LMFDB - Embedded newform 275.2.bm.b.118.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(7,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 14]))

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

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

chi := DirichletCharacter("275.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.bm (of order $20$, 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:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			118.2
Character	$\chi$	$=$	275.118
Dual form			275.2.bm.b.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.482327 - 0.0763931i) q^{2} +(-0.517260 + 1.01518i) q^{3} +(-1.67531 - 0.544341i) q^{4} +(0.327041 - 0.450133i) q^{6} +(2.59854 - 1.32402i) q^{7} +(1.63669 + 0.833936i) q^{8} +(1.00032 + 1.37683i) q^{9} +(-3.15977 + 1.00788i) q^{11} +(1.41917 - 1.41917i) q^{12} +(-0.457808 + 2.89049i) q^{13} +(-1.35449 + 0.440102i) q^{14} +(2.12449 + 1.54353i) q^{16} +(0.824113 + 5.20325i) q^{17} +(-0.377304 - 0.740500i) q^{18} +(1.26677 + 3.89873i) q^{19} +3.32285i q^{21} +(1.60104 - 0.244743i) q^{22} +(2.12046 + 2.12046i) q^{23} +(-1.69319 + 1.23017i) q^{24} +(0.441627 - 1.35919i) q^{26} +(-5.29116 + 0.838037i) q^{27} +(-5.07408 + 0.803656i) q^{28} +(0.817241 - 2.51521i) q^{29} +(5.45328 - 3.96204i) q^{31} +(-3.50456 - 3.50456i) q^{32} +(0.611244 - 3.72907i) q^{33} -2.57262i q^{34} +(-0.926389 - 2.85113i) q^{36} +(0.528116 + 1.03649i) q^{37} +(-0.313163 - 1.97724i) q^{38} +(-2.69755 - 1.95989i) q^{39} +(-3.38136 + 1.09867i) q^{41} +(0.253843 - 1.60270i) q^{42} +(5.07292 - 5.07292i) q^{43} +(5.84223 + 0.0314826i) q^{44} +(-0.860769 - 1.18475i) q^{46} +(3.28041 + 1.67145i) q^{47} +(-2.66588 + 1.35833i) q^{48} +(0.884888 - 1.21794i) q^{49} +(-5.70851 - 1.85481i) q^{51} +(2.34038 - 4.59325i) q^{52} +(1.45955 + 0.231169i) q^{53} +2.61609 q^{54} +5.35716 q^{56} +(-4.61316 - 0.730652i) q^{57} +(-0.586323 + 1.15072i) q^{58} +(-1.52672 - 0.496061i) q^{59} +(-4.07810 + 5.61302i) q^{61} +(-2.93294 + 1.49441i) q^{62} +(4.42234 + 2.25330i) q^{63} +(-1.66445 - 2.29092i) q^{64} +(-0.579695 + 1.75194i) q^{66} +(-1.31471 + 1.31471i) q^{67} +(1.45170 - 9.16564i) q^{68} +(-3.24948 + 1.05582i) q^{69} +(-2.32441 - 1.68878i) q^{71} +(0.489036 + 3.08765i) q^{72} +(-6.71992 - 13.1886i) q^{73} +(-0.175544 - 0.540270i) q^{74} -7.22113i q^{76} +(-6.87635 + 6.80264i) q^{77} +(1.15138 + 1.15138i) q^{78} +(12.3342 - 8.96129i) q^{79} +(0.308439 - 0.949277i) q^{81} +(1.71486 - 0.271606i) q^{82} +(-6.60041 + 1.04540i) q^{83} +(1.80876 - 5.56680i) q^{84} +(-2.83434 + 2.05927i) q^{86} +(2.13066 + 2.13066i) q^{87} +(-6.01208 - 0.985459i) q^{88} +11.1726i q^{89} +(2.63744 + 8.11720i) q^{91} +(-2.39818 - 4.70669i) q^{92} +(1.20142 + 7.58545i) q^{93} +(-1.45454 - 1.05679i) q^{94} +(5.37052 - 1.74499i) q^{96} +(1.57505 - 9.94447i) q^{97} +(-0.519848 + 0.519848i) q^{98} +(-4.54848 - 3.34226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 10 q^{2} + 4 q^{3} - 20 q^{6} + 10 q^{8} - 24 q^{11} - 12 q^{12} + 10 q^{13} - 8 q^{16} + 10 q^{18} - 10 q^{22} + 24 q^{23} + 20 q^{26} + 16 q^{27} - 50 q^{28} - 28 q^{31} - 66 q^{33} + 24 q^{36}+ \cdots + 8 q^{97}+O(q^{100}) $ 32 * q + 10 * q^2 + 4 * q^3 - 20 * q^6 + 10 * q^8 - 24 * q^11 - 12 * q^12 + 10 * q^13 - 8 * q^16 + 10 * q^18 - 10 * q^22 + 24 * q^23 + 20 * q^26 + 16 * q^27 - 50 * q^28 - 28 * q^31 - 66 * q^33 + 24 * q^36 + 8 * q^37 - 10 * q^38 + 40 * q^41 + 10 * q^42 + 60 * q^46 + 28 * q^47 + 54 * q^48 + 20 * q^51 + 50 * q^52 + 24 * q^53 - 80 * q^56 - 30 * q^57 + 50 * q^58 - 60 * q^61 - 100 * q^62 + 30 * q^63 - 100 * q^66 + 8 * q^67 + 30 * q^68 + 24 * q^71 - 80 * q^72 - 50 * q^73 - 70 * q^77 - 60 * q^78 - 12 * q^81 + 10 * q^82 - 90 * q^83 + 100 * q^86 - 170 * q^88 + 20 * q^91 + 68 * q^92 + 8 * q^93 + 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.482327	−	0.0763931i	−0.341057	−	0.0540181i	−0.0164432	−	0.999865i	$-0.505234\pi$
$2$	−0.482327	−	0.0763931i	−0.341057	−	0.0540181i	−0.324614	+	0.945847i	$0.605234\pi$
$3$	−0.517260	+	1.01518i	−0.298640	+	0.586114i	−0.990753	−	0.135675i	$-0.956680\pi$
$3$	−0.517260	+	1.01518i	−0.298640	+	0.586114i	0.692114	+	0.721789i	$0.256680\pi$
$4$	−1.67531	−	0.544341i	−0.837655	−	0.272170i
$5$		0			0
$5$		0			0
$6$	0.327041	−	0.450133i	0.133514	−	0.183766i
$7$	2.59854	−	1.32402i	0.982157	−	0.500434i	0.112266	−	0.993678i	$-0.464189\pi$
$7$	2.59854	−	1.32402i	0.982157	−	0.500434i	0.869891	+	0.493244i	$0.164189\pi$
$8$	1.63669	+	0.833936i	0.578658	+	0.294841i
$9$	1.00032	+	1.37683i	0.333442	+	0.458943i
$10$		0			0
$11$	−3.15977	+	1.00788i	−0.952708	+	0.303888i
$11$	−3.15977	+	1.00788i	−0.952708	+	0.303888i
$12$	1.41917	−	1.41917i	0.409680	−	0.409680i
$13$	−0.457808	+	2.89049i	−0.126973	+	0.801677i	0.839208	+	0.543811i	$0.183019\pi$
$13$	−0.457808	+	2.89049i	−0.126973	+	0.801677i	−0.966181	+	0.257866i	$0.916981\pi$
$14$	−1.35449	+	0.440102i	−0.362004	+	0.117622i
$15$		0			0
$16$	2.12449	+	1.54353i	0.531123	+	0.385884i
$17$	0.824113	+	5.20325i	0.199877	+	1.26197i	0.859797	+	0.510636i	$0.170590\pi$
$17$	0.824113	+	5.20325i	0.199877	+	1.26197i	−0.659920	+	0.751336i	$0.729410\pi$
$18$	−0.377304	−	0.740500i	−0.0889313	−	0.174538i
$19$	1.26677	+	3.89873i	0.290618	+	0.894429i	0.984658	+	0.174494i	$0.0558288\pi$
$19$	1.26677	+	3.89873i	0.290618	+	0.894429i	−0.694041	+	0.719936i	$0.744171\pi$
$20$		0			0
$21$			3.32285i			0.725105i
$22$	1.60104	−	0.244743i	0.341343	−	0.0521795i
$23$	2.12046	+	2.12046i	0.442147	+	0.442147i	0.892733	−	0.450586i	$-0.148785\pi$
$23$	2.12046	+	2.12046i	0.442147	+	0.442147i	−0.450586	+	0.892733i	$0.648785\pi$
$24$	−1.69319	+	1.23017i	−0.345621	+	0.251108i
$25$		0			0
$26$	0.441627	−	1.35919i	0.0866101	−	0.266558i
$27$	−5.29116	+	0.838037i	−1.01828	+	0.161280i
$28$	−5.07408	+	0.803656i	−0.958912	+	0.151877i
$29$	0.817241	−	2.51521i	0.151758	−	0.467063i	−0.846060	−	0.533088i	$-0.821032\pi$
$29$	0.817241	−	2.51521i	0.151758	−	0.467063i	0.997818	+	0.0660248i	$0.0210316\pi$
$30$		0			0
$31$	5.45328	−	3.96204i	0.979438	−	0.711603i	0.0218548	−	0.999761i	$-0.493043\pi$
$31$	5.45328	−	3.96204i	0.979438	−	0.711603i	0.957583	+	0.288158i	$0.0930429\pi$
$32$	−3.50456	−	3.50456i	−0.619524	−	0.619524i
$33$	0.611244	−	3.72907i	0.106404	−	0.649148i
$34$		−	2.57262i		−	0.441201i
$35$		0			0
$36$	−0.926389	−	2.85113i	−0.154398	−	0.475189i
$37$	0.528116	+	1.03649i	0.0868218	+	0.170397i	0.930335	−	0.366712i	$-0.119516\pi$
$37$	0.528116	+	1.03649i	0.0868218	+	0.170397i	−0.843513	+	0.537109i	$0.819516\pi$
$38$	−0.313163	−	1.97724i	−0.0508018	−	0.320750i
$39$	−2.69755	−	1.95989i	−0.431954	−	0.313833i
$40$		0			0
$41$	−3.38136	+	1.09867i	−0.528080	+	0.171584i	−0.560909	−	0.827877i	$-0.689548\pi$
$41$	−3.38136	+	1.09867i	−0.528080	+	0.171584i	0.0328289	+	0.999461i	$0.489548\pi$
$42$	0.253843	−	1.60270i	0.0391688	−	0.247302i
$43$	5.07292	−	5.07292i	0.773613	−	0.773613i	−0.205123	−	0.978736i	$-0.565759\pi$
$43$	5.07292	−	5.07292i	0.773613	−	0.773613i	0.978736	+	0.205123i	$0.0657595\pi$
$44$	5.84223	+	0.0314826i	0.880749	+	0.00474618i
$45$		0			0
$46$	−0.860769	−	1.18475i	−0.126913	−	0.174681i
$47$	3.28041	+	1.67145i	0.478497	+	0.243806i	0.676566	−	0.736382i	$-0.263467\pi$
$47$	3.28041	+	1.67145i	0.478497	+	0.243806i	−0.198070	+	0.980188i	$0.563467\pi$
$48$	−2.66588	+	1.35833i	−0.384786	+	0.196058i
$49$	0.884888	−	1.21794i	0.126413	−	0.173992i
$50$		0			0
$51$	−5.70851	−	1.85481i	−0.799351	−	0.259725i
$52$	2.34038	−	4.59325i	0.324552	−	0.636970i
$53$	1.45955	+	0.231169i	0.200484	+	0.0317536i	0.255869	−	0.966712i	$-0.417639\pi$
$53$	1.45955	+	0.231169i	0.200484	+	0.0317536i	−0.0553847	+	0.998465i	$0.517639\pi$
$54$	2.61609			0.356005
$55$		0			0
$56$	5.35716			0.715881
$57$	−4.61316	−	0.730652i	−0.611028	−	0.0967773i
$58$	−0.586323	+	1.15072i	−0.0769879	+	0.151097i
$59$	−1.52672	−	0.496061i	−0.198762	−	0.0645817i	0.207944	−	0.978141i	$-0.433323\pi$
$59$	−1.52672	−	0.496061i	−0.198762	−	0.0645817i	−0.406706	+	0.913559i	$0.633323\pi$
$60$		0			0
$61$	−4.07810	+	5.61302i	−0.522147	+	0.718674i	−0.985908	−	0.167286i	$-0.946500\pi$
$61$	−4.07810	+	5.61302i	−0.522147	+	0.718674i	0.463761	+	0.885960i	$0.346500\pi$
$62$	−2.93294	+	1.49441i	−0.372483	+	0.189790i
$63$	4.42234	+	2.25330i	0.557163	+	0.283889i
$64$	−1.66445	−	2.29092i	−0.208056	−	0.286365i
$65$		0			0
$66$	−0.579695	+	1.75194i	−0.0713556	+	0.215649i
$67$	−1.31471	+	1.31471i	−0.160617	+	0.160617i	−0.782840	−	0.622223i	$-0.786230\pi$
$67$	−1.31471	+	1.31471i	−0.160617	+	0.160617i	0.622223	+	0.782840i	$0.286230\pi$
$68$	1.45170	−	9.16564i	0.176044	−	1.11150i
$69$	−3.24948	+	1.05582i	−0.391192	+	0.127106i
$70$		0			0
