LMFDB - Embedded newform 275.2.bm.b.7.2

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			7.2
Character	$\chi$	$=$	275.7
Dual form			275.2.bm.b.118.2

$q$-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 $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{4}\right)$

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	−0.324614	−	0.945847i	$-0.605234\pi$
$2$	−0.482327	+	0.0763931i	−0.341057	+	0.0540181i	−0.0164432	+	0.999865i	$0.505234\pi$
$3$	−0.517260	−	1.01518i	−0.298640	−	0.586114i	0.692114	−	0.721789i	$-0.256680\pi$
$3$	−0.517260	−	1.01518i	−0.298640	−	0.586114i	−0.990753	+	0.135675i	$0.956680\pi$
$4$	−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	0.869891	−	0.493244i	$-0.164189\pi$
$7$	2.59854	+	1.32402i	0.982157	+	0.500434i	0.112266	+	0.993678i	$0.464189\pi$
$8$	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	−0.966181	−	0.257866i	$-0.916981\pi$
$13$	−0.457808	−	2.89049i	−0.126973	−	0.801677i	0.839208	−	0.543811i	$-0.183019\pi$
$14$	−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	−0.659920	−	0.751336i	$-0.729410\pi$
$17$	0.824113	−	5.20325i	0.199877	−	1.26197i	0.859797	−	0.510636i	$-0.170590\pi$
$18$	−0.377304	+	0.740500i	−0.0889313	+	0.174538i
$19$	1.26677	−	3.89873i	0.290618	−	0.894429i	−0.694041	−	0.719936i	$-0.744171\pi$
$19$	1.26677	−	3.89873i	0.290618	−	0.894429i	0.984658	−	0.174494i	$-0.0558288\pi$
$20$		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	−0.450586	−	0.892733i	$-0.648785\pi$
$23$	2.12046	−	2.12046i	0.442147	−	0.442147i	0.892733	+	0.450586i	$0.148785\pi$
$24$	−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	0.997818	−	0.0660248i	$-0.0210316\pi$
$29$	0.817241	+	2.51521i	0.151758	+	0.467063i	−0.846060	+	0.533088i	$0.821032\pi$
$30$		0			0
$31$	5.45328	+	3.96204i	0.979438	+	0.711603i	0.957583	−	0.288158i	$-0.0930429\pi$
$31$	5.45328	+	3.96204i	0.979438	+	0.711603i	0.0218548	+	0.999761i	$0.493043\pi$
$32$	−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	−0.843513	−	0.537109i	$-0.819516\pi$
$37$	0.528116	−	1.03649i	0.0868218	−	0.170397i	0.930335	+	0.366712i	$0.119516\pi$
$38$	−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	0.0328289	−	0.999461i	$-0.489548\pi$
$41$	−3.38136	−	1.09867i	−0.528080	−	0.171584i	−0.560909	+	0.827877i	$0.689548\pi$
$42$	0.253843	+	1.60270i	0.0391688	+	0.247302i
$43$	5.07292	+	5.07292i	0.773613	+	0.773613i	0.978736	−	0.205123i	$-0.0657595\pi$
$43$	5.07292	+	5.07292i	0.773613	+	0.773613i	−0.205123	+	0.978736i	$0.565759\pi$
$44$	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	−0.198070	−	0.980188i	$-0.563467\pi$
$47$	3.28041	−	1.67145i	0.478497	−	0.243806i	0.676566	+	0.736382i	$0.263467\pi$
$48$	−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	−0.0553847	−	0.998465i	$-0.517639\pi$
$53$	1.45955	−	0.231169i	0.200484	−	0.0317536i	0.255869	+	0.966712i	$0.417639\pi$
$54$	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	−0.406706	−	0.913559i	$-0.633323\pi$
$59$	−1.52672	+	0.496061i	−0.198762	+	0.0645817i	0.207944	+	0.978141i	$0.433323\pi$
$60$		0			0
$61$	−4.07810	−	5.61302i	−0.522147	−	0.718674i	0.463761	−	0.885960i	$-0.346500\pi$
$61$	−4.07810	−	5.61302i	−0.522147	−	0.718674i	−0.985908	+	0.167286i	$0.946500\pi$
$62$	−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	0.622223	−	0.782840i	$-0.286230\pi$
$67$	−1.31471	−	1.31471i	−0.160617	−	0.160617i	−0.782840	+	0.622223i	$0.786230\pi$
$68$	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	−0.717108	−	0.696962i	$-0.754535\pi$
$71$	−2.32441	+	1.68878i	−0.275857	+	0.200422i	0.441251	+	0.897384i	$0.354535\pi$
$72$	0.489036	−	3.08765i	0.0576334	−	0.363883i
$73$	−6.71992	+	13.1886i	−0.786507	+	1.54361i	0.0519568	+	0.998649i	$0.483454\pi$
$73$	−6.71992	+	13.1886i	−0.786507	+	1.54361i	−0.838464	+	0.544957i	$0.816546\pi$
$74$	−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	0.996113	+	0.0880839i	$0.0280744\pi$
$79$	12.3342	+	8.96129i	1.38770	+	1.00822i	0.391589	+	0.920140i	$0.371926\pi$
