LMFDB - Embedded newform 275.2.z.c.124.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,2,Mod(49,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.z (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			124.3
Character	$\chi$	$=$	275.124
Dual form			275.2.z.c.224.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.776830 - 1.06921i) q^{2} +(-1.92724 + 0.626199i) q^{3} +(0.0782786 - 0.240917i) q^{4} +(2.16668 + 1.57419i) q^{6} +(0.331213 + 0.107618i) q^{7} +(-2.83228 + 0.920262i) q^{8} +(0.895086 - 0.650318i) q^{9} +(-3.25463 + 0.638246i) q^{11} +0.513323i q^{12} +(1.09079 + 1.50135i) q^{13} +(-0.142230 - 0.437738i) q^{14} +(2.77428 + 2.01563i) q^{16} +(1.05786 - 1.45602i) q^{17} +(-1.39066 - 0.451853i) q^{18} +(2.21198 + 6.80779i) q^{19} -0.705717 q^{21} +(3.21072 + 2.98409i) q^{22} +8.41145i q^{23} +(4.88221 - 3.54714i) q^{24} +(0.757902 - 2.33258i) q^{26} +(2.25548 - 3.10441i) q^{27} +(0.0518537 - 0.0713705i) q^{28} +(-1.79251 + 5.51679i) q^{29} +(-4.49489 + 3.26573i) q^{31} +1.42395i q^{32} +(5.87280 - 3.26810i) q^{33} -2.37858 q^{34} +(-0.0866064 - 0.266547i) q^{36} +(-1.75766 - 0.571099i) q^{37} +(5.56065 - 7.65358i) q^{38} +(-3.04236 - 2.21041i) q^{39} +(-2.79149 - 8.59133i) q^{41} +(0.548222 + 0.754563i) q^{42} -6.76370i q^{43} +(-0.101004 + 0.834057i) q^{44} +(8.99364 - 6.53426i) q^{46} +(-6.90656 + 2.24408i) q^{47} +(-6.60890 - 2.14736i) q^{48} +(-5.56500 - 4.04321i) q^{49} +(-1.12700 + 3.46854i) q^{51} +(0.447085 - 0.145267i) q^{52} +(-0.201527 - 0.277378i) q^{53} -5.07141 q^{54} -1.03712 q^{56} +(-8.52606 - 11.7351i) q^{57} +(7.29112 - 2.36903i) q^{58} +(-0.0615923 + 0.189562i) q^{59} +(6.30721 + 4.58245i) q^{61} +(6.98354 + 2.26909i) q^{62} +(0.366449 - 0.119067i) q^{63} +(7.07108 - 5.13744i) q^{64} +(-8.05647 - 3.74052i) q^{66} +12.2451i q^{67} +(-0.267972 - 0.368832i) q^{68} +(-5.26724 - 16.2109i) q^{69} +(-7.95510 - 5.77972i) q^{71} +(-1.93667 + 2.66559i) q^{72} +(0.963578 + 0.313085i) q^{73} +(0.754777 + 2.32297i) q^{74} +1.81326 q^{76} +(-1.14666 - 0.138860i) q^{77} +4.97005i q^{78} +(5.36632 - 3.89886i) q^{79} +(-3.42856 + 10.5520i) q^{81} +(-7.01746 + 9.65870i) q^{82} +(-6.53931 + 9.00058i) q^{83} +(-0.0552425 + 0.170019i) q^{84} +(-7.23185 + 5.25425i) q^{86} -11.7547i q^{87} +(8.63067 - 4.80281i) q^{88} -8.84524 q^{89} +(0.199713 + 0.614654i) q^{91} +(2.02646 + 0.658436i) q^{92} +(6.61775 - 9.10855i) q^{93} +(7.76462 + 5.64133i) q^{94} +(-0.891677 - 2.74430i) q^{96} +(3.64564 + 5.01780i) q^{97} +9.09106i q^{98} +(-2.49811 + 2.68783i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{4} - 6 q^{6} - 16 q^{9} - 10 q^{11} - 6 q^{14} - 8 q^{16} + 26 q^{19} + 20 q^{21} + 86 q^{24} - 68 q^{26} + 22 q^{29} - 20 q^{31} - 40 q^{34} + 6 q^{36} - 6 q^{39} + 50 q^{41} + 2 q^{44} + 80 q^{46}+ \cdots + 20 q^{99}+O(q^{100}) $ 32 * q + 4 * q^4 - 6 * q^6 - 16 * q^9 - 10 * q^11 - 6 * q^14 - 8 * q^16 + 26 * q^19 + 20 * q^21 + 86 * q^24 - 68 * q^26 + 22 * q^29 - 20 * q^31 - 40 * q^34 + 6 * q^36 - 6 * q^39 + 50 * q^41 + 2 * q^44 + 80 * q^46 - 32 * q^49 + 70 * q^51 - 120 * q^54 - 40 * q^56 - 28 * q^59 + 32 * q^61 - 80 * q^64 - 110 * q^66 - 70 * q^69 - 92 * q^71 + 14 * q^74 - 124 * q^76 + 78 * q^79 - 86 * q^81 + 108 * q^84 + 4 * q^86 + 44 * q^89 - 68 * q^91 + 80 * q^94 + 216 * q^96 + 20 * q^99

Character values

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

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.776830	−	1.06921i	−0.549302	−	0.756049i	0.440615	−	0.897696i	$-0.354760\pi$
$2$	−0.776830	−	1.06921i	−0.549302	−	0.756049i	−0.989917	+	0.141647i	$0.954760\pi$
$3$	−1.92724	+	0.626199i	−1.11269	+	0.361536i	−0.806975	−	0.590586i	$-0.798897\pi$
$3$	−1.92724	+	0.626199i	−1.11269	+	0.361536i	−0.305719	+	0.952122i	$0.598897\pi$
$4$	0.0782786	−	0.240917i	0.0391393	−	0.120458i
$5$		0			0
$5$		0			0
$6$	2.16668	+	1.57419i	0.884544	+	0.642659i
$7$	0.331213	+	0.107618i	0.125187	+	0.0406756i	0.370940	−	0.928657i	$-0.379035\pi$
$7$	0.331213	+	0.107618i	0.125187	+	0.0406756i	−0.245754	+	0.969332i	$0.579035\pi$
$8$	−2.83228	+	0.920262i	−1.00136	+	0.325362i
$9$	0.895086	−	0.650318i	0.298362	−	0.216773i
$10$		0			0
$11$	−3.25463	+	0.638246i	−0.981309	+	0.192438i
$11$	−3.25463	+	0.638246i	−0.981309	+	0.192438i
$12$			0.513323i			0.148183i
$13$	1.09079	+	1.50135i	0.302532	+	0.416399i	0.933034	−	0.359788i	$-0.117151\pi$
$13$	1.09079	+	1.50135i	0.302532	+	0.416399i	−0.630502	+	0.776187i	$0.717151\pi$
$14$	−0.142230	−	0.437738i	−0.0380125	−	0.116990i
$15$		0			0
$16$	2.77428	+	2.01563i	0.693571	+	0.503909i
$17$	1.05786	−	1.45602i	0.256569	−	0.353137i	−0.661229	−	0.750184i	$-0.729965\pi$
$17$	1.05786	−	1.45602i	0.256569	−	0.353137i	0.917798	+	0.397047i	$0.129965\pi$
$18$	−1.39066	−	0.451853i	−0.327782	−	0.106503i
$19$	2.21198	+	6.80779i	0.507464	+	1.56181i	0.796588	+	0.604522i	$0.206636\pi$
$19$	2.21198	+	6.80779i	0.507464	+	1.56181i	−0.289124	+	0.957292i	$0.593364\pi$
$20$		0			0
$21$	−0.705717			−0.154000
$22$	3.21072	+	2.98409i	0.684528	+	0.636211i
$23$			8.41145i			1.75391i	0.480574	+	0.876954i	$0.340428\pi$
$23$			8.41145i			1.75391i	−0.480574	+	0.876954i	$0.659572\pi$
$24$	4.88221	−	3.54714i	0.996578	−	0.724056i
$25$		0			0
$26$	0.757902	−	2.33258i	0.148637	−	0.457457i
$27$	2.25548	−	3.10441i	0.434068	−	0.597444i
$28$	0.0518537	−	0.0713705i	0.00979943	−	0.0134878i
$29$	−1.79251	+	5.51679i	−0.332862	+	1.02444i	0.634904	+	0.772591i	$0.281040\pi$
$29$	−1.79251	+	5.51679i	−0.332862	+	1.02444i	−0.967766	+	0.251852i	$0.918960\pi$
$30$		0			0
$31$	−4.49489	+	3.26573i	−0.807307	+	0.586543i	−0.913048	−	0.407851i	$-0.866278\pi$
$31$	−4.49489	+	3.26573i	−0.807307	+	0.586543i	0.105742	+	0.994394i	$0.466278\pi$
$32$			1.42395i			0.251722i
$33$	5.87280	−	3.26810i	1.02232	−	0.568904i
$34$	−2.37858			−0.407923
$35$		0			0
$36$	−0.0866064	−	0.266547i	−0.0144344	−	0.0444245i
$37$	−1.75766	−	0.571099i	−0.288958	−	0.0938881i	0.160952	−	0.986962i	$-0.448544\pi$
$37$	−1.75766	−	0.571099i	−0.288958	−	0.0938881i	−0.449909	+	0.893074i	$0.648544\pi$
$38$	5.56065	−	7.65358i	0.902057	−	1.24157i
$39$	−3.04236	−	2.21041i	−0.487168	−	0.353948i
$40$		0			0
$41$	−2.79149	−	8.59133i	−0.435958	−	1.34174i	−0.892102	−	0.451834i	$-0.850770\pi$
$41$	−2.79149	−	8.59133i	−0.435958	−	1.34174i	0.456144	−	0.889906i	$-0.349230\pi$
$42$	0.548222	+	0.754563i	0.0845925	+	0.116432i
$43$		−	6.76370i		−	1.03145i	−0.856753	−	0.515727i	$-0.827522\pi$
$43$		−	6.76370i		−	1.03145i	0.856753	−	0.515727i	$-0.172478\pi$
$44$	−0.101004	+	0.834057i	−0.0152269	+	0.125739i
$45$		0			0
$46$	8.99364	−	6.53426i	1.32604	−	0.963425i
$47$	−6.90656	+	2.24408i	−1.00742	+	0.327332i	−0.765829	−	0.643045i	$-0.777671\pi$
$47$	−6.90656	+	2.24408i	−1.00742	+	0.327332i	−0.241596	+	0.970377i	$0.577671\pi$
$48$	−6.60890	−	2.14736i	−0.953913	−	0.309945i
$49$	−5.56500	−	4.04321i	−0.795000	−	0.577601i
$50$		0			0
$51$	−1.12700	+	3.46854i	−0.157811	+	0.485693i
$52$	0.447085	−	0.145267i	0.0619996	−	0.0201449i
$53$	−0.201527	−	0.277378i	−0.0276819	−	0.0381009i	0.794952	−	0.606673i	$-0.207496\pi$
$53$	−0.201527	−	0.277378i	−0.0276819	−	0.0381009i	−0.822634	+	0.568572i	$0.807496\pi$
$54$	−5.07141			−0.690131
$55$		0			0
$56$	−1.03712			−0.138591
$57$	−8.52606	−	11.7351i	−1.12930	−	1.55435i
$58$	7.29112	−	2.36903i	0.957370	−	0.311069i
$59$	−0.0615923	+	0.189562i	−0.00801863	+	0.0246788i	−0.954986	−	0.296652i	$-0.904130\pi$
$59$	−0.0615923	+	0.189562i	−0.00801863	+	0.0246788i	0.946967	+	0.321330i	$0.104130\pi$
$60$		0			0
$61$	6.30721	+	4.58245i	0.807555	+	0.586723i	0.913121	−	0.407689i	$-0.133665\pi$
$61$	6.30721	+	4.58245i	0.807555	+	0.586723i	−0.105566	+	0.994412i	$0.533665\pi$
$62$	6.98354	+	2.26909i	0.886910	+	0.288175i
$63$	0.366449	−	0.119067i	0.0461683	−	0.0150010i
$64$	7.07108	−	5.13744i	0.883885	−	0.642180i
$65$		0			0
$66$	−8.05647	−	3.74052i	−0.991683	−	0.460426i
$67$			12.2451i			1.49597i	0.663715	+	0.747986i	$0.268979\pi$
$67$			12.2451i			1.49597i	−0.663715	+	0.747986i	$0.731021\pi$
$68$	−0.267972	−	0.368832i	−0.0324964	−	0.0447275i
$69$	−5.26724	−	16.2109i	−0.634101	−	1.95156i
$70$		0			0
$71$	−7.95510	−	5.77972i	−0.944097	−	0.685927i	0.00530622	−	0.999986i	$-0.498311\pi$