$71$	−2.32441	−	1.68878i	−0.275857	−	0.200422i	0.441251	−	0.897384i	$-0.354535\pi$
$71$	−2.32441	−	1.68878i	−0.275857	−	0.200422i	−0.717108	+	0.696962i	$0.754535\pi$
$72$	0.489036	+	3.08765i	0.0576334	+	0.363883i
$73$	−6.71992	−	13.1886i	−0.786507	−	1.54361i	−0.838464	−	0.544957i	$-0.816546\pi$
$73$	−6.71992	−	13.1886i	−0.786507	−	1.54361i	0.0519568	−	0.998649i	$-0.483454\pi$
$74$	−0.175544	−	0.540270i	−0.0204066	−	0.0628051i
$75$		0			0
$76$		−	7.22113i		−	0.828321i
$77$	−6.87635	+	6.80264i	−0.783633	+	0.775232i
$78$	1.15138	+	1.15138i	0.130368	+	0.130368i
$79$	12.3342	−	8.96129i	1.38770	−	1.00822i	0.391589	−	0.920140i	$-0.371926\pi$
$79$	12.3342	−	8.96129i	1.38770	−	1.00822i	0.996113	−	0.0880839i	$-0.0280744\pi$
$80$		0			0
$81$	0.308439	−	0.949277i	0.0342710	−	0.105475i
$82$	1.71486	−	0.271606i	0.189374	−	0.0299939i
$83$	−6.60041	+	1.04540i	−0.724489	+	0.114748i	−0.507778	−	0.861488i	$-0.669533\pi$
$83$	−6.60041	+	1.04540i	−0.724489	+	0.114748i	−0.216711	+	0.976236i	$0.569533\pi$
$84$	1.80876	−	5.56680i	0.197352	−	0.607388i
$85$		0			0
$86$	−2.83434	+	2.05927i	−0.305635	+	0.222057i
$87$	2.13066	+	2.13066i	0.228431	+	0.228431i
$88$	−6.01208	−	0.985459i	−0.640890	−	0.105050i
$89$			11.1726i			1.18429i	0.805830	+	0.592147i	$0.201719\pi$
$89$			11.1726i			1.18429i	−0.805830	+	0.592147i	$0.798281\pi$
$90$		0			0
$91$	2.63744	+	8.11720i	0.276479	+	0.850914i
$92$	−2.39818	−	4.70669i	−0.250027	−	0.490706i
$93$	1.20142	+	7.58545i	0.124581	+	0.786575i
$94$	−1.45454	−	1.05679i	−0.150025	−	0.108999i
$95$		0			0
$96$	5.37052	−	1.74499i	0.548126	−	0.178097i
$97$	1.57505	−	9.94447i	0.159922	−	1.00971i	−0.768951	−	0.639308i	$-0.779221\pi$
$97$	1.57505	−	9.94447i	0.159922	−	1.00971i	0.928873	−	0.370400i	$-0.120779\pi$
$98$	−0.519848	+	0.519848i	−0.0525126	+	0.0525126i
$99$	−4.54848	−	3.34226i	−0.457140	−	0.335910i
$100$		0			0
$101$	−1.12216	−	1.54452i	−0.111659	−	0.153686i	0.749530	−	0.661971i	$-0.230280\pi$
$101$	−1.12216	−	1.54452i	−0.111659	−	0.153686i	−0.861189	+	0.508285i	$0.830280\pi$
$102$	2.61167	+	1.33071i	0.258594	+	0.131760i
$103$	5.49869	−	2.80172i	0.541802	−	0.276062i	−0.161597	−	0.986857i	$-0.551665\pi$
$103$	5.49869	−	2.80172i	0.541802	−	0.276062i	0.703399	+	0.710795i	$0.251665\pi$
$104$	−3.15977	+	4.34905i	−0.309841	+	0.426459i
$105$		0			0
$106$	−0.686319	−	0.222999i	−0.0666612	−	0.0216595i
$107$	−0.197726	+	0.388059i	−0.0191149	+	0.0375151i	−0.900367	−	0.435132i	$-0.856702\pi$
$107$	−0.197726	+	0.388059i	−0.0191149	+	0.0375151i	0.881252	+	0.472647i	$0.156702\pi$
$108$	9.32051	+	1.47622i	0.896866	+	0.142050i
$109$	−9.46672			−0.906748			−0.453374	−	0.891320i	$-0.649780\pi$
$109$	−9.46672			−0.906748			−0.453374	+	0.891320i	$0.649780\pi$
$110$		0			0
$111$	−1.32539			−0.125801
$112$	7.56426	+	1.19806i	0.714755	+	0.113206i
$113$	−9.20080	+	18.0576i	−0.865538	+	1.69871i	−0.163539	+	0.986537i	$0.552291\pi$
$113$	−9.20080	+	18.0576i	−0.865538	+	1.69871i	−0.701999	+	0.712178i	$0.747709\pi$
$114$	2.16923	+	0.704827i	0.203167	+	0.0660131i
$115$		0			0
$116$	−2.73826	+	3.76890i	−0.254241	+	0.349933i
$117$	−4.43766	+	2.26110i	−0.410262	+	0.209039i
$118$	0.698483	+	0.355895i	0.0643005	+	0.0327628i
$119$	9.03071	+	12.4297i	0.827844	+	1.13943i
$120$		0			0
$121$	8.96835	−	6.36935i	0.815305	−	0.579032i
$122$	2.39578	−	2.39578i	0.216903	−	0.216903i
$123$	0.633694	−	4.00099i	0.0571383	−	0.360757i
$124$	−11.2926	+	3.66920i	−1.01411	+	0.329504i
$125$		0			0
$126$	−1.96088	−	1.42466i	−0.174689	−	0.126919i
$127$	−1.47513	−	9.31359i	−0.130896	−	0.826447i	−0.962540	−	0.271138i	$-0.912600\pi$
$127$	−1.47513	−	9.31359i	−0.130896	−	0.826447i	0.831644	−	0.555309i	$-0.187400\pi$
$128$	5.12793	+	10.0641i	0.453249	+	0.889551i
$129$	2.52591	+	7.77394i	0.222394	+	0.684457i
$130$		0			0
$131$		−	7.51676i		−	0.656743i	−0.944549	−	0.328371i	$-0.893500\pi$
$131$		−	7.51676i		−	0.656743i	0.944549	−	0.328371i	$-0.106500\pi$
$132$	−3.05391	+	5.91462i	−0.265809	+	0.514802i
$133$	8.45377	+	8.45377i	0.733035	+	0.733035i
$134$	0.734554	−	0.533685i	0.0634558	−	0.0461034i
$135$		0			0
$136$	−2.99035	+	9.20336i	−0.256421	+	0.789182i
$137$	15.1801	−	2.40429i	1.29692	−	0.205413i	0.530466	−	0.847706i	$-0.322017\pi$
$137$	15.1801	−	2.40429i	1.29692	−	0.205413i	0.766458	+	0.642294i	$0.222017\pi$
$138$	1.64797	−	0.261013i	0.140285	−	0.0222189i
$139$	1.28625	−	3.95867i	0.109098	−	0.335770i	−0.881572	−	0.472049i	$-0.843514\pi$
$139$	1.28625	−	3.95867i	0.109098	−	0.335770i	0.990670	+	0.136279i	$0.0435145\pi$
$140$		0			0
$141$	−3.39364	+	2.46563i	−0.285796	+	0.207643i
$142$	0.992116	+	0.992116i	0.0832565	+	0.0832565i
$143$	−1.46670	−	9.59470i	−0.122651	−	0.802349i
$144$			4.46910i			0.372425i
$145$		0			0
$146$	2.23368	+	6.87457i	0.184861	+	0.568943i
$147$	0.778714	+	1.52831i	0.0642273	+	0.126053i
$148$	−0.320556	−	2.02391i	−0.0263495	−	0.166364i
$149$	−14.5440	−	10.5669i	−1.19149	−	0.865672i	−0.198073	−	0.980187i	$-0.563468\pi$
$149$	−14.5440	−	10.5669i	−1.19149	−	0.865672i	−0.993421	+	0.114516i	$0.963468\pi$
$150$		0			0
$151$	16.9214	−	5.49808i	1.37704	−	0.447427i	0.475345	−	0.879800i	$-0.342323\pi$
$151$	16.9214	−	5.49808i	1.37704	−	0.447427i	0.901695	+	0.432372i	$0.142323\pi$
$152$	−1.17797	+	7.43742i	−0.0955461	+	0.603254i
$153$	−6.33960	+	6.33960i	−0.512526	+	0.512526i
$154$	3.83633	−	2.75579i	0.309140	−	0.222068i
$155$		0			0
$156$	3.45239	+	4.75181i	0.276413	+	0.380449i
$157$	19.1253	+	9.74483i	1.52636	+	0.777722i	0.997478	−	0.0709708i	$-0.0226097\pi$
$157$	19.1253	+	9.74483i	1.52636	+	0.777722i	0.528887	+	0.848693i	$0.322610\pi$
$158$	−6.63368	+	3.38003i	−0.527748	+	0.268901i
$159$	−0.989642	+	1.36213i	−0.0784837	+	0.108024i
$160$		0			0
$161$	8.31766	+	2.70257i	0.655524	+	0.212993i
$162$	−0.221287	+	0.434300i	−0.0173859	+	0.0341218i
$163$	10.2967	+	1.63083i	0.806497	+	0.127737i	0.546051	−	0.837752i	$-0.316130\pi$
$163$	10.2967	+	1.63083i	0.806497	+	0.127737i	0.260446	+	0.965488i	$0.416130\pi$
$164$	6.26288			0.489049
$165$		0			0
$166$	3.26342			0.253290
$167$	−11.1538	−	1.76660i	−0.863110	−	0.136703i	−0.290843	−	0.956771i	$-0.593936\pi$
$167$	−11.1538	−	1.76660i	−0.863110	−	0.136703i	−0.572267	+	0.820067i	$0.693936\pi$
$168$	−2.77104	+	5.43848i	−0.213791	+	0.419588i
$169$	4.21842	+	1.37065i	0.324493	+	0.105434i
$170$		0			0
$171$	−4.10070	+	5.64412i	−0.313588	+	0.431617i
$172$	−11.2601	+	5.73731i	−0.858575	+	0.437466i
$173$	11.7632	+	5.99367i	0.894343	+	0.455691i	0.839847	−	0.542823i	$-0.182645\pi$
$173$	11.7632	+	5.99367i	0.894343	+	0.455691i	0.0544963	+	0.998514i	$0.482645\pi$
$174$	−0.864909	−	1.19044i	−0.0655686	−	0.0902474i
$175$		0			0
$176$	−8.26862	−	2.73598i	−0.623270	−	0.206233i
$177$	1.29330	−	1.29330i	0.0972104	−	0.0972104i
$178$	0.853510	−	5.38885i	0.0639733	−	0.403912i
$179$	2.11776	−	0.688100i	0.158288	−	0.0514310i	−0.228801	−	0.973473i	$-0.573480\pi$
$179$	2.11776	−	0.688100i	0.158288	−	0.0514310i	0.387089	+	0.922042i	$0.373480\pi$
$180$		0			0
$181$	−3.50687	−	2.54789i	−0.260664	−	0.189383i	0.449776	−	0.893141i	$-0.351504\pi$
$181$	−3.50687	−	2.54789i	−0.260664	−	0.189383i	−0.710440	+	0.703758i	$0.751504\pi$
$182$	−0.652010	−	4.11663i	−0.0483302	−	0.305145i
$183$	−3.58879	−	7.04339i	−0.265291	−	0.520663i
$184$	1.70221	+	5.23888i	0.125489	+	0.386215i
$185$		0			0
$186$		−	3.75045i		−	0.274996i
$187$	−7.84826	−	15.6105i	−0.573922	−	1.14155i
$188$	−4.58586	−	4.58586i	−0.334458	−	0.334458i
$189$	−12.6397	+	9.18329i	−0.919404	+	0.667986i
$190$		0			0
$191$	−1.26010	+	3.87820i	−0.0911779	+	0.280617i	−0.986239	−	0.165327i	$-0.947132\pi$
$191$	−1.26010	+	3.87820i	−0.0911779	+	0.280617i	0.895061	+	0.445944i	$0.147132\pi$
$192$	3.18664	−	0.504715i	0.229976	−	0.0364247i
$193$	−20.6434	+	3.26960i	−1.48595	+	0.235351i	−0.846047	−	0.533108i	$-0.821024\pi$
$193$	−20.6434	+	3.26960i	−1.48595	+	0.235351i	−0.639899	+	0.768459i	$0.721024\pi$
$194$	−1.51938	+	4.67617i	−0.109085	+	0.335729i
$195$		0			0
$196$	−2.14544	+	1.55875i	−0.153246	+	0.111339i
$197$	0.213782	+	0.213782i	0.0152313	+	0.0152313i	0.714681	−	0.699450i	$-0.246572\pi$
$197$	0.213782	+	0.213782i	0.0152313	+	0.0152313i	−0.699450	+	0.714681i	$0.746572\pi$
$198$	1.93853	+	1.95954i	0.137765	+	0.139258i
$199$		−	11.0815i		−	0.785549i	−0.919635	−	0.392775i	$-0.871515\pi$
$199$		−	11.0815i		−	0.785549i	0.919635	−	0.392775i	$-0.128485\pi$
$200$		0			0
$201$	−0.654619	−	2.01471i	−0.0461733	−	0.142107i
$202$	0.423258	+	0.830691i	0.0297803	+	0.0584472i
$203$	−1.20656	−	7.61793i	−0.0846840	−	0.534674i
$204$	8.55387	+	6.21475i	0.598890	+	0.435119i
$205$		0			0
$206$	−2.86620	+	0.931285i	−0.199698	+	0.0648857i
$207$	−0.798364	+	5.04067i	−0.0554901	+	0.350351i
