		−	38.5474i		−	1.44361i
$714$		0			0
$715$			5.78958i			0.216518i
$716$	9.13467	+	41.2247i	0.341379	+	1.54064i
$717$			42.7806i			1.59767i
$718$	4.22447	+	38.5924i	0.157656	+	1.44025i
$719$	1.77790			0.0663045			0.0331523	−	0.999450i	$-0.489445\pi$
$719$	1.77790			0.0663045			0.0331523	+	0.999450i	$0.489445\pi$
$720$	−10.4138	−	22.3450i	−0.388101	−	0.832749i
$721$		0			0
$722$	23.8668	−	2.61255i	0.888230	−	0.0972290i
$723$			65.3336i			2.42978i
$724$	2.64119	+	11.9196i	0.0981590	+	0.442990i
$725$	−0.774233			−0.0287543
$726$	−40.7136	+	4.45667i	−1.51102	+	0.165402i
$727$	−27.1619			−1.00738			−0.503689	−	0.863885i	$-0.668024\pi$
$727$	−27.1619			−1.00738			−0.503689	+	0.863885i	$0.668024\pi$
$728$		0			0
$729$	−22.2718			−0.824883
$730$	−0.150576	+	0.0164826i	−0.00557307	+	0.000610050i
$731$	3.51765			0.130105
$732$	−12.5693	−	56.7250i	−0.464574	−	2.09662i
$733$		−	22.7760i		−	0.841249i	−0.907235	−	0.420625i	$-0.861811\pi$
$733$		−	22.7760i		−	0.841249i	0.907235	−	0.420625i	$-0.138189\pi$
$734$	−28.1763	+	3.08428i	−1.04001	+	0.113843i
$735$		0			0
$736$	17.0324	+	28.0855i	0.627824	+	1.03525i
$737$	12.6345			0.465398
$738$	−7.08171	−	64.6945i	−0.260681	−	2.38144i
$739$		−	32.5176i		−	1.19618i	−0.801429	−	0.598091i	$-0.795926\pi$
$739$		−	32.5176i		−	1.19618i	0.801429	−	0.598091i	$-0.204074\pi$
$740$	−2.21065	−	9.97662i	−0.0812650	−	0.366748i
$741$			20.8243i			0.764999i
$742$		0			0
$743$		−	9.19402i		−	0.337296i	−0.985676	−	0.168648i	$-0.946060\pi$
$743$		−	9.19402i		−	0.337296i	0.985676	−	0.168648i	$-0.0539401\pi$
$744$	−53.8255	+	18.2617i	−1.97334	+	0.669506i
$745$			2.85765i			0.104696i
$746$	−28.9474	+	3.16869i	−1.05984	+	0.116014i
$747$	−97.3942			−3.56347
$748$	5.94894	−	1.31818i	0.217515	−	0.0481975i
$749$		0			0
$750$	−0.465823	−	4.25550i	−0.0170095	−	0.155389i
$751$		−	20.3056i		−	0.740962i	−0.928840	−	0.370481i	$-0.879193\pi$
$751$		−	20.3056i		−	0.740962i	0.928840	−	0.370481i	$-0.120807\pi$
$752$	3.88249	−	1.80942i	0.141580	−	0.0659829i
$753$	3.16207			0.115232
$754$	0.576289	+	5.26465i	0.0209872	+	0.191727i
$755$	6.60903			0.240527
$756$		0			0
$757$	10.9555			0.398184			0.199092	−	0.979981i	$-0.436201\pi$
$757$	10.9555			0.398184			0.199092	+	0.979981i	$0.436201\pi$
$758$	−0.502190	−	4.58772i	−0.0182404	−	0.166634i
$759$	−21.0385			−0.763651
$760$	−1.29246	−	3.80948i	−0.0468826	−	0.138184i
$761$			31.4198i			1.13897i	0.822003	+	0.569484i	$0.192857\pi$
$761$			31.4198i			1.13897i	−0.822003	+	0.569484i	$0.807143\pi$
$762$	−0.997022	−	9.10823i	−0.0361183	−	0.329957i
$763$		0			0
$764$	1.60659	+	7.25052i	0.0581243	+	0.262314i
$765$	15.6870			0.567166
$766$	47.4478	−	5.19382i	1.71436	−	0.187660i