$71$	−7.95510	−	5.77972i	−0.944097	−	0.685927i	−0.949403	+	0.314059i	$0.898311\pi$
$72$	−1.93667	+	2.66559i	−0.228238	+	0.314143i
$73$	0.963578	+	0.313085i	0.112778	+	0.0366439i	0.364862	−	0.931061i	$-0.381116\pi$
$73$	0.963578	+	0.313085i	0.112778	+	0.0366439i	−0.252084	+	0.967705i	$0.581116\pi$
$74$	0.754777	+	2.32297i	0.0877411	+	0.270039i
$75$		0			0
$76$	1.81326			0.207995
$77$	−1.14666	−	0.138860i	−0.130674	−	0.0158246i
$78$			4.97005i			0.562748i
$79$	5.36632	−	3.89886i	0.603758	−	0.438656i	−0.243453	−	0.969913i	$-0.578280\pi$
$79$	5.36632	−	3.89886i	0.603758	−	0.438656i	0.847211	+	0.531257i	$0.178280\pi$
$80$		0			0
$81$	−3.42856	+	10.5520i	−0.380952	+	1.17245i
$82$	−7.01746	+	9.65870i	−0.774949	+	1.06663i
$83$	−6.53931	+	9.00058i	−0.717782	+	0.987942i	0.281813	+	0.959469i	$0.409064\pi$
$83$	−6.53931	+	9.00058i	−0.717782	+	0.987942i	−0.999595	+	0.0284727i	$0.990936\pi$
$84$	−0.0552425	+	0.170019i	−0.00602745	+	0.0185506i
$85$		0			0
$86$	−7.23185	+	5.25425i	−0.779830	+	0.566580i
$87$		−	11.7547i		−	1.26023i
$88$	8.63067	−	4.80281i	0.920032	−	0.511981i
$89$	−8.84524			−0.937594			−0.468797	−	0.883306i	$-0.655312\pi$
$89$	−8.84524			−0.937594			−0.468797	+	0.883306i	$0.655312\pi$
$90$		0			0
$91$	0.199713	+	0.614654i	0.0209356	+	0.0644332i
$92$	2.02646	+	0.658436i	0.211273	+	0.0686467i
$93$	6.61775	−	9.10855i	0.686229	−	0.944513i
$94$	7.76462	+	5.64133i	0.800859	+	0.581858i
$95$		0			0
$96$	−0.891677	−	2.74430i	−0.0910064	−	0.280089i
$97$	3.64564	+	5.01780i	0.370159	+	0.509480i	0.952944	−	0.303146i	$-0.0980370\pi$
$97$	3.64564	+	5.01780i	0.370159	+	0.509480i	−0.582785	+	0.812626i	$0.698037\pi$
$98$			9.09106i			0.918336i
$99$	−2.49811	+	2.68783i	−0.251070	+	0.270137i
$100$		0			0
$101$	2.96734	−	2.15590i	0.295262	−	0.214520i	−0.430285	−	0.902693i	$-0.641587\pi$
$101$	2.96734	−	2.15590i	0.295262	−	0.214520i	0.725547	+	0.688173i	$0.241587\pi$
$102$	4.58410	−	1.48946i	0.453894	−	0.147479i
$103$	−18.7187	−	6.08206i	−1.84440	−	0.599283i	−0.997743	−	0.0671522i	$-0.978609\pi$
$103$	−18.7187	−	6.08206i	−1.84440	−	0.599283i	−0.846662	−	0.532131i	$-0.821391\pi$
$104$	−4.47106	−	3.24842i	−0.438423	−	0.318533i
$105$		0			0
$106$	−0.140025	+	0.430952i	−0.0136004	+	0.0418577i
$107$	−0.286633	+	0.0931327i	−0.0277098	+	0.00900347i	−0.322839	−	0.946454i	$-0.604637\pi$
$107$	−0.286633	+	0.0931327i	−0.0277098	+	0.00900347i	0.295129	+	0.955457i	$0.404637\pi$
$108$	−0.571348	−	0.786392i	−0.0549779	−	0.0756706i
$109$	10.9371			1.04759			0.523794	−	0.851845i	$-0.324516\pi$
$109$	10.9371			1.04759			0.523794	+	0.851845i	$0.324516\pi$
$110$		0			0
$111$	3.74506			0.355466
$112$	0.701960	+	0.966165i	0.0663290	+	0.0912940i
$113$	5.51830	−	1.79300i	0.519118	−	0.168672i	−0.0377271	−	0.999288i	$-0.512012\pi$
$113$	5.51830	−	1.79300i	0.519118	−	0.168672i	0.556845	+	0.830616i	$0.312012\pi$
$114$	−5.92406	+	18.2324i	−0.554839	+	1.70762i
$115$		0			0
$116$	1.18877	+	0.863693i	0.110375	+	0.0801919i
$117$	1.95271	+	0.634473i	0.180528	+	0.0586570i
$118$	0.250529	−	0.0814018i	0.0230630	−	0.00749364i
$119$	0.507071	−	0.368409i	0.0464831	−	0.0337720i
$120$		0			0
$121$	10.1853	−	4.15451i	0.925935	−	0.377683i
$122$		−	10.3035i		−	0.932839i
$123$	10.7598	+	14.8095i	0.970175	+	1.33533i
$124$	0.434915	+	1.33853i	0.0390565	+	0.120204i
$125$		0			0
$126$	−0.411977	−	0.299319i	−0.0367018	−	0.0266654i
$127$	7.25943	−	9.99175i	0.644170	−	0.886625i	−0.354659	−	0.934996i	$-0.615403\pi$
$127$	7.25943	−	9.99175i	0.644170	−	0.886625i	0.998829	+	0.0483711i	$0.0154030\pi$
$128$	−8.27753	−	2.68953i	−0.731637	−	0.237723i
$129$	4.23542	+	13.0353i	0.372908	+	1.14769i
$130$		0			0
$131$	7.81632			0.682915			0.341458	−	0.939897i	$-0.389079\pi$
$131$	7.81632			0.682915			0.341458	+	0.939897i	$0.389079\pi$
$132$	−0.327626	−	1.67068i	−0.0285162	−	0.145414i
$133$			2.49287i			0.216160i
$134$	13.0926	−	9.51233i	1.13103	−	0.821740i
$135$		0			0
$136$	−1.65624	+	5.09737i	−0.142021	+	0.437096i
$137$	5.63141	−	7.75098i	0.481124	−	0.662211i	−0.497596	−	0.867409i	$-0.665784\pi$
$137$	5.63141	−	7.75098i	0.481124	−	0.662211i	0.978720	+	0.205198i	$0.0657839\pi$
$138$	−13.2412	+	18.2249i	−1.12716	+	1.55141i
$139$	−5.91169	+	18.1943i	−0.501423	+	1.54322i	0.305280	+	0.952263i	$0.401250\pi$
$139$	−5.91169	+	18.1943i	−0.501423	+	1.54322i	−0.806702	+	0.590958i	$0.798750\pi$
$140$		0			0
$141$	11.9054	−	8.64976i	1.00261	−	0.728441i
$142$			12.9956i			1.09056i
$143$	−4.50836	−	4.19014i	−0.377008	−	0.350397i
$144$	3.79403			0.316169
$145$		0			0
$146$	−0.413781	−	1.27349i	−0.0342447	−	0.105394i
$147$	13.2570	+	4.30744i	1.09341	+	0.355272i
$148$	−0.275175	+	0.378745i	−0.0226192	+	0.0311327i
$149$	4.67208	+	3.39446i	0.382752	+	0.278085i	0.762479	−	0.647013i	$-0.223982\pi$
$149$	4.67208	+	3.39446i	0.382752	+	0.278085i	−0.379727	+	0.925099i	$0.623982\pi$
$150$		0			0
$151$	4.13098	+	12.7139i	0.336175	+	1.03464i	0.966141	+	0.258016i	$0.0830689\pi$
$151$	4.13098	+	12.7139i	0.336175	+	1.03464i	−0.629966	+	0.776623i	$0.716931\pi$
$152$	−12.5299	−	17.2459i	−1.01631	−	1.39883i
$153$		−	1.99121i		−	0.160980i
$154$	0.742290	+	1.33390i	0.0598155	+	0.107489i
$155$		0			0
$156$	−0.770676	+	0.559929i	−0.0617035	+	0.0448302i
$157$	−12.7870	+	4.15475i	−1.02051	+	0.331585i	−0.771033	−	0.636795i	$-0.780260\pi$
$157$	−12.7870	+	4.15475i	−1.02051	+	0.331585i	−0.249481	+	0.968380i	$0.580260\pi$
$158$	−8.33744	−	2.70900i	−0.663291	−	0.215516i
$159$	0.562086	+	0.408379i	0.0445763	+	0.0323866i
$160$		0			0
$161$	−0.905219	+	2.78598i	−0.0713413	+	0.219566i
$162$	13.9458	−	4.53127i	1.09569	−	0.356010i
$163$	−1.84293	−	2.53658i	−0.144349	−	0.198680i	0.730720	−	0.682677i	$-0.239184\pi$
$163$	−1.84293	−	2.53658i	−0.144349	−	0.198680i	−0.875070	+	0.483997i	$0.839184\pi$
$164$	−2.28831			−0.178687
$165$		0			0
$166$	14.7035			1.14121
$167$	1.54515	+	2.12672i	0.119567	+	0.164570i	0.864605	−	0.502452i	$-0.167569\pi$
$167$	1.54515	+	2.12672i	0.119567	+	0.164570i	−0.745038	+	0.667022i	$0.767569\pi$
$168$	1.99879	−	0.649445i	0.154210	−	0.0501057i
$169$	2.95301	−	9.08842i	0.227154	−	0.699109i
$170$		0			0
$171$	6.40714	+	4.65506i	0.489967	+	0.355982i
$172$	−1.62949	−	0.529453i	−0.124247	−	0.0403704i
$173$	3.73072	−	1.21218i	0.283641	−	0.0921606i	−0.163741	−	0.986503i	$-0.552356\pi$
$173$	3.73072	−	1.21218i	0.283641	−	0.0921606i	0.447383	+	0.894343i	$0.352356\pi$
$174$	−12.5683	+	9.13138i	−0.952798	+	0.692248i
$175$		0			0
$176$	−10.3157	−	4.78948i	−0.777579	−	0.361020i
$177$		−	0.403900i		−	0.0303590i
$178$	6.87125	+	9.45746i	0.515022	+	0.708867i
$179$	1.02435	+	3.15264i	0.0765639	+	0.235639i	0.982012	−	0.188817i	$-0.0604653\pi$
$179$	1.02435	+	3.15264i	0.0765639	+	0.235639i	−0.905448	+	0.424456i	$0.860465\pi$
$180$		0			0
$181$	−13.6763	−	9.93640i	−1.01655	−	0.738567i	−0.0509769	−	0.998700i	$-0.516233\pi$
$181$	−13.6763	−	9.93640i	−1.01655	−	0.738567i	−0.965573	+	0.260133i	$0.916233\pi$
$182$	0.502054	−	0.691018i	0.0372147	−	0.0512216i
$183$	−15.0250	−	4.88193i	−1.11068	−	0.360883i
$184$	−7.74074	−	23.8235i	−0.570655	−	1.75629i
$185$		0			0
$186$	−14.8799			−1.09104
$187$	−2.51365	+	5.41400i	−0.183817	+	0.395911i
$188$			1.83957i			0.134164i
$189$	1.08113	−	0.785490i	0.0786409	−	0.0571360i
$190$		0			0
$191$	−6.49420	+	19.9871i	−0.469903	+	1.44621i	0.382806	+	0.923829i	$0.374958\pi$
$191$	−6.49420	+	19.9871i	−0.469903	+	1.44621i	−0.852709	+	0.522385i	$0.825042\pi$
$192$	−10.4106	+	14.3290i	−0.751322	+	1.03411i
$193$	1.94751	−	2.68051i	0.140184	−	0.192947i	−0.733152	−	0.680065i	$-0.761952\pi$
$193$	1.94751	−	2.68051i	0.140184	−	0.192947i	0.873336	+	0.487117i	$0.161952\pi$
$194$	2.53306	−	7.79595i	0.181863	−	0.559717i
$195$		0			0
$196$	−1.40970	+	1.02420i	−0.100693	+	0.0731575i
$197$			6.97218i			0.496747i	0.968664	+	0.248374i	$0.0798961\pi$
$197$			6.97218i			0.496747i	−0.968664	+	0.248374i	$0.920104\pi$
$198$	4.81448	+	0.583032i	0.342150	+	0.0414343i
$199$	19.2184			1.36236			0.681178	−	0.732118i	$-0.261468\pi$
$199$	19.2184			1.36236			0.681178	+	0.732118i	$0.261468\pi$
$200$		0			0
$201$	−7.66784	−	23.5992i	−0.540848	−	1.66456i
$202$	−4.61024	−	1.49796i	−0.324375	−	0.105396i
$203$	−1.18741	+	1.63433i	−0.0833396	+	0.114707i
