LMFDB - Embedded newform 275.2.h.c.26.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,2,Mod(26,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.26"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.h (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 10 x^{14} - 13 x^{13} + 53 x^{12} - 12 x^{11} + 136 x^{10} + 8 x^{9} + 300 x^{8} + \cdots + 16 $ x^16 - 4x^15 + 10x^14 - 13x^13 + 53x^12 - 12x^11 + 136x^10 + 8x^9 + 300x^8 - 256x^7 + 472x^6 - 48x^5 + 432x^4 + 88x^3 + 128x^2 + 64*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			26.3
Root			$-0.260198 + 0.189045i$ of defining polynomial
Character	$\chi$	$=$	275.26
Dual form			275.2.h.c.201.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.06921 + 0.776830i) q^{2} +(0.626199 - 1.92724i) q^{3} +(-0.0782786 - 0.240917i) q^{4} +(2.16668 - 1.57419i) q^{6} +(-0.107618 - 0.331213i) q^{7} +(0.920262 - 2.83228i) q^{8} +(-0.895086 - 0.650318i) q^{9} +(-3.25463 - 0.638246i) q^{11} -0.513323 q^{12} +(1.50135 + 1.09079i) q^{13} +(0.142230 - 0.437738i) q^{14} +(2.77428 - 2.01563i) q^{16} +(1.45602 - 1.05786i) q^{17} +(-0.451853 - 1.39066i) q^{18} +(-2.21198 + 6.80779i) q^{19} -0.705717 q^{21} +(-2.98409 - 3.21072i) q^{22} +8.41145 q^{23} +(-4.88221 - 3.54714i) q^{24} +(0.757902 + 2.33258i) q^{26} +(3.10441 - 2.25548i) q^{27} +(-0.0713705 + 0.0518537i) q^{28} +(1.79251 + 5.51679i) q^{29} +(-4.49489 - 3.26573i) q^{31} -1.42395 q^{32} +(-3.26810 + 5.87280i) q^{33} +2.37858 q^{34} +(-0.0866064 + 0.266547i) q^{36} +(0.571099 + 1.75766i) q^{37} +(-7.65358 + 5.56065i) q^{38} +(3.04236 - 2.21041i) q^{39} +(-2.79149 + 8.59133i) q^{41} +(-0.754563 - 0.548222i) q^{42} -6.76370 q^{43} +(0.101004 + 0.834057i) q^{44} +(8.99364 + 6.53426i) q^{46} +(-2.24408 + 6.90656i) q^{47} +(-2.14736 - 6.60890i) q^{48} +(5.56500 - 4.04321i) q^{49} +(-1.12700 - 3.46854i) q^{51} +(0.145267 - 0.447085i) q^{52} +(-0.277378 - 0.201527i) q^{53} +5.07141 q^{54} -1.03712 q^{56} +(11.7351 + 8.52606i) q^{57} +(-2.36903 + 7.29112i) q^{58} +(0.0615923 + 0.189562i) q^{59} +(6.30721 - 4.58245i) q^{61} +(-2.26909 - 6.98354i) q^{62} +(-0.119067 + 0.366449i) q^{63} +(-7.07108 - 5.13744i) q^{64} +(-8.05647 + 3.74052i) q^{66} -12.2451 q^{67} +(-0.368832 - 0.267972i) q^{68} +(5.26724 - 16.2109i) q^{69} +(-7.95510 + 5.77972i) q^{71} +(-2.66559 + 1.93667i) q^{72} +(0.313085 + 0.963578i) q^{73} +(-0.754777 + 2.32297i) q^{74} +1.81326 q^{76} +(0.138860 + 1.14666i) q^{77} +4.97005 q^{78} +(-5.36632 - 3.89886i) q^{79} +(-3.42856 - 10.5520i) q^{81} +(-9.65870 + 7.01746i) q^{82} +(9.00058 - 6.53931i) q^{83} +(0.0552425 + 0.170019i) q^{84} +(-7.23185 - 5.25425i) q^{86} +11.7547 q^{87} +(-4.80281 + 8.63067i) q^{88} +8.84524 q^{89} +(0.199713 - 0.614654i) q^{91} +(-0.658436 - 2.02646i) q^{92} +(-9.10855 + 6.61775i) q^{93} +(-7.76462 + 5.64133i) q^{94} +(-0.891677 + 2.74430i) q^{96} +(-5.01780 - 3.64564i) q^{97} +9.09106 q^{98} +(2.49811 + 2.68783i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} - 2 q^{4} - 3 q^{6} + 4 q^{7} + 16 q^{8} + 8 q^{9} - 5 q^{11} - 6 q^{12} + 7 q^{13} + 3 q^{14} - 4 q^{16} + 12 q^{17} + 16 q^{18} - 13 q^{19} + 10 q^{21} + 28 q^{22} - 4 q^{23} - 43 q^{24}+ \cdots - 10 q^{99}+O(q^{100}) $ 16 * q - 2 * q^3 - 2 * q^4 - 3 * q^6 + 4 * q^7 + 16 * q^8 + 8 * q^9 - 5 * q^11 - 6 * q^12 + 7 * q^13 + 3 * q^14 - 4 * q^16 + 12 * q^17 + 16 * q^18 - 13 * q^19 + 10 * q^21 + 28 * q^22 - 4 * q^23 - 43 * q^24 - 34 * q^26 - 11 * q^27 + 47 * q^28 - 11 * q^29 - 10 * q^31 - 58 * q^32 - 34 * q^33 + 20 * q^34 + 3 * q^36 - 4 * q^37 - 36 * q^38 + 3 * q^39 + 25 * q^41 + 13 * q^42 - 28 * q^43 - q^44 + 40 * q^46 + 8 * q^47 - 106 * q^48 + 16 * q^49 + 35 * q^51 + 39 * q^52 - 22 * q^53 + 60 * q^54 - 20 * q^56 + 29 * q^57 + 6 * q^58 + 14 * q^59 + 16 * q^61 - 10 * q^62 + 73 * q^63 + 40 * q^64 - 55 * q^66 - 14 * q^67 + 83 * q^68 + 35 * q^69 - 46 * q^71 + 28 * q^72 + 7 * q^73 - 7 * q^74 - 62 * q^76 - 51 * q^77 + 34 * q^78 - 39 * q^79 - 43 * q^81 - 51 * q^82 + 28 * q^83 - 54 * q^84 + 2 * q^86 - 50 * q^87 - 76 * q^88 - 22 * q^89 - 34 * q^91 + 4 * q^92 + 3 * q^93 - 40 * q^94 + 108 * q^96 - 39 * q^97 - 52 * q^98 - 10 * q^99

Character values

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

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

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 $

$2$	1.06921	+	0.776830i	0.756049	+	0.549302i	0.897696	−	0.440615i	$-0.145240\pi$
$2$	1.06921	+	0.776830i	0.756049	+	0.549302i	−0.141647	+	0.989917i	$0.545240\pi$
$3$	0.626199	−	1.92724i	0.361536	−	1.11269i	−0.590586	−	0.806975i	$-0.701103\pi$
$3$	0.626199	−	1.92724i	0.361536	−	1.11269i	0.952122	−	0.305719i	$-0.0988968\pi$
$4$	−0.0782786	−	0.240917i	−0.0391393	−	0.120458i
$5$		0			0
$5$		0			0
$6$	2.16668	−	1.57419i	0.884544	−	0.642659i
$7$	−0.107618	−	0.331213i	−0.0406756	−	0.125187i	0.928657	−	0.370940i	$-0.120965\pi$
$7$	−0.107618	−	0.331213i	−0.0406756	−	0.125187i	−0.969332	+	0.245754i	$0.920965\pi$
$8$	0.920262	−	2.83228i	0.325362	−	1.00136i
$9$	−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
$12$	−0.513323			−0.148183
$13$	1.50135	+	1.09079i	0.416399	+	0.302532i	0.776187	−	0.630502i	$-0.217151\pi$
$13$	1.50135	+	1.09079i	0.416399	+	0.302532i	−0.359788	+	0.933034i	$0.617151\pi$
$14$	0.142230	−	0.437738i	0.0380125	−	0.116990i
$15$		0			0
$16$	2.77428	−	2.01563i	0.693571	−	0.503909i
$17$	1.45602	−	1.05786i	0.353137	−	0.256569i	−0.397047	−	0.917798i	$-0.629965\pi$
$17$	1.45602	−	1.05786i	0.353137	−	0.256569i	0.750184	+	0.661229i	$0.229965\pi$
$18$	−0.451853	−	1.39066i	−0.106503	−	0.327782i
$19$	−2.21198	+	6.80779i	−0.507464	+	1.56181i	0.289124	+	0.957292i	$0.406636\pi$
$19$	−2.21198	+	6.80779i	−0.507464	+	1.56181i	−0.796588	+	0.604522i	$0.793364\pi$
$20$		0			0
$21$	−0.705717			−0.154000
$22$	−2.98409	−	3.21072i	−0.636211	−	0.684528i
$23$	8.41145			1.75391			0.876954	−	0.480574i	$-0.159572\pi$
$23$	8.41145			1.75391			0.876954	+	0.480574i	$0.159572\pi$
$24$	−4.88221	−	3.54714i	−0.996578	−	0.724056i
$25$		0			0
$26$	0.757902	+	2.33258i	0.148637	+	0.457457i
$27$	3.10441	−	2.25548i	0.597444	−	0.434068i
$28$	−0.0713705	+	0.0518537i	−0.0134878	+	0.00979943i
$29$	1.79251	+	5.51679i	0.332862	+	1.02444i	0.967766	+	0.251852i	$0.0810396\pi$
$29$	1.79251	+	5.51679i	0.332862	+	1.02444i	−0.634904	+	0.772591i	$0.718960\pi$
$30$		0			0
$31$	−4.49489	−	3.26573i	−0.807307	−	0.586543i	0.105742	−	0.994394i	$-0.466278\pi$
$31$	−4.49489	−	3.26573i	−0.807307	−	0.586543i	−0.913048	+	0.407851i	$0.866278\pi$
$32$	−1.42395			−0.251722
$33$	−3.26810	+	5.87280i	−0.568904	+	1.02232i
$34$	2.37858			0.407923
$35$		0			0
$36$	−0.0866064	+	0.266547i	−0.0144344	+	0.0444245i
$37$	0.571099	+	1.75766i	0.0938881	+	0.288958i	0.986962	−	0.160952i	$-0.0514563\pi$
$37$	0.571099	+	1.75766i	0.0938881	+	0.288958i	−0.893074	+	0.449909i	$0.851456\pi$
$38$	−7.65358	+	5.56065i	−1.24157	+	0.902057i
$39$	3.04236	−	2.21041i	0.487168	−	0.353948i
$40$		0			0
$41$	−2.79149	+	8.59133i	−0.435958	+	1.34174i	0.456144	+	0.889906i	$0.349230\pi$
$41$	−2.79149	+	8.59133i	−0.435958	+	1.34174i	−0.892102	+	0.451834i	$0.850770\pi$
$42$	−0.754563	−	0.548222i	−0.116432	−	0.0845925i
$43$	−6.76370			−1.03145			−0.515727	−	0.856753i	$-0.672478\pi$
$43$	−6.76370			−1.03145			−0.515727	+	0.856753i	$0.672478\pi$
$44$	0.101004	+	0.834057i	0.0152269	+	0.125739i
$45$		0			0
$46$	8.99364	+	6.53426i	1.32604	+	0.963425i
$47$	−2.24408	+	6.90656i	−0.327332	+	1.00742i	0.643045	+	0.765829i	$0.277671\pi$
$47$	−2.24408	+	6.90656i	−0.327332	+	1.00742i	−0.970377	+	0.241596i	$0.922329\pi$
$48$	−2.14736	−	6.60890i	−0.309945	−	0.953913i
$49$	5.56500	−	4.04321i	0.795000	−	0.577601i
$50$		0			0
$51$	−1.12700	−	3.46854i	−0.157811	−	0.485693i
$52$	0.145267	−	0.447085i	0.0201449	−	0.0619996i
$53$	−0.277378	−	0.201527i	−0.0381009	−	0.0276819i	0.568572	−	0.822634i	$-0.307496\pi$
$53$	−0.277378	−	0.201527i	−0.0381009	−	0.0276819i	−0.606673	+	0.794952i	$0.707496\pi$
$54$	5.07141			0.690131
$55$		0			0
$56$	−1.03712			−0.138591
$57$	11.7351	+	8.52606i	1.55435	+	1.12930i
$58$	−2.36903	+	7.29112i	−0.311069	+	0.957370i
$59$	0.0615923	+	0.189562i	0.00801863	+	0.0246788i	0.954986	−	0.296652i	$-0.0958700\pi$
$59$	0.0615923	+	0.189562i	0.00801863	+	0.0246788i	−0.946967	+	0.321330i	$0.895870\pi$