$208$	−5.43417	+	5.43417i	−0.376792	+	0.376792i
$209$	−7.93217	−	11.0423i	−0.548680	−	0.763815i
$210$		0			0
$211$	−5.20512	−	7.16423i	−0.358335	−	0.493206i	0.591349	−	0.806416i	$-0.298596\pi$
$211$	−5.20512	−	7.16423i	−0.358335	−	0.493206i	−0.949684	+	0.313210i	$0.898596\pi$
$212$	−2.31936	−	1.18177i	−0.159294	−	0.0811644i
$213$	2.91674	−	1.48615i	0.199852	−	0.101830i
$214$	0.125014	−	0.172067i	0.00854576	−	0.0117622i
$215$		0			0
$216$	−9.35886	−	3.04088i	−0.636790	−	0.206906i
$217$	8.92474	−	17.5158i	0.605851	−	1.18905i
$218$	4.56606	+	0.723193i	0.309253	+	0.0489808i
$219$	16.8647			1.13961
$220$		0			0
$221$	−15.4172			−1.03707
$222$	0.639273	+	0.101251i	0.0429052	+	0.00679551i
$223$	2.80667	−	5.50839i	0.187948	−	0.368869i	−0.777735	−	0.628593i	$-0.783631\pi$
$223$	2.80667	−	5.50839i	0.187948	−	0.368869i	0.965683	+	0.259723i	$0.0836313\pi$
$224$	−13.7469	−	4.46662i	−0.918500	−	0.298439i
$225$		0			0
$226$	5.81727	−	8.00679i	0.386959	−	0.532604i
$227$	2.95522	−	1.50576i	0.196145	−	0.0999406i	−0.353160	−	0.935563i	$-0.614893\pi$
$227$	2.95522	−	1.50576i	0.196145	−	0.0999406i	0.549304	+	0.835622i	$0.314893\pi$
$228$	7.33074	+	3.73520i	0.485490	+	0.247370i
$229$	3.13876	+	4.32013i	0.207415	+	0.285482i	0.900032	−	0.435823i	$-0.143543\pi$
$229$	3.13876	+	4.32013i	0.207415	+	0.285482i	−0.692618	+	0.721305i	$0.743543\pi$
$230$		0			0
$231$	−3.34904	−	10.4995i	−0.220350	−	0.690813i
$232$	3.43509	−	3.43509i	0.225525	−	0.225525i
$233$	0.691167	−	4.36386i	0.0452799	−	0.285886i	−0.954650	−	0.297730i	$-0.903770\pi$
$233$	0.691167	−	4.36386i	0.0452799	−	0.285886i	0.999930	+	0.0118446i	$0.00377033\pi$
$234$	2.31314	−	0.751584i	0.151215	−	0.0491326i
$235$		0			0
$236$	2.28770	+	1.66211i	0.148917	+	0.108194i
$237$	2.71735	+	17.1567i	0.176511	+	1.11445i
$238$	−3.40621	−	6.68507i	−0.220792	−	0.433329i
$239$	−3.23012	−	9.94128i	−0.208939	−	0.643048i	−0.999529	−	0.0307017i	$-0.990226\pi$
$239$	−3.23012	−	9.94128i	−0.208939	−	0.643048i	0.790590	−	0.612346i	$-0.209774\pi$
$240$		0			0
$241$			27.8579i			1.79449i	0.441536	+	0.897243i	$0.354434\pi$
$241$			27.8579i			1.79449i	−0.441536	+	0.897243i	$0.645566\pi$
$242$	−4.81226	+	2.38699i	−0.309344	+	0.153442i
$243$	−10.5600	−	10.5600i	−0.677425	−	0.677425i
$244$	9.88748	−	7.18367i	0.632981	−	0.459888i
$245$		0			0
$246$	−0.611296	+	1.88138i	−0.0389748	+	0.119952i
$247$	−11.8492	+	1.87672i	−0.753944	+	0.119413i
$248$	12.2294	−	1.93695i	0.776569	−	0.122996i
$249$	2.35285	−	7.24134i	0.149106	−	0.458901i
$250$		0			0
$251$	8.04670	−	5.84627i	0.507903	−	0.369013i	−0.304124	−	0.952632i	$-0.598364\pi$
$251$	8.04670	−	5.84627i	0.507903	−	0.369013i	0.812028	+	0.583619i	$0.198364\pi$
$252$	−6.18223	−	6.18223i	−0.389444	−	0.389444i
$253$	−8.83737	−	4.56302i	−0.555601	−	0.286874i
$254$			4.60489i			0.288936i
$255$		0			0
$256$	0.0455968	+	0.140332i	0.00284980	+	0.00877078i
$257$	1.92513	+	3.77828i	0.120086	+	0.235683i	0.943223	−	0.332161i	$-0.107778\pi$
$257$	1.92513	+	3.77828i	0.120086	+	0.235683i	−0.823136	+	0.567844i	$0.807778\pi$
$258$	−0.624438	−	3.94254i	−0.0388758	−	0.245452i
$259$	2.74467	+	1.99412i	0.170545	+	0.123908i
$260$		0			0
$261$	4.28052	−	1.39083i	0.264958	−	0.0860899i
$262$	−0.574229	+	3.62554i	−0.0354760	+	0.223987i
$263$	16.1830	−	16.1830i	0.997884	−	0.997884i	−0.00211364	−	0.999998i	$-0.500673\pi$
$263$	16.1830	−	16.1830i	0.997884	−	0.997884i	0.999998	+	0.00211364i	$0.000672793\pi$
$264$	4.11022	−	5.59360i	0.252967	−	0.344262i
$265$		0			0
$266$	−3.43167	−	4.72330i	−0.210409	−	0.289604i
$267$	−11.3422	−	5.77914i	−0.694131	−	0.353677i
$268$	2.91819	−	1.48689i	0.178257	−	0.0908265i
$269$	13.4435	−	18.5034i	0.819666	−	1.12817i	−0.170094	−	0.985428i	$-0.554407\pi$
$269$	13.4435	−	18.5034i	0.819666	−	1.12817i	0.989759	−	0.142745i	$-0.0455930\pi$
$270$		0			0
$271$	−1.32229	−	0.429640i	−0.0803237	−	0.0260987i	0.268580	−	0.963258i	$-0.413446\pi$
$271$	−1.32229	−	0.429640i	−0.0803237	−	0.0260987i	−0.348903	+	0.937159i	$0.613446\pi$
$272$	−6.28057	+	12.3263i	−0.380815	+	0.747392i
$273$	−9.60465	−	1.52123i	−0.581300	−	0.0920688i
$274$	−7.50545			−0.453421
$275$		0			0
$276$	6.01861			0.362278
$277$	−14.0803	−	2.23010i	−0.846002	−	0.133994i	−0.281639	−	0.959520i	$-0.590878\pi$
$277$	−14.0803	−	2.23010i	−0.846002	−	0.133994i	−0.564363	+	0.825527i	$0.690878\pi$
$278$	−0.922808	+	1.81111i	−0.0553464	+	0.108623i
$279$	10.9101	+	3.54491i	0.653171	+	0.212228i
$280$		0			0
$281$	14.9161	−	20.5302i	0.889818	−	1.22473i	−0.0837853	−	0.996484i	$-0.526701\pi$
$281$	14.9161	−	20.5302i	0.889818	−	1.22473i	0.973604	−	0.228246i	$-0.0732990\pi$
$282$	1.82520	−	0.929988i	0.108689	−	0.0553800i
$283$	−6.60300	−	3.36440i	−0.392508	−	0.199993i	0.246587	−	0.969121i	$-0.420691\pi$
$283$	−6.60300	−	3.36440i	−0.392508	−	0.199993i	−0.639095	+	0.769128i	$0.720691\pi$
$284$	2.97484	+	4.09451i	0.176524	+	0.242964i
$285$		0			0
$286$	−0.0255420	+	4.73983i	−0.00151033	+	0.280272i
$287$	−7.33195	+	7.33195i	−0.432791	+	0.432791i
$288$	1.31948	−	8.33087i	0.0777511	−	0.490901i
$289$	−10.2266	+	3.32284i	−0.601567	+	0.195461i
$290$		0			0
$291$	9.28071	+	6.74283i	0.544045	+	0.395272i
$292$	4.07886	+	25.7529i	0.238697	+	1.50707i
$293$	6.66340	+	13.0777i	0.389280	+	0.764005i	0.999604	−	0.0281472i	$-0.00896072\pi$
$293$	6.66340	+	13.0777i	0.389280	+	0.764005i	−0.610324	+	0.792152i	$0.708961\pi$
$294$	−0.258843	−	0.796636i	−0.0150960	−	0.0464607i
$295$		0			0
$296$			2.13682i			0.124200i
$297$	15.8742	−	7.98087i	0.921116	−	0.463097i
$298$	6.20775	+	6.20775i	0.359606	+	0.359606i
$299$	−7.09994	+	5.15841i	−0.410600	+	0.298318i
$300$		0			0
$301$	6.46553	−	19.8989i	0.372667	−	1.14695i
$302$	−8.58165	+	1.35920i	−0.493818	+	0.0782131i
$303$	2.14842	−	0.340276i	0.123423	−	0.0195483i
$304$	−3.32657	+	10.2381i	−0.190792	+	0.587197i
$305$		0			0
$306$	3.54206	−	2.57346i	0.202486	−	0.147115i
$307$	−0.874954	−	0.874954i	−0.0499363	−	0.0499363i	0.681698	−	0.731634i	$-0.261242\pi$
$307$	−0.874954	−	0.874954i	−0.0499363	−	0.0499363i	−0.731634	+	0.681698i	$0.761242\pi$
$308$	15.2230	−	7.65344i	0.867409	−	0.436095i
$309$			7.03137i			0.400001i
$310$		0			0
$311$	4.37162	+	13.4545i	0.247892	+	0.762933i	0.995147	+	0.0983958i	$0.0313711\pi$
$311$	4.37162	+	13.4545i	0.247892	+	0.762933i	−0.747256	+	0.664537i	$0.768629\pi$
$312$	−2.78064	−	5.45732i	−0.157423	−	0.308960i
$313$	−0.115706	−	0.730542i	−0.00654011	−	0.0412927i	0.984202	−	0.177047i	$-0.0566543\pi$
$313$	−0.115706	−	0.730542i	−0.00654011	−	0.0412927i	−0.990743	+	0.135754i	$0.956654\pi$
$314$	−8.48022	−	6.16124i	−0.478566	−	0.347699i
$315$		0			0
$316$	−25.5415	+	8.29895i	−1.43682	+	0.466852i
$317$	2.66972	−	16.8560i	0.149947	−	0.946726i	−0.791892	−	0.610661i	$-0.790904\pi$
$317$	2.66972	−	16.8560i	0.149947	−	0.946726i	0.941839	−	0.336065i	$-0.109096\pi$
$318$	0.581389	−	0.581389i	0.0326027	−	0.0326027i
$319$	−0.0472661	+	8.77118i	−0.00264640	+	0.491092i
$320$		0			0
$321$	−0.291674	−	0.401454i	−0.0162796	−	0.0224070i
$322$	−3.80538	−	1.93894i	−0.212065	−	0.108053i
$323$	−19.2421	+	9.80433i	−1.07066	+	0.545527i
$324$	−1.03346	+	1.42244i	−0.0574145	+	0.0790243i
$325$		0			0
$326$	−4.84178	−	1.57319i	−0.268161	−	0.0871309i
$327$	4.89675	−	9.61042i	0.270791	−	0.531457i
$328$	−6.45047	−	1.02165i	−0.356168	−	0.0564114i
$329$	10.7373			0.591967
$330$		0			0
$331$	−14.9189			−0.820016			−0.410008	−	0.912082i	$-0.634474\pi$
$331$	−14.9189			−0.820016			−0.410008	+	0.912082i	$0.634474\pi$
$332$	11.6268	+	1.84150i	0.638102	+	0.101065i
$333$	−0.898777	+	1.76395i	−0.0492527	+	0.0966638i
$334$	5.24485	+	1.70415i	0.286985	+	0.0932472i
$335$		0			0
$336$	−5.12893	+	7.05937i	−0.279806	+	0.385120i
$337$	8.40891	−	4.28455i	0.458062	−	0.233394i	−0.209705	−	0.977765i	$-0.567250\pi$
$337$	8.40891	−	4.28455i	0.458062	−	0.233394i	0.667767	+	0.744370i	$0.267250\pi$
$338$	−1.92995	−	0.983358i	−0.104975	−	0.0534876i
$339$	−13.5725	−	18.6809i	−0.737156	−	1.01461i
$340$		0			0
$341$	−13.2379	+	18.0154i	−0.716871	+	0.975589i
$342$	2.40905	−	2.40905i	0.130267	−	0.130267i
$343$	−2.50676	+	15.8271i	−0.135352	+	0.854581i
$344$	12.5333	−	4.07231i	0.675750	−	0.219564i
$345$		0			0
$346$	−5.21586	−	3.78954i	−0.280406	−	0.203727i
$347$	−3.00971	−	19.0026i	−0.161570	−	1.02011i	−0.926581	−	0.376094i	$-0.877267\pi$
$347$	−3.00971	−	19.0026i	−0.161570	−	1.02011i	0.765012	−	0.644016i	$-0.222733\pi$
$348$	−2.40971	−	4.72933i	−0.129174	−	0.253518i
$349$	4.59599	+	14.1450i	0.246018	+	0.757164i	0.995467	+	0.0951031i	$0.0303181\pi$
$349$	4.59599	+	14.1450i	0.246018	+	0.757164i	−0.749450	+	0.662061i	$0.769682\pi$
$350$		0			0
$351$		−	15.6777i		−	0.836813i
$352$	14.6058	+	7.54143i	0.778491	+	0.401960i