$204$	0.747409	+	0.543025i	0.0523291	+	0.0380193i
$205$		0			0
$206$	8.03819	+	24.7390i	0.560047	+	1.72365i
$207$	5.47012	+	7.52897i	0.380199	+	0.523299i
$208$			6.36380i			0.441250i
$209$	−11.5442	−	20.7451i	−0.798532	−	1.43497i
$210$		0			0
$211$	−3.47407	+	2.52406i	−0.239165	+	0.173764i	−0.700911	−	0.713249i	$-0.747223\pi$
$211$	−3.47407	+	2.52406i	−0.239165	+	0.173764i	0.461746	+	0.887012i	$0.347223\pi$
$212$	−0.0826004	+	0.0268385i	−0.00567302	+	0.00184327i
$213$	18.9507	+	6.15745i	1.29848	+	0.421901i
$214$	0.322244	+	0.234124i	0.0220281	+	0.0160044i
$215$		0			0
$216$	−3.53128	+	10.8682i	−0.240273	+	0.739486i
$217$	−1.84022	+	0.597922i	−0.124922	+	0.0405896i
$218$	−8.49629	−	11.6941i	−0.575442	−	0.792027i
$219$	−2.05310			−0.138736
$220$		0			0
$221$	3.33991			0.224666
$222$	−2.90928	−	4.00428i	−0.195258	−	0.268749i
$223$	−10.0702	+	3.27200i	−0.674349	+	0.219109i	−0.626120	−	0.779727i	$-0.715358\pi$
$223$	−10.0702	+	3.27200i	−0.674349	+	0.219109i	−0.0482295	+	0.998836i	$0.515358\pi$
$224$	−0.153242	+	0.471631i	−0.0102389	+	0.0315122i
$225$		0			0
$226$	−6.20389	−	4.50739i	−0.412676	−	0.299827i
$227$	5.49240	+	1.78459i	0.364543	+	0.118447i	0.485560	−	0.874203i	$-0.338616\pi$
$227$	5.49240	+	1.78459i	0.364543	+	0.118447i	−0.121017	+	0.992650i	$0.538616\pi$
$228$	−3.49459	+	1.13546i	−0.231435	+	0.0751978i
$229$	−4.13124	+	3.00152i	−0.273000	+	0.198346i	−0.715858	−	0.698245i	$-0.753964\pi$
$229$	−4.13124	+	3.00152i	−0.273000	+	0.198346i	0.442858	+	0.896592i	$0.353964\pi$
$230$		0			0
$231$	2.29685	−	0.450421i	0.151122	−	0.0296355i
$232$		−	17.2747i		−	1.13414i
$233$	16.3323	+	22.4794i	1.06996	+	1.47268i	0.870115	+	0.492850i	$0.164045\pi$
$233$	16.3323	+	22.4794i	1.06996	+	1.47268i	0.199848	+	0.979827i	$0.435955\pi$
$234$	−0.838534	−	2.58074i	−0.0548167	−	0.168708i
$235$		0			0
$236$	0.0408472	+	0.0296772i	0.00265893	+	0.00193182i
$237$	−7.90074	+	10.8744i	−0.513208	+	0.706370i
$238$	−0.787816	−	0.255977i	−0.0510665	−	0.0165925i
$239$	2.08502	+	6.41702i	0.134868	+	0.415082i	0.995570	−	0.0940282i	$-0.0299744\pi$
$239$	2.08502	+	6.41702i	0.134868	+	0.415082i	−0.860701	+	0.509111i	$0.829974\pi$
$240$		0			0
$241$	−13.0610			−0.841331			−0.420666	−	0.907216i	$-0.638203\pi$
$241$	−13.0610			−0.841331			−0.420666	+	0.907216i	$0.638203\pi$
$242$	−12.3543	−	7.66290i	−0.794165	−	0.492590i
$243$		−	10.9715i		−	0.703823i
$244$	1.59771	−	1.16080i	0.102283	−	0.0743128i
$245$		0			0
$246$	7.47607	−	23.0090i	0.476657	−	1.46700i
$247$	−7.80804	+	10.7468i	−0.496814	+	0.683805i
$248$	9.72545	−	13.3859i	0.617567	−	0.850007i
$249$	6.96667	−	21.4412i	0.441495	−	1.35878i
$250$		0			0
$251$	24.3883	−	17.7191i	1.53938	−	1.11842i	0.588650	−	0.808388i	$-0.299660\pi$
$251$	24.3883	−	17.7191i	1.53938	−	1.11842i	0.950726	−	0.310033i	$-0.100340\pi$
$252$		−	0.0976041i		−	0.00614848i
$253$	−5.36857	−	27.3762i	−0.337519	−	1.72113i
$254$	−16.3227			−1.02418
$255$		0			0
$256$	−1.84728	−	5.68533i	−0.115455	−	0.355333i
$257$	−0.345199	−	0.112162i	−0.0215329	−	0.00699648i	0.298231	−	0.954494i	$-0.403604\pi$
$257$	−0.345199	−	0.112162i	−0.0215329	−	0.00699648i	−0.319764	+	0.947497i	$0.603604\pi$
$258$	10.6473	−	14.6548i	0.662873	−	0.912367i
$259$	−0.520700	−	0.378310i	−0.0323547	−	0.0235071i
$260$		0			0
$261$	1.98322	+	6.10371i	0.122758	+	0.377810i
$262$	−6.07195	−	8.35733i	−0.375127	−	0.516317i
$263$		−	22.5498i		−	1.39048i	−0.718779	−	0.695239i	$-0.755299\pi$
$263$		−	22.5498i		−	1.39048i	0.718779	−	0.695239i	$-0.244701\pi$
$264$	−13.6259	+	14.6607i	−0.838614	+	0.902303i
$265$		0			0
$266$	2.66542	−	1.93654i	0.163427	−	0.118737i
$267$	17.0469	−	5.53888i	1.04325	−	0.338974i
$268$	2.95004	+	0.958525i	0.180202	+	0.0585512i
$269$	−4.97323	−	3.61326i	−0.303223	−	0.220305i	0.425760	−	0.904836i	$-0.360007\pi$
$269$	−4.97323	−	3.61326i	−0.303223	−	0.220305i	−0.728983	+	0.684532i	$0.760007\pi$
$270$		0			0
$271$	5.15939	−	15.8790i	0.313410	−	0.964578i	−0.662993	−	0.748625i	$-0.730714\pi$
$271$	5.15939	−	15.8790i	0.313410	−	0.964578i	0.976404	−	0.215953i	$-0.0692858\pi$
$272$	5.86962	−	1.90715i	0.355898	−	0.115638i
$273$	−0.769791	−	1.05953i	−0.0465899	−	0.0641255i
$274$	−12.6621			−0.764946
$275$		0			0
$276$	−4.31779			−0.259900
$277$	13.1252	+	18.0652i	0.788614	+	1.08543i	0.994279	+	0.106812i	$0.0340643\pi$
$277$	13.1252	+	18.0652i	0.788614	+	1.08543i	−0.205665	+	0.978622i	$0.565936\pi$
$278$	24.0460	−	7.81302i	1.44218	−	0.468594i
$279$	−1.89955	+	5.84622i	−0.113723	+	0.350004i
$280$		0			0
$281$	−19.2992	−	14.0217i	−1.15129	−	0.836463i	−0.162640	−	0.986685i	$-0.552001\pi$
$281$	−19.2992	−	14.0217i	−1.15129	−	0.836463i	−0.988652	+	0.150223i	$0.952001\pi$
$282$	−18.4969	−	6.01000i	−1.10147	−	0.357891i
$283$	0.138749	−	0.0450824i	0.00824779	−	0.00267987i	−0.304890	−	0.952388i	$-0.598620\pi$
$283$	0.138749	−	0.0450824i	0.00824779	−	0.00267987i	0.313138	+	0.949708i	$0.398620\pi$
$284$	−2.01515	+	1.46409i	−0.119577	+	0.0868777i
$285$		0			0
$286$	−0.977932	+	8.07544i	−0.0578264	+	0.477511i
$287$		−	3.14597i		−	0.185701i
$288$	0.926022	+	1.27456i	0.0545664	+	0.0751041i
$289$	4.25236	+	13.0874i	0.250139	+	0.769848i
$290$		0			0
$291$	−10.1682	−	7.38761i	−0.596069	−	0.433070i
$292$	0.150855	−	0.207634i	0.00882812	−	0.0121509i
$293$	7.29917	+	2.37164i	0.426422	+	0.138553i	0.514363	−	0.857573i	$-0.328029\pi$
$293$	7.29917	+	2.37164i	0.426422	+	0.138553i	−0.0879405	+	0.996126i	$0.528029\pi$
$294$	−5.69281	−	17.5207i	−0.332012	−	1.02183i
$295$		0			0
$296$	5.50374			0.319899
$297$	−5.35940	+	11.5433i	−0.310984	+	0.669808i
$298$		−	7.63238i		−	0.442132i
$299$	−12.6285	+	9.17515i	−0.730325	+	0.530612i
$300$		0			0
$301$	0.727893	−	2.24022i	0.0419550	−	0.129124i
$302$	10.3848	−	14.2934i	0.597577	−	0.822494i
$303$	−4.36876	+	6.01309i	−0.250979	+	0.345443i
$304$	−7.58534	+	23.3453i	−0.435049	+	1.33894i
$305$		0			0
$306$	−2.12903	+	1.54683i	−0.121709	+	0.0884266i
$307$		−	9.69537i		−	0.553344i	−0.960964	−	0.276672i	$-0.910768\pi$
$307$		−	9.69537i		−	0.553344i	0.960964	−	0.276672i	$-0.0892315\pi$
$308$	−0.123213	+	0.265380i	−0.00702071	+	0.0151214i
$309$	39.8840			2.26892
$310$		0			0
$311$	7.77436	+	23.9270i	0.440844	+	1.35678i	0.886978	+	0.461811i	$0.152800\pi$
$311$	7.77436	+	23.9270i	0.440844	+	1.35678i	−0.446135	+	0.894966i	$0.647200\pi$
$312$	10.6510	+	3.46071i	0.602992	+	0.195924i
$313$	−6.39138	+	8.79698i	−0.361262	+	0.497235i	−0.950500	−	0.310725i	$-0.899428\pi$
$313$	−6.39138	+	8.79698i	−0.361262	+	0.497235i	0.589238	+	0.807960i	$0.299428\pi$
$314$	14.3757	+	10.4445i	0.811265	+	0.589418i
$315$		0			0
$316$	−0.519233	−	1.59803i	−0.0292091	−	0.0898964i
$317$	14.9499	+	20.5768i	0.839672	+	1.15571i	0.986045	+	0.166480i	$0.0532402\pi$
$317$	14.9499	+	20.5768i	0.839672	+	1.15571i	−0.146373	+	0.989230i	$0.546760\pi$
$318$		−	0.918232i		−	0.0514919i
$319$	2.31291	−	19.0992i	0.129498	−	1.06935i
$320$		0			0
$321$	0.494091	−	0.358978i	0.0275775	−	0.0200362i
$322$	3.68201	−	1.19636i	0.205190	−	0.0666704i
$323$	12.2523	+	3.98100i	0.681734	+	0.221509i
$324$	2.27378	+	1.65200i	0.126321	+	0.0917776i
$325$		0			0
$326$	−1.28050	+	3.94098i	−0.0709204	+	0.218270i
$327$	−21.0785	+	6.84882i	−1.16564	+	0.378741i
$328$	15.8125	+	21.7641i	0.873102	+	1.20172i
$329$	−2.52904			−0.139431
$330$		0			0
$331$	−10.3091			−0.566638			−0.283319	−	0.959026i	$-0.591435\pi$
$331$	−10.3091			−0.566638			−0.283319	+	0.959026i	$0.591435\pi$
$332$	1.65650	+	2.27998i	0.0909124	+	0.125130i
$333$	−1.94465	+	0.631857i	−0.106566	+	0.0346255i
$334$	1.07360	−	3.30420i	0.0587447	−	0.180798i
$335$		0			0
$336$	−1.95786	−	1.42247i	−0.106810	−	0.0776020i
$337$	−2.19127	−	0.711987i	−0.119366	−	0.0387844i	0.248725	−	0.968574i	$-0.419988\pi$
$337$	−2.19127	−	0.711987i	−0.119366	−	0.0387844i	−0.368091	+	0.929790i	$0.619988\pi$
$338$	−12.0115	+	3.90276i	−0.653337	+	0.212282i
$339$	−9.51232	+	6.91111i	−0.516638	+	0.375360i
$340$		0			0
$341$	12.5449	−	13.4976i	0.679344	−	0.730936i
$342$		−	10.4668i		−	0.565980i
$343$	−2.84098	−	3.91028i	−0.153399	−	0.211135i
$344$	6.22438	+	19.1567i	0.335596	+	1.03286i
$345$		0			0
$346$	−4.19422	−	3.04728i	−0.225483	−	0.163823i
$347$	12.1899	−	16.7779i	0.654387	−	0.900686i	−0.344892	−	0.938642i	$-0.612085\pi$