$60$		0			0
$61$	6.30721	−	4.58245i	0.807555	−	0.586723i	−0.105566	−	0.994412i	$-0.533665\pi$
$61$	6.30721	−	4.58245i	0.807555	−	0.586723i	0.913121	+	0.407689i	$0.133665\pi$
$62$	−2.26909	−	6.98354i	−0.288175	−	0.886910i
$63$	−0.119067	+	0.366449i	−0.0150010	+	0.0461683i
$64$	−7.07108	−	5.13744i	−0.883885	−	0.642180i
$65$		0			0
$66$	−8.05647	+	3.74052i	−0.991683	+	0.460426i
$67$	−12.2451			−1.49597			−0.747986	−	0.663715i	$-0.768979\pi$
$67$	−12.2451			−1.49597			−0.747986	+	0.663715i	$0.768979\pi$
$68$	−0.368832	−	0.267972i	−0.0447275	−	0.0324964i
$69$	5.26724	−	16.2109i	0.634101	−	1.95156i
$70$		0			0
$71$	−7.95510	+	5.77972i	−0.944097	+	0.685927i	−0.949403	−	0.314059i	$-0.898311\pi$
$71$	−7.95510	+	5.77972i	−0.944097	+	0.685927i	0.00530622	+	0.999986i	$0.498311\pi$
$72$	−2.66559	+	1.93667i	−0.314143	+	0.228238i
$73$	0.313085	+	0.963578i	0.0366439	+	0.112778i	0.967705	−	0.252084i	$-0.0811160\pi$
$73$	0.313085	+	0.963578i	0.0366439	+	0.112778i	−0.931061	+	0.364862i	$0.881116\pi$
$74$	−0.754777	+	2.32297i	−0.0877411	+	0.270039i
$75$		0			0
$76$	1.81326			0.207995
$77$	0.138860	+	1.14666i	0.0158246	+	0.130674i
$78$	4.97005			0.562748
$79$	−5.36632	−	3.89886i	−0.603758	−	0.438656i	0.243453	−	0.969913i	$-0.421720\pi$
$79$	−5.36632	−	3.89886i	−0.603758	−	0.438656i	−0.847211	+	0.531257i	$0.821720\pi$
$80$		0			0
$81$	−3.42856	−	10.5520i	−0.380952	−	1.17245i
$82$	−9.65870	+	7.01746i	−1.06663	+	0.774949i
$83$	9.00058	−	6.53931i	0.987942	−	0.717782i	0.0284727	−	0.999595i	$-0.490936\pi$
$83$	9.00058	−	6.53931i	0.987942	−	0.717782i	0.959469	+	0.281813i	$0.0909356\pi$
$84$	0.0552425	+	0.170019i	0.00602745	+	0.0185506i
$85$		0			0
$86$	−7.23185	−	5.25425i	−0.779830	−	0.566580i
$87$	11.7547			1.26023
$88$	−4.80281	+	8.63067i	−0.511981	+	0.920032i
$89$	8.84524			0.937594			0.468797	−	0.883306i	$-0.344688\pi$
$89$	8.84524			0.937594			0.468797	+	0.883306i	$0.344688\pi$
$90$		0			0
$91$	0.199713	−	0.614654i	0.0209356	−	0.0644332i
$92$	−0.658436	−	2.02646i	−0.0686467	−	0.211273i
$93$	−9.10855	+	6.61775i	−0.944513	+	0.686229i
$94$	−7.76462	+	5.64133i	−0.800859	+	0.581858i
$95$		0			0
$96$	−0.891677	+	2.74430i	−0.0910064	+	0.280089i
$97$	−5.01780	−	3.64564i	−0.509480	−	0.370159i	0.303146	−	0.952944i	$-0.401963\pi$
$97$	−5.01780	−	3.64564i	−0.509480	−	0.370159i	−0.812626	+	0.582785i	$0.801963\pi$
$98$	9.09106			0.918336
$99$	2.49811	+	2.68783i	0.251070	+	0.270137i
$100$		0			0
$101$	2.96734	+	2.15590i	0.295262	+	0.214520i	0.725547	−	0.688173i	$-0.241587\pi$
$101$	2.96734	+	2.15590i	0.295262	+	0.214520i	−0.430285	+	0.902693i	$0.641587\pi$
$102$	1.48946	−	4.58410i	0.147479	−	0.453894i
$103$	−6.08206	−	18.7187i	−0.599283	−	1.84440i	−0.532131	−	0.846662i	$-0.678609\pi$
$103$	−6.08206	−	18.7187i	−0.599283	−	1.84440i	−0.0671522	−	0.997743i	$-0.521391\pi$
$104$	4.47106	−	3.24842i	0.438423	−	0.318533i
$105$		0			0
$106$	−0.140025	−	0.430952i	−0.0136004	−	0.0418577i
$107$	−0.0931327	+	0.286633i	−0.00900347	+	0.0277098i	−0.955457	−	0.295129i	$-0.904637\pi$
$107$	−0.0931327	+	0.286633i	−0.00900347	+	0.0277098i	0.946454	+	0.322839i	$0.104637\pi$
$108$	−0.786392	−	0.571348i	−0.0756706	−	0.0549779i
$109$	−10.9371			−1.04759			−0.523794	−	0.851845i	$-0.675484\pi$
$109$	−10.9371			−1.04759			−0.523794	+	0.851845i	$0.675484\pi$
$110$		0			0
$111$	3.74506			0.355466
$112$	−0.966165	−	0.701960i	−0.0912940	−	0.0663290i
$113$	−1.79300	+	5.51830i	−0.168672	+	0.519118i	−0.999288	−	0.0377271i	$-0.987988\pi$
$113$	−1.79300	+	5.51830i	−0.168672	+	0.519118i	0.830616	+	0.556845i	$0.187988\pi$
$114$	5.92406	+	18.2324i	0.554839	+	1.70762i
$115$		0			0
$116$	1.18877	−	0.863693i	0.110375	−	0.0801919i
$117$	−0.634473	−	1.95271i	−0.0586570	−	0.180528i
$118$	−0.0814018	+	0.250529i	−0.00749364	+	0.0230630i
$119$	−0.507071	−	0.368409i	−0.0464831	−	0.0337720i
$120$		0			0
$121$	10.1853	+	4.15451i	0.925935	+	0.377683i
$122$	10.3035			0.932839
$123$	14.8095	+	10.7598i	1.33533	+	0.970175i
$124$	−0.434915	+	1.33853i	−0.0390565	+	0.120204i
$125$		0			0
$126$	−0.411977	+	0.299319i	−0.0367018	+	0.0266654i
$127$	9.99175	−	7.25943i	0.886625	−	0.644170i	−0.0483711	−	0.998829i	$-0.515403\pi$
$127$	9.99175	−	7.25943i	0.886625	−	0.644170i	0.934996	+	0.354659i	$0.115403\pi$
$128$	−2.68953	−	8.27753i	−0.237723	−	0.731637i
$129$	−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	$0.389079\pi$
$132$	1.67068	+	0.327626i	0.145414	+	0.0285162i
$133$	2.49287			0.216160
$134$	−13.0926	−	9.51233i	−1.13103	−	0.821740i
$135$		0			0
$136$	−1.65624	−	5.09737i	−0.142021	−	0.437096i
$137$	7.75098	−	5.63141i	0.662211	−	0.481124i	−0.205198	−	0.978720i	$-0.565784\pi$
$137$	7.75098	−	5.63141i	0.662211	−	0.481124i	0.867409	+	0.497596i	$0.165784\pi$
$138$	18.2249	−	13.2412i	1.55141	−	1.12716i
$139$	5.91169	+	18.1943i	0.501423	+	1.54322i	0.806702	+	0.590958i	$0.201250\pi$
$139$	5.91169	+	18.1943i	0.501423	+	1.54322i	−0.305280	+	0.952263i	$0.598750\pi$
$140$		0			0
$141$	11.9054	+	8.64976i	1.00261	+	0.728441i
$142$	−12.9956			−1.09056
$143$	−4.19014	−	4.50836i	−0.350397	−	0.377008i
$144$	−3.79403			−0.316169
$145$		0			0
$146$	−0.413781	+	1.27349i	−0.0342447	+	0.105394i
$147$	−4.30744	−	13.2570i	−0.355272	−	1.09341i
$148$	0.378745	−	0.275175i	0.0311327	−	0.0226192i
$149$	−4.67208	+	3.39446i	−0.382752	+	0.278085i	−0.762479	−	0.647013i	$-0.776018\pi$
$149$	−4.67208	+	3.39446i	−0.382752	+	0.278085i	0.379727	+	0.925099i	$0.376018\pi$
$150$		0			0
$151$	4.13098	−	12.7139i	0.336175	−	1.03464i	−0.629966	−	0.776623i	$-0.716931\pi$
$151$	4.13098	−	12.7139i	0.336175	−	1.03464i	0.966141	−	0.258016i	$-0.0830689\pi$
$152$	17.2459	+	12.5299i	1.39883	+	1.01631i
$153$	−1.99121			−0.160980
$154$	−0.742290	+	1.33390i	−0.0598155	+	0.107489i
$155$		0			0
$156$	−0.770676	−	0.559929i	−0.0617035	−	0.0448302i
$157$	−4.15475	+	12.7870i	−0.331585	+	1.02051i	0.636795	+	0.771033i	$0.280260\pi$
$157$	−4.15475	+	12.7870i	−0.331585	+	1.02051i	−0.968380	+	0.249481i	$0.919740\pi$
$158$	−2.70900	−	8.33744i	−0.215516	−	0.663291i
$159$	−0.562086	+	0.408379i	−0.0445763	+	0.0323866i
$160$		0			0
$161$	−0.905219	−	2.78598i	−0.0713413	−	0.219566i
$162$	4.53127	−	13.9458i	0.356010	−	1.09569i
$163$	−2.53658	−	1.84293i	−0.198680	−	0.144349i	0.483997	−	0.875070i	$-0.339184\pi$
$163$	−2.53658	−	1.84293i	−0.198680	−	0.144349i	−0.682677	+	0.730720i	$0.739184\pi$
$164$	2.28831			0.178687
$165$		0			0
$166$	14.7035			1.14121
$167$	−2.12672	−	1.54515i	−0.164570	−	0.119567i	0.502452	−	0.864605i	$-0.332431\pi$
$167$	−2.12672	−	1.54515i	−0.164570	−	0.119567i	−0.667022	+	0.745038i	$0.732431\pi$
$168$	−0.649445	+	1.99879i	−0.0501057	+	0.154210i
$169$	−2.95301	−	9.08842i	−0.227154	−	0.699109i
$170$		0			0
$171$	6.40714	−	4.65506i	0.489967	−	0.355982i
$172$	0.529453	+	1.62949i	0.0403704	+	0.124247i
$173$	−1.21218	+	3.73072i	−0.0921606	+	0.283641i	−0.986503	−	0.163741i	$-0.947644\pi$
$173$	−1.21218	+	3.73072i	−0.0921606	+	0.283641i	0.894343	+	0.447383i	$0.147644\pi$
$174$	12.5683	+	9.13138i	0.952798	+	0.692248i
$175$		0			0
$176$	−10.3157	+	4.78948i	−0.777579	+	0.361020i
$177$	0.403900			0.0303590
$178$	9.45746	+	6.87125i	0.708867	+	0.515022i
$179$	−1.02435	+	3.15264i	−0.0765639	+	0.235639i	−0.982012	−	0.188817i	$-0.939535\pi$
$179$	−1.02435	+	3.15264i	−0.0765639	+	0.235639i	0.905448	+	0.424456i	$0.139535\pi$
$180$		0			0
$181$	−13.6763	+	9.93640i	−1.01655	+	0.738567i	−0.965573	−	0.260133i	$-0.916233\pi$
$181$	−13.6763	+	9.93640i	−1.01655	+	0.738567i	−0.0509769	+	0.998700i	$0.516233\pi$
$182$	0.691018	−	0.502054i	0.0512216	−	0.0372147i
$183$	−4.88193	−	15.0250i	−0.360883	−	1.11068i
$184$	7.74074	−	23.8235i	0.570655	−	1.75629i
$185$		0			0
$186$	−14.8799			−1.09104
$187$	−5.41400	+	2.51365i	−0.395911	+	0.183817i
$188$	1.83957			0.134164
$189$	−1.08113	−	0.785490i	−0.0786409	−	0.0571360i
$190$		0			0
$191$	−6.49420	−	19.9871i	−0.469903	−	1.44621i	−0.852709	−	0.522385i	$-0.825042\pi$
$191$	−6.49420	−	19.9871i	−0.469903	−	1.44621i	0.382806	−	0.923829i	$-0.374958\pi$
$192$	−14.3290	+	10.4106i	−1.03411	+	0.751322i
$193$	−2.68051	+	1.94751i	−0.192947	+	0.140184i	−0.680065	−	0.733152i	$-0.738048\pi$
$193$	−2.68051	+	1.94751i	−0.192947	+	0.140184i	0.487117	+	0.873336i	$0.338048\pi$