$353$	−1.78406	−	1.78406i	−0.0949560	−	0.0949560i	0.658033	−	0.752989i	$-0.271389\pi$
$353$	−1.78406	−	1.78406i	−0.0949560	−	0.0949560i	−0.752989	+	0.658033i	$0.771389\pi$
$354$	−0.722594	+	0.524995i	−0.0384054	+	0.0279032i
$355$		0			0
$356$	6.08171	−	18.7176i	0.322330	−	0.992029i
$357$	−17.2896	+	2.73840i	−0.915063	+	0.144932i
$358$	−1.07402	+	0.170108i	−0.0567636	+	0.00899047i
$359$	−2.62416	+	8.07635i	−0.138498	+	0.426253i	−0.996118	−	0.0880312i	$-0.971942\pi$
$359$	−2.62416	+	8.07635i	−0.138498	+	0.426253i	0.857620	+	0.514285i	$0.171942\pi$
$360$		0			0
$361$	1.77596	−	1.29031i	0.0934717	−	0.0679111i
$362$	1.49682	+	1.49682i	0.0786711	+	0.0786711i
$363$	1.82707	+	12.3991i	0.0958962	+	0.650783i
$364$		−	15.0345i		−	0.788021i
$365$		0			0
$366$	1.19290	+	3.67138i	0.0623541	+	0.191906i
$367$	9.63799	+	18.9156i	0.503099	+	0.987387i	0.993277	+	0.115765i	$0.0369318\pi$
$367$	9.63799	+	18.9156i	0.503099	+	0.987387i	−0.490178	+	0.871622i	$0.663068\pi$
$368$	1.23190	+	7.77792i	0.0642173	+	0.405452i
$369$	−4.89515	−	3.55653i	−0.254831	−	0.185146i
$370$		0			0
$371$	4.09877	−	1.33177i	0.212797	−	0.0691420i
$372$	2.11633	−	13.3620i	0.109726	−	0.692786i
$373$	2.57445	−	2.57445i	0.133300	−	0.133300i	−0.637309	−	0.770609i	$-0.719952\pi$
$373$	2.57445	−	2.57445i	0.133300	−	0.133300i	0.770609	+	0.637309i	$0.219952\pi$
$374$	2.59290	+	8.12891i	0.134076	+	0.420336i
$375$		0			0
$376$	3.97513	+	5.47130i	0.205002	+	0.282161i
$377$	6.89604	+	3.51371i	0.355164	+	0.180965i
$378$	6.79802	−	3.46377i	0.349653	−	0.178157i
$379$	−9.74713	+	13.4158i	−0.500677	+	0.689122i	−0.982312	−	0.187249i	$-0.940043\pi$
$379$	−9.74713	+	13.4158i	−0.500677	+	0.689122i	0.481636	+	0.876371i	$0.340043\pi$
$380$		0			0
$381$	10.2180	+	3.32002i	0.523483	+	0.170090i
$382$	0.904051	−	1.77430i	0.0462553	−	0.0907810i
$383$	−11.2007	−	1.77402i	−0.572330	−	0.0906481i	−0.136440	−	0.990648i	$-0.543566\pi$
$383$	−11.2007	−	1.77402i	−0.572330	−	0.0906481i	−0.435890	+	0.900000i	$0.643566\pi$
$384$	−12.8694			−0.656736
$385$		0			0
$386$	10.2067			0.519505
$387$	12.0591	+	1.90998i	0.612999	+	0.0970895i
$388$	−8.05188	+	15.8027i	−0.408772	+	0.802260i
$389$	0.777554	+	0.252643i	0.0394236	+	0.0128095i	0.328662	−	0.944447i	$-0.393402\pi$
$389$	0.777554	+	0.252643i	0.0394236	+	0.0128095i	−0.289239	+	0.957257i	$0.593402\pi$
$390$		0			0
$391$	−9.28580	+	12.7808i	−0.469603	+	0.646353i
$392$	2.46398	−	1.25546i	0.124450	−	0.0634102i
$393$	7.63086	+	3.88812i	0.384926	+	0.196130i
$394$	−0.0867814	−	0.119444i	−0.00437198	−	0.00601752i
$395$		0			0
$396$	5.80078	+	8.07525i	0.291500	+	0.405796i
$397$	−11.8504	+	11.8504i	−0.594752	+	0.594752i	−0.938911	−	0.344159i	$-0.888164\pi$
$397$	−11.8504	+	11.8504i	−0.594752	+	0.594752i	0.344159	+	0.938911i	$0.388164\pi$
$398$	−0.846553	+	5.34493i	−0.0424339	+	0.267917i
$399$	−12.9549	+	4.20930i	−0.648555	+	0.210728i
$400$		0			0
$401$	23.0228	+	16.7270i	1.14970	+	0.835308i	0.988441	−	0.151603i	$-0.0484436\pi$
$401$	23.0228	+	16.7270i	1.14970	+	0.835308i	0.161262	+	0.986912i	$0.448444\pi$
$402$	0.161831	+	1.02176i	0.00807137	+	0.0509607i
$403$	8.95566	+	17.5765i	0.446113	+	0.875547i
$404$	1.03922	+	3.19839i	0.0517032	+	0.159126i
$405$		0			0
$406$			3.76651i			0.186929i
$407$	−2.71338	−	2.74279i	−0.134497	−	0.135955i
$408$	−7.79627	−	7.79627i	−0.385973	−	0.385973i
$409$	1.95998	−	1.42401i	0.0969146	−	0.0704126i	−0.538273	−	0.842771i	$-0.680923\pi$
$409$	1.95998	−	1.42401i	0.0969146	−	0.0704126i	0.635187	+	0.772358i	$0.280923\pi$
$410$		0			0
$411$	−5.41127	+	16.6542i	−0.266918	+	0.821490i
$412$	−10.7371	+	1.70059i	−0.528979	+	0.0837820i
$413$	−4.62404	+	0.732376i	−0.227534	+	0.0360379i
$414$	0.770145	−	2.37026i	0.0378506	−	0.116492i
$415$		0			0
$416$	11.7343	−	8.52546i	0.575321	−	0.417995i
$417$	3.35343	+	3.35343i	0.164218	+	0.164218i
$418$	2.98234	+	5.93199i	0.145871	+	0.290143i
$419$			16.4371i			0.803006i	0.915858	+	0.401503i	$0.131512\pi$
$419$			16.4371i			0.803006i	−0.915858	+	0.401503i	$0.868488\pi$
$420$		0			0
$421$	−3.85294	−	11.8581i	−0.187781	−	0.577930i	0.812204	−	0.583373i	$-0.198267\pi$
$421$	−3.85294	−	11.8581i	−0.187781	−	0.577930i	−0.999985	+	0.00544310i	$0.998267\pi$
$422$	1.96327	+	3.85314i	0.0955707	+	0.187568i
$423$	0.980171	+	6.18855i	0.0476575	+	0.300898i
$424$	2.19605	+	1.59552i	0.106649	+	0.0774853i
$425$		0			0
$426$	−1.52036	+	0.493994i	−0.0736615	+	0.0239341i
$427$	−3.16534	+	19.9852i	−0.153182	+	0.967151i
$428$	0.542488	−	0.542488i	0.0262222	−	0.0262222i
$429$	10.4990	+	3.47399i	0.506896	+	0.167726i
$430$		0			0
$431$	−11.6588	−	16.0470i	−0.561586	−	0.772957i	0.429941	−	0.902857i	$-0.358534\pi$
$431$	−11.6588	−	16.0470i	−0.561586	−	0.772957i	−0.991527	+	0.129900i	$0.958534\pi$
$432$	−12.5346	−	6.38668i	−0.603070	−	0.307279i
$433$	25.5054	−	12.9956i	1.22571	−	0.624531i	0.283314	−	0.959027i	$-0.408566\pi$
$433$	25.5054	−	12.9956i	1.22571	−	0.624531i	0.942397	+	0.334496i	$0.108566\pi$
$434$	−5.64273	+	7.76656i	−0.270860	+	0.372807i
$435$		0			0
$436$	15.8597	+	5.15313i	0.759541	+	0.246790i
$437$	−5.58097	+	10.9533i	−0.266974	+	0.523966i
$438$	−8.13431	−	1.28835i	−0.388672	−	0.0615597i
$439$	3.12279			0.149043			0.0745214	−	0.997219i	$-0.476257\pi$
$439$	3.12279			0.149043			0.0745214	+	0.997219i	$0.476257\pi$
$440$		0			0
$441$	2.56208			0.122004
$442$	7.43613	+	1.17777i	0.353701	+	0.0560207i
$443$	14.4087	−	28.2787i	0.684579	−	1.34356i	−0.243033	−	0.970018i	$-0.578142\pi$
$443$	14.4087	−	28.2787i	0.684579	−	1.34356i	0.927612	−	0.373545i	$-0.121858\pi$
$444$	2.22044	+	0.721465i	0.105378	+	0.0342392i
$445$		0			0
$446$	−1.77454	+	2.44244i	−0.0840267	+	0.115653i
$447$	18.2503	−	9.29900i	0.863210	−	0.439827i
$448$	−7.35837	−	3.74928i	−0.347650	−	0.177137i
$449$	−20.5693	−	28.3112i	−0.970726	−	1.33609i	−0.941679	−	0.336511i	$-0.890753\pi$
$449$	−20.5693	−	28.3112i	−0.970726	−	1.33609i	−0.0290462	−	0.999578i	$-0.509247\pi$
$450$		0			0
$451$	9.57702	−	6.87957i	0.450964	−	0.323946i
$452$	25.2437	−	25.2437i	1.18736	−	1.18736i
$453$	−3.17119	+	20.0221i	−0.148996	+	0.940722i
$454$	−1.54041	+	0.500510i	−0.0722951	+	0.0234901i
$455$		0			0
$456$	−6.94099	−	5.04293i	−0.325042	−	0.236157i
$457$	−0.797826	−	5.03728i	−0.0373207	−	0.235634i	0.961976	−	0.273134i	$-0.0880604\pi$
$457$	−0.797826	−	5.03728i	−0.0373207	−	0.235634i	−0.999297	+	0.0375006i	$0.988060\pi$
$458$	−1.18388	−	2.32350i	−0.0553191	−	0.108570i
$459$	−8.72103	−	26.8406i	−0.407063	−	1.25281i
$460$		0			0
$461$			12.4703i			0.580801i	0.956905	+	0.290400i	$0.0937885\pi$
$461$			12.4703i			0.580801i	−0.956905	+	0.290400i	$0.906211\pi$
$462$	0.813245	+	5.32002i	0.0378356	+	0.247510i
$463$	19.2728	+	19.2728i	0.895684	+	0.895684i	0.995051	−	0.0993669i	$-0.0316818\pi$
$463$	19.2728	+	19.2728i	0.895684	+	0.895684i	−0.0993669	+	0.995051i	$0.531682\pi$
$464$	5.61854	−	4.08211i	0.260834	−	0.189507i
$465$		0			0
$466$	−0.666738	+	2.05201i	−0.0308860	+	0.0950574i
$467$	39.2044	−	6.20937i	1.81416	−	0.287335i	0.845184	−	0.534476i	$-0.179491\pi$
$467$	39.2044	−	6.20937i	1.81416	−	0.287335i	0.968980	+	0.247141i	$0.0794911\pi$
$468$	8.66527	−	1.37244i	0.400552	−	0.0634412i
$469$	−1.67562	+	5.15703i	−0.0773730	+	0.238130i
$470$		0			0
$471$	−19.7855	+	14.3750i	−0.911667	+	0.662365i
$472$	−2.08508	−	2.08508i	−0.0959738	−	0.0959738i
$473$	−10.9164	+	21.1422i	−0.501936	+	0.972119i
$474$		−	8.48273i		−	0.389625i
$475$		0			0
$476$	−8.36324	−	25.7394i	−0.383328	−	1.17976i
$477$	1.14174	+	2.24079i	0.0522767	+	0.102599i
$478$	0.798528	+	5.04171i	0.0365238	+	0.230602i
$479$	30.9491	+	22.4858i	1.41410	+	1.02740i	0.992711	+	0.120523i	$0.0384570\pi$
$479$	30.9491	+	22.4858i	1.41410	+	1.02740i	0.421388	+	0.906880i	$0.361543\pi$
$480$		0			0
$481$	−3.23773	+	1.05200i	−0.147628	+	0.0479671i
$482$	2.12815	−	13.4366i	0.0969348	−	0.612022i
$483$	−7.04599	+	7.04599i	−0.320603	+	0.320603i
$484$	−18.4919	+	5.78879i	−0.840539	+	0.263127i
$485$		0			0
$486$	4.28667	+	5.90009i	0.194447	+	0.267634i
$487$	−24.2169	−	12.3391i	−1.09737	−	0.559139i	−0.190987	−	0.981593i	$-0.561169\pi$
$487$	−24.2169	−	12.3391i	−1.09737	−	0.559139i	−0.906384	+	0.422454i	$0.861169\pi$
$488$	−11.3555	+	5.78591i	−0.514039	+	0.261916i
$489$	−6.98164	+	9.60940i	−0.315720	+	0.434552i
$490$		0			0
$491$	3.77748	+	1.22738i	0.170475	+	0.0553907i	0.393011	−	0.919534i	$-0.371433\pi$
$491$	3.77748	+	1.22738i	0.170475	+	0.0553907i	−0.222536	+	0.974925i	$0.571433\pi$
$492$	−3.23954	+	6.35795i	−0.146050	+	0.286638i
$493$	13.7608	+	2.17949i	0.619753	+	0.0981593i
$494$	5.85854			0.263588
$495$		0			0
$496$	17.7010			0.794798
$497$	−8.27608	−	1.31080i	−0.371233	−	0.0587975i