$347$	12.1899	−	16.7779i	0.654387	−	0.900686i	0.999279	+	0.0379558i	$0.0120846\pi$
$348$	−2.83189	−	0.920138i	−0.151806	−	0.0493246i
$349$	−1.14723	−	3.53080i	−0.0614097	−	0.189000i	0.915645	−	0.401988i	$-0.131680\pi$
$349$	−1.14723	−	3.53080i	−0.0614097	−	0.189000i	−0.977055	+	0.212988i	$0.931680\pi$
$350$		0			0
$351$	7.12106			0.380094
$352$	−0.908832	−	4.63444i	−0.0484409	−	0.247017i
$353$		−	3.01441i		−	0.160441i	−0.996777	−	0.0802203i	$-0.974438\pi$
$353$		−	3.01441i		−	0.160441i	0.996777	−	0.0802203i	$-0.0255624\pi$
$354$	−0.431856	+	0.313762i	−0.0229529	+	0.0166763i
$355$		0			0
$356$	−0.692393	+	2.13097i	−0.0366967	+	0.112941i
$357$	−0.746551	+	1.02754i	−0.0395117	+	0.0543832i
$358$	2.57510	−	3.54432i	0.136098	−	0.187323i
$359$	7.02678	−	21.6262i	0.370859	−	1.14139i	−0.575371	−	0.817893i	$-0.695142\pi$
$359$	7.02678	−	21.6262i	0.370859	−	1.14139i	0.946230	−	0.323494i	$-0.104858\pi$
$360$		0			0
$361$	−26.0818	+	18.9495i	−1.37273	+	0.997344i
$362$			22.3418i			1.17426i
$363$	−17.0280	+	14.3848i	−0.893736	+	0.755005i
$364$	0.163714			0.00858092
$365$		0			0
$366$	6.45207	+	19.8574i	0.337255	+	1.03796i
$367$	−12.8806	−	4.18516i	−0.672362	−	0.218464i	−0.0471138	−	0.998890i	$-0.515002\pi$
$367$	−12.8806	−	4.18516i	−0.672362	−	0.218464i	−0.625248	+	0.780426i	$0.715002\pi$
$368$	−16.9544	+	23.3357i	−0.883809	+	1.21646i
$369$	−8.08572	−	5.87462i	−0.420926	−	0.305820i
$370$		0			0
$371$	−0.0368976	−	0.113559i	−0.00191563	−	0.00589570i
$372$	−1.67637	−	2.30733i	−0.0869159	−	0.119630i
$373$			24.8281i			1.28555i	0.766056	+	0.642774i	$0.222217\pi$
$373$			24.8281i			1.28555i	−0.766056	+	0.642774i	$0.777783\pi$
$374$	7.74141	−	1.51812i	0.400299	−	0.0785001i
$375$		0			0
$376$	17.4961	−	12.7117i	0.902294	−	0.655555i
$377$	−10.2379	+	3.32649i	−0.527278	+	0.171323i
$378$	−1.67971	−	0.545772i	−0.0863952	−	0.0280715i
$379$	4.98407	+	3.62114i	0.256015	+	0.186005i	0.708388	−	0.705823i	$-0.249423\pi$
$379$	4.98407	+	3.62114i	0.256015	+	0.186005i	−0.452374	+	0.891829i	$0.649423\pi$
$380$		0			0
$381$	−7.73386	+	23.8024i	−0.396218	+	1.21943i
$382$	26.4154	−	8.58287i	1.35153	−	0.439138i
$383$	0.213759	+	0.294214i	0.0109226	+	0.0150337i	0.814443	−	0.580243i	$-0.197042\pi$
$383$	0.213759	+	0.294214i	0.0109226	+	0.0150337i	−0.803521	+	0.595277i	$0.797042\pi$
$384$	17.6370			0.900034
$385$		0			0
$386$	−4.37892			−0.222881
$387$	−4.39856	−	6.05409i	−0.223591	−	0.307747i
$388$	1.49425	−	0.485510i	0.0758589	−	0.0246481i
$389$	0.577201	−	1.77644i	0.0292653	−	0.0900693i	−0.935357	−	0.353705i	$-0.884922\pi$
$389$	0.577201	−	1.77644i	0.0292653	−	0.0900693i	0.964622	+	0.263636i	$0.0849217\pi$
$390$		0			0
$391$	12.2473	+	8.89815i	0.619370	+	0.449999i
$392$	19.4824	+	6.33022i	0.984011	+	0.319725i
$393$	−15.0639	+	4.89457i	−0.759875	+	0.246898i
$394$	7.45476	−	5.41620i	0.375565	−	0.272864i
$395$		0			0
$396$	0.451995	+	0.812237i	0.0227136	+	0.0408164i
$397$			0.384172i			0.0192811i	0.999954	+	0.00964053i	$0.00306872\pi$
$397$			0.384172i			0.0192811i	−0.999954	+	0.00964053i	$0.996931\pi$
$398$	−14.9294	−	20.5486i	−0.748345	−	1.03001i
$399$	−1.56104	−	4.80437i	−0.0781495	−	0.240519i
$400$		0			0
$401$	18.3270	+	13.3153i	0.915206	+	0.664936i	0.942326	−	0.334696i	$-0.108634\pi$
$401$	18.3270	+	13.3153i	0.915206	+	0.664936i	−0.0271201	+	0.999632i	$0.508634\pi$
$402$	−19.2760	+	26.5311i	−0.961399	+	1.32325i
$403$	−9.80600	−	3.18616i	−0.488471	−	0.158714i
$404$	−0.287113	−	0.883643i	−0.0142844	−	0.0439629i
$405$		0			0
$406$	2.66986			0.132503
$407$	6.08505	+	0.736897i	0.301625	+	0.0365266i
$408$		−	10.8610i		−	0.537699i
$409$	−23.6348	+	17.1717i	−1.16866	+	0.849085i	−0.990848	−	0.134979i	$-0.956903\pi$
$409$	−23.6348	+	17.1717i	−1.16866	+	0.849085i	−0.177816	+	0.984064i	$0.556903\pi$
$410$		0			0
$411$	−5.99944	+	18.4644i	−0.295931	+	0.910781i
$412$	−2.93054	+	4.03354i	−0.144377	+	0.198718i
$413$	−0.0408003	+	0.0561568i	−0.00200765	+	0.00276330i
$414$	3.80073	−	11.6975i	0.186796	−	0.574899i
$415$		0			0
$416$	−2.13785	+	1.55324i	−0.104817	+	0.0761537i
$417$		−	38.7667i		−	1.89841i
$418$	−13.2130	+	28.4587i	−0.646270	+	1.39196i
$419$	0.720765			0.0352117			0.0176058	−	0.999845i	$-0.494396\pi$
$419$	0.720765			0.0352117			0.0176058	+	0.999845i	$0.494396\pi$
$420$		0			0
$421$	−7.24859	−	22.3089i	−0.353275	−	1.08727i	−0.957003	−	0.290078i	$-0.906319\pi$
$421$	−7.24859	−	22.3089i	−0.353275	−	1.08727i	0.603728	−	0.797190i	$-0.293681\pi$
$422$	5.39753	+	1.75376i	0.262747	+	0.0853718i
$423$	−4.72260	+	6.50010i	−0.229621	+	0.316046i
$424$	0.826042	+	0.600154i	0.0401161	+	0.0291461i
$425$		0			0
$426$	−8.13782	−	25.0456i	−0.394278	−	1.21346i
$427$	1.59587	+	2.19653i	0.0772298	+	0.106298i
$428$			0.0763449i			0.00369027i
$429$	11.3126	+	5.25229i	0.546176	+	0.253583i
$430$		0			0
$431$	−3.04083	+	2.20930i	−0.146472	+	0.106418i	−0.658608	−	0.752486i	$-0.728854\pi$
$431$	−3.04083	+	2.20930i	−0.146472	+	0.106418i	0.512136	+	0.858904i	$0.328854\pi$
$432$	12.5147	−	4.06627i	0.602114	−	0.195639i
$433$	−12.9409	−	4.20476i	−0.621901	−	0.202068i	−0.0189169	−	0.999821i	$-0.506022\pi$
$433$	−12.9409	−	4.20476i	−0.621901	−	0.202068i	−0.602984	+	0.797753i	$0.706022\pi$
$434$	2.06884	+	1.50310i	0.0993076	+	0.0721512i
$435$		0			0
$436$	0.856143	−	2.63494i	0.0410018	−	0.126191i
$437$	−57.2634	+	18.6060i	−2.73928	+	0.890045i
$438$	1.59491	+	2.19521i	0.0762078	+	0.104891i
$439$	−15.6217			−0.745584			−0.372792	−	0.927915i	$-0.621600\pi$
$439$	−15.6217			−0.745584			−0.372792	+	0.927915i	$0.621600\pi$
$440$		0			0
$441$	−7.61052			−0.362406
$442$	−2.59454	−	3.57108i	−0.123410	−	0.169859i
$443$	1.34652	−	0.437512i	0.0639753	−	0.0207868i	−0.276855	−	0.960912i	$-0.589292\pi$
$443$	1.34652	−	0.437512i	0.0639753	−	0.0207868i	0.340830	+	0.940125i	$0.389292\pi$
$444$	0.293158	−	0.902248i	0.0139127	−	0.0428188i
$445$		0			0
$446$	11.3213	+	8.22540i	0.536079	+	0.389484i
$447$	−11.1298	−	3.61630i	−0.526423	−	0.171045i
$448$	2.89491	−	0.940613i	0.136772	−	0.0444398i
$449$	5.58939	−	4.06093i	0.263780	−	0.191647i	−0.448032	−	0.894017i	$-0.647875\pi$
$449$	5.58939	−	4.06093i	0.263780	−	0.191647i	0.711812	+	0.702370i	$0.247875\pi$
$450$		0			0
$451$	14.5687	+	26.1800i	0.686012	+	1.23277i
$452$		−	1.46980i		−	0.0691338i
$453$	−15.9228	−	21.9159i	−0.748119	−	1.02970i
$454$	−2.35855	−	7.25887i	−0.110692	−	0.340676i
$455$		0			0
$456$	34.9475	+	25.3909i	1.63657	+	1.18904i
$457$	24.8949	−	34.2649i	1.16453	−	1.60284i	0.471669	−	0.881776i	$-0.343652\pi$
$457$	24.8949	−	34.2649i	1.16453	−	1.60284i	0.692865	−	0.721068i	$-0.256348\pi$
$458$	6.41854	+	2.08551i	0.299919	+	0.0974496i
$459$	−2.13410	−	6.56807i	−0.0996111	−	0.306571i
$460$		0			0
$461$	25.1563			1.17165			0.585823	−	0.810439i	$-0.300772\pi$
$461$	25.1563			1.17165			0.585823	+	0.810439i	$0.300772\pi$
$462$	−2.26586	−	2.10593i	−0.105417	−	0.0979765i
$463$			7.89251i			0.366796i	0.983039	+	0.183398i	$0.0587097\pi$
$463$			7.89251i			0.366796i	−0.983039	+	0.183398i	$0.941290\pi$
$464$	−16.0928	+	11.6921i	−0.747089	+	0.542792i
$465$		0			0
$466$	11.3479	−	34.9254i	0.525684	−	1.61789i
$467$	9.38761	−	12.9209i	0.434407	−	0.597909i	−0.534551	−	0.845136i	$-0.679519\pi$
$467$	9.38761	−	12.9209i	0.434407	−	0.597909i	0.968958	+	0.247227i	$0.0795193\pi$
$468$	0.305710	−	0.420774i	0.0141315	−	0.0194503i
$469$	−1.31778	+	4.05572i	−0.0608495	+	0.187276i
$470$		0			0
$471$	22.0420	−	16.0144i	1.01564	−	0.737905i
$472$		−	0.593572i		−	0.0273214i
$473$	4.31691	+	22.0134i	0.198492	+	1.01218i
$474$	17.7646			0.815957
$475$		0			0
$476$	−0.0490630	−	0.151000i	−0.00224880	−	0.00692109i
$477$	−0.360768	−	0.117221i	−0.0165185	−	0.00536717i
$478$	5.24147	−	7.21426i	0.239739	−	0.329973i
$479$	11.6195	+	8.44209i	0.530910	+	0.385729i	0.820698	−	0.571362i	$-0.193585\pi$
$479$	11.6195	+	8.44209i	0.530910	+	0.385729i	−0.289788	+	0.957091i	$0.593585\pi$
$480$		0			0
$481$	−1.05983	−	3.26181i	−0.0483240	−	0.148726i
$482$	10.1462	+	13.9650i	0.462145	+	0.636088i
$483$		−	5.93610i		−	0.270102i
$484$	−0.203602	−	2.77901i	−0.00925465	−	0.126319i
$485$		0			0
$486$	−11.7309	+	8.52300i	−0.532125	+	0.386611i
$487$	34.1729	−	11.1034i	1.54852	−	0.503145i	0.594808	−	0.803868i	$-0.297228\pi$