$80$		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	−0.216711	−	0.976236i	$-0.569533\pi$
$83$	−6.60041	−	1.04540i	−0.724489	−	0.114748i	−0.507778	+	0.861488i	$0.669533\pi$
$84$	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	$-0.798281\pi$
$89$		−	11.1726i		−	1.18429i	0.805830	−	0.592147i	$-0.201719\pi$
$90$		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	0.928873	+	0.370400i	$0.120779\pi$
$97$	1.57505	+	9.94447i	0.159922	+	1.00971i	−0.768951	+	0.639308i	$0.779221\pi$
$98$	−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	−0.861189	−	0.508285i	$-0.830280\pi$
$101$	−1.12216	+	1.54452i	−0.111659	+	0.153686i	0.749530	+	0.661971i	$0.230280\pi$
$102$	2.61167	−	1.33071i	0.258594	−	0.131760i
$103$	5.49869	+	2.80172i	0.541802	+	0.276062i	0.703399	−	0.710795i	$-0.251665\pi$
$103$	5.49869	+	2.80172i	0.541802	+	0.276062i	−0.161597	+	0.986857i	$0.551665\pi$
$104$	−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	0.881252	−	0.472647i	$-0.156702\pi$
$107$	−0.197726	−	0.388059i	−0.0191149	−	0.0375151i	−0.900367	+	0.435132i	$0.856702\pi$
$108$	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	−0.701999	−	0.712178i	$-0.747709\pi$
$113$	−9.20080	−	18.0576i	−0.865538	−	1.69871i	−0.163539	−	0.986537i	$-0.552291\pi$
$114$	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	0.831644	+	0.555309i	$0.187400\pi$
$127$	−1.47513	+	9.31359i	−0.130896	+	0.826447i	−0.962540	+	0.271138i	$0.912600\pi$
$128$	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	$0.106500\pi$
$131$			7.51676i			0.656743i	−0.944549	+	0.328371i	$0.893500\pi$
$132$	−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	0.766458	−	0.642294i	$-0.222017\pi$
$137$	15.1801	+	2.40429i	1.29692	+	0.205413i	0.530466	+	0.847706i	$0.322017\pi$
$138$	1.64797	+	0.261013i	0.140285	+	0.0222189i
$139$	1.28625	+	3.95867i	0.109098	+	0.335770i	0.990670	−	0.136279i	$-0.0435145\pi$
$139$	1.28625	+	3.95867i	0.109098	+	0.335770i	−0.881572	+	0.472049i	$0.843514\pi$
$140$		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	−0.993421	−	0.114516i	$-0.963468\pi$
$149$	−14.5440	+	10.5669i	−1.19149	+	0.865672i	−0.198073	+	0.980187i	$0.563468\pi$
$150$		0			0
$151$	16.9214	+	5.49808i	1.37704	+	0.447427i	0.901695	−	0.432372i	$-0.142323\pi$
$151$	16.9214	+	5.49808i	1.37704	+	0.447427i	0.475345	+	0.879800i	$0.342323\pi$
$152$	−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	0.528887	−	0.848693i	$-0.322610\pi$
$157$	19.1253	−	9.74483i	1.52636	−	0.777722i	0.997478	+	0.0709708i	$0.0226097\pi$
$158$	−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	0.260446	−	0.965488i	$-0.416130\pi$
$163$	10.2967	−	1.63083i	0.806497	−	0.127737i	0.546051	+	0.837752i	$0.316130\pi$
$164$	6.26288			0.489049
$165$		0			0
$166$	3.26342			0.253290
$167$	−11.1538	+	1.76660i	−0.863110	+	0.136703i	−0.572267	−	0.820067i	$-0.693936\pi$
$167$	−11.1538	+	1.76660i	−0.863110	+	0.136703i	−0.290843	+	0.956771i	$0.593936\pi$
$168$	−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	0.0544963	−	0.998514i	$-0.482645\pi$
$173$	11.7632	−	5.99367i	0.894343	−	0.455691i	0.839847	+	0.542823i	$0.182645\pi$
$174$	−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	0.387089	−	0.922042i	$-0.373480\pi$
$179$	2.11776	+	0.688100i	0.158288	+	0.0514310i	−0.228801	+	0.973473i	$0.573480\pi$
$180$		0			0
$181$	−3.50687	+	2.54789i	−0.260664	+	0.189383i	−0.710440	−	0.703758i	$-0.751504\pi$
$181$	−3.50687	+	2.54789i	−0.260664	+	0.189383i	0.449776	+	0.893141i	$0.351504\pi$
$182$	−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	0.895061	−	0.445944i	$-0.147132\pi$
$191$	−1.26010	−	3.87820i	−0.0911779	−	0.280617i	−0.986239	+	0.165327i	$0.947132\pi$
$192$	3.18664	+	0.504715i	0.229976	+	0.0364247i
$193$	−20.6434	−	3.26960i	−1.48595	−	0.235351i	−0.639899	−	0.768459i	$-0.721024\pi$
$193$	−20.6434	−	3.26960i	−1.48595	−	0.235351i	−0.846047	+	0.533108i	$0.821024\pi$
$194$	−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	−0.699450	−	0.714681i	$-0.746572\pi$