$767$			47.8087i			1.72627i
$768$	31.1480	−	37.0886i	1.12396	−	1.33832i
$769$			23.9511i			0.863700i	0.901945	+	0.431850i	$0.142139\pi$
$769$			23.9511i			0.863700i	−0.901945	+	0.431850i	$0.857861\pi$
$770$		0			0
$771$		−	14.8444i		−	0.534606i
$772$	29.9357	−	6.63323i	1.07741	−	0.238735i
$773$		−	15.1850i		−	0.546165i	−0.961991	−	0.273083i	$-0.911957\pi$
$773$		−	15.1850i		−	0.546165i	0.961991	−	0.273083i	$-0.0880433\pi$
$774$	1.31073	+	11.9741i	0.0471133	+	0.430401i
$775$	−6.63865			−0.238467
$776$	7.91864	+	23.3398i	0.284263	+	0.837851i
$777$		0			0
$778$	5.07793	−	0.555850i	0.182053	−	0.0199282i
$779$		−	10.6198i		−	0.380494i
$780$	−28.5899	+	6.33503i	−1.02368	+	0.226830i
$781$	19.5436			0.699324
$782$	−20.7770	+	2.27433i	−0.742986	+	0.0813300i
$783$	7.41329			0.264929
$784$		0			0
$785$	−15.5831			−0.556185
$786$	−41.1326	+	4.50253i	−1.46715	+	0.160600i
$787$	18.2996			0.652312			0.326156	−	0.945316i	$-0.394247\pi$
$787$	18.2996			0.652312			0.326156	+	0.945316i	$0.394247\pi$
$788$	−47.7620	+	10.5832i	−1.70145	+	0.377012i
$789$		−	23.6001i		−	0.840187i
$790$	−15.1390	+	1.65717i	−0.538622	+	0.0589596i
$791$		0			0
$792$	6.70376	+	19.7590i	0.238208	+	0.702107i
$793$	−46.4194			−1.64840
$794$	−1.15064	−	10.5116i	−0.0408348	−	0.373044i
$795$		−	10.1769i		−	0.360939i
$796$	25.1231	−	5.56683i	0.890463	−	0.197311i
$797$		−	15.0960i		−	0.534728i	−0.963596	−	0.267364i	$-0.913847\pi$
$797$		−	15.0960i		−	0.534728i	0.963596	−	0.267364i	$-0.0861526\pi$
$798$		0			0
$799$			2.72566i			0.0964268i
$800$	4.83689	−	2.93333i	0.171010	−	0.103709i
$801$			24.2906i			0.858266i
$802$	13.4210	−	1.46911i	0.473911	−	0.0518761i
$803$	0.128205			0.00452426
$804$	13.8248	+	62.3912i	0.487563	+	2.20037i
$805$		0			0
$806$	4.94138	+	45.1417i	0.174053	+	1.59005i
$807$		−	63.9085i		−	2.24969i
$808$	2.73116	+	8.04998i	0.0960819	+	0.283197i
$809$	44.4480			1.56271			0.781355	−	0.624087i	$-0.214529\pi$
$809$	44.4480			1.56271			0.781355	+	0.624087i	$0.214529\pi$
$810$	1.61500	+	14.7537i	0.0567453	+	0.518393i
$811$	34.6449			1.21655			0.608274	−	0.793727i	$-0.291862\pi$
$811$	34.6449			1.21655			0.608274	+	0.793727i	$0.291862\pi$
$812$		0			0
$813$	−65.1449			−2.28473
$814$	0.941107	+	8.59743i	0.0329858	+	0.301340i
$815$	−9.64030			−0.337685
$816$	13.0188	+	27.9345i	0.455749	+	0.977902i
$817$			1.96559i			0.0687672i
$818$	−3.33496	−	30.4663i	−0.116604	−	1.06523i
$819$		0			0
$820$	14.5801	−	3.23069i	0.509158	−	0.112821i
$821$	23.7100			0.827484			0.413742	−	0.910394i	$-0.364222\pi$
$821$	23.7100			0.827484			0.413742	+	0.910394i	$0.364222\pi$
$822$	−18.1951	+	1.99171i	−0.634629	+	0.0694688i
$823$			6.49176i			0.226289i	0.993579	+	0.113144i	$0.0360922\pi$