$487$	34.1729	−	11.1034i	1.54852	−	0.503145i	0.953712	+	0.300723i	$0.0972279\pi$
$488$	−22.0808	−	7.17449i	−0.999551	−	0.324774i
$489$	5.14017	+	3.73455i	0.232447	+	0.168882i
$490$		0			0
$491$	10.8828	−	33.4939i	0.491135	−	1.51156i	−0.331760	−	0.943364i	$-0.607642\pi$
$491$	10.8828	−	33.4939i	0.491135	−	1.51156i	0.822895	−	0.568194i	$-0.192358\pi$
$492$	4.41012	−	1.43294i	0.198824	−	0.0646017i
$493$	6.13634	+	8.44595i	0.276367	+	0.380386i
$494$	17.5562			0.789891
$495$		0			0
$496$	−19.0526			−0.855488
$497$	−2.01283	−	2.77043i	−0.0902879	−	0.124271i
$498$	−28.3372	+	9.20731i	−1.26982	+	0.412589i
$499$	−8.18654	+	25.1956i	−0.366480	+	1.12791i	0.582569	+	0.812781i	$0.302048\pi$
$499$	−8.18654	+	25.1956i	−0.366480	+	1.12791i	−0.949049	+	0.315128i	$0.897952\pi$
$500$		0			0
$501$	−4.30963	−	3.13113i	−0.192540	−	0.139888i
$502$	−37.8911	−	12.3116i	−1.69116	−	0.549492i
$503$	16.8751	−	5.48306i	0.752424	−	0.244478i	0.0924004	−	0.995722i	$-0.470546\pi$
$503$	16.8751	−	5.48306i	0.752424	−	0.244478i	0.660024	+	0.751244i	$0.270546\pi$
$504$	−0.928313	+	0.674459i	−0.0413504	+	0.0300428i
$505$		0			0
$506$	−25.1005	+	27.0068i	−1.11586	+	1.20060i
$507$			19.3647i			0.860019i
$508$	−1.83892	−	2.53106i	−0.0815889	−	0.112298i
$509$	4.25018	+	13.0807i	0.188386	+	0.579793i	0.999990	−	0.00441502i	$-0.00140535\pi$
$509$	4.25018	+	13.0807i	0.188386	+	0.579793i	−0.811604	+	0.584208i	$0.801405\pi$
$510$		0			0
$511$	0.285456	+	0.207396i	0.0126278	+	0.00917465i
$512$	−14.8754	+	20.4742i	−0.657406	+	0.904842i
$513$	26.1232	+	8.48796i	1.15337	+	0.374753i
$514$	0.148236	+	0.456223i	0.00653840	+	0.0201231i
$515$		0			0
$516$	3.47196			0.152845
$517$	21.0460	−	11.7117i	0.925604	−	0.515081i
$518$			0.850623i			0.0373742i
$519$	−6.43093	+	4.67234i	−0.282286	+	0.205093i
$520$		0			0
$521$	3.88720	−	11.9636i	0.170301	−	0.524133i	−0.829087	−	0.559120i	$-0.811139\pi$
$521$	3.88720	−	11.9636i	0.170301	−	0.524133i	0.999388	+	0.0349870i	$0.0111390\pi$
$522$	4.98555	−	6.86203i	0.218212	−	0.300343i
$523$	23.9797	−	33.0052i	1.04856	−	1.44322i	0.158508	−	0.987358i	$-0.449331\pi$
$523$	23.9797	−	33.0052i	1.04856	−	1.44322i	0.890051	−	0.455861i	$-0.150669\pi$
$524$	0.611850	−	1.88308i	0.0267288	−	0.0822628i
$525$		0			0
$526$	−24.1105	+	17.5173i	−1.05127	+	0.763792i
$527$			9.99936i			0.435579i
$528$	22.8801	+	2.77077i	0.995729	+	0.120582i
$529$	−47.7524			−2.07619
$530$		0			0
$531$	0.0681449	+	0.209729i	0.00295724	+	0.00910144i
$532$	0.600575	+	0.195139i	0.0260382	+	0.00846033i
$533$	9.85363	−	13.5624i	0.426808	−	0.587451i
$534$	−19.1648	−	13.9241i	−0.829342	−	0.602553i
$535$		0			0
$536$	−11.2687	−	34.6814i	−0.486732	−	1.49801i
$537$	−3.94836	−	5.43445i	−0.170384	−	0.234514i
$538$			8.12434i			0.350265i
$539$	20.6926	+	9.60732i	0.891293	+	0.413817i
$540$		0			0
$541$	−26.3873	+	19.1715i	−1.13448	+	0.824247i	−0.986340	−	0.164720i	$-0.947328\pi$
$541$	−26.3873	+	19.1715i	−1.13448	+	0.824247i	−0.148138	+	0.988967i	$0.547328\pi$
$542$	−20.9860	+	6.81876i	−0.901425	+	0.292891i
$543$	32.5797	+	10.5858i	1.39813	+	0.454279i
$544$	2.07331	+	1.50635i	0.0888923	+	0.0645840i
$545$		0			0
$546$	−0.534865	+	1.64614i	−0.0228901	+	0.0704485i
$547$	−5.44942	+	1.77062i	−0.233000	+	0.0757064i	−0.423190	−	0.906041i	$-0.639090\pi$
$547$	−5.44942	+	1.77062i	−0.233000	+	0.0757064i	0.190190	+	0.981747i	$0.439090\pi$
$548$	−1.42652	−	1.96344i	−0.0609379	−	0.0838739i
$549$	8.62555			0.368129
$550$		0			0
$551$	−41.5222			−1.76890
$552$	29.8365	+	41.0665i	1.26993	+	1.74791i
$553$	2.19698	−	0.713842i	0.0934251	−	0.0303556i
$554$	9.11960	−	28.0672i	0.387454	−	1.19246i
$555$		0			0
$556$	3.92055	+	2.84845i	0.166268	+	0.120801i
$557$	38.6418	+	12.5555i	1.63731	+	0.531993i	0.975935	−	0.218064i	$-0.0699741\pi$
$557$	38.6418	+	12.5555i	1.63731	+	0.531993i	0.661373	+	0.750057i	$0.269974\pi$
$558$	7.72649	−	2.51049i	0.327089	−	0.106278i
$559$	10.1547	−	7.37780i	0.429497	−	0.312048i
$560$		0			0
$561$	1.45418	−	12.0081i	0.0613955	−	0.506984i
$562$			31.5274i			1.32990i
$563$	−8.63316	−	11.8825i	−0.363844	−	0.500788i	0.587371	−	0.809318i	$-0.300163\pi$
$563$	−8.63316	−	11.8825i	−0.363844	−	0.500788i	−0.951215	+	0.308530i	$0.900163\pi$
$564$	−1.15194	−	3.54529i	−0.0485052	−	0.149284i
$565$		0			0
$566$	−0.155987	−	0.113332i	−0.00655664	−	0.00476368i
$567$	−2.27117	+	3.12600i	−0.0953801	+	0.131279i
$568$	27.8499	+	9.04898i	1.16856	+	0.379687i
$569$	7.60025	+	23.3912i	0.318619	+	0.980609i	0.974239	+	0.225518i	$0.0724073\pi$
$569$	7.60025	+	23.3912i	0.318619	+	0.980609i	−0.655620	+	0.755091i	$0.727593\pi$
$570$		0			0
$571$	−22.4923			−0.941273			−0.470637	−	0.882327i	$-0.655976\pi$
$571$	−22.4923			−0.941273			−0.470637	+	0.882327i	$0.655976\pi$
$572$	−1.36238	+	0.758141i	−0.0569641	+	0.0316995i
$573$		−	42.5866i		−	1.77908i
$574$	−3.36372	+	2.44388i	−0.140399	+	0.102006i
$575$		0			0
$576$	2.98825	−	9.19690i	0.124511	−	0.383204i
$577$	22.0616	−	30.3652i	0.918435	−	1.26412i	−0.0457674	−	0.998952i	$-0.514573\pi$
$577$	22.0616	−	30.3652i	0.918435	−	1.26412i	0.964203	−	0.265166i	$-0.0854267\pi$
$578$	10.6899	−	14.7134i	0.444641	−	0.611996i
$579$	−2.07478	+	6.38552i	−0.0862249	+	0.265373i
$580$		0			0
$581$	−3.13452	+	2.27736i	−0.130042	+	0.0944809i
$582$			16.6109i			0.688543i
$583$	0.832933	+	0.774141i	0.0344966	+	0.0320617i
$584$	−3.01724			−0.124854
$585$		0			0
$586$	−3.13442	−	9.64675i	−0.129482	−	0.398503i
$587$	−26.6393	−	8.65563i	−1.09952	−	0.357256i	−0.297603	−	0.954690i	$-0.596187\pi$
$587$	−26.6393	−	8.65563i	−1.09952	−	0.357256i	−0.801918	+	0.597434i	$0.796187\pi$
$588$	2.07547	−	2.85664i	0.0855910	−	0.117806i
$589$	−32.1750	−	23.3765i	−1.32575	−	0.963213i
$590$		0			0
$591$	−4.36597	−	13.4371i	−0.179592	−	0.552728i
$592$	−3.72512	−	5.12719i	−0.153102	−	0.210726i
$593$			17.7522i			0.728996i	0.931204	+	0.364498i	$0.118759\pi$
$593$			17.7522i			0.728996i	−0.931204	+	0.364498i	$0.881241\pi$
$594$	16.5056	−	3.23681i	0.677232	−	0.132808i
$595$		0			0
$596$	1.18351	−	0.859868i	0.0484783	−	0.0352216i
$597$	−37.0385	+	12.0345i	−1.51589	+	0.492541i
$598$	19.6204	+	6.37506i	0.802338	+	0.260695i
$599$	−19.7594	−	14.3561i	−0.807348	−	0.586573i	0.105713	−	0.994397i	$-0.466288\pi$
$599$	−19.7594	−	14.3561i	−0.807348	−	0.586573i	−0.913061	+	0.407824i	$0.866288\pi$
$600$		0			0
$601$	−1.34725	+	4.14640i	−0.0549553	+	0.169135i	−0.974767	−	0.223225i	$-0.928341\pi$
$601$	−1.34725	+	4.14640i	−0.0549553	+	0.169135i	0.919812	+	0.392360i	$0.128341\pi$
$602$	−2.96073	+	0.961999i	−0.120670	+	0.0392082i
$603$	7.96318	+	10.9604i	0.324286	+	0.446341i
$604$	3.38635			0.137789
$605$		0			0
$606$	9.82307			0.399035
$607$	−23.2869	−	32.0516i	−0.945185	−	1.30094i	−0.953633	−	0.300971i	$-0.902689\pi$
$607$	−23.2869	−	32.0516i	−0.945185	−	1.30094i	0.00844827	−	0.999964i	$-0.497311\pi$
$608$	−9.69396	+	3.14976i	−0.393142	+	0.127740i
$609$	1.26501	−	3.89329i	0.0512607	−	0.157764i
$610$		0			0
$611$	−10.9028	−	7.92132i	−0.441078	−	0.320462i
$612$	−0.479716	−	0.155869i	−0.0193914	−	0.00630064i
$613$	−2.48151	+	0.806291i	−0.100227	+	0.0325658i	−0.358701	−	0.933452i	$-0.616780\pi$
$613$	−2.48151	+	0.806291i	−0.100227	+	0.0325658i	0.258474	+	0.966018i	$0.416780\pi$
$614$	−10.3664	+	7.53165i	−0.418355	+	0.303953i
$615$		0			0
$616$	3.37545	−	0.661939i	0.136001	−	0.0266703i
$617$		−	3.53110i		−	0.142157i	−0.997471	−	0.0710783i	$-0.977356\pi$
$617$		−	3.53110i		−	0.142157i	0.997471	−	0.0710783i	$-0.0226440\pi$
$618$	−30.9831	−	42.6445i	−1.24632	−	1.71541i
$619$	1.86509	+	5.74014i	0.0749641	+	0.230716i	0.981517	−	0.191377i	$-0.0612955\pi$
$619$	1.86509	+	5.74014i	0.0749641	+	0.230716i	−0.906552	+	0.422093i	$0.861295\pi$
$620$		0			0
$621$	26.1126	+	18.9719i	1.04786	+	0.761316i
$622$	19.5438	−	26.8997i	0.783634	−	1.07858i
$623$	−2.92966	−	0.951903i	−0.117374	−	0.0381372i
$624$	−3.98501	−	12.2646i	−0.159528	−	0.490977i
$625$		0			0
$626$	14.3709			0.574376
$627$	35.2391	+	32.7518i	1.40731	+	1.30798i
$628$			3.40583i			0.135907i
$629$	−2.69090	+	1.95505i	−0.107293	+	0.0779530i
$630$		0			0
$631$	0.333740	−	1.02714i	0.0132860	−	0.0408900i	−0.944194	−	0.329391i	$-0.893157\pi$