$498$	−1.68803	+	3.31295i	−0.0756426	+	0.148457i
$499$	−6.11060	−	1.98546i	−0.273548	−	0.0888812i	0.169031	−	0.985611i	$-0.445936\pi$
$499$	−6.11060	−	1.98546i	−0.273548	−	0.0888812i	−0.442579	+	0.896730i	$0.645936\pi$
$500$		0			0
$501$	7.56284	−	10.4094i	0.337883	−	0.465056i
$502$	−4.32776	+	2.20510i	−0.193157	+	0.0984186i
$503$	−36.2878	−	18.4896i	−1.61799	−	0.824409i	−0.999246	−	0.0388190i	$-0.987640\pi$
$503$	−36.2878	−	18.4896i	−1.61799	−	0.824409i	−0.618747	−	0.785590i	$-0.712360\pi$
$504$	5.35890	+	7.37590i	0.238704	+	0.328549i
$505$		0			0
$506$	3.91392	+	2.87598i	0.173995	+	0.127853i
$507$	−3.57347	+	3.57347i	−0.158703	+	0.158703i
$508$	−2.59847	+	16.4061i	−0.115289	+	0.727904i
$509$	8.83124	−	2.86944i	0.391438	−	0.127186i	−0.106684	−	0.994293i	$-0.534023\pi$
$509$	8.83124	−	2.86944i	0.391438	−	0.127186i	0.498122	+	0.867107i	$0.334023\pi$
$510$		0			0
$511$	−34.9240	−	25.3738i	−1.54495	−	1.12247i
$512$	−3.54520	−	22.3835i	−0.156677	−	0.989220i
$513$	−9.96998	−	19.5672i	−0.440185	−	0.863912i
$514$	−0.639909	−	1.96944i	−0.0282252	−	0.0868681i
$515$		0			0
$516$		−	14.3987i		−	0.633868i
$517$	−12.0500	−	1.97515i	−0.529957	−	0.0868669i
$518$	−1.17149	−	1.17149i	−0.0514723	−	0.0514723i
$519$	−12.1693	+	8.84152i	−0.534173	+	0.388099i
$520$		0			0
$521$	−4.57564	+	14.0824i	−0.200462	+	0.616960i	0.799407	+	0.600790i	$0.205147\pi$
$521$	−4.57564	+	14.0824i	−0.200462	+	0.616960i	−0.999869	+	0.0161698i	$0.994853\pi$
$522$	−2.17086	+	0.343831i	−0.0950160	+	0.0150491i
$523$	38.3651	−	6.07643i	1.67759	−	0.265704i	0.756197	−	0.654344i	$-0.227055\pi$
$523$	38.3651	−	6.07643i	1.67759	−	0.265704i	0.921390	+	0.388640i	$0.127055\pi$
$524$	−4.09168	+	12.5929i	−0.178746	+	0.550124i
$525$		0			0
$526$	−9.04175	+	6.56922i	−0.394239	+	0.286431i
$527$	25.1096	+	25.1096i	1.09379	+	1.09379i
$528$	7.05453	−	6.97891i	0.307009	−	0.303718i
$529$		−	14.0073i		−	0.609011i
$530$		0			0
$531$	−0.844224	−	2.59825i	−0.0366362	−	0.112755i
$532$	−9.56095	−	18.7644i	−0.414520	−	0.813541i
$533$	−1.62768	−	10.2768i	−0.0705027	−	0.445136i
$534$	5.02916	+	3.65390i	0.217633	+	0.158120i
$535$		0			0
$536$	−3.24815	+	1.05539i	−0.140299	+	0.0455859i
$537$	−0.396884	+	2.50583i	−0.0171268	+	0.108134i
$538$	−7.89771	+	7.89771i	−0.340495	+	0.340495i
$539$	−1.56850	+	4.74029i	−0.0675603	+	0.204179i
$540$		0			0
$541$	10.2392	+	14.0930i	0.440217	+	0.605907i	0.970260	−	0.242064i	$-0.0778243\pi$
$541$	10.2392	+	14.0930i	0.440217	+	0.605907i	−0.530043	+	0.847971i	$0.677824\pi$
$542$	0.604957	+	0.308241i	0.0259851	+	0.0132401i
$543$	4.40053	−	2.24218i	0.188845	−	0.0962213i
$544$	15.3469	−	21.1232i	0.657994	−	0.905650i
$545$		0			0
$546$	4.51637	+	1.46746i	0.193283	+	0.0628014i
$547$	−17.7994	+	34.9333i	−0.761048	+	1.49364i	0.105430	+	0.994427i	$0.466378\pi$
$547$	−17.7994	+	34.9333i	−0.761048	+	1.49364i	−0.866478	+	0.499215i	$0.833622\pi$
$548$	−26.7401	−	4.23522i	−1.14228	−	0.180920i
$549$	−11.8076			−0.503936
$550$		0			0
$551$	10.8414			0.461858
$552$	−6.19888	−	0.981807i	−0.263842	−	0.0417885i
$553$	20.1859	−	39.6170i	0.858391	−	1.68469i
$554$	6.62094	+	2.15127i	0.281297	+	0.0913989i
$555$		0			0
$556$	−4.30973	+	5.93184i	−0.182773	+	0.251566i
$557$	−32.7010	+	16.6620i	−1.38558	+	0.705991i	−0.978277	−	0.207301i	$-0.933532\pi$
$557$	−32.7010	+	16.6620i	−1.38558	+	0.705991i	−0.407307	+	0.913291i	$0.633532\pi$
$558$	−4.99143	−	2.54326i	−0.211304	−	0.107665i
$559$	12.3408	+	16.9856i	0.521959	+	0.718416i
$560$		0			0
$561$	19.9070	+	0.107275i	0.840475	+	0.00452915i
$562$	−8.76280	+	8.76280i	−0.369636	+	0.369636i
$563$	2.64077	−	16.6732i	0.111295	−	0.702690i	−0.867437	−	0.497547i	$-0.834234\pi$
$563$	2.64077	−	16.6732i	0.111295	−	0.702690i	0.978732	−	0.205143i	$-0.0657659\pi$
$564$	7.02754	−	2.28339i	0.295913	−	0.0961480i
$565$		0			0
$566$	2.92779	+	2.12716i	0.123064	+	0.0894114i
$567$	−0.455374	−	2.87512i	−0.0191239	−	0.120744i
$568$	−2.39601	−	4.70243i	−0.100534	−	0.197310i
$569$	0.818531	+	2.51918i	0.0343146	+	0.105609i	0.966747	−	0.255736i	$-0.0823176\pi$
$569$	0.818531	+	2.51918i	0.0343146	+	0.105609i	−0.932432	+	0.361345i	$0.882318\pi$
$570$		0			0
$571$		−	29.8675i		−	1.24992i	−0.780658	−	0.624959i	$-0.785116\pi$
$571$		−	29.8675i		−	1.24992i	0.780658	−	0.624959i	$-0.214884\pi$
$572$	−2.76562	+	16.8725i	−0.115636	+	0.705473i
$573$	−3.28527	−	3.28527i	−0.137244	−	0.137244i
$574$	4.09651	−	2.97629i	0.170985	−	0.124228i
$575$		0			0
$576$	1.48921	−	4.58332i	0.0620505	−	0.190972i
$577$	0.354477	−	0.0561437i	0.0147571	−	0.00233729i	−0.149052	−	0.988829i	$-0.547622\pi$
$577$	0.354477	−	0.0561437i	0.0147571	−	0.00233729i	0.163809	+	0.986492i	$0.447622\pi$
$578$	5.18643	−	0.821450i	0.215727	−	0.0341678i
$579$	7.35878	−	22.6480i	0.305821	−	0.941219i
$580$		0			0
$581$	−15.7673	+	11.4556i	−0.654138	+	0.475259i
$582$	−3.96123	−	3.96123i	−0.164198	−	0.164198i
$583$	−4.84483	+	0.740605i	−0.200652	+	0.0306727i
$584$		−	27.1896i		−	1.12511i
$585$		0			0
$586$	−2.21490	−	6.81675i	−0.0914965	−	0.281597i
$587$	−11.7343	−	23.0298i	−0.484326	−	0.950543i	−0.995827	−	0.0912603i	$-0.970910\pi$
$587$	−11.7343	−	23.0298i	−0.484326	−	0.950543i	0.511501	−	0.859282i	$-0.329090\pi$
$588$	−0.472664	−	2.98428i	−0.0194923	−	0.123070i
$589$	22.3550	+	16.2418i	0.921121	+	0.669233i
$590$		0			0
$591$	−0.327608	+	0.106446i	−0.0134760	+	0.00437861i
$592$	−0.477873	+	3.01717i	−0.0196405	+	0.124005i
$593$	−9.56872	+	9.56872i	−0.392940	+	0.392940i	−0.875734	−	0.482794i	$-0.839622\pi$
$593$	−9.56872	+	9.56872i	−0.392940	+	0.392940i	0.482794	+	0.875734i	$0.339622\pi$
$594$	−8.26626	+	2.63671i	−0.339169	+	0.108185i
$595$		0			0
$596$	18.6138	+	25.6197i	0.762451	+	1.04942i
$597$	11.2497	+	5.73203i	0.460421	+	0.234596i
$598$	3.81856	−	1.94565i	0.156153	−	0.0795637i
$599$	6.65542	−	9.16040i	0.271933	−	0.374284i	−0.651108	−	0.758985i	$-0.725696\pi$
$599$	6.65542	−	9.16040i	0.271933	−	0.374284i	0.923041	+	0.384701i	$0.125696\pi$
$600$		0			0
$601$	−15.6822	−	5.09545i	−0.639689	−	0.207848i	−0.0288267	−	0.999584i	$-0.509177\pi$
$601$	−15.6822	−	5.09545i	−0.639689	−	0.207848i	−0.610862	+	0.791737i	$0.709177\pi$
$602$	−4.63864	+	9.10384i	−0.189057	+	0.371045i
$603$	−3.12526	−	0.494993i	−0.127271	−	0.0201577i
$604$	−31.3413			−1.27526
$605$		0			0
$606$	−1.06223			−0.0431503
$607$	−4.92298	−	0.779724i	−0.199818	−	0.0316480i	0.0557232	−	0.998446i	$-0.482254\pi$
$607$	−4.92298	−	0.779724i	−0.199818	−	0.0316480i	−0.255541	+	0.966798i	$0.582254\pi$
$608$	9.22383	−	18.1028i	0.374076	−	0.734165i
$609$	8.35766	+	2.71557i	0.338670	+	0.110040i
$610$		0			0
$611$	−6.33310	+	8.71677i	−0.256210	+	0.352643i
$612$	14.0717	−	7.16989i	0.568814	−	0.289825i
$613$	−16.2873	−	8.29879i	−0.657837	−	0.335185i	0.0930058	−	0.995666i	$-0.470352\pi$
$613$	−16.2873	−	8.29879i	−0.657837	−	0.335185i	−0.750843	+	0.660481i	$0.770352\pi$
$614$	0.355174	+	0.488855i	0.0143337	+	0.0197286i
$615$		0			0
$616$	−16.9274	+	5.39938i	−0.682025	+	0.217547i
$617$	−15.4942	+	15.4942i	−0.623773	+	0.623773i	−0.946494	−	0.322721i	$-0.895402\pi$
$617$	−15.4942	+	15.4942i	−0.623773	+	0.623773i	0.322721	+	0.946494i	$0.395402\pi$
$618$	0.537149	−	3.39142i	0.0216073	−	0.136423i
$619$	46.8070	−	15.2085i	1.88133	−	0.611282i	0.895114	−	0.445837i	$-0.147094\pi$
$619$	46.8070	−	15.2085i	1.88133	−	0.611282i	0.986219	−	0.165445i	$-0.0529061\pi$
$620$		0			0
$621$	−12.9967	−	9.44269i	−0.521541	−	0.378922i
$622$	−1.08072	−	6.82342i	−0.0433330	−	0.273594i
$623$	14.7928	+	29.0325i	0.592661	+	1.16316i
$624$	−2.70578	−	8.32754i	−0.108318	−	0.333368i
$625$		0			0
$626$			0.361199i			0.0144364i
$627$	15.3129	−	2.34082i	0.611540	−	0.0934832i
$628$	−26.7363	−	26.7363i	−1.06689	−	1.06689i
$629$	−4.95787	+	3.60210i	−0.197683	+	0.143625i
$630$		0			0
$631$	−2.79731	+	8.60924i	−0.111359	+	0.342729i	−0.991170	−	0.132595i	$-0.957669\pi$
$631$	−2.79731	+	8.60924i	−0.111359	+	0.342729i	0.879811	+	0.475324i	$0.157669\pi$
$632$	27.6604	−	4.38097i	1.10027	−	0.174266i
$633$	9.96538	−	1.57836i	0.396088	−	0.0627342i
$634$	−2.57536	+	7.92615i	−0.102281	+	0.314788i
$635$		0			0
$636$	2.39942	−	1.74328i	0.0951431	−	0.0691255i
$637$	3.11534	+	3.11534i	0.123434	+	0.123434i
$638$	0.692856	−	4.22697i	0.0274304	−	0.167347i
$639$		−	4.88965i		−	0.193432i
$640$		0			0
$641$	−8.63030	−	26.5613i	−0.340876	−	1.04911i	−0.963755	−	0.266791i	$-0.914037\pi$
$641$	−8.63030	−	26.5613i	−0.340876	−	1.04911i	0.622878	−	0.782319i	$-0.285963\pi$
$642$	0.110014	+	0.215914i	0.00434190	+	0.00852146i
$643$	1.50637	+	9.51085i	0.0594055	+	0.375071i	0.999424	+	0.0339470i	$0.0108078\pi$
$643$	1.50637	+	9.51085i	0.0594055	+	0.375071i	−0.940018	+	0.341124i	$0.889192\pi$