$823$			6.49176i			0.226289i	−0.993579	+	0.113144i	$0.963908\pi$
$824$	1.02518	−	0.347819i	0.0357138	−	0.0121168i
$825$			3.62326i			0.126146i
$826$		0			0
$827$		−	39.4872i		−	1.37310i	−0.727081	−	0.686552i	$-0.759123\pi$
$827$		−	39.4872i		−	1.37310i	0.727081	−	0.686552i	$-0.240877\pi$
$828$	−15.4837	−	69.8777i	−0.538095	−	2.42842i
$829$		−	3.26274i		−	0.113320i	−0.998394	−	0.0566598i	$-0.981955\pi$
$829$		−	3.26274i		−	0.113320i	0.998394	−	0.0566598i	$-0.0180451\pi$
$830$	−2.43182	−	22.2157i	−0.0844096	−	0.771119i
$831$	−15.6422			−0.542621
$832$	−23.5464	−	30.7067i	−0.816325	−	1.06456i
$833$		0			0
$834$	32.0755	−	3.51110i	1.11068	−	0.121580i
$835$			4.94876i			0.171259i
$836$	0.736572	+	3.32414i	0.0254749	+	0.114968i
$837$	63.5651			2.19713
$838$	18.3216	−	2.00555i	0.632909	−	0.0692807i
$839$	−5.39522			−0.186264			−0.0931318	−	0.995654i	$-0.529688\pi$
$839$	−5.39522			−0.186264			−0.0931318	+	0.995654i	$0.529688\pi$
$840$		0			0
$841$	−28.4006			−0.979330
$842$	48.1914	−	5.27521i	1.66078	−	0.181796i
$843$	47.3197			1.62978
$844$	7.32875	+	33.0746i	0.252266	+	1.13847i
$845$			10.3958i			0.357627i
$846$	−9.27814	+	1.01562i	−0.318989	+	0.0349178i
$847$		0			0
$848$	12.1892	−	5.68074i	0.418578	−	0.195077i
$849$	−86.4834			−2.96810
$850$	0.391687	+	3.57823i	0.0134347	+	0.122732i
$851$		−	29.6672i		−	1.01698i
$852$	21.3848	+	96.5094i	0.732632	+	3.30636i
$853$			10.7675i			0.368672i	0.982863	+	0.184336i	$0.0590134\pi$
$853$			10.7675i			0.368672i	−0.982863	+	0.184336i	$0.940987\pi$
$854$		0			0
$855$			8.76558i			0.299776i
$856$	0.765585	+	2.25653i	0.0261672	+	0.0771265i
$857$		−	35.1897i		−	1.20206i	−0.799227	−	0.601029i	$-0.794758\pi$
$857$		−	35.1897i		−	1.20206i	0.799227	−	0.601029i	$-0.205242\pi$
$858$	24.6376	−	2.69692i	0.841112	−	0.0920714i
$859$	−41.2385			−1.40704			−0.703520	−	0.710675i	$-0.748390\pi$
$859$	−41.2385			−1.40704			−0.703520	+	0.710675i	$0.748390\pi$
$860$	−2.69858	+	0.597958i	−0.0920208	+	0.0203902i
$861$		0			0
$862$	0.438960	+	4.01010i	0.0149510	+	0.136584i
$863$		−	23.0295i		−	0.783933i	−0.919980	−	0.391966i	$-0.871795\pi$
$863$		−	23.0295i		−	0.783933i	0.919980	−	0.391966i	$-0.128205\pi$
$864$	−46.3133	+	28.0867i	−1.57561	+	0.955528i
$865$	6.93069			0.235651
$866$	−5.32721	−	48.6664i	−0.181026	−	1.65375i
$867$	31.8491			1.08165
$868$		0			0
$869$	12.8898			0.437258
$870$	0.360656	+	3.29475i	0.0122274	+	0.111702i
$871$	51.0562			1.72997
$872$	−10.5818	+	3.59014i	−0.358344	+	0.121578i
$873$		−	53.7047i		−	1.81763i
$874$	−1.27085	−	11.6098i	−0.0429871	−	0.392706i
$875$		0			0
$876$	0.140284	+	0.633098i	0.00473974	+	0.0213904i
$877$	4.06272			0.137188			0.0685941	−	0.997645i	$-0.478149\pi$