$631$	0.333740	−	1.02714i	0.0132860	−	0.0408900i	0.957480	+	0.288501i	$0.0931567\pi$
$632$	−11.6109	+	15.9811i	−0.461858	+	0.635693i
$633$	5.11481	−	7.03994i	0.203296	−	0.279812i
$634$	10.3875	−	31.9694i	0.412540	−	1.26967i
$635$		0			0
$636$	0.142385	−	0.103449i	0.00564592	−	0.00410200i
$637$		−	12.7653i		−	0.505780i
$638$	−22.2179	+	12.3638i	−0.879615	+	0.489489i
$639$	−10.8792			−0.430373
$640$		0			0
$641$	3.05474	+	9.40153i	0.120655	+	0.371338i	0.993084	−	0.117402i	$-0.0374566\pi$
$641$	3.05474	+	9.40153i	0.120655	+	0.371338i	−0.872429	+	0.488740i	$0.837457\pi$
$642$	−0.767650	−	0.249425i	−0.0302967	−	0.00984400i
$643$	−16.9284	+	23.2999i	−0.667589	+	0.918858i	−0.999703	−	0.0243814i	$-0.992238\pi$
$643$	−16.9284	+	23.2999i	−0.667589	+	0.918858i	0.332113	+	0.943240i	$0.392238\pi$
$644$	0.600329	+	0.436165i	0.0236563	+	0.0171873i
$645$		0			0
$646$	−5.26138	−	16.1929i	−0.207006	−	0.637100i
$647$	−10.7614	−	14.8118i	−0.423074	−	0.582311i	0.543272	−	0.839557i	$-0.317185\pi$
$647$	−10.7614	−	14.8118i	−0.423074	−	0.582311i	−0.966346	+	0.257245i	$0.917185\pi$
$648$		−	33.0415i		−	1.29799i
$649$	0.0794734	−	0.656265i	0.00311961	−	0.0257606i
$650$		0			0
$651$	3.17212	−	2.30468i	0.124325	−	0.0903276i
$652$	−0.755365	+	0.245433i	−0.0295824	+	0.00961190i
$653$	30.3775	+	9.87025i	1.18876	+	0.386253i	0.835616	−	0.549315i	$-0.185111\pi$
$653$	30.3775	+	9.87025i	1.18876	+	0.386253i	0.353148	+	0.935567i	$0.385111\pi$
$654$	23.6973	+	17.2171i	0.926637	+	0.673241i
$655$		0			0
$656$	9.57259	−	29.4614i	0.373747	−	1.15027i
$657$	1.06609	−	0.346394i	0.0415921	−	0.0135141i
$658$	1.96463	+	2.70409i	0.0765894	+	0.105416i
$659$	−27.0408			−1.05336			−0.526679	−	0.850064i	$-0.676563\pi$
$659$	−27.0408			−1.05336			−0.526679	+	0.850064i	$0.676563\pi$
$660$		0			0
$661$	47.2504			1.83783			0.918915	−	0.394456i	$-0.129067\pi$
$661$	47.2504			1.83783			0.918915	+	0.394456i	$0.129067\pi$
$662$	8.00839	+	11.0226i	0.311255	+	0.428406i
$663$	−6.43681	+	2.09144i	−0.249985	+	0.0812250i
$664$	10.2382	−	31.5100i	0.397320	−	1.22283i
$665$		0			0
$666$	2.18626	+	1.58841i	0.0847157	+	0.0615496i
$667$	−46.4042	−	15.0776i	−1.79678	−	0.583809i
$668$	0.633314	−	0.205776i	0.0245036	−	0.00796172i
$669$	17.3588	−	12.6119i	0.671128	−	0.487603i
$670$		0			0
$671$	−23.4524	−	10.8887i	−0.905369	−	0.420352i
$672$		−	1.00491i		−	0.0387651i
$673$	−22.2631	−	30.6425i	−0.858179	−	1.18118i	−0.982001	−	0.188878i	$-0.939515\pi$
$673$	−22.2631	−	30.6425i	−0.858179	−	1.18118i	0.123821	−	0.992305i	$-0.460485\pi$
$674$	0.940977	+	2.89603i	0.0362451	+	0.111551i
$675$		0			0
$676$	−1.95839	−	1.42286i	−0.0753228	−	0.0547252i
$677$	−19.9281	+	27.4287i	−0.765900	+	1.05417i	0.230800	+	0.973001i	$0.425866\pi$
$677$	−19.9281	+	27.4287i	−0.765900	+	1.05417i	−0.996700	+	0.0811701i	$0.974134\pi$
$678$	14.7789	+	4.80196i	0.567581	+	0.184418i
$679$	0.667481	+	2.05429i	0.0256156	+	0.0788366i
$680$		0			0
$681$	−11.7027			−0.448448
$682$	−24.1771	−	2.92784i	−0.925789	−	0.112113i
$683$			38.6515i			1.47896i	0.673178	+	0.739480i	$0.264929\pi$
$683$			38.6515i			1.47896i	−0.673178	+	0.739480i	$0.735071\pi$
$684$	1.62302	−	1.17920i	0.0620579	−	0.0450877i
$685$		0			0
$686$	−1.97397	+	6.07524i	−0.0753664	+	0.231954i
$687$	6.08235	−	8.37164i	0.232056	−	0.319398i
$688$	13.6331	−	18.7644i	0.519759	−	0.715387i
$689$	0.196617	−	0.605125i	0.00749051	−	0.0230534i
$690$		0			0
$691$	−21.3377	+	15.5027i	−0.811723	+	0.589751i	−0.914330	−	0.404971i	$-0.867282\pi$
$691$	−21.3377	+	15.5027i	−0.811723	+	0.589751i	0.102607	+	0.994722i	$0.467282\pi$
$692$		−	0.993680i		−	0.0377741i
$693$	−1.11666	+	0.621403i	−0.0424186	+	0.0236052i
$694$	−27.4087			−1.04042
$695$		0			0
$696$	10.8174	+	33.2925i	0.410032	+	1.26195i
$697$	−15.4622	−	5.02397i	−0.585672	−	0.190296i
$698$	−2.88399	+	3.96947i	−0.109161	+	0.150247i
$699$	−45.5528	−	33.0961i	−1.72297	−	1.25181i
$700$		0			0
$701$	5.74279	+	17.6745i	0.216902	+	0.667556i	0.999013	+	0.0444171i	$0.0141430\pi$
$701$	5.74279	+	17.6745i	0.216902	+	0.667556i	−0.782111	+	0.623139i	$0.785857\pi$
$702$	−5.53186	−	7.61395i	−0.208786	−	0.287370i
$703$		−	13.2291i		−	0.498943i
$704$	−19.7348	+	21.2336i	−0.743784	+	0.800270i
$705$		0			0
$706$	−3.22305	+	2.34168i	−0.121301	+	0.0881303i
$707$	1.21483	−	0.394723i	0.0456885	−	0.0148451i
$708$	−0.0973063	−	0.0316167i	−0.00365699	−	0.00118823i
$709$	19.1789	+	13.9343i	0.720280	+	0.523314i	0.886474	−	0.462779i	$-0.153148\pi$
$709$	19.1789	+	13.9343i	0.720280	+	0.523314i	−0.166194	+	0.986093i	$0.553148\pi$
$710$		0			0
$711$	2.26782	−	6.97963i	0.0850499	−	0.261757i
$712$	25.0522	−	8.13994i	0.938869	−	0.305057i
$713$	−27.4695	−	37.8086i	−1.02874	−	1.41594i
$714$	1.67860			0.0628202
$715$		0			0
$716$	0.839708			0.0313814
$717$	−8.03666	−	11.0615i	−0.300135	−	0.413100i
$718$	−28.5817	+	9.28674i	−1.06666	+	0.346578i
$719$	9.53420	−	29.3432i	0.355566	−	1.09432i	−0.600115	−	0.799914i	$-0.704879\pi$
$719$	9.53420	−	29.3432i	0.355566	−	1.09432i	0.955681	−	0.294405i	$-0.0951214\pi$
$720$		0			0
$721$	−5.54532	−	4.02891i	−0.206519	−	0.150045i
$722$	40.5222	+	13.1665i	1.50808	+	0.490005i
$723$	25.1717	−	8.17877i	0.936144	−	0.304172i
$724$	−3.46440	+	2.51704i	−0.128754	+	0.0935449i
$725$		0			0
$726$	28.6082	+	7.03202i	1.06175	+	0.260983i
$727$			24.1222i			0.894642i	0.894373	+	0.447321i	$0.147622\pi$
$727$			24.1222i			0.894642i	−0.894373	+	0.447321i	$0.852378\pi$
$728$	−1.13129	−	1.55708i	−0.0419282	−	0.0577092i
$729$	−3.41534	−	10.5113i	−0.126494	−	0.389309i
$730$		0			0
$731$	−9.84810	−	7.15506i	−0.364245	−	0.264640i
$732$	−2.35228	+	3.23763i	−0.0869427	+	0.119666i
$733$	−13.1699	−	4.27917i	−0.486442	−	0.158055i	0.0555200	−	0.998458i	$-0.482318\pi$
$733$	−13.1699	−	4.27917i	−0.486442	−	0.158055i	−0.541962	+	0.840403i	$0.682318\pi$
$734$	5.53120	+	17.0233i	0.204160	+	0.628341i
$735$		0			0
$736$	−11.9775			−0.441496
$737$	−7.81536	−	39.8532i	−0.287882	−	1.46801i
$738$			13.2090i			0.486228i
$739$	22.2549	−	16.1692i	0.818661	−	0.594792i	−0.0976674	−	0.995219i	$-0.531138\pi$
$739$	22.2549	−	16.1692i	0.818661	−	0.594792i	0.916329	+	0.400427i	$0.131138\pi$
$740$		0			0
$741$	8.31832	−	25.6012i	0.305581	−	0.940482i
$742$	−0.0927559	+	0.127668i	−0.00340518	+	0.00468683i
$743$	−1.58429	+	2.18058i	−0.0581218	+	0.0799979i	−0.837089	−	0.547067i	$-0.815744\pi$
$743$	−1.58429	+	2.18058i	−0.0581218	+	0.0799979i	0.778967	+	0.627065i	$0.215744\pi$
$744$	−10.3610	+	31.8880i	−0.379854	+	1.16907i
$745$		0			0
$746$	26.5465	−	19.2872i	0.971937	−	0.706154i
$747$			12.3089i			0.450360i
$748$	1.10756	+	1.02938i	0.0404963	+	0.0376379i
$749$	−0.104959			−0.00383512
$750$		0			0
$751$	7.10258	+	21.8595i	0.259177	+	0.797664i	0.992978	+	0.118300i	$0.0377443\pi$
$751$	7.10258	+	21.8595i	0.259177	+	0.797664i	−0.733801	+	0.679364i	$0.762256\pi$
$752$	−23.6840	−	7.69539i	−0.863666	−	0.280622i
$753$	−35.9064	+	49.4210i	−1.30850	+	1.80100i
$754$	11.5098	+	8.36238i	0.419163	+	0.304540i
$755$		0			0
$756$	−0.104608	−	0.321950i	−0.00380455	−	0.0117092i
$757$	20.5466	+	28.2800i	0.746780	+	1.02785i	0.998200	+	0.0599765i	$0.0191026\pi$
$757$	20.5466	+	28.2800i	0.746780	+	1.02785i	−0.251420	+	0.967878i	$0.580897\pi$
$758$		−	8.14205i		−	0.295733i
$759$	27.4895	+	49.3987i	0.997805	+	1.79306i
$760$		0			0
$761$	−30.1151	+	21.8799i	−1.09167	+	0.793145i	−0.979681	−	0.200564i	$-0.935723\pi$
$761$	−30.1151	+	21.8799i	−1.09167	+	0.793145i	−0.111990	+	0.993709i	$0.535723\pi$
$762$	31.4577	−	10.2212i	1.13959	−	0.370276i
$763$	3.62252	+	1.17703i	0.131144	+	0.0426112i
$764$	4.30686	+	3.12912i	0.155817	+	0.113208i
$765$		0			0
$766$	0.148524	−	0.457109i	0.00536638	−	0.0165160i
$767$	−0.351782	+	0.114301i	−0.0127021	+	0.00412717i
$768$	7.12029	+	9.80024i	0.256931	+	0.353636i
$769$	−30.1272			−1.08642			−0.543208	−	0.839598i	$-0.682790\pi$
$769$	−30.1272			−1.08642			−0.543208	+	0.839598i	$0.682790\pi$
$770$		0			0
$771$	0.735518			0.0264890
$772$	−0.493332	−	0.679013i	−0.0177554	−	0.0244382i
$773$	−29.3954	+	9.55113i	−1.05728	+	0.343530i	−0.785521	−	0.618836i	$-0.787605\pi$
$773$	−29.3954	+	9.55113i	−1.05728	+	0.343530i	−0.271757	+	0.962366i	$0.587605\pi$
$774$	−3.05620	+	9.40600i	−0.109853	+	0.338092i
$775$		0			0