$194$	−2.53306	−	7.79595i	−0.181863	−	0.559717i
$195$		0			0
$196$	−1.40970	−	1.02420i	−0.100693	−	0.0731575i
$197$	−6.97218			−0.496747			−0.248374	−	0.968664i	$-0.579896\pi$
$197$	−6.97218			−0.496747			−0.248374	+	0.968664i	$0.579896\pi$
$198$	0.583032	+	4.81448i	0.0414343	+	0.342150i
$199$	−19.2184			−1.36236			−0.681178	−	0.732118i	$-0.738532\pi$
$199$	−19.2184			−1.36236			−0.681178	+	0.732118i	$0.738532\pi$
$200$		0			0
$201$	−7.66784	+	23.5992i	−0.540848	+	1.66456i
$202$	1.49796	+	4.61024i	0.105396	+	0.324375i
$203$	1.63433	−	1.18741i	0.114707	−	0.0833396i
$204$	−0.747409	+	0.543025i	−0.0523291	+	0.0380193i
$205$		0			0
$206$	8.03819	−	24.7390i	0.560047	−	1.72365i
$207$	−7.52897	−	5.47012i	−0.523299	−	0.380199i
$208$	6.36380			0.441250
$209$	11.5442	−	20.7451i	0.798532	−	1.43497i
$210$		0			0
$211$	−3.47407	−	2.52406i	−0.239165	−	0.173764i	0.461746	−	0.887012i	$-0.347223\pi$
$211$	−3.47407	−	2.52406i	−0.239165	−	0.173764i	−0.700911	+	0.713249i	$0.747223\pi$
$212$	−0.0268385	+	0.0826004i	−0.00184327	+	0.00567302i
$213$	6.15745	+	18.9507i	0.421901	+	1.29848i
$214$	−0.322244	+	0.234124i	−0.0220281	+	0.0160044i
$215$		0			0
$216$	−3.53128	−	10.8682i	−0.240273	−	0.739486i
$217$	−0.597922	+	1.84022i	−0.0405896	+	0.124922i
$218$	−11.6941	−	8.49629i	−0.792027	−	0.575442i
$219$	2.05310			0.138736
$220$		0			0
$221$	3.33991			0.224666
$222$	4.00428	+	2.90928i	0.268749	+	0.195258i
$223$	3.27200	−	10.0702i	0.219109	−	0.674349i	−0.779727	−	0.626120i	$-0.784642\pi$
$223$	3.27200	−	10.0702i	0.219109	−	0.674349i	0.998836	−	0.0482295i	$-0.0153579\pi$
$224$	0.153242	+	0.471631i	0.0102389	+	0.0315122i
$225$		0			0
$226$	−6.20389	+	4.50739i	−0.412676	+	0.299827i
$227$	−1.78459	−	5.49240i	−0.118447	−	0.364543i	0.874203	−	0.485560i	$-0.161384\pi$
$227$	−1.78459	−	5.49240i	−0.118447	−	0.364543i	−0.992650	+	0.121017i	$0.961384\pi$
$228$	1.13546	−	3.49459i	0.0751978	−	0.231435i
$229$	4.13124	+	3.00152i	0.273000	+	0.198346i	0.715858	−	0.698245i	$-0.246036\pi$
$229$	4.13124	+	3.00152i	0.273000	+	0.198346i	−0.442858	+	0.896592i	$0.646036\pi$
$230$		0			0
$231$	2.29685	+	0.450421i	0.151122	+	0.0296355i
$232$	17.2747			1.13414
$233$	22.4794	+	16.3323i	1.47268	+	1.06996i	0.979827	+	0.199848i	$0.0640447\pi$
$233$	22.4794	+	16.3323i	1.47268	+	1.06996i	0.492850	+	0.870115i	$0.335955\pi$
$234$	0.838534	−	2.58074i	0.0548167	−	0.168708i
$235$		0			0
$236$	0.0408472	−	0.0296772i	0.00265893	−	0.00193182i
$237$	−10.8744	+	7.90074i	−0.706370	+	0.513208i
$238$	−0.255977	−	0.787816i	−0.0165925	−	0.0510665i
$239$	−2.08502	+	6.41702i	−0.134868	+	0.415082i	−0.995570	−	0.0940282i	$-0.970026\pi$
$239$	−2.08502	+	6.41702i	−0.134868	+	0.415082i	0.860701	+	0.509111i	$0.170026\pi$
$240$		0			0
$241$	−13.0610			−0.841331			−0.420666	−	0.907216i	$-0.638203\pi$
$241$	−13.0610			−0.841331			−0.420666	+	0.907216i	$0.638203\pi$
$242$	7.66290	+	12.3543i	0.492590	+	0.794165i
$243$	−10.9715			−0.703823
$244$	−1.59771	−	1.16080i	−0.102283	−	0.0743128i
$245$		0			0
$246$	7.47607	+	23.0090i	0.476657	+	1.46700i
$247$	−10.7468	+	7.80804i	−0.683805	+	0.496814i
$248$	−13.3859	+	9.72545i	−0.850007	+	0.617567i
$249$	−6.96667	−	21.4412i	−0.441495	−	1.35878i
$250$		0			0
$251$	24.3883	+	17.7191i	1.53938	+	1.11842i	0.950726	+	0.310033i	$0.100340\pi$
$251$	24.3883	+	17.7191i	1.53938	+	1.11842i	0.588650	+	0.808388i	$0.299660\pi$
$252$	0.0976041			0.00614848
$253$	−27.3762	−	5.36857i	−1.72113	−	0.337519i
$254$	16.3227			1.02418
$255$		0			0
$256$	−1.84728	+	5.68533i	−0.115455	+	0.355333i
$257$	0.112162	+	0.345199i	0.00699648	+	0.0215329i	0.954494	−	0.298231i	$-0.0963965\pi$
$257$	0.112162	+	0.345199i	0.00699648	+	0.0215329i	−0.947497	+	0.319764i	$0.896396\pi$
$258$	−14.6548	+	10.6473i	−0.912367	+	0.662873i
$259$	0.520700	−	0.378310i	0.0323547	−	0.0235071i
$260$		0			0
$261$	1.98322	−	6.10371i	0.122758	−	0.377810i
$262$	8.35733	+	6.07195i	0.516317	+	0.375127i
$263$	−22.5498			−1.39048			−0.695239	−	0.718779i	$-0.744701\pi$
$263$	−22.5498			−1.39048			−0.695239	+	0.718779i	$0.744701\pi$
$264$	13.6259	+	14.6607i	0.838614	+	0.902303i
$265$		0			0
$266$	2.66542	+	1.93654i	0.163427	+	0.118737i
$267$	5.53888	−	17.0469i	0.338974	−	1.04325i
$268$	0.958525	+	2.95004i	0.0585512	+	0.180202i
$269$	4.97323	−	3.61326i	0.303223	−	0.220305i	−0.425760	−	0.904836i	$-0.639993\pi$
$269$	4.97323	−	3.61326i	0.303223	−	0.220305i	0.728983	+	0.684532i	$0.239993\pi$
$270$		0			0
$271$	5.15939	+	15.8790i	0.313410	+	0.964578i	0.976404	+	0.215953i	$0.0692858\pi$
$271$	5.15939	+	15.8790i	0.313410	+	0.964578i	−0.662993	+	0.748625i	$0.730714\pi$
$272$	1.90715	−	5.86962i	0.115638	−	0.355898i
$273$	−1.05953	−	0.769791i	−0.0641255	−	0.0465899i
$274$	12.6621			0.764946
$275$		0			0
$276$	−4.31779			−0.259900
$277$	−18.0652	−	13.1252i	−1.08543	−	0.788614i	−0.106812	−	0.994279i	$-0.534064\pi$
$277$	−18.0652	−	13.1252i	−1.08543	−	0.788614i	−0.978622	+	0.205665i	$0.934064\pi$
$278$	−7.81302	+	24.0460i	−0.468594	+	1.44218i
$279$	1.89955	+	5.84622i	0.113723	+	0.350004i
$280$		0			0
$281$	−19.2992	+	14.0217i	−1.15129	+	0.836463i	−0.988652	−	0.150223i	$-0.952001\pi$
$281$	−19.2992	+	14.0217i	−1.15129	+	0.836463i	−0.162640	+	0.986685i	$0.552001\pi$
$282$	6.01000	+	18.4969i	0.357891	+	1.10147i
$283$	−0.0450824	+	0.138749i	−0.00267987	+	0.00824779i	−0.952388	−	0.304890i	$-0.901380\pi$
$283$	−0.0450824	+	0.138749i	−0.00267987	+	0.00824779i	0.949708	+	0.313138i	$0.101380\pi$
$284$	2.01515	+	1.46409i	0.119577	+	0.0868777i
$285$		0			0
$286$	−0.977932	−	8.07544i	−0.0578264	−	0.477511i
$287$	3.14597			0.185701
$288$	1.27456	+	0.926022i	0.0751041	+	0.0545664i
$289$	−4.25236	+	13.0874i	−0.250139	+	0.769848i
$290$		0			0
$291$	−10.1682	+	7.38761i	−0.596069	+	0.433070i
$292$	0.207634	−	0.150855i	0.0121509	−	0.00882812i
$293$	2.37164	+	7.29917i	0.138553	+	0.426422i	0.996126	−	0.0879405i	$-0.0280285\pi$
$293$	2.37164	+	7.29917i	0.138553	+	0.426422i	−0.857573	+	0.514363i	$0.828029\pi$
$294$	5.69281	−	17.5207i	0.332012	−	1.02183i
$295$		0			0
$296$	5.50374			0.319899
$297$	−11.5433	+	5.35940i	−0.669808	+	0.310984i
$298$	−7.63238			−0.442132
$299$	12.6285	+	9.17515i	0.730325	+	0.530612i
$300$		0			0
$301$	0.727893	+	2.24022i	0.0419550	+	0.129124i
$302$	14.2934	−	10.3848i	0.822494	−	0.597577i
$303$	6.01309	−	4.36876i	0.345443	−	0.250979i
$304$	7.58534	+	23.3453i	0.435049	+	1.33894i
$305$		0			0
$306$	−2.12903	−	1.54683i	−0.121709	−	0.0884266i
$307$	9.69537			0.553344			0.276672	−	0.960964i	$-0.410768\pi$
$307$	9.69537			0.553344			0.276672	+	0.960964i	$0.410768\pi$
$308$	0.265380	−	0.123213i	0.0151214	−	0.00702071i
$309$	−39.8840			−2.26892
$310$		0			0
$311$	7.77436	−	23.9270i	0.440844	−	1.35678i	−0.446135	−	0.894966i	$-0.647200\pi$
$311$	7.77436	−	23.9270i	0.440844	−	1.35678i	0.886978	−	0.461811i	$-0.152800\pi$
$312$	−3.46071	−	10.6510i	−0.195924	−	0.602992i
$313$	8.79698	−	6.39138i	0.497235	−	0.361262i	−0.310725	−	0.950500i	$-0.600572\pi$
$313$	8.79698	−	6.39138i	0.497235	−	0.361262i	0.807960	+	0.589238i	$0.200572\pi$
$314$	−14.3757	+	10.4445i	−0.811265	+	0.589418i
$315$		0			0
$316$	−0.519233	+	1.59803i	−0.0292091	+	0.0898964i
$317$	−20.5768	−	14.9499i	−1.15571	−	0.839672i	−0.166480	−	0.986045i	$-0.553240\pi$
$317$	−20.5768	−	14.9499i	−1.15571	−	0.839672i	−0.989230	+	0.146373i	$0.953240\pi$
$318$	−0.918232			−0.0514919
$319$	−2.31291	−	19.0992i	−0.129498	−	1.06935i
$320$		0			0
$321$	0.494091	+	0.358978i	0.0275775	+	0.0200362i
$322$	1.19636	−	3.68201i	0.0666704	−	0.205190i
$323$	3.98100	+	12.2523i	0.221509	+	0.681734i
$324$	−2.27378	+	1.65200i	−0.126321	+	0.0917776i
$325$		0			0
$326$	−1.28050	−	3.94098i	−0.0709204	−	0.218270i
$327$	−6.84882	+	21.0785i	−0.378741	+	1.16564i
$328$	21.7641	+	15.8125i	1.20172	+	0.873102i
$329$	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	$0.591435\pi$
$332$	−2.27998	−	1.65650i	−0.125130	−	0.0909124i
$333$	0.631857	−	1.94465i	0.0346255	−	0.106566i
$334$	−1.07360	−	3.30420i	−0.0587447	−	0.180798i
$335$		0			0
$336$	−1.95786	+	1.42247i	−0.106810	+	0.0776020i
$337$	0.711987	+	2.19127i	0.0387844	+	0.119366i	0.968574	−	0.248725i	$-0.0800115\pi$
$337$	0.711987	+	2.19127i	0.0387844	+	0.119366i	−0.929790	+	0.368091i	$0.880012\pi$
$338$	3.90276	−	12.0115i	0.212282	−	0.653337i