$197$	0.213782	−	0.213782i	0.0152313	−	0.0152313i	0.714681	+	0.699450i	$0.246572\pi$
$198$	1.93853	−	1.95954i	0.137765	−	0.139258i
$199$			11.0815i			0.785549i	0.919635	+	0.392775i	$0.128485\pi$
$199$			11.0815i			0.785549i	−0.919635	+	0.392775i	$0.871515\pi$
$200$		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	−0.949684	−	0.313210i	$-0.898596\pi$
$211$	−5.20512	+	7.16423i	−0.358335	+	0.493206i	0.591349	+	0.806416i	$0.298596\pi$
$212$	−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	0.965683	−	0.259723i	$-0.0836313\pi$
$223$	2.80667	+	5.50839i	0.187948	+	0.368869i	−0.777735	+	0.628593i	$0.783631\pi$
$224$	−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	0.549304	−	0.835622i	$-0.314893\pi$
$227$	2.95522	+	1.50576i	0.196145	+	0.0999406i	−0.353160	+	0.935563i	$0.614893\pi$
$228$	7.33074	−	3.73520i	0.485490	−	0.247370i
$229$	3.13876	−	4.32013i	0.207415	−	0.285482i	−0.692618	−	0.721305i	$-0.743543\pi$
$229$	3.13876	−	4.32013i	0.207415	−	0.285482i	0.900032	+	0.435823i	$0.143543\pi$
$230$		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	0.999930	−	0.0118446i	$-0.00377033\pi$
$233$	0.691167	+	4.36386i	0.0452799	+	0.285886i	−0.954650	+	0.297730i	$0.903770\pi$
$234$	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	0.790590	+	0.612346i	$0.209774\pi$
$239$	−3.23012	+	9.94128i	−0.208939	+	0.643048i	−0.999529	+	0.0307017i	$0.990226\pi$
$240$		0			0
$241$		−	27.8579i		−	1.79449i	−0.441536	−	0.897243i	$-0.645566\pi$
$241$		−	27.8579i		−	1.79449i	0.441536	−	0.897243i	$-0.354434\pi$
$242$	−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	0.812028	−	0.583619i	$-0.198364\pi$
$251$	8.04670	+	5.84627i	0.507903	+	0.369013i	−0.304124	+	0.952632i	$0.598364\pi$
$252$	−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	−0.823136	−	0.567844i	$-0.807778\pi$
$257$	1.92513	−	3.77828i	0.120086	−	0.235683i	0.943223	+	0.332161i	$0.107778\pi$
$258$	−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	0.999998	−	0.00211364i	$-0.000672793\pi$
$263$	16.1830	+	16.1830i	0.997884	+	0.997884i	−0.00211364	+	0.999998i	$0.500673\pi$
$264$	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	0.989759	+	0.142745i	$0.0455930\pi$
$269$	13.4435	+	18.5034i	0.819666	+	1.12817i	−0.170094	+	0.985428i	$0.554407\pi$
$270$		0			0
$271$	−1.32229	+	0.429640i	−0.0803237	+	0.0260987i	−0.348903	−	0.937159i	$-0.613446\pi$
$271$	−1.32229	+	0.429640i	−0.0803237	+	0.0260987i	0.268580	+	0.963258i	$0.413446\pi$
$272$	−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	−0.564363	−	0.825527i	$-0.690878\pi$
$277$	−14.0803	+	2.23010i	−0.846002	+	0.133994i	−0.281639	+	0.959520i	$0.590878\pi$
$278$	−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	0.973604	+	0.228246i	$0.0732990\pi$
$281$	14.9161	+	20.5302i	0.889818	+	1.22473i	−0.0837853	+	0.996484i	$0.526701\pi$
$282$	1.82520	+	0.929988i	0.108689	+	0.0553800i
$283$	−6.60300	+	3.36440i	−0.392508	+	0.199993i	−0.639095	−	0.769128i	$-0.720691\pi$
$283$	−6.60300	+	3.36440i	−0.392508	+	0.199993i	0.246587	+	0.969121i	$0.420691\pi$
$284$	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	−0.610324	−	0.792152i	$-0.708961\pi$
$293$	6.66340	−	13.0777i	0.389280	−	0.764005i	0.999604	+	0.0281472i	$0.00896072\pi$
$294$	−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	−0.731634	−	0.681698i	$-0.761242\pi$
$307$	−0.874954	+	0.874954i	−0.0499363	+	0.0499363i	0.681698	+	0.731634i	$0.261242\pi$
$308$	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	−0.747256	−	0.664537i	$-0.768629\pi$
$311$	4.37162	−	13.4545i	0.247892	−	0.762933i	0.995147	−	0.0983958i	$-0.0313711\pi$
$312$	−2.78064	+	5.45732i	−0.157423	+	0.308960i
$313$	−0.115706	+	0.730542i	−0.00654011	+	0.0412927i	−0.990743	−	0.135754i	$-0.956654\pi$
$313$	−0.115706	+	0.730542i	−0.00654011	+	0.0412927i	0.984202	+	0.177047i	$0.0566543\pi$
$314$	−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	0.941839	+	0.336065i	$0.109096\pi$
$317$	2.66972	+	16.8560i	0.149947	+	0.946726i	−0.791892	+	0.610661i	$0.790904\pi$