$877$	4.06272			0.137188			0.0685941	+	0.997645i	$0.478149\pi$
$878$	15.3770	−	1.68322i	0.518947	−	0.0568059i
$879$		−	1.98931i		−	0.0670978i
$880$	−4.33967	+	2.02250i	−0.146290	+	0.0681783i
$881$			42.0606i			1.41706i	0.705682	+	0.708529i	$0.250641\pi$
$881$			42.0606i			1.41706i	−0.705682	+	0.708529i	$0.749359\pi$
$882$		0			0
$883$			54.8918i			1.84725i	0.383291	+	0.923627i	$0.374790\pi$
$883$			54.8918i			1.84725i	−0.383291	+	0.923627i	$0.625210\pi$
$884$	24.0398	−	5.32680i	0.808546	−	0.179160i
$885$			29.9199i			1.00575i
$886$	−5.44666	−	49.7577i	−0.182984	−	1.67164i
$887$	38.1245			1.28009			0.640047	−	0.768336i	$-0.278915\pi$
$887$	38.1245			1.28009			0.640047	+	0.768336i	$0.278915\pi$
$888$	−41.4257	+	14.0547i	−1.39016	+	0.471646i
$889$		0			0
$890$	−5.54071	+	0.606507i	−0.185725	+	0.0203302i
$891$		−	12.5618i		−	0.420836i
$892$	−37.0390	+	8.20720i	−1.24016	+	0.274798i
$893$	−1.52304			−0.0509665
$894$	12.1607	−	1.33116i	0.406715	−	0.0445206i
$895$	21.1123			0.705706
$896$		0			0
$897$	−85.0171			−2.83864
$898$	−39.3669	+	4.30925i	−1.31369	+	0.143801i
$899$	5.13987			0.171424
$900$	−12.0344	+	2.66661i	−0.401145	+	0.0888869i
$901$			8.55727i			0.285084i
$902$	−12.5645	+	1.37536i	−0.418351	+	0.0457943i
$903$		0			0
$904$	−7.18369	+	2.43725i	−0.238926	+	0.0810617i
$905$	6.10438			0.202917
$906$	−3.07864	−	28.1247i	−0.102281	−	0.934381i
$907$		−	0.354708i		−	0.0117779i	−0.999983	−	0.00588894i	$-0.998125\pi$
$907$		−	0.354708i		−	0.0117779i	0.999983	−	0.00588894i	$-0.00187452\pi$
$908$	1.82465	−	0.404312i	0.0605533	−	0.0134176i
$909$		−	18.5229i		−	0.614366i
$910$		0			0
$911$			12.2958i			0.407379i	0.979036	+	0.203690i	$0.0652934\pi$
$911$			12.2958i			0.407379i	−0.979036	+	0.203690i	$0.934707\pi$
$912$	−15.6092	+	7.27462i	−0.516872	+	0.240887i
$913$			18.9152i			0.626001i
$914$	−28.3832	+	3.10693i	−0.938831	+	0.102768i
$915$	−29.0504			−0.960378
$916$	5.65967	+	25.5420i	0.187001	+	0.843932i
$917$		0			0
$918$	−3.75040	−	34.2616i	−0.123782	−	1.13080i
$919$			0.280729i			0.00926038i	0.999989	+	0.00463019i	$0.00147384\pi$
$919$			0.280729i			0.00926038i	−0.999989	+	0.00463019i	$0.998526\pi$
$920$	15.5526	−	5.27661i	0.512753	−	0.173965i
$921$	−14.7734			−0.486799
$922$	−0.0196735	−	0.179727i	−0.000647914	−	0.00591898i
$923$	78.9760			2.59953
$924$		0			0
$925$	−5.10930			−0.167993
$926$	−2.74926	−	25.1157i	−0.0903462	−	0.825352i
$927$	−2.35893			−0.0774774
$928$	−3.74489	+	2.27109i	−0.122932	+	0.0745520i
$929$		−	32.4836i		−	1.06575i	−0.846194	−	0.532875i	$-0.821111\pi$
$929$		−	32.4836i		−	1.06575i	0.846194	−	0.532875i	$-0.178889\pi$
$930$	3.09244	+	28.2508i	0.101405	+	0.926379i
$931$		0			0
$932$	−30.4643	+	6.75036i	−0.997891	+	0.221115i