$339$	9.51232	+	6.91111i	0.516638	+	0.375360i
$340$		0			0
$341$	12.5449	+	13.4976i	0.679344	+	0.730936i
$342$	10.4668			0.565980
$343$	−3.91028	−	2.84098i	−0.211135	−	0.153399i
$344$	−6.22438	+	19.1567i	−0.335596	+	1.03286i
$345$		0			0
$346$	−4.19422	+	3.04728i	−0.225483	+	0.163823i
$347$	16.7779	−	12.1899i	0.900686	−	0.654387i	−0.0379558	−	0.999279i	$-0.512085\pi$
$347$	16.7779	−	12.1899i	0.900686	−	0.654387i	0.938642	+	0.344892i	$0.112085\pi$
$348$	−0.920138	−	2.83189i	−0.0493246	−	0.151806i
$349$	1.14723	−	3.53080i	0.0614097	−	0.189000i	−0.915645	−	0.401988i	$-0.868320\pi$
$349$	1.14723	−	3.53080i	0.0614097	−	0.189000i	0.977055	+	0.212988i	$0.0683195\pi$
$350$		0			0
$351$	7.12106			0.380094
$352$	4.63444	+	0.908832i	0.247017	+	0.0484409i
$353$	−3.01441			−0.160441			−0.0802203	−	0.996777i	$-0.525562\pi$
$353$	−3.01441			−0.160441			−0.0802203	+	0.996777i	$0.525562\pi$
$354$	0.431856	+	0.313762i	0.0229529	+	0.0166763i
$355$		0			0
$356$	−0.692393	−	2.13097i	−0.0366967	−	0.112941i
$357$	−1.02754	+	0.746551i	−0.0543832	+	0.0395117i
$358$	−3.54432	+	2.57510i	−0.187323	+	0.136098i
$359$	−7.02678	−	21.6262i	−0.370859	−	1.14139i	−0.946230	−	0.323494i	$-0.895142\pi$
$359$	−7.02678	−	21.6262i	−0.370859	−	1.14139i	0.575371	−	0.817893i	$-0.304858\pi$
$360$		0			0
$361$	−26.0818	−	18.9495i	−1.37273	−	0.997344i
$362$	−22.3418			−1.17426
$363$	14.3848	−	17.0280i	0.755005	−	0.893736i
$364$	−0.163714			−0.00858092
$365$		0			0
$366$	6.45207	−	19.8574i	0.337255	−	1.03796i
$367$	4.18516	+	12.8806i	0.218464	+	0.672362i	0.998890	+	0.0471138i	$0.0150024\pi$
$367$	4.18516	+	12.8806i	0.218464	+	0.672362i	−0.780426	+	0.625248i	$0.784998\pi$
$368$	23.3357	−	16.9544i	1.21646	−	0.883809i
$369$	8.08572	−	5.87462i	0.420926	−	0.305820i
$370$		0			0
$371$	−0.0368976	+	0.113559i	−0.00191563	+	0.00589570i
$372$	2.30733	+	1.67637i	0.119630	+	0.0869159i
$373$	24.8281			1.28555			0.642774	−	0.766056i	$-0.277783\pi$
$373$	24.8281			1.28555			0.642774	+	0.766056i	$0.277783\pi$
$374$	−7.74141	−	1.51812i	−0.400299	−	0.0785001i
$375$		0			0
$376$	17.4961	+	12.7117i	0.902294	+	0.655555i
$377$	−3.32649	+	10.2379i	−0.171323	+	0.527278i
$378$	−0.545772	−	1.67971i	−0.0280715	−	0.0863952i
$379$	−4.98407	+	3.62114i	−0.256015	+	0.186005i	−0.708388	−	0.705823i	$-0.750577\pi$
$379$	−4.98407	+	3.62114i	−0.256015	+	0.186005i	0.452374	+	0.891829i	$0.350577\pi$
$380$		0			0
$381$	−7.73386	−	23.8024i	−0.396218	−	1.21943i
$382$	8.58287	−	26.4154i	0.439138	−	1.35153i
$383$	0.294214	+	0.213759i	0.0150337	+	0.0109226i	0.595277	−	0.803521i	$-0.297042\pi$
$383$	0.294214	+	0.213759i	0.0150337	+	0.0109226i	−0.580243	+	0.814443i	$0.697042\pi$
$384$	−17.6370			−0.900034
$385$		0			0
$386$	−4.37892			−0.222881
$387$	6.05409	+	4.39856i	0.307747	+	0.223591i
$388$	−0.485510	+	1.49425i	−0.0246481	+	0.0758589i
$389$	−0.577201	−	1.77644i	−0.0292653	−	0.0900693i	0.935357	−	0.353705i	$-0.115078\pi$
$389$	−0.577201	−	1.77644i	−0.0292653	−	0.0900693i	−0.964622	+	0.263636i	$0.915078\pi$
$390$		0			0
$391$	12.2473	−	8.89815i	0.619370	−	0.449999i
$392$	−6.33022	−	19.4824i	−0.319725	−	0.984011i
$393$	4.89457	−	15.0639i	0.246898	−	0.759875i
$394$	−7.45476	−	5.41620i	−0.375565	−	0.272864i
$395$		0			0
$396$	0.451995	−	0.812237i	0.0227136	−	0.0408164i
$397$	−0.384172			−0.0192811			−0.00964053	−	0.999954i	$-0.503069\pi$
$397$	−0.384172			−0.0192811			−0.00964053	+	0.999954i	$0.503069\pi$
$398$	−20.5486	−	14.9294i	−1.03001	−	0.748345i
$399$	1.56104	−	4.80437i	0.0781495	−	0.240519i
$400$		0			0
$401$	18.3270	−	13.3153i	0.915206	−	0.664936i	−0.0271201	−	0.999632i	$-0.508634\pi$
$401$	18.3270	−	13.3153i	0.915206	−	0.664936i	0.942326	+	0.334696i	$0.108634\pi$
$402$	−26.5311	+	19.2760i	−1.32325	+	0.961399i
$403$	−3.18616	−	9.80600i	−0.158714	−	0.488471i
$404$	0.287113	−	0.883643i	0.0142844	−	0.0439629i
$405$		0			0
$406$	2.66986			0.132503
$407$	−0.736897	−	6.08505i	−0.0365266	−	0.301625i
$408$	−10.8610			−0.537699
$409$	23.6348	+	17.1717i	1.16866	+	0.849085i	0.990848	−	0.134979i	$-0.0430967\pi$
$409$	23.6348	+	17.1717i	1.16866	+	0.849085i	0.177816	+	0.984064i	$0.443097\pi$
$410$		0			0
$411$	−5.99944	−	18.4644i	−0.295931	−	0.910781i
$412$	−4.03354	+	2.93054i	−0.198718	+	0.144377i
$413$	0.0561568	−	0.0408003i	0.00276330	−	0.00200765i
$414$	−3.80073	−	11.6975i	−0.186796	−	0.574899i
$415$		0			0
$416$	−2.13785	−	1.55324i	−0.104817	−	0.0761537i
$417$	38.7667			1.89841
$418$	28.4587	−	13.2130i	1.39196	−	0.646270i
$419$	−0.720765			−0.0352117			−0.0176058	−	0.999845i	$-0.505604\pi$
$419$	−0.720765			−0.0352117			−0.0176058	+	0.999845i	$0.505604\pi$
$420$		0			0
$421$	−7.24859	+	22.3089i	−0.353275	+	1.08727i	0.603728	+	0.797190i	$0.293681\pi$
$421$	−7.24859	+	22.3089i	−0.353275	+	1.08727i	−0.957003	+	0.290078i	$0.906319\pi$
$422$	−1.75376	−	5.39753i	−0.0853718	−	0.262747i
$423$	6.50010	−	4.72260i	0.316046	−	0.229621i
$424$	−0.826042	+	0.600154i	−0.0401161	+	0.0291461i
$425$		0			0
$426$	−8.13782	+	25.0456i	−0.394278	+	1.21346i
$427$	−2.19653	−	1.59587i	−0.106298	−	0.0772298i
$428$	0.0763449			0.00369027
$429$	−11.3126	+	5.25229i	−0.546176	+	0.253583i
$430$		0			0
$431$	−3.04083	−	2.20930i	−0.146472	−	0.106418i	0.512136	−	0.858904i	$-0.328854\pi$
$431$	−3.04083	−	2.20930i	−0.146472	−	0.106418i	−0.658608	+	0.752486i	$0.728854\pi$
$432$	4.06627	−	12.5147i	0.195639	−	0.602114i
$433$	−4.20476	−	12.9409i	−0.202068	−	0.621901i	−0.999821	−	0.0189169i	$-0.993978\pi$
$433$	−4.20476	−	12.9409i	−0.202068	−	0.621901i	0.797753	−	0.602984i	$-0.206022\pi$
$434$	−2.06884	+	1.50310i	−0.0993076	+	0.0721512i
$435$		0			0
$436$	0.856143	+	2.63494i	0.0410018	+	0.126191i
$437$	−18.6060	+	57.2634i	−0.890045	+	2.73928i
$438$	2.19521	+	1.59491i	0.104891	+	0.0762078i
$439$	15.6217			0.745584			0.372792	−	0.927915i	$-0.378400\pi$
$439$	15.6217			0.745584			0.372792	+	0.927915i	$0.378400\pi$
$440$		0			0
$441$	−7.61052			−0.362406
$442$	3.57108	+	2.59454i	0.169859	+	0.123410i
$443$	−0.437512	+	1.34652i	−0.0207868	+	0.0639753i	−0.960912	−	0.276855i	$-0.910708\pi$
$443$	−0.437512	+	1.34652i	−0.0207868	+	0.0639753i	0.940125	+	0.340830i	$0.110708\pi$
$444$	−0.293158	−	0.902248i	−0.0139127	−	0.0428188i
$445$		0			0
$446$	11.3213	−	8.22540i	0.536079	−	0.389484i
$447$	3.61630	+	11.1298i	0.171045	+	0.526423i
$448$	−0.940613	+	2.89491i	−0.0444398	+	0.136772i
$449$	−5.58939	−	4.06093i	−0.263780	−	0.191647i	0.448032	−	0.894017i	$-0.352125\pi$
$449$	−5.58939	−	4.06093i	−0.263780	−	0.191647i	−0.711812	+	0.702370i	$0.752125\pi$
$450$		0			0
$451$	14.5687	−	26.1800i	0.686012	−	1.23277i
$452$	1.46980			0.0691338
$453$	−21.9159	−	15.9228i	−1.02970	−	0.748119i
$454$	2.35855	−	7.25887i	0.110692	−	0.340676i
$455$		0			0
$456$	34.9475	−	25.3909i	1.63657	−	1.18904i
$457$	34.2649	−	24.8949i	1.60284	−	1.16453i	0.721068	−	0.692865i	$-0.243652\pi$
$457$	34.2649	−	24.8949i	1.60284	−	1.16453i	0.881776	−	0.471669i	$-0.156348\pi$
$458$	2.08551	+	6.41854i	0.0974496	+	0.299919i
$459$	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	$0.300772\pi$
$462$	2.10593	+	2.26586i	0.0979765	+	0.105417i
$463$	7.89251			0.366796			0.183398	−	0.983039i	$-0.441290\pi$
$463$	7.89251			0.366796			0.183398	+	0.983039i	$0.441290\pi$
$464$	16.0928	+	11.6921i	0.747089	+	0.542792i
$465$		0			0
$466$	11.3479	+	34.9254i	0.525684	+	1.61789i
$467$	12.9209	−	9.38761i	0.597909	−	0.434407i	−0.247227	−	0.968958i	$-0.579519\pi$
$467$	12.9209	−	9.38761i	0.597909	−	0.434407i	0.845136	+	0.534551i	$0.179519\pi$
$468$	−0.420774	+	0.305710i	−0.0194503	+	0.0141315i
$469$	1.31778	+	4.05572i	0.0608495	+	0.187276i
$470$		0			0
$471$	22.0420	+	16.0144i	1.01564	+	0.737905i
$472$	0.593572			0.0273214
$473$	22.0134	+	4.31691i	1.01218	+	0.198492i
$474$	−17.7646			−0.815957
$475$		0			0
$476$	−0.0490630	+	0.151000i	−0.00224880	+	0.00692109i
$477$	0.117221	+	0.360768i	0.00536717	+	0.0165185i
$478$	−7.21426	+	5.24147i	−0.329973	+	0.239739i
$479$	−11.6195	+	8.44209i	−0.530910	+	0.385729i	−0.820698	−	0.571362i	$-0.806415\pi$
$479$	−11.6195	+	8.44209i	−0.530910	+	0.385729i	0.289788	+	0.957091i	$0.406415\pi$
$480$		0			0
$481$	−1.05983	+	3.26181i	−0.0483240	+	0.148726i
$482$	−13.9650	−	10.1462i	−0.636088	−	0.462145i
$483$	−5.93610			−0.270102
$484$	0.203602	−	2.77901i	0.00925465	−	0.126319i