$318$	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	0.667767	−	0.744370i	$-0.267250\pi$
$337$	8.40891	+	4.28455i	0.458062	+	0.233394i	−0.209705	+	0.977765i	$0.567250\pi$
$338$	−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	0.765012	+	0.644016i	$0.222733\pi$
$347$	−3.00971	+	19.0026i	−0.161570	+	1.02011i	−0.926581	+	0.376094i	$0.877267\pi$
$348$	−2.40971	+	4.72933i	−0.129174	+	0.253518i
$349$	4.59599	−	14.1450i	0.246018	−	0.757164i	−0.749450	−	0.662061i	$-0.769682\pi$
$349$	4.59599	−	14.1450i	0.246018	−	0.757164i	0.995467	−	0.0951031i	$-0.0303181\pi$
$350$		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	−0.752989	−	0.658033i	$-0.771389\pi$
$353$	−1.78406	+	1.78406i	−0.0949560	+	0.0949560i	0.658033	+	0.752989i	$0.271389\pi$
$354$	−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	0.857620	−	0.514285i	$-0.171942\pi$
$359$	−2.62416	−	8.07635i	−0.138498	−	0.426253i	−0.996118	+	0.0880312i	$0.971942\pi$
$360$		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	−0.490178	−	0.871622i	$-0.663068\pi$
$367$	9.63799	−	18.9156i	0.503099	−	0.987387i	0.993277	−	0.115765i	$-0.0369318\pi$
$368$	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	0.770609	−	0.637309i	$-0.219952\pi$
$373$	2.57445	+	2.57445i	0.133300	+	0.133300i	−0.637309	+	0.770609i	$0.719952\pi$
$374$	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	0.481636	−	0.876371i	$-0.340043\pi$
$379$	−9.74713	−	13.4158i	−0.500677	−	0.689122i	−0.982312	+	0.187249i	$0.940043\pi$
$380$		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	−0.435890	−	0.900000i	$-0.643566\pi$
$383$	−11.2007	+	1.77402i	−0.572330	+	0.0906481i	−0.136440	+	0.990648i	$0.543566\pi$
$384$	−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	−0.289239	−	0.957257i	$-0.593402\pi$
$389$	0.777554	−	0.252643i	0.0394236	−	0.0128095i	0.328662	+	0.944447i	$0.393402\pi$
$390$		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	0.344159	−	0.938911i	$-0.388164\pi$
$397$	−11.8504	−	11.8504i	−0.594752	−	0.594752i	−0.938911	+	0.344159i	$0.888164\pi$
$398$	−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	0.161262	−	0.986912i	$-0.448444\pi$
$401$	23.0228	−	16.7270i	1.14970	−	0.835308i	0.988441	+	0.151603i	$0.0484436\pi$
$402$	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	0.635187	−	0.772358i	$-0.280923\pi$
$409$	1.95998	+	1.42401i	0.0969146	+	0.0704126i	−0.538273	+	0.842771i	$0.680923\pi$
$410$		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	$-0.868488\pi$
$419$		−	16.4371i		−	0.803006i	0.915858	−	0.401503i	$-0.131512\pi$
$420$		0			0
$421$	−3.85294	+	11.8581i	−0.187781	+	0.577930i	−0.999985	−	0.00544310i	$-0.998267\pi$
$421$	−3.85294	+	11.8581i	−0.187781	+	0.577930i	0.812204	+	0.583373i	$0.198267\pi$
$422$	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	−0.991527	−	0.129900i	$-0.958534\pi$
$431$	−11.6588	+	16.0470i	−0.561586	+	0.772957i	0.429941	+	0.902857i	$0.358534\pi$
$432$	−12.5346	+	6.38668i	−0.603070	+	0.307279i
$433$	25.5054	+	12.9956i	1.22571	+	0.624531i	0.942397	−	0.334496i	$-0.108566\pi$
$433$	25.5054	+	12.9956i	1.22571	+	0.624531i	0.283314	+	0.959027i	$0.408566\pi$
$434$	−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	0.927612	+	0.373545i	$0.121858\pi$
$443$	14.4087	+	28.2787i	0.684579	+	1.34356i	−0.243033	+	0.970018i	$0.578142\pi$
$444$	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	−0.0290462	+	0.999578i	$0.509247\pi$
$449$	−20.5693	+	28.3112i	−0.970726	+	1.33609i	−0.941679	+	0.336511i	$0.890753\pi$
$450$		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	−0.999297	−	0.0375006i	$-0.988060\pi$
$457$	−0.797826	+	5.03728i	−0.0373207	+	0.235634i	0.961976	+	0.273134i	$0.0880604\pi$
$458$	−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	$-0.906211\pi$
$461$		−	12.4703i		−	0.580801i	0.956905	−	0.290400i	$-0.0937885\pi$
$462$	0.813245	−	5.32002i	0.0378356	−	0.247510i
$463$	19.2728	−	19.2728i	0.895684	−	0.895684i	−0.0993669	−	0.995051i	$-0.531682\pi$