$933$	36.0124			1.17899
$934$	−20.6227	+	2.25744i	−0.674795	+	0.0738656i
$935$		−	3.04662i		−	0.0996350i
$936$	27.0900	+	79.8467i	0.885466	+	2.60987i
$937$			59.7020i			1.95038i	0.221368	+	0.975190i	$0.428948\pi$
$937$			59.7020i			1.95038i	−0.221368	+	0.975190i	$0.571052\pi$
$938$		0			0
$939$		−	80.5424i		−	2.62840i
$940$	−0.463328	−	2.09099i	−0.0151121	−	0.0682007i
$941$			14.2458i			0.464401i	0.972668	+	0.232201i	$0.0745926\pi$
$941$			14.2458i			0.464401i	−0.972668	+	0.232201i	$0.925407\pi$
$942$	7.25897	+	66.3139i	0.236510	+	2.16062i
$943$	43.3564			1.41188
$944$	−35.8358	+	16.7012i	−1.16636	+	0.543578i
$945$		0			0
$946$	2.32552	−	0.254560i	0.0756092	−	0.00827647i
$947$		−	30.1026i		−	0.978202i	−0.872227	−	0.489101i	$-0.837325\pi$
$947$		−	30.1026i		−	0.978202i	0.872227	−	0.489101i	$-0.162675\pi$
$948$	14.1042	+	63.6521i	0.458083	+	2.06732i
$949$	0.518080			0.0168176
$950$	−1.99944	+	0.218866i	−0.0648703	+	0.00710095i
$951$	−80.0831			−2.59687
$952$		0			0
$953$	3.58515			0.116134			0.0580672	−	0.998313i	$-0.481506\pi$
$953$	3.58515			0.116134			0.0580672	+	0.998313i	$0.481506\pi$
$954$	−29.1290	+	3.18857i	−0.943086	+	0.103234i
$955$	3.71319			0.120156
$956$	6.11480	+	27.5960i	0.197767	+	0.892519i
$957$		−	2.80525i		−	0.0906809i
$958$	−36.7640	+	4.02433i	−1.18779	+	0.130020i
$959$		0			0
$960$	−14.7359	−	19.2170i	−0.475600	−	0.620225i
$961$	13.0717			0.421668
$962$	3.80303	+	34.7424i	0.122615	+	1.12014i
$963$		−	5.19225i		−	0.167318i
$964$	9.33840	+	42.1441i	0.300770	+	1.35737i
$965$		−	15.3309i		−	0.493519i
$966$		0			0
$967$		−	46.1614i		−	1.48445i	−0.670150	−	0.742226i	$-0.733770\pi$
$967$		−	46.1614i		−	1.48445i	0.670150	−	0.742226i	$-0.266230\pi$
$968$	−25.6257	+	8.69418i	−0.823641	+	0.279441i
$969$		−	10.9582i		−	0.352029i
$970$	12.2501	−	1.34094i	0.393327	−	0.0430551i
$971$	11.6623			0.374260			0.187130	−	0.982335i	$-0.440081\pi$
$971$	11.6623			0.374260			0.187130	+	0.982335i	$0.440081\pi$
$972$	5.94261	−	1.31678i	0.190609	−	0.0422357i
$973$		0			0
$974$	−2.55828	−	23.3710i	−0.0819727	−	0.748856i
$975$			14.6417i			0.468909i
$976$	−16.2159	−	34.7944i	−0.519057	−	1.11374i
$977$	−42.4830			−1.35915			−0.679575	−	0.733606i	$-0.737836\pi$
$977$	−42.4830			−1.35915			−0.679575	+	0.733606i	$0.737836\pi$
$978$	4.49067	+	41.0243i	0.143596	+	1.31181i
$979$	4.71754			0.150773
$980$		0			0
$981$	24.3486			0.777390
$982$	−3.37155	−	30.8006i	−0.107591	−	0.982887i
$983$	31.7431			1.01245			0.506223	−	0.862402i	$-0.331041\pi$
$983$	31.7431			1.01245			0.506223	+	0.862402i	$0.331041\pi$
$984$	−20.5399	−	60.5405i	−0.654789	−	1.92996i
$985$			24.4602i			0.779368i
$986$	−0.303257	−	2.77039i	−0.00965767	−	0.0882270i