$644$	−12.4635	−	9.05529i	−0.491132	−	0.356828i
$645$		0			0
$646$	10.0300	−	3.25893i	0.394624	−	0.128221i
$647$	−4.84185	+	30.5702i	−0.190353	+	1.20184i	0.688675	+	0.725070i	$0.258193\pi$
$647$	−4.84185	+	30.5702i	−0.190353	+	1.20184i	−0.879028	+	0.476770i	$0.841807\pi$
$648$	1.29645	−	1.29645i	0.0509296	−	0.0509296i
$649$	5.32406	+	0.0286903i	0.208988	+	0.00112619i
$650$		0			0
$651$	13.1653	+	18.1204i	0.515987	+	0.710195i
$652$	−16.3624	−	8.33705i	−0.640800	−	0.326504i
$653$	5.44440	−	2.77406i	0.213056	−	0.108557i	−0.344206	−	0.938894i	$-0.611852\pi$
$653$	5.44440	−	2.77406i	0.213056	−	0.108557i	0.557262	+	0.830337i	$0.311852\pi$
$654$	−3.09601	+	4.26129i	−0.121063	+	0.166630i
$655$		0			0
$656$	−8.87952	−	2.88513i	−0.346687	−	0.112645i
$657$	11.4363	−	22.4450i	0.446173	−	0.875665i
$658$	−5.17890	−	0.820257i	−0.201895	−	0.0319770i
$659$	−12.0647			−0.469975			−0.234988	−	0.971998i	$-0.575505\pi$
$659$	−12.0647			−0.469975			−0.234988	+	0.971998i	$0.575505\pi$
$660$		0			0
$661$	−29.6228			−1.15219			−0.576097	−	0.817382i	$-0.695425\pi$
$661$	−29.6228			−1.15219			−0.576097	+	0.817382i	$0.695425\pi$
$662$	7.19579	+	1.13970i	0.279672	+	0.0442957i
$663$	7.97469	−	15.6512i	0.309711	−	0.607843i
$664$	−11.6746	−	3.79331i	−0.453063	−	0.147209i
$665$		0			0
$666$	0.568258	−	0.782140i	0.0220196	−	0.0303073i
$667$	7.06635	−	3.60048i	0.273610	−	0.139411i
$668$	17.7245	+	9.03109i	0.685782	+	0.349423i
$669$	4.14023	+	5.69854i	0.160071	+	0.220318i
$670$		0			0
$671$	7.22862	−	21.8461i	0.279058	−	0.843361i
$672$	11.6451	−	11.6451i	0.449220	−	0.449220i
$673$	−0.787773	+	4.97380i	−0.0303664	+	0.191726i	−0.998208	−	0.0598329i	$-0.980943\pi$
$673$	−0.787773	+	4.97380i	−0.0303664	+	0.191726i	0.967842	+	0.251559i	$0.0809432\pi$
$674$	−4.38316	+	1.42417i	−0.168833	+	0.0548571i
$675$		0			0
$676$	−6.32105	−	4.59251i	−0.243117	−	0.176635i
$677$	−5.69516	−	35.9579i	−0.218883	−	1.38197i	−0.815180	−	0.579208i	$-0.803362\pi$
$677$	−5.69516	−	35.9579i	−0.218883	−	1.38197i	0.596297	−	0.802764i	$-0.296638\pi$
$678$	5.11928	+	10.0472i	0.196605	+	0.385859i
$679$	−9.07388	−	27.9265i	−0.348223	−	1.07172i
$680$		0			0
$681$			3.77894i			0.144809i
$682$	7.76124	−	7.67804i	0.297193	−	0.294007i
$683$	8.07353	+	8.07353i	0.308925	+	0.308925i	0.844492	−	0.535567i	$-0.179902\pi$
$683$	8.07353	+	8.07353i	0.308925	+	0.308925i	−0.535567	+	0.844492i	$0.679902\pi$
$684$	9.94226	−	7.22348i	0.380152	−	0.276197i
$685$		0			0
$686$	2.41816	−	7.44232i	0.0923257	−	0.284149i
$687$	−6.00926	+	0.951773i	−0.229267	+	0.0363124i
$688$	18.6076	−	2.94716i	0.709408	−	0.112359i
$689$	−1.33638	+	4.11297i	−0.0509122	+	0.156692i
$690$		0			0
$691$	9.61076	−	6.98263i	0.365611	−	0.265632i	−0.389778	−	0.920909i	$-0.627448\pi$
$691$	9.61076	−	6.98263i	0.365611	−	0.265632i	0.755388	+	0.655277i	$0.227448\pi$
$692$	−16.4445	−	16.4445i	−0.625125	−	0.625125i
$693$	−16.2447	−	2.66271i	−0.617083	−	0.101148i
$694$			9.39538i			0.356644i
$695$		0			0
$696$	1.71040	+	5.26407i	0.0648326	+	0.199534i
$697$	−8.50329	−	16.6886i	−0.322085	−	0.632127i
$698$	−1.13619	−	7.17362i	−0.0430054	−	0.271526i
$699$	4.07258	+	2.95891i	0.154039	+	0.111916i
$700$		0			0
$701$	−25.2475	+	8.20342i	−0.953586	+	0.309839i	−0.744172	−	0.667988i	$-0.767156\pi$
$701$	−25.2475	+	8.20342i	−0.953586	+	0.309839i	−0.209414	+	0.977827i	$0.567156\pi$
$702$	−1.19767	+	7.56177i	−0.0452030	+	0.285401i
$703$	−3.37197	+	3.37197i	−0.127176	+	0.127176i
$704$	7.56826	+	5.56122i	0.285239	+	0.209596i
$705$		0			0
$706$	0.724212	+	0.996792i	0.0272561	+	0.0375148i
$707$	−4.96097	−	2.52774i	−0.186576	−	0.0950654i
$708$	−2.87068	+	1.46268i	−0.107887	+	0.0549710i
$709$	−10.4984	+	14.4498i	−0.394275	+	0.542673i	−0.959296	−	0.282404i	$-0.908868\pi$
$709$	−10.4984	+	14.4498i	−0.394275	+	0.542673i	0.565021	+	0.825077i	$0.308868\pi$
$710$		0			0
$711$	24.6763	+	8.01783i	0.925435	+	0.300692i
$712$	−9.31723	+	18.2861i	−0.349178	+	0.685301i
$713$	19.9648	+	3.16212i	0.747689	+	0.118422i
$714$	8.54844			0.319917
$715$		0			0
$716$	−3.92246			−0.146589
$717$	11.7630	+	1.86307i	0.439297	+	0.0695778i
$718$	1.88268	−	3.69497i	0.0702611	−	0.137895i
$719$	−31.1609	−	10.1248i	−1.16211	−	0.377592i	−0.336416	−	0.941714i	$-0.609215\pi$
$719$	−31.1609	−	10.1248i	−1.16211	−	0.377592i	−0.825691	+	0.564122i	$0.809215\pi$
$720$		0			0
$721$	10.5790	−	14.5608i	0.393984	−	0.542272i
$722$	−0.955166	+	0.486681i	−0.0355476	+	0.0181124i
$723$	−28.2808	−	14.4098i	−1.05177	−	0.535905i
$724$	4.48818	+	6.17744i	0.166802	+	0.229583i
$725$		0			0
$726$	0.0659608	−	6.12000i	0.00244803	−	0.227134i
$727$	−0.964903	+	0.964903i	−0.0357863	+	0.0357863i	−0.724773	−	0.688987i	$-0.758056\pi$
$727$	−0.964903	+	0.964903i	−0.0357863	+	0.0357863i	0.688987	+	0.724773i	$0.258056\pi$
$728$	−2.45255	+	15.4848i	−0.0908976	+	0.573905i
$729$	19.0304	−	6.18335i	0.704830	−	0.229013i
$730$		0			0
$731$	30.5763	+	22.2150i	1.13091	+	0.821651i
$732$	2.17832	+	13.7534i	0.0805131	+	0.508340i
$733$	5.35405	+	10.5079i	0.197756	+	0.388119i	0.968495	−	0.249033i	$-0.0801126\pi$
$733$	5.35405	+	10.5079i	0.197756	+	0.388119i	−0.770739	+	0.637151i	$0.780113\pi$
$734$	−3.20364	−	9.85979i	−0.118249	−	0.363932i
$735$		0			0
$736$		−	14.8626i		−	0.547842i
$737$	2.82911	−	5.47925i	0.104212	−	0.201831i
$738$	2.08937	+	2.08937i	0.0769107	+	0.0769107i
$739$	−34.8645	+	25.3305i	−1.28251	+	0.931798i	−0.999626	−	0.0273561i	$-0.991291\pi$
$739$	−34.8645	+	25.3305i	−1.28251	+	0.931798i	−0.282884	+	0.959154i	$0.591291\pi$
$740$		0			0
$741$	4.22388	−	12.9998i	0.155168	−	0.477558i
$742$	−2.07868	+	0.329231i	−0.0763109	+	0.0120865i
$743$	−37.4472	+	5.93105i	−1.37380	+	0.217589i	−0.799309	−	0.600920i	$-0.794801\pi$
$743$	−37.4472	+	5.93105i	−1.37380	+	0.217589i	−0.574494	+	0.818509i	$0.694801\pi$
$744$	−4.35943	+	13.4170i	−0.159825	+	0.491889i
$745$		0			0
$746$	−1.43840	+	1.04506i	−0.0526636	+	0.0382623i
$747$	−8.04189	−	8.04189i	−0.294237	−	0.294237i
$748$	4.65085	+	30.4245i	0.170052	+	1.11243i
$749$			1.27018i			0.0464114i
$750$		0			0
$751$	10.7881	+	33.2025i	0.393665	+	1.21158i	0.929996	+	0.367569i	$0.119810\pi$
$751$	10.7881	+	33.2025i	0.393665	+	1.21158i	−0.536331	+	0.844008i	$0.680190\pi$
$752$	4.38926	+	8.61441i	0.160060	+	0.314135i
$753$	1.77278	+	11.1929i	0.0646036	+	0.407891i
$754$	−3.05772	−	2.22157i	−0.111356	−	0.0809047i
$755$		0			0
$756$	26.1743	−	8.50454i	0.951950	−	0.309307i
$757$	−5.39320	+	34.0513i	−0.196019	+	1.23762i	0.671798	+	0.740734i	$0.265522\pi$
$757$	−5.39320	+	34.0513i	−0.196019	+	1.23762i	−0.867818	+	0.496883i	$0.834478\pi$
$758$	5.72618	−	5.72618i	0.207984	−	0.207984i
$759$	9.20349	−	6.61125i	0.334065	−	0.239973i
$760$		0			0
$761$	−8.17878	−	11.2571i	−0.296481	−	0.408071i	0.634625	−	0.772820i	$-0.281155\pi$
$761$	−8.17878	−	11.2571i	−0.296481	−	0.408071i	−0.931106	+	0.364750i	$0.881155\pi$
$762$	−4.67478	−	2.38192i	−0.169350	−	0.0862879i
$763$	−24.5997	+	12.5342i	−0.890568	+	0.453767i
$764$	4.22213	−	5.81126i	0.152751	−	0.210244i
$765$		0			0
$766$	5.26689	+	1.71132i	0.190300	+	0.0618323i
$767$	2.13280	−	4.18586i	0.0770110	−	0.151143i
$768$	−0.166048	−	0.0262994i	−0.00599174	−	0.000948998i
$769$	13.3273			0.480596			0.240298	−	0.970699i	$-0.422755\pi$
$769$	13.3273			0.480596			0.240298	+	0.970699i	$0.422755\pi$
$770$		0			0
$771$	−4.83143			−0.174000
$772$	36.3639	+	5.75948i	1.30877	+	0.207288i
$773$	5.67471	−	11.1372i	0.204105	−	0.400579i	−0.766151	−	0.642661i	$-0.777830\pi$
$773$	5.67471	−	11.1372i	0.204105	−	0.400579i	0.970256	+	0.242082i	$0.0778304\pi$
$774$	−5.67053	−	1.84247i	−0.203823	−	0.0662261i
$775$		0			0
$776$	10.8709	−	14.9625i	0.390243	−	0.537124i
$777$	−3.44409	+	1.75485i	−0.123556	+	0.0629549i
$778$	−0.355735	−	0.181256i	−0.0127537	−	0.00649835i
$779$	−8.56685	−	11.7913i	−0.306939	−	0.422465i
$780$		0			0
$781$	9.04671	+	2.99345i	0.323717	+	0.107114i
$782$	5.45516	−	5.45516i	0.195076	−	0.195076i
$783$	−2.21631	+	13.9933i	−0.0792046	+	0.500078i
$784$	3.75988	−	1.22166i	0.134281	−	0.0436306i
$785$		0			0
$786$	−3.38355	−	2.45829i	−0.120687	−	0.0876843i
$787$	−0.984406	−	6.21530i	−0.0350903	−	0.221551i	0.963911	−	0.266223i	$-0.0857758\pi$
$787$	−0.984406	−	6.21530i	−0.0350903	−	0.221551i	−0.999002	+	0.0446718i	$0.985776\pi$
$788$	−0.241781	−	0.474521i	−0.00861308	−	0.0169041i
$789$	8.05781	+	24.7994i	0.286866	+	0.882882i
$790$		0			0
$791$			59.1055i			2.10155i
$792$	−4.65723	−	9.26339i	−0.165487	−	0.329160i
$793$	−14.3574	−	14.3574i	−0.509846	−	0.509846i
$794$	6.62104	−	4.81046i	0.234972	−	0.170717i
$795$		0			0
$796$	−6.03213	+	18.5650i	−0.213803	+	0.658019i
$797$	1.74680	−	0.276667i	0.0618750	−	0.00980003i	−0.125420	−	0.992104i	$-0.540028\pi$