$463$	19.2728	−	19.2728i	0.895684	−	0.895684i	0.995051	+	0.0993669i	$0.0316818\pi$
$464$	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	0.968980	−	0.247141i	$-0.0794911\pi$
$467$	39.2044	+	6.20937i	1.81416	+	0.287335i	0.845184	+	0.534476i	$0.179491\pi$
$468$	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	0.421388	−	0.906880i	$-0.361543\pi$
$479$	30.9491	−	22.4858i	1.41410	−	1.02740i	0.992711	−	0.120523i	$-0.0384570\pi$
$480$		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	−0.906384	−	0.422454i	$-0.861169\pi$
$487$	−24.2169	+	12.3391i	−1.09737	+	0.559139i	−0.190987	+	0.981593i	$0.561169\pi$
$488$	−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	−0.222536	−	0.974925i	$-0.571433\pi$
$491$	3.77748	−	1.22738i	0.170475	−	0.0553907i	0.393011	+	0.919534i	$0.371433\pi$
$492$	−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	−0.442579	−	0.896730i	$-0.645936\pi$
$499$	−6.11060	+	1.98546i	−0.273548	+	0.0888812i	0.169031	+	0.985611i	$0.445936\pi$
$500$		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	−0.618747	+	0.785590i	$0.712360\pi$
$503$	−36.2878	+	18.4896i	−1.61799	+	0.824409i	−0.999246	+	0.0388190i	$0.987640\pi$
$504$	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	0.498122	−	0.867107i	$-0.334023\pi$
$509$	8.83124	+	2.86944i	0.391438	+	0.127186i	−0.106684	+	0.994293i	$0.534023\pi$
$510$		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	−0.999869	−	0.0161698i	$-0.994853\pi$
$521$	−4.57564	−	14.0824i	−0.200462	−	0.616960i	0.799407	−	0.600790i	$-0.205147\pi$
$522$	−2.17086	−	0.343831i	−0.0950160	−	0.0150491i
$523$	38.3651	+	6.07643i	1.67759	+	0.265704i	0.921390	−	0.388640i	$-0.127055\pi$
$523$	38.3651	+	6.07643i	1.67759	+	0.265704i	0.756197	+	0.654344i	$0.227055\pi$
$524$	−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	−0.530043	−	0.847971i	$-0.677824\pi$
$541$	10.2392	−	14.0930i	0.440217	−	0.605907i	0.970260	+	0.242064i	$0.0778243\pi$
$542$	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	−0.866478	−	0.499215i	$-0.833622\pi$
$547$	−17.7994	−	34.9333i	−0.761048	−	1.49364i	0.105430	−	0.994427i	$-0.466378\pi$
$548$	−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	−0.407307	−	0.913291i	$-0.633532\pi$
$557$	−32.7010	−	16.6620i	−1.38558	−	0.705991i	−0.978277	+	0.207301i	$0.933532\pi$
$558$	−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	0.978732	+	0.205143i	$0.0657659\pi$
$563$	2.64077	+	16.6732i	0.111295	+	0.702690i	−0.867437	+	0.497547i	$0.834234\pi$
$564$	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	−0.932432	−	0.361345i	$-0.882318\pi$
$569$	0.818531	−	2.51918i	0.0343146	−	0.105609i	0.966747	+	0.255736i	$0.0823176\pi$
$570$		0			0
$571$			29.8675i			1.24992i	0.780658	+	0.624959i	$0.214884\pi$
$571$			29.8675i			1.24992i	−0.780658	+	0.624959i	$0.785116\pi$
$572$	−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	0.163809	−	0.986492i	$-0.447622\pi$
$577$	0.354477	+	0.0561437i	0.0147571	+	0.00233729i	−0.149052	+	0.988829i	$0.547622\pi$
$578$	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	0.511501	+	0.859282i	$0.329090\pi$
$587$	−11.7343	+	23.0298i	−0.484326	+	0.950543i	−0.995827	+	0.0912603i	$0.970910\pi$
$588$	−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	0.482794	−	0.875734i	$-0.339622\pi$
$593$	−9.56872	−	9.56872i	−0.392940	−	0.392940i	−0.875734	+	0.482794i	$0.839622\pi$
$594$	−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	0.923041	−	0.384701i	$-0.125696\pi$
$599$	6.65542	+	9.16040i	0.271933	+	0.374284i	−0.651108	+	0.758985i	$0.725696\pi$
$600$		0			0
$601$	−15.6822	+	5.09545i	−0.639689	+	0.207848i	−0.610862	−	0.791737i	$-0.709177\pi$
$601$	−15.6822	+	5.09545i	−0.639689	+	0.207848i	−0.0288267	+	0.999584i	$0.509177\pi$
$602$	−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	−0.255541	−	0.966798i	$-0.582254\pi$
$607$	−4.92298	+	0.779724i	−0.199818	+	0.0316480i	0.0557232	+	0.998446i	$0.482254\pi$
$608$	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	−0.750843	−	0.660481i	$-0.770352\pi$