$987$		0			0
$988$	2.97650	+	13.4329i	0.0946951	+	0.427358i
$989$	−8.02470			−0.255171
$990$	10.3707	−	1.13522i	0.329602	−	0.0360795i
$991$		−	29.3504i		−	0.932347i	−0.884693	−	0.466173i	$-0.845632\pi$
$991$		−	29.3504i		−	0.932347i	0.884693	−	0.466173i	$-0.154368\pi$
$992$	−32.1105	+	19.4734i	−1.01951	+	0.618281i
$993$			73.5053i			2.33262i
$994$		0			0
$995$		−	12.8662i		−	0.407886i
$996$	−93.4062	+	20.6972i	−2.95969	+	0.655816i
$997$			10.8068i			0.342256i	0.985249	+	0.171128i	$0.0547411\pi$
$997$			10.8068i			0.342256i	−0.985249	+	0.171128i	$0.945259\pi$
$998$	6.26147	+	57.2012i	0.198203	+	1.81067i
$999$	48.9216			1.54781

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.g.a.391.4		32
4.3	odd	2	inner	980.2.g.a.391.1		32
7.2	even	3		980.2.o.f.31.11		32
7.3	odd	6		980.2.o.f.411.10		32
7.4	even	3		140.2.o.a.131.10	yes	32
7.5	odd	6		140.2.o.a.31.11	yes	32
7.6	odd	2	inner	980.2.g.a.391.3		32
28.3	even	6		980.2.o.f.411.11		32
28.11	odd	6		140.2.o.a.131.11	yes	32
28.19	even	6		140.2.o.a.31.10	✓	32
28.23	odd	6		980.2.o.f.31.10		32
28.27	even	2	inner	980.2.g.a.391.2		32
35.4	even	6		700.2.p.c.551.7		32
35.12	even	12		700.2.t.d.199.4		32
35.18	odd	12		700.2.t.d.299.3		32
35.19	odd	6		700.2.p.c.451.6		32
35.32	odd	12		700.2.t.c.299.14		32
35.33	even	12		700.2.t.c.199.13		32
140.19	even	6		700.2.p.c.451.7		32
140.39	odd	6		700.2.p.c.551.6		32
140.47	odd	12		700.2.t.d.199.3		32
140.67	even	12		700.2.t.c.299.13		32
140.103	odd	12		700.2.t.c.199.14		32
140.123	even	12		700.2.t.d.299.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.10	✓	32	28.19	even	6
140.2.o.a.31.11	yes	32	7.5	odd	6
140.2.o.a.131.10	yes	32	7.4	even	3
140.2.o.a.131.11	yes	32	28.11	odd	6
700.2.p.c.451.6		32	35.19	odd	6
700.2.p.c.451.7		32	140.19	even	6
700.2.p.c.551.6		32	140.39	odd	6
700.2.p.c.551.7		32	35.4	even	6
700.2.t.c.199.13		32	35.33	even	12
700.2.t.c.199.14		32	140.103	odd	12
700.2.t.c.299.13		32	140.67	even	12
700.2.t.c.299.14		32	35.32	odd	12
700.2.t.d.199.3		32	140.47	odd	12
700.2.t.d.199.4		32	35.12	even	12
700.2.t.d.299.3		32	35.18	odd	12
700.2.t.d.299.4		32	140.123	even	12
980.2.g.a.391.1		32	4.3	odd	2	inner
980.2.g.a.391.2		32	28.27	even	2	inner
980.2.g.a.391.3		32	7.6	odd	2	inner
980.2.g.a.391.4		32	1.1	even	1	trivial
980.2.o.f.31.10		32	28.23	odd	6
980.2.o.f.31.11		32	7.2	even	3
980.2.o.f.411.10		32	7.3	odd	6