$485$		0			0
$486$	−11.7309	−	8.52300i	−0.532125	−	0.386611i
$487$	11.1034	−	34.1729i	0.503145	−	1.54852i	−0.300723	−	0.953712i	$-0.597228\pi$
$487$	11.1034	−	34.1729i	0.503145	−	1.54852i	0.803868	−	0.594808i	$-0.202772\pi$
$488$	−7.17449	−	22.0808i	−0.324774	−	0.999551i
$489$	−5.14017	+	3.73455i	−0.232447	+	0.168882i
$490$		0			0
$491$	10.8828	+	33.4939i	0.491135	+	1.51156i	0.822895	+	0.568194i	$0.192358\pi$
$491$	10.8828	+	33.4939i	0.491135	+	1.51156i	−0.331760	+	0.943364i	$0.607642\pi$
$492$	1.43294	−	4.41012i	0.0646017	−	0.198824i
$493$	8.44595	+	6.13634i	0.380386	+	0.276367i
$494$	−17.5562			−0.789891
$495$		0			0
$496$	−19.0526			−0.855488
$497$	2.77043	+	2.01283i	0.124271	+	0.0902879i
$498$	9.20731	−	28.3372i	0.412589	−	1.26982i
$499$	8.18654	+	25.1956i	0.366480	+	1.12791i	0.949049	+	0.315128i	$0.102048\pi$
$499$	8.18654	+	25.1956i	0.366480	+	1.12791i	−0.582569	+	0.812781i	$0.697952\pi$
$500$		0			0
$501$	−4.30963	+	3.13113i	−0.192540	+	0.139888i
$502$	12.3116	+	37.8911i	0.549492	+	1.69116i
$503$	−5.48306	+	16.8751i	−0.244478	+	0.752424i	0.751244	+	0.660024i	$0.229454\pi$
$503$	−5.48306	+	16.8751i	−0.244478	+	0.752424i	−0.995722	+	0.0924004i	$0.970546\pi$
$504$	0.928313	+	0.674459i	0.0413504	+	0.0300428i
$505$		0			0
$506$	−25.1005	−	27.0068i	−1.11586	−	1.20060i
$507$	−19.3647			−0.860019
$508$	−2.53106	−	1.83892i	−0.112298	−	0.0815889i
$509$	−4.25018	+	13.0807i	−0.188386	+	0.579793i	−0.999990	−	0.00441502i	$-0.998595\pi$
$509$	−4.25018	+	13.0807i	−0.188386	+	0.579793i	0.811604	+	0.584208i	$0.198595\pi$
$510$		0			0
$511$	0.285456	−	0.207396i	0.0126278	−	0.00917465i
$512$	−20.4742	+	14.8754i	−0.904842	+	0.657406i
$513$	8.48796	+	26.1232i	0.374753	+	1.15337i
$514$	−0.148236	+	0.456223i	−0.00653840	+	0.0201231i
$515$		0			0
$516$	3.47196			0.152845
$517$	11.7117	−	21.0460i	0.515081	−	0.925604i
$518$	0.850623			0.0373742
$519$	6.43093	+	4.67234i	0.282286	+	0.205093i
$520$		0			0
$521$	3.88720	+	11.9636i	0.170301	+	0.524133i	0.999388	−	0.0349870i	$-0.0111390\pi$
$521$	3.88720	+	11.9636i	0.170301	+	0.524133i	−0.829087	+	0.559120i	$0.811139\pi$
$522$	6.86203	−	4.98555i	0.300343	−	0.218212i
$523$	−33.0052	+	23.9797i	−1.44322	+	1.04856i	−0.455861	+	0.890051i	$0.650669\pi$
$523$	−33.0052	+	23.9797i	−1.44322	+	1.04856i	−0.987358	+	0.158508i	$0.949331\pi$
$524$	−0.611850	−	1.88308i	−0.0267288	−	0.0822628i
$525$		0			0
$526$	−24.1105	−	17.5173i	−1.05127	−	0.763792i
$527$	−9.99936			−0.435579
$528$	2.77077	+	22.8801i	0.120582	+	0.995729i
$529$	47.7524			2.07619
$530$		0			0
$531$	0.0681449	−	0.209729i	0.00295724	−	0.00910144i
$532$	−0.195139	−	0.600575i	−0.00846033	−	0.0260382i
$533$	−13.5624	+	9.85363i	−0.587451	+	0.426808i
$534$	19.1648	−	13.9241i	0.829342	−	0.602553i
$535$		0			0
$536$	−11.2687	+	34.6814i	−0.486732	+	1.49801i
$537$	5.43445	+	3.94836i	0.234514	+	0.170384i
$538$	8.12434			0.350265
$539$	−20.6926	+	9.60732i	−0.891293	+	0.413817i
$540$		0			0
$541$	−26.3873	−	19.1715i	−1.13448	−	0.824247i	−0.148138	−	0.988967i	$-0.547328\pi$
$541$	−26.3873	−	19.1715i	−1.13448	−	0.824247i	−0.986340	+	0.164720i	$0.947328\pi$
$542$	−6.81876	+	20.9860i	−0.292891	+	0.901425i
$543$	10.5858	+	32.5797i	0.454279	+	1.39813i
$544$	−2.07331	+	1.50635i	−0.0888923	+	0.0645840i
$545$		0			0
$546$	−0.534865	−	1.64614i	−0.0228901	−	0.0704485i
$547$	−1.77062	+	5.44942i	−0.0757064	+	0.233000i	−0.981747	−	0.190190i	$-0.939090\pi$
$547$	−1.77062	+	5.44942i	−0.0757064	+	0.233000i	0.906041	+	0.423190i	$0.139090\pi$
$548$	−1.96344	−	1.42652i	−0.0838739	−	0.0609379i
$549$	−8.62555			−0.368129
$550$		0			0
$551$	−41.5222			−1.76890
$552$	−41.0665	−	29.8365i	−1.74791	−	1.26993i
$553$	−0.713842	+	2.19698i	−0.0303556	+	0.0934251i
$554$	−9.11960	−	28.0672i	−0.387454	−	1.19246i
$555$		0			0
$556$	3.92055	−	2.84845i	0.166268	−	0.120801i
$557$	−12.5555	−	38.6418i	−0.531993	−	1.63731i	−0.750057	−	0.661373i	$-0.769974\pi$
$557$	−12.5555	−	38.6418i	−0.531993	−	1.63731i	0.218064	−	0.975935i	$-0.430026\pi$
$558$	−2.51049	+	7.72649i	−0.106278	+	0.327089i
$559$	−10.1547	−	7.37780i	−0.429497	−	0.312048i
$560$		0			0
$561$	1.45418	+	12.0081i	0.0613955	+	0.506984i
$562$	−31.5274			−1.32990
$563$	−11.8825	−	8.63316i	−0.500788	−	0.363844i	0.308530	−	0.951215i	$-0.400163\pi$
$563$	−11.8825	−	8.63316i	−0.500788	−	0.363844i	−0.809318	+	0.587371i	$0.800163\pi$
$564$	1.15194	−	3.54529i	0.0485052	−	0.149284i
$565$		0			0
$566$	−0.155987	+	0.113332i	−0.00655664	+	0.00476368i
$567$	−3.12600	+	2.27117i	−0.131279	+	0.0953801i
$568$	9.04898	+	27.8499i	0.379687	+	1.16856i
$569$	−7.60025	+	23.3912i	−0.318619	+	0.980609i	0.655620	+	0.755091i	$0.272407\pi$
$569$	−7.60025	+	23.3912i	−0.318619	+	0.980609i	−0.974239	+	0.225518i	$0.927593\pi$
$570$		0			0
$571$	−22.4923			−0.941273			−0.470637	−	0.882327i	$-0.655976\pi$
$571$	−22.4923			−0.941273			−0.470637	+	0.882327i	$0.655976\pi$
$572$	−0.758141	+	1.36238i	−0.0316995	+	0.0569641i
$573$	−42.5866			−1.77908
$574$	3.36372	+	2.44388i	0.140399	+	0.102006i
$575$		0			0
$576$	2.98825	+	9.19690i	0.124511	+	0.383204i
$577$	30.3652	−	22.0616i	1.26412	−	0.918435i	0.265166	−	0.964203i	$-0.414573\pi$
$577$	30.3652	−	22.0616i	1.26412	−	0.918435i	0.998952	+	0.0457674i	$0.0145733\pi$
$578$	−14.7134	+	10.6899i	−0.611996	+	0.444641i
$579$	2.07478	+	6.38552i	0.0862249	+	0.265373i
$580$		0			0
$581$	−3.13452	−	2.27736i	−0.130042	−	0.0944809i
$582$	−16.6109			−0.688543
$583$	0.774141	+	0.832933i	0.0320617	+	0.0344966i
$584$	3.01724			0.124854
$585$		0			0
$586$	−3.13442	+	9.64675i	−0.129482	+	0.398503i
$587$	8.65563	+	26.6393i	0.357256	+	1.09952i	0.954690	+	0.297603i	$0.0961871\pi$
$587$	8.65563	+	26.6393i	0.357256	+	1.09952i	−0.597434	+	0.801918i	$0.703813\pi$
$588$	−2.85664	+	2.07547i	−0.117806	+	0.0855910i
$589$	32.1750	−	23.3765i	1.32575	−	0.963213i
$590$		0			0
$591$	−4.36597	+	13.4371i	−0.179592	+	0.552728i
$592$	5.12719	+	3.72512i	0.210726	+	0.153102i
$593$	17.7522			0.728996			0.364498	−	0.931204i	$-0.381241\pi$
$593$	17.7522			0.728996			0.364498	+	0.931204i	$0.381241\pi$
$594$	−16.5056	−	3.23681i	−0.677232	−	0.132808i
$595$		0			0
$596$	1.18351	+	0.859868i	0.0484783	+	0.0352216i
$597$	−12.0345	+	37.0385i	−0.492541	+	1.51589i
$598$	6.37506	+	19.6204i	0.260695	+	0.802338i
$599$	19.7594	−	14.3561i	0.807348	−	0.586573i	−0.105713	−	0.994397i	$-0.533712\pi$
$599$	19.7594	−	14.3561i	0.807348	−	0.586573i	0.913061	+	0.407824i	$0.133712\pi$
$600$		0			0
$601$	−1.34725	−	4.14640i	−0.0549553	−	0.169135i	0.919812	−	0.392360i	$-0.128341\pi$
$601$	−1.34725	−	4.14640i	−0.0549553	−	0.169135i	−0.974767	+	0.223225i	$0.928341\pi$
$602$	−0.961999	+	2.96073i	−0.0392082	+	0.120670i
$603$	10.9604	+	7.96318i	0.446341	+	0.324286i
$604$	−3.38635			−0.137789
$605$		0			0
$606$	9.82307			0.399035
$607$	32.0516	+	23.2869i	1.30094	+	0.945185i	0.999964	−	0.00844827i	$-0.00268920\pi$
$607$	32.0516	+	23.2869i	1.30094	+	0.945185i	0.300971	+	0.953633i	$0.402689\pi$
$608$	3.14976	−	9.69396i	0.127740	−	0.393142i
$609$	−1.26501	−	3.89329i	−0.0512607	−	0.157764i
$610$		0			0
$611$	−10.9028	+	7.92132i	−0.441078	+	0.320462i
$612$	0.155869	+	0.479716i	0.00630064	+	0.0193914i
$613$	0.806291	−	2.48151i	0.0325658	−	0.100227i	−0.933452	−	0.358701i	$-0.883220\pi$
$613$	0.806291	−	2.48151i	0.0325658	−	0.100227i	0.966018	+	0.258474i	$0.0832197\pi$
$614$	10.3664	+	7.53165i	0.418355	+	0.303953i
$615$		0			0
$616$	3.37545	+	0.661939i	0.136001	+	0.0266703i
$617$	3.53110			0.142157			0.0710783	−	0.997471i	$-0.477356\pi$
$617$	3.53110			0.142157			0.0710783	+	0.997471i	$0.477356\pi$
$618$	−42.6445	−	30.9831i	−1.71541	−	1.24632i
$619$	−1.86509	+	5.74014i	−0.0749641	+	0.230716i	−0.981517	−	0.191377i	$-0.938705\pi$
$619$	−1.86509	+	5.74014i	−0.0749641	+	0.230716i	0.906552	+	0.422093i	$0.138705\pi$
$620$		0			0
$621$	26.1126	−	18.9719i	1.04786	−	0.761316i
$622$	26.8997	−	19.5438i	1.07858	−	0.783634i
$623$	−0.951903	−	2.92966i	−0.0381372	−	0.117374i
$624$	3.98501	−	12.2646i	0.159528	−	0.490977i
$625$		0			0
$626$	14.3709			0.574376
$627$	−32.7518	−	35.2391i	−1.30798	−	1.40731i
$628$	3.40583			0.135907
$629$	2.69090	+	1.95505i	0.107293	+	0.0779530i
$630$		0			0
$631$	0.333740	+	1.02714i	0.0132860	+	0.0408900i	0.957480	−	0.288501i	$-0.0931567\pi$