$613$	−16.2873	+	8.29879i	−0.657837	+	0.335185i	0.0930058	+	0.995666i	$0.470352\pi$
$614$	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	0.322721	−	0.946494i	$-0.395402\pi$
$617$	−15.4942	−	15.4942i	−0.623773	−	0.623773i	−0.946494	+	0.322721i	$0.895402\pi$
$618$	0.537149	+	3.39142i	0.0216073	+	0.136423i
$619$	46.8070	+	15.2085i	1.88133	+	0.611282i	0.986219	+	0.165445i	$0.0529061\pi$
$619$	46.8070	+	15.2085i	1.88133	+	0.611282i	0.895114	+	0.445837i	$0.147094\pi$
$620$		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	0.879811	−	0.475324i	$-0.157669\pi$
$631$	−2.79731	−	8.60924i	−0.111359	−	0.342729i	−0.991170	+	0.132595i	$0.957669\pi$
$632$	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	0.622878	+	0.782319i	$0.285963\pi$
$641$	−8.63030	+	26.5613i	−0.340876	+	1.04911i	−0.963755	+	0.266791i	$0.914037\pi$
$642$	0.110014	−	0.215914i	0.00434190	−	0.00852146i
$643$	1.50637	−	9.51085i	0.0594055	−	0.375071i	−0.940018	−	0.341124i	$-0.889192\pi$
$643$	1.50637	−	9.51085i	0.0594055	−	0.375071i	0.999424	−	0.0339470i	$-0.0108078\pi$
$644$	−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	−0.879028	−	0.476770i	$-0.841807\pi$
$647$	−4.84185	−	30.5702i	−0.190353	−	1.20184i	0.688675	−	0.725070i	$-0.258193\pi$
$648$	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	0.557262	−	0.830337i	$-0.311852\pi$
$653$	5.44440	+	2.77406i	0.213056	+	0.108557i	−0.344206	+	0.938894i	$0.611852\pi$
$654$	−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	0.967842	−	0.251559i	$-0.0809432\pi$
$673$	−0.787773	−	4.97380i	−0.0303664	−	0.191726i	−0.998208	+	0.0598329i	$0.980943\pi$
$674$	−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	0.596297	+	0.802764i	$0.296638\pi$
$677$	−5.69516	+	35.9579i	−0.218883	+	1.38197i	−0.815180	+	0.579208i	$0.803362\pi$
$678$	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	−0.535567	−	0.844492i	$-0.679902\pi$
$683$	8.07353	−	8.07353i	0.308925	−	0.308925i	0.844492	+	0.535567i	$0.179902\pi$
$684$	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	0.755388	−	0.655277i	$-0.227448\pi$
$691$	9.61076	+	6.98263i	0.365611	+	0.265632i	−0.389778	+	0.920909i	$0.627448\pi$
$692$	−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	−0.209414	−	0.977827i	$-0.567156\pi$
$701$	−25.2475	−	8.20342i	−0.953586	−	0.309839i	−0.744172	+	0.667988i	$0.767156\pi$
$702$	−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	0.565021	−	0.825077i	$-0.308868\pi$
$709$	−10.4984	−	14.4498i	−0.394275	−	0.542673i	−0.959296	+	0.282404i	$0.908868\pi$
$710$		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	−0.825691	−	0.564122i	$-0.809215\pi$
$719$	−31.1609	+	10.1248i	−1.16211	+	0.377592i	−0.336416	+	0.941714i	$0.609215\pi$
$720$		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	0.688987	−	0.724773i	$-0.258056\pi$
$727$	−0.964903	−	0.964903i	−0.0357863	−	0.0357863i	−0.724773	+	0.688987i	$0.758056\pi$
$728$	−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	−0.770739	−	0.637151i	$-0.780113\pi$
$733$	5.35405	−	10.5079i	0.197756	−	0.388119i	0.968495	+	0.249033i	$0.0801126\pi$
$734$	−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	−0.282884	−	0.959154i	$-0.591291\pi$
$739$	−34.8645	−	25.3305i	−1.28251	−	0.931798i	−0.999626	+	0.0273561i	$0.991291\pi$
$740$		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	−0.574494	−	0.818509i	$-0.694801\pi$
$743$	−37.4472	−	5.93105i	−1.37380	−	0.217589i	−0.799309	+	0.600920i	$0.794801\pi$
$744$	−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	−0.536331	−	0.844008i	$-0.680190\pi$
$751$	10.7881	−	33.2025i	0.393665	−	1.21158i	0.929996	−	0.367569i	$-0.119810\pi$
$752$	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	−0.867818	−	0.496883i	$-0.834478\pi$
$757$	−5.39320	−	34.0513i	−0.196019	−	1.23762i	0.671798	−	0.740734i	$-0.265522\pi$
$758$	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	−0.931106	−	0.364750i	$-0.881155\pi$
$761$	−8.17878	+	11.2571i	−0.296481	+	0.408071i	0.634625	+	0.772820i	$0.281155\pi$