980.2.o.f.411.11		32	28.3	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40582 + 0.153886i) q^{2} +3.02707 q^{3} +(1.95264 - 0.432671i) q^{4} -1.00000i q^{5} +(-4.25550 + 0.465823i) q^{6} +(-2.67847 + 0.908739i) q^{8} +6.16313 q^{9} +O(q^{10})\)	\(q+(-1.40582 + 0.153886i) q^{2} +3.02707 q^{3} +(1.95264 - 0.432671i) q^{4} -1.00000i q^{5} +(-4.25550 + 0.465823i) q^{6} +(-2.67847 + 0.908739i) q^{8} +6.16313 q^{9} +(0.153886 + 1.40582i) q^{10} -1.19696i q^{11} +(5.91077 - 1.30972i) q^{12} -4.83692i q^{13} -3.02707i q^{15} +(3.62559 - 1.68970i) q^{16} +2.54530i q^{17} +(-8.66423 + 0.948419i) q^{18} -1.42226 q^{19} +(-0.432671 - 1.95264i) q^{20} +(0.184195 + 1.68270i) q^{22} -5.80651i q^{23} +(-8.10790 + 2.75081i) q^{24} -1.00000 q^{25} +(0.744335 + 6.79982i) q^{26} +9.57500 q^{27} +0.774233 q^{29} +(0.465823 + 4.25550i) q^{30} +6.63865 q^{31} +(-4.83689 + 2.93333i) q^{32} -3.62326i q^{33} +(-0.391687 - 3.57823i) q^{34} +(12.0344 - 2.66661i) q^{36} +5.10930 q^{37} +(1.99944 - 0.218866i) q^{38} -14.6417i q^{39} +(0.908739 + 2.67847i) q^{40} +7.46685i q^{41} -1.38202i q^{43} +(-0.517888 - 2.33722i) q^{44} -6.16313i q^{45} +(0.893541 + 8.16289i) q^{46} +1.07086 q^{47} +(10.9749 - 5.11483i) q^{48} +(1.40582 - 0.153886i) q^{50} +7.70480i q^{51} +(-2.09280 - 9.44476i) q^{52} +3.36198 q^{53} +(-13.4607 + 1.47346i) q^{54} -1.19696 q^{55} -4.30528 q^{57} +(-1.08843 + 0.119144i) q^{58} -9.88412 q^{59} +(-1.30972 - 5.91077i) q^{60} -9.59690i q^{61} +(-9.33272 + 1.02160i) q^{62} +(6.34839 - 4.86806i) q^{64} -4.83692 q^{65} +(0.557570 + 5.09364i) q^{66} +10.5555i q^{67} +(1.10128 + 4.97006i) q^{68} -17.5767i q^{69} +16.3277i q^{71} +(-16.5077 + 5.60068i) q^{72} +0.107109i q^{73} +(-7.18274 + 0.786250i) q^{74} -3.02707 q^{75} +(-2.77716 + 0.615371i) q^{76} +(2.25315 + 20.5835i) q^{78} +10.7688i q^{79} +(-1.68970 - 3.62559i) q^{80} +10.4948 q^{81} +(-1.14904 - 10.4970i) q^{82} -15.8027 q^{83} +2.54530 q^{85} +(0.212673 + 1.94286i) q^{86} +2.34366 q^{87} +(1.08772 + 3.20601i) q^{88} +3.94128i q^{89} +(0.948419 + 8.66423i) q^{90} +(-2.51231 - 11.3380i) q^{92} +20.0956 q^{93} +(-1.50543 + 0.164790i) q^{94} +1.42226i q^{95} +(-14.6416 + 8.87940i) q^{96} -8.71387i q^{97} -7.37699i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9	\( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9} + 28 q^{16} - 8 q^{22} - 32 q^{25} - 40 q^{29} - 4 q^{32} + 60 q^{36} - 16 q^{37} + 36 q^{44} - 4 q^{46} + 4 q^{50} + 16 q^{53} + 48 q^{57} - 4 q^{58} - 28 q^{60} + 4 q^{64} - 8 q^{65} - 8 q^{72} - 76 q^{74} + 120 q^{78} + 72 q^{81} - 56 q^{86} - 8 q^{88} - 4 q^{92} + 16 q^{93}+O(q^{100}) \) 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9 + 28 * q^16 - 8 * q^22 - 32 * q^25 - 40 * q^29 - 4 * q^32 + 60 * q^36 - 16 * q^37 + 36 * q^44 - 4 * q^46 + 4 * q^50 + 16 * q^53 + 48 * q^57 - 4 * q^58 - 28 * q^60 + 4 * q^64 - 8 * q^65 - 8 * q^72 - 76 * q^74 + 120 * q^78 + 72 * q^81 - 56 * q^86 - 8 * q^88 - 4 * q^92 + 16 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more