$631$	0.333740	+	1.02714i	0.0132860	+	0.0408900i	−0.944194	+	0.329391i	$0.893157\pi$
$632$	−15.9811	+	11.6109i	−0.635693	+	0.461858i
$633$	−7.03994	+	5.11481i	−0.279812	+	0.203296i
$634$	−10.3875	−	31.9694i	−0.412540	−	1.26967i
$635$		0			0
$636$	0.142385	+	0.103449i	0.00564592	+	0.00410200i
$637$	12.7653			0.505780
$638$	12.3638	−	22.2179i	0.489489	−	0.879615i
$639$	10.8792			0.430373
$640$		0			0
$641$	3.05474	−	9.40153i	0.120655	−	0.371338i	−0.872429	−	0.488740i	$-0.837457\pi$
$641$	3.05474	−	9.40153i	0.120655	−	0.371338i	0.993084	+	0.117402i	$0.0374566\pi$
$642$	0.249425	+	0.767650i	0.00984400	+	0.0302967i
$643$	23.2999	−	16.9284i	0.918858	−	0.667589i	−0.0243814	−	0.999703i	$-0.507762\pi$
$643$	23.2999	−	16.9284i	0.918858	−	0.667589i	0.943240	+	0.332113i	$0.107762\pi$
$644$	−0.600329	+	0.436165i	−0.0236563	+	0.0171873i
$645$		0			0
$646$	−5.26138	+	16.1929i	−0.207006	+	0.637100i
$647$	14.8118	+	10.7614i	0.582311	+	0.423074i	0.839557	−	0.543272i	$-0.182815\pi$
$647$	14.8118	+	10.7614i	0.582311	+	0.423074i	−0.257245	+	0.966346i	$0.582815\pi$
$648$	−33.0415			−1.29799
$649$	−0.0794734	−	0.656265i	−0.00311961	−	0.0257606i
$650$		0			0
$651$	3.17212	+	2.30468i	0.124325	+	0.0903276i
$652$	−0.245433	+	0.755365i	−0.00961190	+	0.0295824i
$653$	9.87025	+	30.3775i	0.386253	+	1.18876i	0.935567	+	0.353148i	$0.114889\pi$
$653$	9.87025	+	30.3775i	0.386253	+	1.18876i	−0.549315	+	0.835616i	$0.685111\pi$
$654$	−23.6973	+	17.2171i	−0.926637	+	0.673241i
$655$		0			0
$656$	9.57259	+	29.4614i	0.373747	+	1.15027i
$657$	0.346394	−	1.06609i	0.0135141	−	0.0415921i
$658$	2.70409	+	1.96463i	0.105416	+	0.0765894i
$659$	27.0408			1.05336			0.526679	−	0.850064i	$-0.323437\pi$
$659$	27.0408			1.05336			0.526679	+	0.850064i	$0.323437\pi$
$660$		0			0
$661$	47.2504			1.83783			0.918915	−	0.394456i	$-0.129067\pi$
$661$	47.2504			1.83783			0.918915	+	0.394456i	$0.129067\pi$
$662$	−11.0226	−	8.00839i	−0.428406	−	0.311255i
$663$	2.09144	−	6.43681i	0.0812250	−	0.249985i
$664$	−10.2382	−	31.5100i	−0.397320	−	1.22283i
$665$		0			0
$666$	2.18626	−	1.58841i	0.0847157	−	0.0615496i
$667$	15.0776	+	46.4042i	0.583809	+	1.79678i
$668$	−0.205776	+	0.633314i	−0.00796172	+	0.0245036i
$669$	−17.3588	−	12.6119i	−0.671128	−	0.487603i
$670$		0			0
$671$	−23.4524	+	10.8887i	−0.905369	+	0.420352i
$672$	1.00491			0.0387651
$673$	−30.6425	−	22.2631i	−1.18118	−	0.858179i	−0.188878	−	0.982001i	$-0.560485\pi$
$673$	−30.6425	−	22.2631i	−1.18118	−	0.858179i	−0.992305	+	0.123821i	$0.960485\pi$
$674$	−0.940977	+	2.89603i	−0.0362451	+	0.111551i
$675$		0			0
$676$	−1.95839	+	1.42286i	−0.0753228	+	0.0547252i
$677$	−27.4287	+	19.9281i	−1.05417	+	0.765900i	−0.973001	−	0.230800i	$-0.925866\pi$
$677$	−27.4287	+	19.9281i	−1.05417	+	0.765900i	−0.0811701	+	0.996700i	$0.525866\pi$
$678$	4.80196	+	14.7789i	0.184418	+	0.567581i
$679$	−0.667481	+	2.05429i	−0.0256156	+	0.0788366i
$680$		0			0
$681$	−11.7027			−0.448448
$682$	2.92784	+	24.1771i	0.112113	+	0.925789i
$683$	38.6515			1.47896			0.739480	−	0.673178i	$-0.235071\pi$
$683$	38.6515			1.47896			0.739480	+	0.673178i	$0.235071\pi$
$684$	−1.62302	−	1.17920i	−0.0620579	−	0.0450877i
$685$		0			0
$686$	−1.97397	−	6.07524i	−0.0753664	−	0.231954i
$687$	8.37164	−	6.08235i	0.319398	−	0.232056i
$688$	−18.7644	+	13.6331i	−0.715387	+	0.519759i
$689$	−0.196617	−	0.605125i	−0.00749051	−	0.0230534i
$690$		0			0
$691$	−21.3377	−	15.5027i	−0.811723	−	0.589751i	0.102607	−	0.994722i	$-0.467282\pi$
$691$	−21.3377	−	15.5027i	−0.811723	−	0.589751i	−0.914330	+	0.404971i	$0.867282\pi$
$692$	0.993680			0.0377741
$693$	0.621403	−	1.11666i	0.0236052	−	0.0424186i
$694$	27.4087			1.04042
$695$		0			0
$696$	10.8174	−	33.2925i	0.410032	−	1.26195i
$697$	5.02397	+	15.4622i	0.190296	+	0.585672i
$698$	3.96947	−	2.88399i	0.150247	−	0.109161i
$699$	45.5528	−	33.0961i	1.72297	−	1.25181i
$700$		0			0
$701$	5.74279	−	17.6745i	0.216902	−	0.667556i	−0.782111	−	0.623139i	$-0.785857\pi$
$701$	5.74279	−	17.6745i	0.216902	−	0.667556i	0.999013	−	0.0444171i	$-0.0141430\pi$
$702$	7.61395	+	5.53186i	0.287370	+	0.208786i
$703$	−13.2291			−0.498943
$704$	19.7348	+	21.2336i	0.743784	+	0.800270i
$705$		0			0
$706$	−3.22305	−	2.34168i	−0.121301	−	0.0881303i
$707$	0.394723	−	1.21483i	0.0148451	−	0.0456885i
$708$	−0.0316167	−	0.0973063i	−0.00118823	−	0.00365699i
$709$	−19.1789	+	13.9343i	−0.720280	+	0.523314i	−0.886474	−	0.462779i	$-0.846852\pi$
$709$	−19.1789	+	13.9343i	−0.720280	+	0.523314i	0.166194	+	0.986093i	$0.446852\pi$
$710$		0			0
$711$	2.26782	+	6.97963i	0.0850499	+	0.261757i
$712$	8.13994	−	25.0522i	0.305057	−	0.938869i
$713$	−37.8086	−	27.4695i	−1.41594	−	1.02874i
$714$	−1.67860			−0.0628202
$715$		0			0
$716$	0.839708			0.0313814
$717$	11.0615	+	8.03666i	0.413100	+	0.300135i
$718$	9.28674	−	28.5817i	0.346578	−	1.06666i
$719$	−9.53420	−	29.3432i	−0.355566	−	1.09432i	−0.955681	−	0.294405i	$-0.904879\pi$
$719$	−9.53420	−	29.3432i	−0.355566	−	1.09432i	0.600115	−	0.799914i	$-0.295121\pi$
$720$		0			0
$721$	−5.54532	+	4.02891i	−0.206519	+	0.150045i
$722$	−13.1665	−	40.5222i	−0.490005	−	1.50808i
$723$	−8.17877	+	25.1717i	−0.304172	+	0.936144i
$724$	3.46440	+	2.51704i	0.128754	+	0.0935449i
$725$		0			0
$726$	28.6082	−	7.03202i	1.06175	−	0.260983i
$727$	−24.1222			−0.894642			−0.447321	−	0.894373i	$-0.647622\pi$
$727$	−24.1222			−0.894642			−0.447321	+	0.894373i	$0.647622\pi$
$728$	−1.55708	−	1.13129i	−0.0577092	−	0.0419282i
$729$	3.41534	−	10.5113i	0.126494	−	0.389309i
$730$		0			0
$731$	−9.84810	+	7.15506i	−0.364245	+	0.264640i
$732$	−3.23763	+	2.35228i	−0.119666	+	0.0869427i
$733$	−4.27917	−	13.1699i	−0.158055	−	0.486442i	0.840403	−	0.541962i	$-0.182318\pi$
$733$	−4.27917	−	13.1699i	−0.158055	−	0.486442i	−0.998458	+	0.0555200i	$0.982318\pi$
$734$	−5.53120	+	17.0233i	−0.204160	+	0.628341i
$735$		0			0
$736$	−11.9775			−0.441496
$737$	39.8532	+	7.81536i	1.46801	+	0.287882i
$738$	13.2090			0.486228
$739$	−22.2549	−	16.1692i	−0.818661	−	0.594792i	0.0976674	−	0.995219i	$-0.468862\pi$
$739$	−22.2549	−	16.1692i	−0.818661	−	0.594792i	−0.916329	+	0.400427i	$0.868862\pi$
$740$		0			0
$741$	8.31832	+	25.6012i	0.305581	+	0.940482i
$742$	−0.127668	+	0.0927559i	−0.00468683	+	0.00340518i
$743$	2.18058	−	1.58429i	0.0799979	−	0.0581218i	−0.547067	−	0.837089i	$-0.684256\pi$
$743$	2.18058	−	1.58429i	0.0799979	−	0.0581218i	0.627065	+	0.778967i	$0.284256\pi$
$744$	10.3610	+	31.8880i	0.379854	+	1.16907i
$745$		0			0
$746$	26.5465	+	19.2872i	0.971937	+	0.706154i
$747$	−12.3089			−0.450360
$748$	1.02938	+	1.10756i	0.0376379	+	0.0404963i
$749$	0.104959			0.00383512
$750$		0			0
$751$	7.10258	−	21.8595i	0.259177	−	0.797664i	−0.733801	−	0.679364i	$-0.762256\pi$
$751$	7.10258	−	21.8595i	0.259177	−	0.797664i	0.992978	−	0.118300i	$-0.0377443\pi$
$752$	7.69539	+	23.6840i	0.280622	+	0.863666i
$753$	49.4210	−	35.9064i	1.80100	−	1.30850i
$754$	−11.5098	+	8.36238i	−0.419163	+	0.304540i
$755$		0			0
$756$	−0.104608	+	0.321950i	−0.00380455	+	0.0117092i
$757$	−28.2800	−	20.5466i	−1.02785	−	0.746780i	−0.0599765	−	0.998200i	$-0.519103\pi$
$757$	−28.2800	−	20.5466i	−1.02785	−	0.746780i	−0.967878	+	0.251420i	$0.919103\pi$
$758$	−8.14205			−0.295733
$759$	−27.4895	+	49.3987i	−0.997805	+	1.79306i
$760$		0			0
$761$	−30.1151	−	21.8799i	−1.09167	−	0.793145i	−0.111990	−	0.993709i	$-0.535723\pi$
$761$	−30.1151	−	21.8799i	−1.09167	−	0.793145i	−0.979681	+	0.200564i	$0.935723\pi$
$762$	10.2212	−	31.4577i	0.370276	−	1.13959i
$763$	1.17703	+	3.62252i	0.0426112	+	0.131144i
$764$	−4.30686	+	3.12912i	−0.155817	+	0.113208i
$765$		0			0
$766$	0.148524	+	0.457109i	0.00536638	+	0.0165160i
$767$	−0.114301	+	0.351782i	−0.00412717	+	0.0127021i
$768$	9.80024	+	7.12029i	0.353636	+	0.256931i
$769$	30.1272			1.08642			0.543208	−	0.839598i	$-0.317210\pi$
$769$	30.1272			1.08642			0.543208	+	0.839598i	$0.317210\pi$
$770$		0			0
$771$	0.735518			0.0264890
$772$	0.679013	+	0.493332i	0.0244382	+	0.0177554i
$773$	9.55113	−	29.3954i	0.343530	−	1.05728i	−0.618836	−	0.785521i	$-0.712395\pi$
$773$	9.55113	−	29.3954i	0.343530	−	1.05728i	0.962366	−	0.271757i	$-0.0876047\pi$
$774$	3.05620	+	9.40600i	0.109853	+	0.338092i
$775$		0			0
$776$	−14.9432	+	10.8568i	−0.536428	+	0.389738i
$777$	−0.403034	−	1.24041i	−0.0144588	−	0.0444995i