$776$	−14.9432	−	10.8568i	−0.536428	−	0.389738i
$777$	1.24041	+	0.403034i	0.0444995	+	0.0144588i
$778$	−2.34779	+	0.762842i	−0.0841722	+	0.0273492i
$779$	52.3132	−	38.0078i	1.87431	−	1.36177i
$780$		0			0
$781$	29.5798	+	13.7336i	1.05845	+	0.491426i
$782$		−	20.0073i		−	0.715460i
$783$	13.0834	+	18.0077i	0.467562	+	0.643544i
$784$	−7.28925	−	22.4340i	−0.260330	−	0.801214i
$785$		0			0
$786$	16.9355	+	12.3043i	0.604068	+	0.438881i
$787$	−20.2891	+	27.9255i	−0.723227	+	0.995437i	0.276183	+	0.961105i	$0.410930\pi$
$787$	−20.2891	+	27.9255i	−0.723227	+	0.995437i	−0.999410	+	0.0343320i	$0.989070\pi$
$788$	1.67972	+	0.545773i	0.0598374	+	0.0194423i
$789$	14.1206	+	43.4588i	0.502708	+	1.54718i
$790$		0			0
$791$	2.02069			0.0718474
$792$	4.60184	−	9.91160i	0.163519	−	0.352193i
$793$			14.4678i			0.513767i
$794$	0.410763	−	0.298437i	0.0145774	−	0.0105911i
$795$		0			0
$796$	1.50439	−	4.63003i	0.0533217	−	0.164107i
$797$	6.01617	−	8.28055i	0.213104	−	0.293312i	−0.689061	−	0.724703i	$-0.741977\pi$
$797$	6.01617	−	8.28055i	0.213104	−	0.293312i	0.902165	+	0.431391i	$0.141977\pi$
$798$	−3.92425	+	5.40126i	−0.138917	+	0.191203i
$799$	−4.03876	+	12.4300i	−0.142881	+	0.439743i
$800$		0			0
$801$	−7.91725	+	5.75222i	−0.279742	+	0.203245i
$802$		−	29.9392i		−	1.05719i
$803$	−3.33592	−	0.403979i	−0.117722	−	0.0142561i
$804$	−6.28566			−0.221678
$805$		0			0
$806$	4.21090	+	12.9598i	0.148323	+	0.456490i
$807$	11.8472	+	3.84940i	0.417043	+	0.135505i
$808$	−6.42034	+	8.83683i	−0.225867	+	0.310879i
$809$	29.0143	+	21.0801i	1.02009	+	0.741139i	0.966301	−	0.257414i	$-0.0828704\pi$
$809$	29.0143	+	21.0801i	1.02009	+	0.741139i	0.0537884	+	0.998552i	$0.482870\pi$
$810$		0			0
$811$	5.71683	+	17.5946i	0.200745	+	0.617830i	0.999861	+	0.0166535i	$0.00530122\pi$
$811$	5.71683	+	17.5946i	0.200745	+	0.617830i	−0.799116	+	0.601177i	$0.794699\pi$
$812$	0.300788	+	0.413999i	0.0105556	+	0.0145285i
$813$			33.8334i			1.18659i
$814$	−3.93915	−	7.07867i	−0.138067	−	0.248107i
$815$		0			0
$816$	−10.1179	+	7.35110i	−0.354198	+	0.257340i
$817$	46.0458	−	14.9612i	1.61094	−	0.523426i
$818$	36.7204	+	11.9312i	1.28390	+	0.417164i
$819$	0.578481	+	0.420291i	0.0202138	+	0.0146862i
$820$		0			0
$821$	−8.43005	+	25.9450i	−0.294211	+	0.905488i	0.689275	+	0.724500i	$0.257929\pi$
$821$	−8.43005	+	25.9450i	−0.294211	+	0.905488i	−0.983485	+	0.180987i	$0.942071\pi$
$822$	24.4030	−	7.92900i	0.851151	−	0.276556i
$823$	−1.16646	−	1.60549i	−0.0406602	−	0.0559639i	0.788203	−	0.615416i	$-0.211012\pi$
$823$	−1.16646	−	1.60549i	−0.0406602	−	0.0559639i	−0.828863	+	0.559452i	$0.811012\pi$
$824$	58.6135			2.04190
$825$		0			0
$826$	0.0917386			0.00319199
$827$	7.24783	+	9.97578i	0.252032	+	0.346892i	0.916222	−	0.400672i	$-0.131223\pi$
$827$	7.24783	+	9.97578i	0.252032	+	0.346892i	−0.664190	+	0.747564i	$0.731223\pi$
$828$	2.24205	−	0.728485i	0.0779165	−	0.0253166i
$829$	−0.0956826	+	0.294481i	−0.00332319	+	0.0102277i	−0.952704	−	0.303899i	$-0.901712\pi$
$829$	−0.0956826	+	0.294481i	−0.00332319	+	0.0102277i	0.949381	+	0.314126i	$0.101712\pi$
$830$		0			0
$831$	−36.6078	−	26.5971i	−1.26991	−	0.922644i
$832$	15.4262	+	5.01226i	0.534806	+	0.173769i
$833$	−11.7740	+	3.82561i	−0.407945	+	0.132549i
$834$	−41.4499	+	30.1151i	−1.43529	+	1.04280i
$835$		0			0
$836$	−5.90150	+	1.15731i	−0.204108	+	0.0400263i
$837$			21.3198i			0.736920i
$838$	−0.559912	−	0.770653i	−0.0193418	−	0.0266218i
$839$	2.07149	+	6.37539i	0.0715158	+	0.220103i	0.980426	−	0.196890i	$-0.0630841\pi$
$839$	2.07149	+	6.37539i	0.0715158	+	0.220103i	−0.908910	+	0.416993i	$0.863084\pi$
$840$		0			0
$841$	−3.76040	−	2.73209i	−0.129669	−	0.0942101i
$842$	−18.2220	+	25.0805i	−0.627973	+	0.864331i
$843$	45.9745	+	14.9380i	1.58345	+	0.514493i
$844$	0.336143	+	1.03454i	0.0115705	+	0.0356104i
$845$		0			0
$846$	10.6187			0.365077
$847$	3.82059	−	0.279913i	0.131277	−	0.00961792i
$848$		−	1.17573i		−	0.0403748i
$849$	−0.239173	+	0.173769i	−0.00820840	+	0.00596375i
$850$		0			0
$851$	4.80377	−	14.7845i	0.164671	−	0.506806i
$852$	2.96686	−	4.08354i	0.101643	−	0.139900i
$853$	−26.1984	+	36.0590i	−0.897015	+	1.23464i	0.0743953	+	0.997229i	$0.476297\pi$
$853$	−26.1984	+	36.0590i	−0.897015	+	1.23464i	−0.971410	+	0.237407i	$0.923703\pi$
$854$	1.10884	−	3.41267i	0.0379438	−	0.116779i
$855$		0			0
$856$	0.726117	−	0.527555i	0.0248182	−	0.0180314i
$857$			32.2444i			1.10145i	0.834688	+	0.550723i	$0.185648\pi$
$857$			32.2444i			1.10145i	−0.834688	+	0.550723i	$0.814352\pi$
$858$	−3.17212	−	16.1757i	−0.108294	−	0.552229i
$859$	18.1192			0.618220			0.309110	−	0.951026i	$-0.399969\pi$
$859$	18.1192			0.618220			0.309110	+	0.951026i	$0.399969\pi$
$860$		0			0
$861$	1.97000	+	6.06305i	0.0671375	+	0.206628i
$862$	4.72442	+	1.53506i	0.160915	+	0.0522843i
$863$	−4.82918	+	6.64680i	−0.164387	+	0.226260i	−0.883262	−	0.468880i	$-0.844658\pi$
$863$	−4.82918	+	6.64680i	−0.164387	+	0.226260i	0.718874	+	0.695140i	$0.244658\pi$
$864$	4.42053	+	3.21170i	0.150389	+	0.109264i
$865$		0			0
$866$	5.55711	+	17.1030i	0.188838	+	0.581184i
$867$	−16.3907	−	22.5598i	−0.556656	−	0.766171i
$868$			0.490143i			0.0166365i
$869$	−14.9770	+	16.1144i	−0.508059	+	0.546643i
$870$		0			0
$871$	−18.3841	+	13.3568i	−0.622921	+	0.452579i
$872$	−30.9770	+	10.0650i	−1.04901	+	0.340845i
$873$	6.52633	+	2.12053i	0.220883	+	0.0717692i
$874$	64.3777	+	46.7731i	2.17761	+	1.58212i
$875$		0			0
$876$	−0.160714	+	0.494626i	−0.00543002	+	0.0167119i
$877$	31.4147	−	10.2073i	1.06080	−	0.344675i	0.273901	−	0.961758i	$-0.411686\pi$
$877$	31.4147	−	10.2073i	1.06080	−	0.344675i	0.786898	+	0.617083i	$0.211686\pi$
$878$	12.1354	+	16.7030i	0.409551	+	0.563698i
$879$	−15.5524			−0.524569
$880$		0			0
$881$	30.1182			1.01471			0.507354	−	0.861738i	$-0.330624\pi$
$881$	30.1182			1.01471			0.507354	+	0.861738i	$0.330624\pi$
$882$	5.91208	+	8.13728i	0.199070	+	0.273997i
$883$	−18.1246	+	5.88905i	−0.609943	+	0.198182i	−0.597670	−	0.801742i	$-0.703907\pi$
$883$	−18.1246	+	5.88905i	−0.609943	+	0.198182i	−0.0122728	+	0.999925i	$0.503907\pi$
$884$	0.261443	−	0.804639i	0.00879328	−	0.0270629i
$885$		0			0
$886$	−1.51381	−	1.09985i	−0.0508576	−	0.0369502i
$887$	21.2737	+	6.91223i	0.714300	+	0.232090i	0.643550	−	0.765404i	$-0.277461\pi$
$887$	21.2737	+	6.91223i	0.714300	+	0.232090i	0.0707497	+	0.997494i	$0.477461\pi$
$888$	−10.6070	+	3.44644i	−0.355949	+	0.115655i
$889$	3.47970	−	2.52815i	0.116706	−	0.0847915i
$890$		0			0
$891$	4.42393	−	36.5313i	0.148207	−	1.22384i
$892$			2.68220i			0.0898068i
$893$	−30.5544	−	42.0545i	−1.02246	−	1.40730i
$894$	4.77939	+	14.7094i	0.159847	+	0.491957i
$895$		0			0
$896$	−2.45218	−	1.78161i	−0.0819217	−	0.0595196i
$897$	18.5927	−	25.5907i	0.620793	−	0.854448i
$898$	−8.68401	−	2.82161i	−0.289789	−	0.0941582i
$899$	−9.95920	−	30.6513i	−0.332158	−	1.02228i
$900$		0			0
$901$	−0.617057			−0.0205572
$902$	16.6746	−	35.9144i	0.555204	−	1.19582i
$903$			4.77326i			0.158844i
$904$	−13.9793	+	10.1566i	−0.464945	+	0.337802i
$905$		0			0
$906$	−11.0635	+	34.0498i	−0.367559	+	1.13123i
$907$	−25.0745	+	34.5121i	−0.832586	+	1.14596i	0.154850	+	0.987938i	$0.450511\pi$
$907$	−25.0745	+	34.5121i	−0.832586	+	1.14596i	−0.987436	+	0.158019i	$0.949489\pi$
$908$	0.859874	−	1.18351i	0.0285359	−	0.0392763i
$909$	1.25401	−	3.85943i	0.0415927	−	0.128009i
$910$		0			0
$911$	30.0340	−	21.8210i	0.995070	−	0.722960i	0.0340443	−	0.999420i	$-0.489161\pi$
$911$	30.0340	−	21.8210i	0.995070	−	0.722960i	0.961025	+	0.276460i	$0.0891613\pi$
$912$		−	49.7419i		−	1.64712i
$913$	15.5385	−	33.4673i	0.514248	−	1.10761i
$914$	−55.9756			−1.85151
$915$		0			0
$916$	0.399729	+	1.23024i	0.0132074	+	0.0406483i
$917$	2.58886	+	0.841173i	0.0854918	+	0.0277780i
$918$	−5.36485	+	7.38408i	−0.177066	+	0.243711i
$919$	2.71707	+	1.97406i	0.0896278	+	0.0651184i	0.631697	−	0.775216i	$-0.282359\pi$
$919$	2.71707	+	1.97406i	0.0896278	+	0.0651184i	−0.542069	+	0.840334i	$0.682359\pi$
$920$		0			0
$921$	6.07123	+	18.6853i	0.200054	+	0.615702i
$922$	−19.5422	−	26.8975i	−0.643587	−	0.885821i
$923$		−	18.2479i		−	0.600636i
$924$	0.0712802	−	0.588608i	0.00234495	−	0.0193638i
$925$		0			0
$926$	8.43879	−	6.13114i	0.277316	−	0.201482i
$927$	−20.7101	+	6.72912i	−0.680209	+	0.221013i