$762$	−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	0.970256	−	0.242082i	$-0.0778304\pi$
$773$	5.67471	+	11.1372i	0.204105	+	0.400579i	−0.766151	+	0.642661i	$0.777830\pi$
$774$	−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	−0.999002	−	0.0446718i	$-0.985776\pi$
$787$	−0.984406	+	6.21530i	−0.0350903	+	0.221551i	0.963911	+	0.266223i	$0.0857758\pi$
$788$	−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	0.187295	−	0.982304i	$-0.440028\pi$
$797$	1.74680	+	0.276667i	0.0618750	+	0.00980003i	−0.125420	+	0.992104i	$0.540028\pi$
$798$	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	−0.818443	−	0.574588i	$-0.805162\pi$
$809$	−14.9294	+	10.8468i	−0.524889	+	0.381354i	0.293553	+	0.955943i	$0.405162\pi$
$810$		0			0
$811$	−12.4057	−	4.03086i	−0.435624	−	0.141543i	0.0829918	−	0.996550i	$-0.473552\pi$
$811$	−12.4057	−	4.03086i	−0.435624	−	0.141543i	−0.518616	+	0.855007i	$0.673552\pi$
$812$	−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	−0.707502	−	0.706711i	$-0.750178\pi$
$821$	−24.7703	+	8.04835i	−0.864489	+	0.280889i	−0.156987	+	0.987601i	$0.550178\pi$
$822$	3.88227	+	7.61938i	0.135410	+	0.265756i
$823$	−4.96237	+	0.785962i	−0.172977	+	0.0273969i	−0.242322	−	0.970196i	$-0.577909\pi$
$823$	−4.96237	+	0.785962i	−0.172977	+	0.0273969i	0.0693449	+	0.997593i	$0.477909\pi$
$824$	11.3361			0.394912
$825$		0			0
$826$	2.28625			0.0795488
$827$	12.0210	−	1.90393i	0.418010	−	0.0662062i	0.0561130	−	0.998424i	$-0.482129\pi$
$827$	12.0210	−	1.90393i	0.418010	−	0.0662062i	0.361897	+	0.932218i	$0.382129\pi$
$828$	4.08135	+	8.01010i	0.141837	+	0.278370i
$829$	10.4727	−	3.40277i	0.363730	−	0.118183i	−0.121449	−	0.992598i	$-0.538754\pi$
$829$	10.4727	−	3.40277i	0.363730	−	0.118183i	0.485180	+	0.874415i	$0.338754\pi$
$830$		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	0.152475	−	0.988307i	$-0.451276\pi$
$839$	−8.83685	−	2.87127i	−0.305082	−	0.0991272i	−0.457557	+	0.889180i	$0.651276\pi$
$840$		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	0.595978	−	0.803001i	$-0.296765\pi$
$853$	26.7133	+	4.23097i	0.914645	+	0.144866i	0.318667	+	0.947867i	$0.396765\pi$
$854$	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	0.142591	−	0.989782i	$-0.454457\pi$
$857$	33.1497	−	33.1497i	1.13237	−	1.13237i	0.989782	−	0.142591i	$-0.0455432\pi$
$858$	−4.79856	+	2.47765i	−0.163820	+	0.0845857i
$859$		−	47.2517i		−	1.61221i	−0.591775	−	0.806103i	$-0.701573\pi$
$859$		−	47.2517i		−	1.61221i	0.591775	−	0.806103i	$-0.298427\pi$
$860$		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	0.910988	+	0.412432i	$0.135321\pi$
$863$	−2.43422	+	15.3690i	−0.0828617	+	0.523168i	−0.993850	+	0.110736i	$0.964679\pi$
$864$	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	0.999077	+	0.0429592i	$0.0136785\pi$
$877$	13.2254	+	25.9562i	0.446589	+	0.876480i	−0.552488	+	0.833521i	$0.686321\pi$
$878$	−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	−0.918530	−	0.395351i	$-0.870623\pi$
$883$	−20.7555	−	40.7349i	−0.698477	−	1.37084i	0.220053	−	0.975488i	$-0.429377\pi$
$884$	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	0.885760	−	0.464144i	$-0.153638\pi$
$887$	30.7027	+	15.6438i	1.03090	+	0.525267i	0.145136	+	0.989412i	$0.453638\pi$
$888$	−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	−0.511249	−	0.859433i	$-0.670817\pi$
$907$	−38.0387	−	6.02474i	−1.26306	−	0.200048i	−0.751806	+	0.659384i	$0.770817\pi$
$908$	−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	0.959536	−	0.281586i	$-0.0908605\pi$
$911$	29.8280	+	21.6713i	0.988244	+	0.718002i	0.0287085	+	0.999588i	$0.490861\pi$
$912$	−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	−0.914234	−	0.405187i	$-0.867206\pi$
$919$	−24.5973	+	17.8710i	−0.811392	+	0.589510i	0.102842	+	0.994698i	$0.467206\pi$
$920$		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	0.972241	−	0.233981i	$-0.0751752\pi$
$929$	13.6936	+	18.8477i	0.449273	+	0.618372i	−0.522968	+	0.852352i	$0.675175\pi$