$778$	0.762842	−	2.34779i	0.0273492	−	0.0841722i
$779$	−52.3132	−	38.0078i	−1.87431	−	1.36177i
$780$		0			0
$781$	29.5798	−	13.7336i	1.05845	−	0.491426i
$782$	20.0073			0.715460
$783$	18.0077	+	13.0834i	0.643544	+	0.467562i
$784$	7.28925	−	22.4340i	0.260330	−	0.801214i
$785$		0			0
$786$	16.9355	−	12.3043i	0.604068	−	0.438881i
$787$	−27.9255	+	20.2891i	−0.995437	+	0.723227i	−0.961105	−	0.276183i	$-0.910930\pi$
$787$	−27.9255	+	20.2891i	−0.995437	+	0.723227i	−0.0343320	+	0.999410i	$0.510930\pi$
$788$	0.545773	+	1.67972i	0.0194423	+	0.0598374i
$789$	−14.1206	+	43.4588i	−0.502708	+	1.54718i
$790$		0			0
$791$	2.02069			0.0718474
$792$	9.91160	−	4.60184i	0.352193	−	0.163519i
$793$	14.4678			0.513767
$794$	−0.410763	−	0.298437i	−0.0145774	−	0.0105911i
$795$		0			0
$796$	1.50439	+	4.63003i	0.0533217	+	0.164107i
$797$	8.28055	−	6.01617i	0.293312	−	0.213104i	−0.431391	−	0.902165i	$-0.641977\pi$
$797$	8.28055	−	6.01617i	0.293312	−	0.213104i	0.724703	+	0.689061i	$0.241977\pi$
$798$	5.40126	−	3.92425i	0.191203	−	0.138917i
$799$	4.03876	+	12.4300i	0.142881	+	0.439743i
$800$		0			0
$801$	−7.91725	−	5.75222i	−0.279742	−	0.203245i
$802$	29.9392			1.05719
$803$	−0.403979	−	3.33592i	−0.0142561	−	0.117722i
$804$	6.28566			0.221678
$805$		0			0
$806$	4.21090	−	12.9598i	0.148323	−	0.456490i
$807$	−3.84940	−	11.8472i	−0.135505	−	0.417043i
$808$	8.83683	−	6.42034i	0.310879	−	0.225867i
$809$	−29.0143	+	21.0801i	−1.02009	+	0.741139i	−0.966301	−	0.257414i	$-0.917130\pi$
$809$	−29.0143	+	21.0801i	−1.02009	+	0.741139i	−0.0537884	+	0.998552i	$0.517130\pi$
$810$		0			0
$811$	5.71683	−	17.5946i	0.200745	−	0.617830i	−0.799116	−	0.601177i	$-0.794699\pi$
$811$	5.71683	−	17.5946i	0.200745	−	0.617830i	0.999861	−	0.0166535i	$-0.00530122\pi$
$812$	−0.413999	−	0.300788i	−0.0145285	−	0.0105556i
$813$	33.8334			1.18659
$814$	3.93915	−	7.07867i	0.138067	−	0.248107i
$815$		0			0
$816$	−10.1179	−	7.35110i	−0.354198	−	0.257340i
$817$	14.9612	−	46.0458i	0.523426	−	1.61094i
$818$	11.9312	+	36.7204i	0.417164	+	1.28390i
$819$	−0.578481	+	0.420291i	−0.0202138	+	0.0146862i
$820$		0			0
$821$	−8.43005	−	25.9450i	−0.294211	−	0.905488i	−0.983485	−	0.180987i	$-0.942071\pi$
$821$	−8.43005	−	25.9450i	−0.294211	−	0.905488i	0.689275	−	0.724500i	$-0.257929\pi$
$822$	7.92900	−	24.4030i	0.276556	−	0.851151i
$823$	−1.60549	−	1.16646i	−0.0559639	−	0.0406602i	0.559452	−	0.828863i	$-0.311012\pi$
$823$	−1.60549	−	1.16646i	−0.0559639	−	0.0406602i	−0.615416	+	0.788203i	$0.711012\pi$
$824$	−58.6135			−2.04190
$825$		0			0
$826$	0.0917386			0.00319199
$827$	−9.97578	−	7.24783i	−0.346892	−	0.252032i	0.400672	−	0.916222i	$-0.368777\pi$
$827$	−9.97578	−	7.24783i	−0.346892	−	0.252032i	−0.747564	+	0.664190i	$0.768777\pi$
$828$	−0.728485	+	2.24205i	−0.0253166	+	0.0779165i
$829$	0.0956826	+	0.294481i	0.00332319	+	0.0102277i	0.952704	−	0.303899i	$-0.0982884\pi$
$829$	0.0956826	+	0.294481i	0.00332319	+	0.0102277i	−0.949381	+	0.314126i	$0.898288\pi$
$830$		0			0
$831$	−36.6078	+	26.5971i	−1.26991	+	0.922644i
$832$	−5.01226	−	15.4262i	−0.173769	−	0.534806i
$833$	3.82561	−	11.7740i	0.132549	−	0.407945i
$834$	41.4499	+	30.1151i	1.43529	+	1.04280i
$835$		0			0
$836$	−5.90150	−	1.15731i	−0.204108	−	0.0400263i
$837$	−21.3198			−0.736920
$838$	−0.770653	−	0.559912i	−0.0266218	−	0.0193418i
$839$	−2.07149	+	6.37539i	−0.0715158	+	0.220103i	−0.980426	−	0.196890i	$-0.936916\pi$
$839$	−2.07149	+	6.37539i	−0.0715158	+	0.220103i	0.908910	+	0.416993i	$0.136916\pi$
$840$		0			0
$841$	−3.76040	+	2.73209i	−0.129669	+	0.0942101i
$842$	−25.0805	+	18.2220i	−0.864331	+	0.627973i
$843$	14.9380	+	45.9745i	0.514493	+	1.58345i
$844$	−0.336143	+	1.03454i	−0.0115705	+	0.0356104i
$845$		0			0
$846$	10.6187			0.365077
$847$	0.279913	−	3.82059i	0.00961792	−	0.131277i
$848$	−1.17573			−0.0403748
$849$	0.239173	+	0.173769i	0.00820840	+	0.00596375i
$850$		0			0
$851$	4.80377	+	14.7845i	0.164671	+	0.506806i
$852$	4.08354	−	2.96686i	0.139900	−	0.101643i
$853$	36.0590	−	26.1984i	1.23464	−	0.897015i	0.237407	−	0.971410i	$-0.423703\pi$
$853$	36.0590	−	26.1984i	1.23464	−	0.897015i	0.997229	+	0.0743953i	$0.0237027\pi$
$854$	−1.10884	−	3.41267i	−0.0379438	−	0.116779i
$855$		0			0
$856$	0.726117	+	0.527555i	0.0248182	+	0.0180314i
$857$	−32.2444			−1.10145			−0.550723	−	0.834688i	$-0.685648\pi$
$857$	−32.2444			−1.10145			−0.550723	+	0.834688i	$0.685648\pi$
$858$	−16.1757	−	3.17212i	−0.552229	−	0.108294i
$859$	−18.1192			−0.618220			−0.309110	−	0.951026i	$-0.600031\pi$
$859$	−18.1192			−0.618220			−0.309110	+	0.951026i	$0.600031\pi$
$860$		0			0
$861$	1.97000	−	6.06305i	0.0671375	−	0.206628i
$862$	−1.53506	−	4.72442i	−0.0522843	−	0.160915i
$863$	6.64680	−	4.82918i	0.226260	−	0.164387i	−0.468880	−	0.883262i	$-0.655342\pi$
$863$	6.64680	−	4.82918i	0.226260	−	0.164387i	0.695140	+	0.718874i	$0.255342\pi$
$864$	−4.42053	+	3.21170i	−0.150389	+	0.109264i
$865$		0			0
$866$	5.55711	−	17.1030i	0.188838	−	0.581184i
$867$	22.5598	+	16.3907i	0.766171	+	0.556656i
$868$	0.490143			0.0166365
$869$	14.9770	+	16.1144i	0.508059	+	0.546643i
$870$		0			0
$871$	−18.3841	−	13.3568i	−0.622921	−	0.452579i
$872$	−10.0650	+	30.9770i	−0.340845	+	1.04901i
$873$	2.12053	+	6.52633i	0.0717692	+	0.220883i
$874$	−64.3777	+	46.7731i	−2.17761	+	1.58212i
$875$		0			0
$876$	−0.160714	−	0.494626i	−0.00543002	−	0.0167119i
$877$	10.2073	−	31.4147i	0.344675	−	1.06080i	−0.617083	−	0.786898i	$-0.711686\pi$
$877$	10.2073	−	31.4147i	0.344675	−	1.06080i	0.961758	−	0.273901i	$-0.0883142\pi$
$878$	16.7030	+	12.1354i	0.563698	+	0.409551i
$879$	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	$0.330624\pi$
$882$	−8.13728	−	5.91208i	−0.273997	−	0.199070i
$883$	5.88905	−	18.1246i	0.198182	−	0.609943i	−0.801742	−	0.597670i	$-0.796093\pi$
$883$	5.88905	−	18.1246i	0.198182	−	0.609943i	0.999925	−	0.0122728i	$-0.00390665\pi$
$884$	−0.261443	−	0.804639i	−0.00879328	−	0.0270629i
$885$		0			0
$886$	−1.51381	+	1.09985i	−0.0508576	+	0.0369502i
$887$	−6.91223	−	21.2737i	−0.232090	−	0.714300i	−0.997494	−	0.0707497i	$-0.977461\pi$
$887$	−6.91223	−	21.2737i	−0.232090	−	0.714300i	0.765404	−	0.643550i	$-0.222539\pi$
$888$	3.44644	−	10.6070i	0.115655	−	0.355949i
$889$	−3.47970	−	2.52815i	−0.116706	−	0.0847915i
$890$		0			0
$891$	4.42393	+	36.5313i	0.148207	+	1.22384i
$892$	−2.68220			−0.0898068
$893$	−42.0545	−	30.5544i	−1.40730	−	1.02246i
$894$	−4.77939	+	14.7094i	−0.159847	+	0.491957i
$895$		0			0
$896$	−2.45218	+	1.78161i	−0.0819217	+	0.0595196i
$897$	25.5907	−	18.5927i	0.854448	−	0.620793i
$898$	−2.82161	−	8.68401i	−0.0941582	−	0.289789i
$899$	9.95920	−	30.6513i	0.332158	−	1.02228i
$900$		0			0
$901$	−0.617057			−0.0205572
$902$	35.9144	−	16.6746i	1.19582	−	0.555204i
$903$	4.77326			0.158844
$904$	13.9793	+	10.1566i	0.464945	+	0.337802i
$905$		0			0
$906$	−11.0635	−	34.0498i	−0.367559	−	1.13123i
$907$	−34.5121	+	25.0745i	−1.14596	+	0.832586i	−0.987938	−	0.154850i	$-0.950511\pi$
$907$	−34.5121	+	25.0745i	−1.14596	+	0.832586i	−0.158019	+	0.987436i	$0.550511\pi$
$908$	−1.18351	+	0.859874i	−0.0392763	+	0.0285359i
$909$	−1.25401	−	3.85943i	−0.0415927	−	0.128009i
$910$		0			0
$911$	30.0340	+	21.8210i	0.995070	+	0.722960i	0.961025	−	0.276460i	$-0.0891613\pi$
$911$	30.0340	+	21.8210i	0.995070	+	0.722960i	0.0340443	+	0.999420i	$0.489161\pi$
$912$	49.7419			1.64712
$913$	−33.4673	+	15.5385i	−1.10761	+	0.514248i
$914$	55.9756			1.85151
$915$		0			0
$916$	0.399729	−	1.23024i	0.0132074	−	0.0406483i
$917$	−0.841173	−	2.58886i	−0.0277780	−	0.0854918i
$918$	7.38408	−	5.36485i	0.243711	−	0.177066i
$919$	−2.71707	+	1.97406i	−0.0896278	+	0.0651184i	−0.631697	−	0.775216i	$-0.717641\pi$
$919$	−2.71707	+	1.97406i	−0.0896278	+	0.0651184i	0.542069	+	0.840334i	$0.317641\pi$
$920$		0			0
$921$	6.07123	−	18.6853i	0.200054	−	0.615702i
$922$	26.8975	+	19.5422i	0.885821	+	0.643587i
$923$	−18.2479			−0.600636
$924$	−0.0712802	−	0.588608i	−0.00234495	−	0.0193638i
$925$		0			0
$926$	8.43879	+	6.13114i	0.277316	+	0.201482i
$927$	−6.72912	+	20.7101i	−0.221013	+	0.680209i
$928$	−2.55245	−	7.85565i	−0.0837884	−	0.257874i
$929$	16.2929	−	11.8375i	0.534552	−	0.388375i	−0.287506	−	0.957779i	$-0.592826\pi$
$929$	16.2929	−	11.8375i	0.534552	−	0.388375i	0.822058	+	0.569404i	$0.192826\pi$