$928$	−7.85565	−	2.55245i	−0.257874	−	0.0837884i
$929$	−16.2929	−	11.8375i	−0.534552	−	0.388375i	0.287506	−	0.957779i	$-0.407174\pi$
$929$	−16.2929	−	11.8375i	−0.534552	−	0.388375i	−0.822058	+	0.569404i	$0.807174\pi$
$930$		0			0
$931$	15.2156	−	46.8288i	0.498672	−	1.53475i
$932$	6.69414	−	2.17506i	0.219274	−	0.0712463i
$933$	−29.9661	−	41.2449i	−0.981048	−	1.35030i
$934$	−21.1078			−0.690669
$935$		0			0
$936$	−6.11449			−0.199858
$937$	−6.18937	−	8.51894i	−0.202198	−	0.278302i	0.695861	−	0.718176i	$-0.255023\pi$
$937$	−6.18937	−	8.51894i	−0.202198	−	0.278302i	−0.898059	+	0.439875i	$0.855023\pi$
$938$	5.36013	−	1.74161i	0.175014	−	0.0568656i
$939$	6.80908	−	20.9562i	0.222206	−	0.683879i
$940$		0			0
$941$	15.6743	+	11.3880i	0.510966	+	0.371239i	0.813190	−	0.581998i	$-0.197729\pi$
$941$	15.6743	+	11.3880i	0.510966	+	0.371239i	−0.302224	+	0.953237i	$0.597729\pi$
$942$	−34.2457	−	11.1271i	−1.11579	−	0.362541i
$943$	72.2655	−	23.4805i	2.35329	−	0.764630i
$944$	−0.552961	+	0.401750i	−0.0179974	+	0.0130758i
$945$		0			0
$946$	20.1835	−	21.7163i	0.656223	−	0.706059i
$947$		−	3.79793i		−	0.123416i	−0.998094	−	0.0617081i	$-0.980345\pi$
$947$		−	3.79793i		−	0.123416i	0.998094	−	0.0617081i	$-0.0196548\pi$
$948$	2.00137	+	2.75465i	0.0650016	+	0.0894670i
$949$	0.581014	+	1.78818i	0.0188605	+	0.0580467i
$950$		0			0
$951$	−41.6973	−	30.2949i	−1.35213	−	0.982379i
$952$	−1.09713	+	1.51007i	−0.0355583	+	0.0489417i
$953$	−0.509545	−	0.165561i	−0.0165058	−	0.00536305i	0.300752	−	0.953702i	$-0.402762\pi$
$953$	−0.509545	−	0.165561i	−0.0165058	−	0.00536305i	−0.317258	+	0.948339i	$0.602762\pi$
$954$	0.154922	+	0.476800i	0.00501577	+	0.0154370i
$955$		0			0
$956$	1.70918			0.0552788
$957$	7.50237	+	38.2571i	0.242517	+	1.23668i
$958$		−	18.9819i		−	0.613276i
$959$	2.69934	−	1.96118i	0.0871661	−	0.0633299i
$960$		0			0
$961$	−0.0404620	+	0.124529i	−0.00130523	+	0.00401707i
$962$	−2.66427	+	3.66706i	−0.0858996	+	0.118231i
$963$	−0.195995	+	0.269764i	−0.00631586	+	0.00869303i
$964$	−1.02239	+	3.14661i	−0.0329291	+	0.101345i
$965$		0			0
$966$	−6.34697	+	4.61134i	−0.204210	+	0.148367i
$967$			36.5291i			1.17470i	0.809335	+	0.587348i	$0.199828\pi$
$967$			36.5291i			1.17470i	−0.809335	+	0.587348i	$0.800172\pi$
$968$	−25.0243	+	21.1399i	−0.804311	+	0.679461i
$969$	−26.1060			−0.838645
$970$		0			0
$971$	6.37443	+	19.6185i	0.204565	+	0.629587i	0.999731	+	0.0231946i	$0.00738372\pi$
$971$	6.37443	+	19.6185i	0.204565	+	0.629587i	−0.795166	+	0.606392i	$0.792616\pi$
$972$	−2.64322	−	0.858835i	−0.0847814	−	0.0275471i
$973$	−3.91605	+	5.38998i	−0.125543	+	0.172795i
$974$	−38.4185	−	27.9126i	−1.23101	−	0.894379i
$975$		0			0
$976$	8.26142	+	25.4261i	0.264442	+	0.813868i
$977$	−13.8335	−	19.0402i	−0.442573	−	0.609149i	0.528209	−	0.849115i	$-0.322864\pi$
$977$	−13.8335	−	19.0402i	−0.442573	−	0.609149i	−0.970781	+	0.239965i	$0.922864\pi$
$978$		−	8.39706i		−	0.268508i
$979$	28.7880	−	5.64544i	0.920069	−	0.180429i
$980$		0			0
$981$	9.78967	−	7.11261i	0.312560	−	0.227088i
$982$	−44.2663	+	14.3830i	−1.41259	+	0.458979i
$983$	−38.6829	−	12.5688i	−1.23379	−	0.400883i	−0.381706	−	0.924284i	$-0.624663\pi$
$983$	−38.6829	−	12.5688i	−1.23379	−	0.400883i	−0.852087	+	0.523400i	$0.824663\pi$
$984$	−44.1033	−	32.0429i	−1.40596	−	1.02149i
$985$		0			0
$986$	4.26364	−	13.1221i	0.135782	−	0.417894i
$987$	4.87407	−	1.58368i	0.155143	−	0.0504092i
$988$	1.97789	+	2.72233i	0.0629251	+	0.0866090i
$989$	56.8925			1.80908
$990$		0			0
$991$	23.1498			0.735377			0.367688	−	0.929949i	$-0.380149\pi$
$991$	23.1498			0.735377			0.367688	+	0.929949i	$0.380149\pi$
$992$	−4.65024	−	6.40051i	−0.147645	−	0.203216i
$993$	19.8681	−	6.45553i	0.630494	−	0.204860i
$994$	−1.39855	+	4.30430i	−0.0443594	+	0.136524i
$995$		0			0
$996$	−4.62020	−	3.35677i	−0.146397	−	0.106363i
$997$	−5.06765	−	1.64658i	−0.160494	−	0.0521477i	0.227668	−	0.973739i	$-0.426890\pi$
$997$	−5.06765	−	1.64658i	−0.160494	−	0.0521477i	−0.388162	+	0.921591i	$0.626890\pi$
$998$	33.2991	−	10.8195i	1.05406	−	0.342486i
$999$	−5.73730	+	4.16840i	−0.181520	+	0.131882i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.z.c.124.3		32
5.2	odd	4		275.2.h.c.201.3	yes	16
5.3	odd	4		275.2.h.e.201.2	yes	16
5.4	even	2	inner	275.2.z.c.124.6		32
11.4	even	5	inner	275.2.z.c.224.6		32
55.2	even	20		3025.2.a.bm.1.5		8
55.4	even	10	inner	275.2.z.c.224.3		32
55.13	even	20		3025.2.a.bj.1.4		8
55.37	odd	20		275.2.h.c.26.3	✓	16
55.42	odd	20		3025.2.a.bi.1.4		8
55.48	odd	20		275.2.h.e.26.2	yes	16
55.53	odd	20		3025.2.a.bn.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.h.c.26.3	✓	16	55.37	odd	20
275.2.h.c.201.3	yes	16	5.2	odd	4
275.2.h.e.26.2	yes	16	55.48	odd	20
275.2.h.e.201.2	yes	16	5.3	odd	4
275.2.z.c.124.3		32	1.1	even	1	trivial
275.2.z.c.124.6		32	5.4	even	2	inner
275.2.z.c.224.3		32	55.4	even	10	inner
275.2.z.c.224.6		32	11.4	even	5	inner
3025.2.a.bi.1.4		8	55.42	odd	20
3025.2.a.bj.1.4		8	55.13	even	20
3025.2.a.bm.1.5		8	55.2	even	20
3025.2.a.bn.1.5		8	55.53	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.z (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.776830 - 1.06921i) q^{2} +(-1.92724 + 0.626199i) q^{3} +(0.0782786 - 0.240917i) q^{4} +(2.16668 + 1.57419i) q^{6} +(0.331213 + 0.107618i) q^{7} +(-2.83228 + 0.920262i) q^{8} +(0.895086 - 0.650318i) q^{9} +(-3.25463 + 0.638246i) q^{11} +0.513323i q^{12} +(1.09079 + 1.50135i) q^{13} +(-0.142230 - 0.437738i) q^{14} +(2.77428 + 2.01563i) q^{16} +(1.05786 - 1.45602i) q^{17} +(-1.39066 - 0.451853i) q^{18} +(2.21198 + 6.80779i) q^{19} -0.705717 q^{21} +(3.21072 + 2.98409i) q^{22} +8.41145i q^{23} +(4.88221 - 3.54714i) q^{24} +(0.757902 - 2.33258i) q^{26} +(2.25548 - 3.10441i) q^{27} +(0.0518537 - 0.0713705i) q^{28} +(-1.79251 + 5.51679i) q^{29} +(-4.49489 + 3.26573i) q^{31} +1.42395i q^{32} +(5.87280 - 3.26810i) q^{33} -2.37858 q^{34} +(-0.0866064 - 0.266547i) q^{36} +(-1.75766 - 0.571099i) q^{37} +(5.56065 - 7.65358i) q^{38} +(-3.04236 - 2.21041i) q^{39} +(-2.79149 - 8.59133i) q^{41} +(0.548222 + 0.754563i) q^{42} -6.76370i q^{43} +(-0.101004 + 0.834057i) q^{44} +(8.99364 - 6.53426i) q^{46} +(-6.90656 + 2.24408i) q^{47} +(-6.60890 - 2.14736i) q^{48} +(-5.56500 - 4.04321i) q^{49} +(-1.12700 + 3.46854i) q^{51} +(0.447085 - 0.145267i) q^{52} +(-0.201527 - 0.277378i) q^{53} -5.07141 q^{54} -1.03712 q^{56} +(-8.52606 - 11.7351i) q^{57} +(7.29112 - 2.36903i) q^{58} +(-0.0615923 + 0.189562i) q^{59} +(6.30721 + 4.58245i) q^{61} +(6.98354 + 2.26909i) q^{62} +(0.366449 - 0.119067i) q^{63} +(7.07108 - 5.13744i) q^{64} +(-8.05647 - 3.74052i) q^{66} +12.2451i q^{67} +(-0.267972 - 0.368832i) q^{68} +(-5.26724 - 16.2109i) q^{69} +(-7.95510 - 5.77972i) q^{71} +(-1.93667 + 2.66559i) q^{72} +(0.963578 + 0.313085i) q^{73} +(0.754777 + 2.32297i) q^{74} +1.81326 q^{76} +(-1.14666 - 0.138860i) q^{77} +4.97005i q^{78} +(5.36632 - 3.89886i) q^{79} +(-3.42856 + 10.5520i) q^{81} +(-7.01746 + 9.65870i) q^{82} +(-6.53931 + 9.00058i) q^{83} +(-0.0552425 + 0.170019i) q^{84} +(-7.23185 + 5.25425i) q^{86} -11.7547i q^{87} +(8.63067 - 4.80281i) q^{88} -8.84524 q^{89} +(0.199713 + 0.614654i) q^{91} +(2.02646 + 0.658436i) q^{92} +(6.61775 - 9.10855i) q^{93} +(7.76462 + 5.64133i) q^{94} +(-0.891677 - 2.74430i) q^{96} +(3.64564 + 5.01780i) q^{97} +9.09106i q^{98} +(-2.49811 + 2.68783i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{4} - 6 q^{6} - 16 q^{9} - 10 q^{11} - 6 q^{14} - 8 q^{16} + 26 q^{19} + 20 q^{21} + 86 q^{24} - 68 q^{26} + 22 q^{29} - 20 q^{31} - 40 q^{34} + 6 q^{36} - 6 q^{39} + 50 q^{41} + 2 q^{44} + 80 q^{46}+ \cdots + 20 q^{99}+O(q^{100}) \) 32 * q + 4 * q^4 - 6 * q^6 - 16 * q^9 - 10 * q^11 - 6 * q^14 - 8 * q^16 + 26 * q^19 + 20 * q^21 + 86 * q^24 - 68 * q^26 + 22 * q^29 - 20 * q^31 - 40 * q^34 + 6 * q^36 - 6 * q^39 + 50 * q^41 + 2 * q^44 + 80 * q^46 - 32 * q^49 + 70 * q^51 - 120 * q^54 - 40 * q^56 - 28 * q^59 + 32 * q^61 - 80 * q^64 - 110 * q^66 - 70 * q^69 - 92 * q^71 + 14 * q^74 - 124 * q^76 + 78 * q^79 - 86 * q^81 + 108 * q^84 + 4 * q^86 + 44 * q^89 - 68 * q^91 + 80 * q^94 + 216 * q^96 + 20 * q^99

Introduction

L-functions

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