$797$	1.74680	−	0.276667i	0.0618750	−	0.00980003i	0.187295	+	0.982304i	$0.440028\pi$
$798$	6.57006	−	1.04059i	0.232577	−	0.0368367i
$799$	−5.99354	+	18.4462i	−0.212036	+	0.652581i
$800$		0			0
$801$	−15.3828	+	11.1762i	−0.543523	+	0.394893i
$802$	−9.82669	−	9.82669i	−0.346992	−	0.346992i
$803$	34.5259	+	34.9001i	1.21839	+	1.23160i
$804$			3.73160i			0.131603i
$805$		0			0
$806$	−2.97684	−	9.16176i	−0.104855	−	0.322709i
$807$	11.8305	+	23.2186i	0.416453	+	0.817335i
$808$	−0.548599	−	3.46372i	−0.0192996	−	0.121853i
$809$	−14.9294	−	10.8468i	−0.524889	−	0.381354i	0.293553	−	0.955943i	$-0.405162\pi$
$809$	−14.9294	−	10.8468i	−0.524889	−	0.381354i	−0.818443	+	0.574588i	$0.805162\pi$
$810$		0			0
$811$	−12.4057	+	4.03086i	−0.435624	+	0.141543i	−0.518616	−	0.855007i	$-0.673552\pi$
$811$	−12.4057	+	4.03086i	−0.435624	+	0.141543i	0.0829918	+	0.996550i	$0.473552\pi$
$812$	−2.12539	+	13.4192i	−0.0745865	+	0.470920i
$813$	1.12013	−	1.12013i	0.0392847	−	0.0392847i
$814$	1.09921	+	1.53020i	0.0385273	+	0.0536336i
$815$		0			0
$816$	−9.26472	−	12.7518i	−0.324330	−	0.446402i
$817$	26.2042	+	13.3517i	0.916768	+	0.467117i
$818$	−1.05413	+	0.537108i	−0.0368569	+	0.0187796i
$819$	−8.53770	+	11.7511i	−0.298331	+	0.410618i
$820$		0			0
$821$	−24.7703	−	8.04835i	−0.864489	−	0.280889i	−0.156987	−	0.987601i	$-0.550178\pi$
$821$	−24.7703	−	8.04835i	−0.864489	−	0.280889i	−0.707502	+	0.706711i	$0.750178\pi$
$822$	3.88227	−	7.61938i	0.135410	−	0.265756i
$823$	−4.96237	−	0.785962i	−0.172977	−	0.0273969i	0.0693449	−	0.997593i	$-0.477909\pi$
$823$	−4.96237	−	0.785962i	−0.172977	−	0.0273969i	−0.242322	+	0.970196i	$0.577909\pi$
$824$	11.3361			0.394912
$825$		0			0
$826$	2.28625			0.0795488
$827$	12.0210	+	1.90393i	0.418010	+	0.0662062i	0.361897	−	0.932218i	$-0.382129\pi$
$827$	12.0210	+	1.90393i	0.418010	+	0.0662062i	0.0561130	+	0.998424i	$0.482129\pi$
$828$	4.08135	−	8.01010i	0.141837	−	0.278370i
$829$	10.4727	+	3.40277i	0.363730	+	0.118183i	0.485180	−	0.874415i	$-0.338754\pi$
$829$	10.4727	+	3.40277i	0.363730	+	0.118183i	−0.121449	+	0.992598i	$0.538754\pi$
$830$		0			0
$831$	9.54711	−	13.1405i	0.331185	−	0.455838i
$832$	7.38386	−	3.76227i	0.255989	−	0.130433i
$833$	7.06651	+	3.60057i	0.244840	+	0.124752i
$834$	−1.36127	−	1.87363i	−0.0471370	−	0.0648785i
$835$		0			0
$836$	7.27804	+	22.8171i	0.251716	+	0.789148i
$837$	−25.5338	+	25.5338i	−0.882578	+	0.882578i
$838$	1.25568	−	7.92807i	0.0433769	−	0.273871i
$839$	−8.83685	+	2.87127i	−0.305082	+	0.0991272i	−0.457557	−	0.889180i	$-0.651276\pi$
$839$	−8.83685	+	2.87127i	−0.305082	+	0.0991272i	0.152475	+	0.988307i	$0.451276\pi$
$840$		0			0
$841$	17.8031	+	12.9347i	0.613900	+	0.446024i
$842$	0.952498	+	6.01384i	0.0328253	+	0.207251i
$843$	13.1264	+	25.7619i	0.452096	+	0.887288i
$844$	4.82040	+	14.8357i	0.165925	+	0.510665i
$845$		0			0
$846$		−	3.05979i		−	0.105198i
$847$	14.8715	−	28.4253i	0.510990	−	0.976706i
$848$	2.74398	+	2.74398i	0.0942286	+	0.0942286i
$849$	6.83093	−	4.96296i	0.234437	−	0.170328i
$850$		0			0
$851$	−1.07798	+	3.31768i	−0.0369527	+	0.113729i
$852$	−5.69542	+	0.902066i	−0.195122	+	0.0309043i
$853$	26.7133	−	4.23097i	0.914645	−	0.144866i	0.318667	−	0.947867i	$-0.396765\pi$
$853$	26.7133	−	4.23097i	0.914645	−	0.144866i	0.595978	+	0.803001i	$0.296765\pi$
$854$	3.05346	−	9.39759i	0.104487	−	0.321579i
$855$		0			0
$856$	−0.647232	+	0.470242i	−0.0221220	+	0.0160725i
$857$	33.1497	+	33.1497i	1.13237	+	1.13237i	0.989782	+	0.142591i	$0.0455432\pi$
$857$	33.1497	+	33.1497i	1.13237	+	1.13237i	0.142591	+	0.989782i	$0.454457\pi$
$858$	−4.79856	−	2.47765i	−0.163820	−	0.0845857i
$859$			47.2517i			1.61221i	0.591775	+	0.806103i	$0.298427\pi$
$859$			47.2517i			1.61221i	−0.591775	+	0.806103i	$0.701573\pi$
$860$		0			0
$861$	−3.65072	−	11.2358i	−0.124416	−	0.382914i
$862$	4.39749	+	8.63057i	0.149779	+	0.293958i
$863$	−2.43422	−	15.3690i	−0.0828617	−	0.523168i	−0.993850	−	0.110736i	$-0.964679\pi$
$863$	−2.43422	−	15.3690i	−0.0828617	−	0.523168i	0.910988	−	0.412432i	$-0.135321\pi$
$864$	21.4801	+	15.6062i	0.730768	+	0.530934i
$865$		0			0
$866$	−13.2947	+	4.31972i	−0.451773	+	0.146790i
$867$	1.91655	−	12.1006i	0.0650896	−	0.410959i
$868$	−24.4863	+	24.4863i	−0.831118	+	0.831118i
$869$	−29.9413	+	40.7470i	−1.01569	+	1.38225i
$870$		0			0
$871$	−3.19826	−	4.40203i	−0.108369	−	0.149157i
$872$	−15.4941	−	7.89464i	−0.524696	−	0.267346i
$873$	15.2674	−	7.77913i	0.516723	−	0.263284i
$874$	3.52861	−	4.85671i	0.119357	−	0.164281i
$875$		0			0
$876$	−28.2536	−	9.18015i	−0.954601	−	0.310169i
$877$	13.2254	−	25.9562i	0.446589	−	0.876480i	−0.552488	−	0.833521i	$-0.686321\pi$
$877$	13.2254	−	25.9562i	0.446589	−	0.876480i	0.999077	−	0.0429592i	$-0.0136785\pi$
$878$	−1.50621	−	0.238560i	−0.0508321	−	0.00805101i
$879$	−16.7229			−0.564048
$880$		0			0
$881$	4.18815			0.141102			0.0705512	−	0.997508i	$-0.477524\pi$
$881$	4.18815			0.141102			0.0705512	+	0.997508i	$0.477524\pi$
$882$	−1.23576	−	0.195725i	−0.0416102	−	0.00659041i
$883$	−20.7555	+	40.7349i	−0.698477	+	1.37084i	0.220053	+	0.975488i	$0.429377\pi$
$883$	−20.7555	+	40.7349i	−0.698477	+	1.37084i	−0.918530	+	0.395351i	$0.870623\pi$
$884$	25.8286	+	8.39221i	0.868709	+	0.282261i
$885$		0			0
$886$	−9.11003	+	12.5389i	−0.306057	+	0.421252i
$887$	30.7027	−	15.6438i	1.03090	−	0.525267i	0.145136	−	0.989412i	$-0.453638\pi$
$887$	30.7027	−	15.6438i	1.03090	−	0.525267i	0.885760	+	0.464144i	$0.153638\pi$
$888$	−2.16926	−	1.10529i	−0.0727955	−	0.0370912i
$889$	−16.1646	−	22.2487i	−0.542143	−	0.746196i
$890$		0			0
$891$	−0.0178389	+	3.31037i	−0.000597626	+	0.110902i
$892$	−7.70048	+	7.70048i	−0.257831	+	0.257831i
$893$	−2.36100	+	14.9068i	−0.0790078	+	0.498836i
$894$	−9.51300	+	3.09096i	−0.318162	+	0.103377i
$895$		0			0
$896$	26.6503	+	19.3626i	0.890323	+	0.646857i
$897$	−1.56420	−	9.87594i	−0.0522270	−	0.329748i
$898$	7.75836	+	15.2266i	0.258900	+	0.508119i
$899$	−5.50871	−	16.9541i	−0.183726	−	0.565450i
$900$		0			0
$901$			7.78489i			0.259352i
$902$	−5.14481	+	2.58659i	−0.171303	+	0.0861239i
$903$	16.8566	+	16.8566i	0.560951	+	0.560951i
$904$	−30.1177	+	21.8818i	−1.00170	+	0.727778i
$905$		0			0
$906$	3.05911	−	9.41497i	0.101632	−	0.312791i
$907$	−38.0387	+	6.02474i	−1.26306	+	0.200048i	−0.751806	−	0.659384i	$-0.770817\pi$
$907$	−38.0387	+	6.02474i	−1.26306	+	0.200048i	−0.511249	+	0.859433i	$0.670817\pi$
$908$	−5.77055	+	0.913965i	−0.191502	+	0.0303310i
$909$	1.00402	−	3.09005i	0.0333012	−	0.102490i
$910$		0			0
$911$	29.8280	−	21.6713i	0.988244	−	0.718002i	0.0287085	−	0.999588i	$-0.490861\pi$
$911$	29.8280	−	21.6713i	0.988244	−	0.718002i	0.959536	+	0.281586i	$0.0908605\pi$
$912$	−8.67283	−	8.67283i	−0.287186	−	0.287186i
$913$	19.8022	−	9.95566i	0.655356	−	0.329484i
$914$			2.49056i			0.0823805i
$915$		0			0
$916$	−2.90677	−	8.94611i	−0.0960423	−	0.295588i
$917$	−9.95237	−	19.5326i	−0.328656	−	0.645024i
$918$	2.15595	+	13.6122i	0.0711571	+	0.449268i
$919$	−24.5973	−	17.8710i	−0.811392	−	0.589510i	0.102842	−	0.994698i	$-0.467206\pi$
$919$	−24.5973	−	17.8710i	−0.811392	−	0.589510i	−0.914234	+	0.405187i	$0.867206\pi$
$920$		0			0
$921$	1.34081	−	0.435657i	0.0441813	−	0.0143554i
$922$	0.952647	−	6.01478i	0.0313738	−	0.198086i
$923$	5.94554	−	5.94554i	0.195700	−	0.195700i
$924$	−0.104612	+	19.4129i	−0.00344148	+	0.638636i
$925$		0			0
$926$	−7.82350	−	10.7681i	−0.257096	−	0.353862i
$927$	9.35797	+	4.76812i	0.307356	+	0.156606i
$928$	−11.6788	+	5.95063i	−0.383374	+	0.195339i
$929$	13.6936	−	18.8477i	0.449273	−	0.618372i	−0.522968	−	0.852352i	$-0.675175\pi$
$929$	13.6936	−	18.8477i	0.449273	−	0.618372i	0.972241	+	0.233981i	$0.0751752\pi$
$930$		0			0
$931$	5.86938	+	1.90708i	0.192361	+	0.0625020i
$932$	−3.53335	+	6.93458i	−0.115739	+	0.227150i
$933$	−15.9199	−	2.52147i	−0.521196	−	0.0825493i
$934$	−19.3837			−0.634254
$935$		0			0
$936$	−9.14869			−0.299034
$937$	7.94449	+	1.25828i	0.259535	+	0.0411063i	0.284846	−	0.958573i	$-0.408058\pi$
$937$	7.94449	+	1.25828i	0.259535	+	0.0411063i	−0.0253108	+	0.999680i	$0.508058\pi$
$938$	1.20216	−	2.35937i	0.0392519	−	0.0770362i
$939$	0.801481	+	0.260417i	0.0261553	+	0.00849838i
$940$		0			0
$941$	28.1490	−	38.7438i	0.917631	−	1.26301i	−0.0468615	−	0.998901i	$-0.514922\pi$
$941$	28.1490	−	38.7438i	0.917631	−	1.26301i	0.964493	−	0.264110i	$-0.0850781\pi$
$942$	10.6412	−	5.42198i	0.346710	−	0.176658i
$943$	−9.49976	−	4.84037i	−0.309355	−	0.157624i
$944$	−2.47782	−	3.41042i	−0.0806460	−	0.111000i
$945$		0			0
$946$	6.88039	−	9.36352i	0.223701	−	0.304434i
$947$	−9.38618	+	9.38618i	−0.305010	+	0.305010i	−0.842970	−	0.537960i	$-0.819195\pi$