$930$		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	−0.0253108	−	0.999680i	$-0.508058\pi$
$937$	7.94449	−	1.25828i	0.259535	−	0.0411063i	0.284846	+	0.958573i	$0.408058\pi$
$938$	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	0.964493	+	0.264110i	$0.0850781\pi$
$941$	28.1490	+	38.7438i	0.917631	+	1.26301i	−0.0468615	+	0.998901i	$0.514922\pi$
$942$	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	0.537960	−	0.842970i	$-0.319195\pi$
$947$	−9.38618	−	9.38618i	−0.305010	−	0.305010i	−0.842970	+	0.537960i	$0.819195\pi$
$948$	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	0.0595128	+	0.998228i	$0.481045\pi$
$953$	−24.1733	+	47.4428i	−0.783051	+	1.53682i	−0.842564	+	0.538597i	$0.818955\pi$
$954$	−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	−0.283994	+	0.958826i	$0.591660\pi$
$967$	−38.6475	+	38.6475i	−1.24282	+	1.24282i	−0.958826	+	0.283994i	$0.908340\pi$
$968$	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	−0.901640	−	0.432487i	$-0.857636\pi$
$971$	2.55556	−	7.86521i	0.0820119	−	0.252407i	0.983652	+	0.180081i	$0.0576360\pi$
$972$	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	0.613610	+	0.789610i	$0.289717\pi$
$977$	8.56551	+	54.0805i	0.274035	+	1.73019i	−0.339575	+	0.940579i	$0.610283\pi$
$978$	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	0.249318	−	0.968422i	$-0.419793\pi$
$983$	−12.1525	−	6.19202i	−0.387606	−	0.197495i	−0.636924	+	0.770927i	$0.719793\pi$
$984$	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	0.727643	−	0.685956i	$-0.240616\pi$
$997$	18.9575	+	9.65934i	0.600391	+	0.305914i	−0.127252	+	0.991870i	$0.540616\pi$
$998$	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.7.2		32
5.2	odd	4		55.2.l.a.18.2	yes	32
5.3	odd	4	inner	275.2.bm.b.18.3		32
5.4	even	2		55.2.l.a.7.3	✓	32
11.8	odd	10	inner	275.2.bm.b.107.3		32
15.2	even	4		495.2.bj.a.73.3		32
15.14	odd	2		495.2.bj.a.172.2		32
20.7	even	4		880.2.cm.a.513.3		32
20.19	odd	2		880.2.cm.a.337.2		32
55.2	even	20		605.2.m.c.578.3		32
55.4	even	10		605.2.m.c.112.3		32
55.7	even	20		605.2.m.d.233.2		32
55.8	even	20	inner	275.2.bm.b.118.2		32
55.9	even	10		605.2.m.d.457.2		32
55.14	even	10		605.2.m.e.602.3		32
55.17	even	20		605.2.e.b.483.8		32
55.19	odd	10		55.2.l.a.52.2	yes	32
55.24	odd	10		605.2.m.c.457.3		32
55.27	odd	20		605.2.e.b.483.9		32
55.29	odd	10		605.2.m.d.112.2		32
55.32	even	4		605.2.m.e.403.3		32
55.37	odd	20		605.2.m.c.233.3		32
55.39	odd	10		605.2.e.b.362.9		32
55.42	odd	20		605.2.m.d.578.2		32
55.47	odd	20		605.2.m.e.118.2		32
55.49	even	10		605.2.e.b.362.8		32
55.52	even	20		55.2.l.a.8.3	yes	32
55.54	odd	2		605.2.m.e.282.2		32
165.74	even	10		495.2.bj.a.217.3		32
165.107	odd	20		495.2.bj.a.118.2		32
220.19	even	10		880.2.cm.a.657.3		32
220.107	odd	20		880.2.cm.a.833.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.3	✓	32	5.4	even	2
55.2.l.a.8.3	yes	32	55.52	even	20
55.2.l.a.18.2	yes	32	5.2	odd	4
55.2.l.a.52.2	yes	32	55.19	odd	10
275.2.bm.b.7.2		32	1.1	even	1	trivial
275.2.bm.b.18.3		32	5.3	odd	4	inner
275.2.bm.b.107.3		32	11.8	odd	10	inner
275.2.bm.b.118.2		32	55.8	even	20	inner
495.2.bj.a.73.3		32	15.2	even	4
495.2.bj.a.118.2		32	165.107	odd	20
495.2.bj.a.172.2		32	15.14	odd	2
495.2.bj.a.217.3		32	165.74	even	10
605.2.e.b.362.8		32	55.49	even	10
605.2.e.b.362.9		32	55.39	odd	10
605.2.e.b.483.8		32	55.17	even	20
605.2.e.b.483.9		32	55.27	odd	20
605.2.m.c.112.3		32	55.4	even	10
605.2.m.c.233.3		32	55.37	odd	20
605.2.m.c.457.3		32	55.24	odd	10
605.2.m.c.578.3		32	55.2	even	20
605.2.m.d.112.2		32	55.29	odd	10
605.2.m.d.233.2		32	55.7	even	20
605.2.m.d.457.2		32	55.9	even	10
605.2.m.d.578.2		32	55.42	odd	20
605.2.m.e.118.2		32	55.47	odd	20
605.2.m.e.282.2		32	55.54	odd	2
605.2.m.e.403.3		32	55.32	even	4
605.2.m.e.602.3		32	55.14	even	10
880.2.cm.a.337.2		32	20.19	odd	2
880.2.cm.a.513.3		32	20.7	even	4
880.2.cm.a.657.3		32	220.19	even	10
880.2.cm.a.833.2		32	220.107	odd	20

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

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