$930$		0			0
$931$	15.2156	+	46.8288i	0.498672	+	1.53475i
$932$	2.17506	−	6.69414i	0.0712463	−	0.219274i
$933$	−41.2449	−	29.9661i	−1.35030	−	0.981048i
$934$	21.1078			0.690669
$935$		0			0
$936$	−6.11449			−0.199858
$937$	8.51894	+	6.18937i	0.278302	+	0.202198i	0.718176	−	0.695861i	$-0.244977\pi$
$937$	8.51894	+	6.18937i	0.278302	+	0.202198i	−0.439875	+	0.898059i	$0.644977\pi$
$938$	−1.74161	+	5.36013i	−0.0568656	+	0.175014i
$939$	−6.80908	−	20.9562i	−0.222206	−	0.683879i
$940$		0			0
$941$	15.6743	−	11.3880i	0.510966	−	0.371239i	−0.302224	−	0.953237i	$-0.597729\pi$
$941$	15.6743	−	11.3880i	0.510966	−	0.371239i	0.813190	+	0.581998i	$0.197729\pi$
$942$	11.1271	+	34.2457i	0.362541	+	1.11579i
$943$	−23.4805	+	72.2655i	−0.764630	+	2.35329i
$944$	0.552961	+	0.401750i	0.0179974	+	0.0130758i
$945$		0			0
$946$	20.1835	+	21.7163i	0.656223	+	0.706059i
$947$	3.79793			0.123416			0.0617081	−	0.998094i	$-0.480345\pi$
$947$	3.79793			0.123416			0.0617081	+	0.998094i	$0.480345\pi$
$948$	2.75465	+	2.00137i	0.0894670	+	0.0650016i
$949$	−0.581014	+	1.78818i	−0.0188605	+	0.0580467i
$950$		0			0
$951$	−41.6973	+	30.2949i	−1.35213	+	0.982379i
$952$	−1.51007	+	1.09713i	−0.0489417	+	0.0355583i
$953$	−0.165561	−	0.509545i	−0.00536305	−	0.0165058i	0.948339	−	0.317258i	$-0.102762\pi$
$953$	−0.165561	−	0.509545i	−0.00536305	−	0.0165058i	−0.953702	+	0.300752i	$0.902762\pi$
$954$	−0.154922	+	0.476800i	−0.00501577	+	0.0154370i
$955$		0			0
$956$	1.70918			0.0552788
$957$	−38.2571	−	7.50237i	−1.23668	−	0.242517i
$958$	−18.9819			−0.613276
$959$	−2.69934	−	1.96118i	−0.0871661	−	0.0633299i
$960$		0			0
$961$	−0.0404620	−	0.124529i	−0.00130523	−	0.00401707i
$962$	−3.66706	+	2.66427i	−0.118231	+	0.0858996i
$963$	0.269764	−	0.195995i	0.00869303	−	0.00631586i
$964$	1.02239	+	3.14661i	0.0329291	+	0.101345i
$965$		0			0
$966$	−6.34697	−	4.61134i	−0.204210	−	0.148367i
$967$	−36.5291			−1.17470			−0.587348	−	0.809335i	$-0.699828\pi$
$967$	−36.5291			−1.17470			−0.587348	+	0.809335i	$0.699828\pi$
$968$	21.1399	−	25.0243i	0.679461	−	0.804311i
$969$	26.1060			0.838645
$970$		0			0
$971$	6.37443	−	19.6185i	0.204565	−	0.629587i	−0.795166	−	0.606392i	$-0.792616\pi$
$971$	6.37443	−	19.6185i	0.204565	−	0.629587i	0.999731	−	0.0231946i	$-0.00738372\pi$
$972$	0.858835	+	2.64322i	0.0275471	+	0.0847814i
$973$	5.38998	−	3.91605i	0.172795	−	0.125543i
$974$	38.4185	−	27.9126i	1.23101	−	0.894379i
$975$		0			0
$976$	8.26142	−	25.4261i	0.264442	−	0.813868i
$977$	19.0402	+	13.8335i	0.609149	+	0.442573i	0.849115	−	0.528209i	$-0.177136\pi$
$977$	19.0402	+	13.8335i	0.609149	+	0.442573i	−0.239965	+	0.970781i	$0.577136\pi$
$978$	−8.39706			−0.268508
$979$	−28.7880	−	5.64544i	−0.920069	−	0.180429i
$980$		0			0
$981$	9.78967	+	7.11261i	0.312560	+	0.227088i
$982$	−14.3830	+	44.2663i	−0.458979	+	1.41259i
$983$	−12.5688	−	38.6829i	−0.400883	−	1.23379i	−0.924284	−	0.381706i	$-0.875337\pi$
$983$	−12.5688	−	38.6829i	−0.400883	−	1.23379i	0.523400	−	0.852087i	$-0.324663\pi$
$984$	44.1033	−	32.0429i	1.40596	−	1.02149i
$985$		0			0
$986$	4.26364	+	13.1221i	0.135782	+	0.417894i
$987$	1.58368	−	4.87407i	0.0504092	−	0.155143i
$988$	2.72233	+	1.97789i	0.0866090	+	0.0629251i
$989$	−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	$0.380149\pi$
$992$	6.40051	+	4.65024i	0.203216	+	0.147645i
$993$	−6.45553	+	19.8681i	−0.204860	+	0.630494i
$994$	1.39855	+	4.30430i	0.0443594	+	0.136524i
$995$		0			0
$996$	−4.62020	+	3.35677i	−0.146397	+	0.106363i
$997$	1.64658	+	5.06765i	0.0521477	+	0.160494i	0.973739	−	0.227668i	$-0.0731101\pi$
$997$	1.64658	+	5.06765i	0.0521477	+	0.160494i	−0.921591	+	0.388162i	$0.873110\pi$
$998$	−10.8195	+	33.2991i	−0.342486	+	1.05406i
$999$	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.h.c.26.3	✓	16
5.2	odd	4		275.2.z.c.224.3		32
5.3	odd	4		275.2.z.c.224.6		32
5.4	even	2		275.2.h.e.26.2	yes	16
11.3	even	5	inner	275.2.h.c.201.3	yes	16
11.5	even	5		3025.2.a.bi.1.4		8
11.6	odd	10		3025.2.a.bm.1.5		8
55.3	odd	20		275.2.z.c.124.3		32
55.14	even	10		275.2.h.e.201.2	yes	16
55.39	odd	10		3025.2.a.bj.1.4		8
55.47	odd	20		275.2.z.c.124.6		32
55.49	even	10		3025.2.a.bn.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.h.c.26.3	✓	16	1.1	even	1	trivial
275.2.h.c.201.3	yes	16	11.3	even	5	inner
275.2.h.e.26.2	yes	16	5.4	even	2
275.2.h.e.201.2	yes	16	55.14	even	10
275.2.z.c.124.3		32	55.3	odd	20
275.2.z.c.124.6		32	55.47	odd	20
275.2.z.c.224.3		32	5.2	odd	4
275.2.z.c.224.6		32	5.3	odd	4
3025.2.a.bi.1.4		8	11.5	even	5
3025.2.a.bj.1.4		8	55.39	odd	10
3025.2.a.bm.1.5		8	11.6	odd	10
3025.2.a.bn.1.5		8	55.49	even	10

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.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06921 + 0.776830i) q^{2} +(0.626199 - 1.92724i) q^{3} +(-0.0782786 - 0.240917i) q^{4} +(2.16668 - 1.57419i) q^{6} +(-0.107618 - 0.331213i) q^{7} +(0.920262 - 2.83228i) q^{8} +(-0.895086 - 0.650318i) q^{9} +(-3.25463 - 0.638246i) q^{11} -0.513323 q^{12} +(1.50135 + 1.09079i) q^{13} +(0.142230 - 0.437738i) q^{14} +(2.77428 - 2.01563i) q^{16} +(1.45602 - 1.05786i) q^{17} +(-0.451853 - 1.39066i) q^{18} +(-2.21198 + 6.80779i) q^{19} -0.705717 q^{21} +(-2.98409 - 3.21072i) q^{22} +8.41145 q^{23} +(-4.88221 - 3.54714i) q^{24} +(0.757902 + 2.33258i) q^{26} +(3.10441 - 2.25548i) q^{27} +(-0.0713705 + 0.0518537i) q^{28} +(1.79251 + 5.51679i) q^{29} +(-4.49489 - 3.26573i) q^{31} -1.42395 q^{32} +(-3.26810 + 5.87280i) q^{33} +2.37858 q^{34} +(-0.0866064 + 0.266547i) q^{36} +(0.571099 + 1.75766i) q^{37} +(-7.65358 + 5.56065i) q^{38} +(3.04236 - 2.21041i) q^{39} +(-2.79149 + 8.59133i) q^{41} +(-0.754563 - 0.548222i) q^{42} -6.76370 q^{43} +(0.101004 + 0.834057i) q^{44} +(8.99364 + 6.53426i) q^{46} +(-2.24408 + 6.90656i) q^{47} +(-2.14736 - 6.60890i) q^{48} +(5.56500 - 4.04321i) q^{49} +(-1.12700 - 3.46854i) q^{51} +(0.145267 - 0.447085i) q^{52} +(-0.277378 - 0.201527i) q^{53} +5.07141 q^{54} -1.03712 q^{56} +(11.7351 + 8.52606i) q^{57} +(-2.36903 + 7.29112i) q^{58} +(0.0615923 + 0.189562i) q^{59} +(6.30721 - 4.58245i) q^{61} +(-2.26909 - 6.98354i) q^{62} +(-0.119067 + 0.366449i) q^{63} +(-7.07108 - 5.13744i) q^{64} +(-8.05647 + 3.74052i) q^{66} -12.2451 q^{67} +(-0.368832 - 0.267972i) q^{68} +(5.26724 - 16.2109i) q^{69} +(-7.95510 + 5.77972i) q^{71} +(-2.66559 + 1.93667i) q^{72} +(0.313085 + 0.963578i) q^{73} +(-0.754777 + 2.32297i) q^{74} +1.81326 q^{76} +(0.138860 + 1.14666i) q^{77} +4.97005 q^{78} +(-5.36632 - 3.89886i) q^{79} +(-3.42856 - 10.5520i) q^{81} +(-9.65870 + 7.01746i) q^{82} +(9.00058 - 6.53931i) q^{83} +(0.0552425 + 0.170019i) q^{84} +(-7.23185 - 5.25425i) q^{86} +11.7547 q^{87} +(-4.80281 + 8.63067i) q^{88} +8.84524 q^{89} +(0.199713 - 0.614654i) q^{91} +(-0.658436 - 2.02646i) q^{92} +(-9.10855 + 6.61775i) q^{93} +(-7.76462 + 5.64133i) q^{94} +(-0.891677 + 2.74430i) q^{96} +(-5.01780 - 3.64564i) q^{97} +9.09106 q^{98} +(2.49811 + 2.68783i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} - 2 q^{4} - 3 q^{6} + 4 q^{7} + 16 q^{8} + 8 q^{9} - 5 q^{11} - 6 q^{12} + 7 q^{13} + 3 q^{14} - 4 q^{16} + 12 q^{17} + 16 q^{18} - 13 q^{19} + 10 q^{21} + 28 q^{22} - 4 q^{23} - 43 q^{24}+ \cdots - 10 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 - 2 * q^4 - 3 * q^6 + 4 * q^7 + 16 * q^8 + 8 * q^9 - 5 * q^11 - 6 * q^12 + 7 * q^13 + 3 * q^14 - 4 * q^16 + 12 * q^17 + 16 * q^18 - 13 * q^19 + 10 * q^21 + 28 * q^22 - 4 * q^23 - 43 * q^24 - 34 * q^26 - 11 * q^27 + 47 * q^28 - 11 * q^29 - 10 * q^31 - 58 * q^32 - 34 * q^33 + 20 * q^34 + 3 * q^36 - 4 * q^37 - 36 * q^38 + 3 * q^39 + 25 * q^41 + 13 * q^42 - 28 * q^43 - q^44 + 40 * q^46 + 8 * q^47 - 106 * q^48 + 16 * q^49 + 35 * q^51 + 39 * q^52 - 22 * q^53 + 60 * q^54 - 20 * q^56 + 29 * q^57 + 6 * q^58 + 14 * q^59 + 16 * q^61 - 10 * q^62 + 73 * q^63 + 40 * q^64 - 55 * q^66 - 14 * q^67 + 83 * q^68 + 35 * q^69 - 46 * q^71 + 28 * q^72 + 7 * q^73 - 7 * q^74 - 62 * q^76 - 51 * q^77 + 34 * q^78 - 39 * q^79 - 43 * q^81 - 51 * q^82 + 28 * q^83 - 54 * q^84 + 2 * q^86 - 50 * q^87 - 76 * q^88 - 22 * q^89 - 34 * q^91 + 4 * q^92 + 3 * q^93 - 40 * q^94 + 108 * q^96 - 39 * q^97 - 52 * q^98 - 10 * q^99

Introduction

L-functions

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