$947$	−9.38618	+	9.38618i	−0.305010	+	0.305010i	0.537960	+	0.842970i	$0.319195\pi$
$948$	4.78668	−	30.2219i	0.155464	−	0.981563i
$949$	41.1978	−	13.3860i	1.33734	−	0.434528i
$950$		0			0
$951$	15.7309	+	11.4292i	0.510109	+	0.370616i
$952$	4.41491	+	27.8746i	0.143088	+	0.903422i
$953$	−24.1733	−	47.4428i	−0.783051	−	1.53682i	−0.842564	−	0.538597i	$-0.818955\pi$
$953$	−24.1733	−	47.4428i	−0.783051	−	1.53682i	0.0595128	−	0.998228i	$-0.481045\pi$
$954$	−0.379511	−	1.16802i	−0.0122871	−	0.0378159i
$955$		0			0
$956$			18.4130i			0.595519i
$957$	−8.87987	−	4.58496i	−0.287045	−	0.148211i
$958$	−13.2098	−	13.2098i	−0.426790	−	0.426790i
$959$	36.2628	−	26.3465i	1.17099	−	0.850772i
$960$		0			0
$961$	4.46097	−	13.7294i	0.143902	−	0.442885i
$962$	1.64201	−	0.260069i	0.0529405	−	0.00838495i
$963$	−0.732081	+	0.115950i	−0.0235910	+	0.00373644i
$964$	15.1642	−	46.6706i	0.488406	−	1.50316i
$965$		0			0
$966$	3.93674	−	2.86021i	0.126662	−	0.0920256i
$967$	−38.6475	−	38.6475i	−1.24282	−	1.24282i	−0.958826	−	0.283994i	$-0.908340\pi$
$967$	−38.6475	−	38.6475i	−1.24282	−	1.24282i	−0.283994	−	0.958826i	$-0.591660\pi$
$968$	19.9901	−	2.94563i	0.642505	−	0.0946763i
$969$		−	24.6055i		−	0.790443i
$970$		0			0
$971$	2.55556	+	7.86521i	0.0820119	+	0.252407i	0.983652	−	0.180081i	$-0.0576360\pi$
$971$	2.55556	+	7.86521i	0.0820119	+	0.252407i	−0.901640	+	0.432487i	$0.857636\pi$
$972$	11.9430	+	23.4395i	0.383073	+	0.751823i
$973$	−1.89900	−	11.9898i	−0.0608790	−	0.384375i
$974$	10.7378	+	7.80149i	0.344062	+	0.249976i
$975$		0			0
$976$	−17.3278	+	5.63014i	−0.554649	+	0.180216i
$977$	8.56551	−	54.0805i	0.274035	−	1.73019i	−0.339575	−	0.940579i	$-0.610283\pi$
$977$	8.56551	−	54.0805i	0.274035	−	1.73019i	0.613610	−	0.789610i	$-0.289717\pi$
$978$	4.10153	−	4.10153i	0.131152	−	0.131152i
$979$	−11.2607	−	35.3029i	−0.359892	−	1.12829i
$980$		0			0
$981$	−9.46980	−	13.0341i	−0.302347	−	0.416145i
$982$	−1.72822	−	0.880571i	−0.0551496	−	0.0281001i
$983$	−12.1525	+	6.19202i	−0.387606	+	0.197495i	−0.636924	−	0.770927i	$-0.719793\pi$
$983$	−12.1525	+	6.19202i	−0.387606	+	0.197495i	0.249318	+	0.968422i	$0.419793\pi$
$984$	4.37373	−	6.01992i	0.139429	−	0.191908i
$985$		0			0
$986$	−6.47069	−	2.10245i	−0.206069	−	0.0669558i
$987$	−5.55398	+	10.9003i	−0.176785	+	0.346960i
$988$	20.8726	+	3.30589i	0.664045	+	0.105174i
$989$	21.5139			0.684102
$990$		0			0
$991$	6.43457			0.204401			0.102200	−	0.994764i	$-0.467412\pi$
$991$	6.43457			0.204401			0.102200	+	0.994764i	$0.467412\pi$
$992$	−32.9965	−	5.22613i	−1.04764	−	0.165930i
$993$	7.71694	−	15.1453i	0.244890	−	0.480623i
$994$	3.89164	+	1.26447i	0.123435	+	0.0401066i
$995$		0			0
$996$	−7.88351	+	10.8507i	−0.249799	+	0.343818i
$997$	18.9575	−	9.65934i	0.600391	−	0.305914i	−0.127252	−	0.991870i	$-0.540616\pi$
$997$	18.9575	−	9.65934i	0.600391	−	0.305914i	0.727643	+	0.685956i	$0.240616\pi$
$998$	2.79564	+	1.42445i	0.0884943	+	0.0450901i
$999$	−3.66296	−	5.04163i	−0.115891	−	0.159510i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.bm.b.118.2		32
5.2	odd	4	inner	275.2.bm.b.107.3		32
5.3	odd	4		55.2.l.a.52.2	yes	32
5.4	even	2		55.2.l.a.8.3	yes	32
11.7	odd	10	inner	275.2.bm.b.18.3		32
15.8	even	4		495.2.bj.a.217.3		32
15.14	odd	2		495.2.bj.a.118.2		32
20.3	even	4		880.2.cm.a.657.3		32
20.19	odd	2		880.2.cm.a.833.2		32
55.3	odd	20		605.2.m.c.457.3		32
55.4	even	10		605.2.m.e.403.3		32
55.7	even	20	inner	275.2.bm.b.7.2		32
55.8	even	20		605.2.m.d.457.2		32
55.9	even	10		605.2.e.b.483.8		32
55.13	even	20		605.2.e.b.362.8		32
55.14	even	10		605.2.m.c.578.3		32
55.18	even	20		55.2.l.a.7.3	✓	32
55.19	odd	10		605.2.m.d.578.2		32
55.24	odd	10		605.2.e.b.483.9		32
55.28	even	20		605.2.m.c.112.3		32
55.29	odd	10		55.2.l.a.18.2	yes	32
55.38	odd	20		605.2.m.d.112.2		32
55.39	odd	10		605.2.m.c.233.3		32
55.43	even	4		605.2.m.e.602.3		32
55.48	odd	20		605.2.m.e.282.2		32
55.49	even	10		605.2.m.d.233.2		32
55.53	odd	20		605.2.e.b.362.9		32
55.54	odd	2		605.2.m.e.118.2		32
165.29	even	10		495.2.bj.a.73.3		32
165.128	odd	20		495.2.bj.a.172.2		32
220.139	even	10		880.2.cm.a.513.3		32
220.183	odd	20		880.2.cm.a.337.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.3	✓	32	55.18	even	20
55.2.l.a.8.3	yes	32	5.4	even	2
55.2.l.a.18.2	yes	32	55.29	odd	10
55.2.l.a.52.2	yes	32	5.3	odd	4
275.2.bm.b.7.2		32	55.7	even	20	inner
275.2.bm.b.18.3		32	11.7	odd	10	inner
275.2.bm.b.107.3		32	5.2	odd	4	inner
275.2.bm.b.118.2		32	1.1	even	1	trivial
495.2.bj.a.73.3		32	165.29	even	10
495.2.bj.a.118.2		32	15.14	odd	2
495.2.bj.a.172.2		32	165.128	odd	20
495.2.bj.a.217.3		32	15.8	even	4
605.2.e.b.362.8		32	55.13	even	20
605.2.e.b.362.9		32	55.53	odd	20
605.2.e.b.483.8		32	55.9	even	10
605.2.e.b.483.9		32	55.24	odd	10
605.2.m.c.112.3		32	55.28	even	20
605.2.m.c.233.3		32	55.39	odd	10
605.2.m.c.457.3		32	55.3	odd	20
605.2.m.c.578.3		32	55.14	even	10
605.2.m.d.112.2		32	55.38	odd	20
605.2.m.d.233.2		32	55.49	even	10
605.2.m.d.457.2		32	55.8	even	20
605.2.m.d.578.2		32	55.19	odd	10
605.2.m.e.118.2		32	55.54	odd	2
605.2.m.e.282.2		32	55.48	odd	20
605.2.m.e.403.3		32	55.4	even	10
605.2.m.e.602.3		32	55.43	even	4
880.2.cm.a.337.2		32	220.183	odd	20
880.2.cm.a.513.3		32	220.139	even	10
880.2.cm.a.657.3		32	20.3	even	4
880.2.cm.a.833.2		32	20.19	odd	2

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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.bm (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.482327 - 0.0763931i) q^{2} +(-0.517260 + 1.01518i) q^{3} +(-1.67531 - 0.544341i) q^{4} +(0.327041 - 0.450133i) q^{6} +(2.59854 - 1.32402i) q^{7} +(1.63669 + 0.833936i) q^{8} +(1.00032 + 1.37683i) q^{9} +(-3.15977 + 1.00788i) q^{11} +(1.41917 - 1.41917i) q^{12} +(-0.457808 + 2.89049i) q^{13} +(-1.35449 + 0.440102i) q^{14} +(2.12449 + 1.54353i) q^{16} +(0.824113 + 5.20325i) q^{17} +(-0.377304 - 0.740500i) q^{18} +(1.26677 + 3.89873i) q^{19} +3.32285i q^{21} +(1.60104 - 0.244743i) q^{22} +(2.12046 + 2.12046i) q^{23} +(-1.69319 + 1.23017i) q^{24} +(0.441627 - 1.35919i) q^{26} +(-5.29116 + 0.838037i) q^{27} +(-5.07408 + 0.803656i) q^{28} +(0.817241 - 2.51521i) q^{29} +(5.45328 - 3.96204i) q^{31} +(-3.50456 - 3.50456i) q^{32} +(0.611244 - 3.72907i) q^{33} -2.57262i q^{34} +(-0.926389 - 2.85113i) q^{36} +(0.528116 + 1.03649i) q^{37} +(-0.313163 - 1.97724i) q^{38} +(-2.69755 - 1.95989i) q^{39} +(-3.38136 + 1.09867i) q^{41} +(0.253843 - 1.60270i) q^{42} +(5.07292 - 5.07292i) q^{43} +(5.84223 + 0.0314826i) q^{44} +(-0.860769 - 1.18475i) q^{46} +(3.28041 + 1.67145i) q^{47} +(-2.66588 + 1.35833i) q^{48} +(0.884888 - 1.21794i) q^{49} +(-5.70851 - 1.85481i) q^{51} +(2.34038 - 4.59325i) q^{52} +(1.45955 + 0.231169i) q^{53} +2.61609 q^{54} +5.35716 q^{56} +(-4.61316 - 0.730652i) q^{57} +(-0.586323 + 1.15072i) q^{58} +(-1.52672 - 0.496061i) q^{59} +(-4.07810 + 5.61302i) q^{61} +(-2.93294 + 1.49441i) q^{62} +(4.42234 + 2.25330i) q^{63} +(-1.66445 - 2.29092i) q^{64} +(-0.579695 + 1.75194i) q^{66} +(-1.31471 + 1.31471i) q^{67} +(1.45170 - 9.16564i) q^{68} +(-3.24948 + 1.05582i) q^{69} +(-2.32441 - 1.68878i) q^{71} +(0.489036 + 3.08765i) q^{72} +(-6.71992 - 13.1886i) q^{73} +(-0.175544 - 0.540270i) q^{74} -7.22113i q^{76} +(-6.87635 + 6.80264i) q^{77} +(1.15138 + 1.15138i) q^{78} +(12.3342 - 8.96129i) q^{79} +(0.308439 - 0.949277i) q^{81} +(1.71486 - 0.271606i) q^{82} +(-6.60041 + 1.04540i) q^{83} +(1.80876 - 5.56680i) q^{84} +(-2.83434 + 2.05927i) q^{86} +(2.13066 + 2.13066i) q^{87} +(-6.01208 - 0.985459i) q^{88} +11.1726i q^{89} +(2.63744 + 8.11720i) q^{91} +(-2.39818 - 4.70669i) q^{92} +(1.20142 + 7.58545i) q^{93} +(-1.45454 - 1.05679i) q^{94} +(5.37052 - 1.74499i) q^{96} +(1.57505 - 9.94447i) q^{97} +(-0.519848 + 0.519848i) q^{98} +(-4.54848 - 3.34226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{2} + 4 q^{3} - 20 q^{6} + 10 q^{8} - 24 q^{11} - 12 q^{12} + 10 q^{13} - 8 q^{16} + 10 q^{18} - 10 q^{22} + 24 q^{23} + 20 q^{26} + 16 q^{27} - 50 q^{28} - 28 q^{31} - 66 q^{33} + 24 q^{36}+ \cdots + 8 q^{97}+O(q^{100}) \) 32 * q + 10 * q^2 + 4 * q^3 - 20 * q^6 + 10 * q^8 - 24 * q^11 - 12 * q^12 + 10 * q^13 - 8 * q^16 + 10 * q^18 - 10 * q^22 + 24 * q^23 + 20 * q^26 + 16 * q^27 - 50 * q^28 - 28 * q^31 - 66 * q^33 + 24 * q^36 + 8 * q^37 - 10 * q^38 + 40 * q^41 + 10 * q^42 + 60 * q^46 + 28 * q^47 + 54 * q^48 + 20 * q^51 + 50 * q^52 + 24 * q^53 - 80 * q^56 - 30 * q^57 + 50 * q^58 - 60 * q^61 - 100 * q^62 + 30 * q^63 - 100 * q^66 + 8 * q^67 + 30 * q^68 + 24 * q^71 - 80 * q^72 - 50 * q^73 - 70 * q^77 - 60 * q^78 - 12 * q^81 + 10 * q^82 - 90 * q^83 + 100 * q^86 - 170 * q^88 + 20 * q^91 + 68 * q^92 + 8 * q^93 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more