LMFDB - Embedded newform 275.2.h.c.201.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(26,275)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$16$
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			201.3
Root			$-0.260198 - 0.189045i$ of defining polynomial
Character	$\chi$	$=$	275.201
Dual form			275.2.h.c.26.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06921 - 0.776830i) q^{2} +(0.626199 + 1.92724i) q^{3} +(-0.0782786 + 0.240917i) q^{4} +(2.16668 + 1.57419i) q^{6} +(-0.107618 + 0.331213i) q^{7} +(0.920262 + 2.83228i) q^{8} +(-0.895086 + 0.650318i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 16 * q - 2 * q^3 - 2 * q^4 - 3 * q^6 + 4 * q^7 + 16 * q^8 + 8 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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 $

$2$	1.06921	−	0.776830i	0.756049	−	0.549302i	−0.141647	−	0.989917i	$-0.545240\pi$
$2$	1.06921	−	0.776830i	0.756049	−	0.549302i	0.897696	+	0.440615i	$0.145240\pi$
$3$	0.626199	+	1.92724i	0.361536	+	1.11269i	0.952122	+	0.305719i	$0.0988968\pi$
$3$	0.626199	+	1.92724i	0.361536	+	1.11269i	−0.590586	+	0.806975i	$0.701103\pi$
$4$	−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	−0.969332	−	0.245754i	$-0.920965\pi$
$7$	−0.107618	+	0.331213i	−0.0406756	+	0.125187i	0.928657	+	0.370940i	$0.120965\pi$
$8$	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	−0.359788	−	0.933034i	$-0.617151\pi$
$13$	1.50135	−	1.09079i	0.416399	−	0.302532i	0.776187	+	0.630502i	$0.217151\pi$
$14$	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	0.750184	−	0.661229i	$-0.229965\pi$
$17$	1.45602	+	1.05786i	0.353137	+	0.256569i	−0.397047	+	0.917798i	$0.629965\pi$
$18$	−0.451853	+	1.39066i	−0.106503	+	0.327782i
$19$	−2.21198	−	6.80779i	−0.507464	−	1.56181i	−0.796588	−	0.604522i	$-0.793364\pi$
$19$	−2.21198	−	6.80779i	−0.507464	−	1.56181i	0.289124	−	0.957292i	$-0.406636\pi$
$20$		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	−0.634904	−	0.772591i	$-0.718960\pi$
$29$	1.79251	−	5.51679i	0.332862	−	1.02444i	0.967766	−	0.251852i	$-0.0810396\pi$
$30$		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	$0.466278\pi$
$32$	−1.42395			−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	−0.893074	−	0.449909i	$-0.851456\pi$
$37$	0.571099	−	1.75766i	0.0938881	−	0.288958i	0.986962	+	0.160952i	$0.0514563\pi$
$38$	−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	−0.892102	−	0.451834i	$-0.850770\pi$
$41$	−2.79149	−	8.59133i	−0.435958	−	1.34174i	0.456144	−	0.889906i	$-0.349230\pi$
$42$	−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	−0.970377	−	0.241596i	$-0.922329\pi$
$47$	−2.24408	−	6.90656i	−0.327332	−	1.00742i	0.643045	−	0.765829i	$-0.277671\pi$
$48$	−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	−0.606673	−	0.794952i	$-0.707496\pi$
$53$	−0.277378	+	0.201527i	−0.0381009	+	0.0276819i	0.568572	+	0.822634i	$0.307496\pi$
$54$	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	−0.946967	−	0.321330i	$-0.895870\pi$
$59$	0.0615923	−	0.189562i	0.00801863	−	0.0246788i	0.954986	+	0.296652i	$0.0958700\pi$
$60$		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	$0.533665\pi$
$62$	−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	0.00530622	−	0.999986i	$-0.498311\pi$
$71$	−7.95510	−	5.77972i	−0.944097	−	0.685927i	−0.949403	+	0.314059i	$0.898311\pi$
$72$	−2.66559	−	1.93667i	−0.314143	−	0.228238i
$73$	0.313085	−	0.963578i	0.0366439	−	0.112778i	−0.931061	−	0.364862i	$-0.881116\pi$
$73$	0.313085	−	0.963578i	0.0366439	−	0.112778i	0.967705	+	0.252084i	$0.0811160\pi$
$74$	−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	−0.847211	−	0.531257i	$-0.821720\pi$
$79$	−5.36632	+	3.89886i	−0.603758	+	0.438656i	0.243453	+	0.969913i	$0.421720\pi$
$80$		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	0.959469	−	0.281813i	$-0.0909356\pi$
$83$	9.00058	+	6.53931i	0.987942	+	0.717782i	0.0284727	+	0.999595i	$0.490936\pi$
$84$	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	−0.812626	−	0.582785i	$-0.801963\pi$
$97$	−5.01780	+	3.64564i	−0.509480	+	0.370159i	0.303146	+	0.952944i	$0.401963\pi$
$98$	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	−0.430285	−	0.902693i	$-0.641587\pi$
$101$	2.96734	−	2.15590i	0.295262	−	0.214520i	0.725547	+	0.688173i	$0.241587\pi$
$102$	1.48946	+	4.58410i	0.147479	+	0.453894i
$103$	−6.08206	+	18.7187i	−0.599283	+	1.84440i	−0.0671522	+	0.997743i	$0.521391\pi$
$103$	−6.08206	+	18.7187i	−0.599283	+	1.84440i	−0.532131	+	0.846662i	$0.678609\pi$
$104$	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	0.946454	−	0.322839i	$-0.104637\pi$
$107$	−0.0931327	−	0.286633i	−0.00900347	−	0.0277098i	−0.955457	+	0.295129i	$0.904637\pi$
$108$	−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	0.830616	−	0.556845i	$-0.187988\pi$
$113$	−1.79300	−	5.51830i	−0.168672	−	0.519118i	−0.999288	+	0.0377271i	$0.987988\pi$
$114$	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	0.934996	−	0.354659i	$-0.115403\pi$
$127$	9.99175	+	7.25943i	0.886625	+	0.644170i	−0.0483711	+	0.998829i	$0.515403\pi$
$128$	−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	0.867409	−	0.497596i	$-0.165784\pi$
$137$	7.75098	+	5.63141i	0.662211	+	0.481124i	−0.205198	+	0.978720i	$0.565784\pi$
$138$	18.2249	+	13.2412i	1.55141	+	1.12716i
$139$	5.91169	−	18.1943i	0.501423	−	1.54322i	−0.305280	−	0.952263i	$-0.598750\pi$
$139$	5.91169	−	18.1943i	0.501423	−	1.54322i	0.806702	−	0.590958i	$-0.201250\pi$
$140$		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	0.379727	−	0.925099i	$-0.376018\pi$
$149$	−4.67208	−	3.39446i	−0.382752	−	0.278085i	−0.762479	+	0.647013i	$0.776018\pi$
$150$		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	$0.716931\pi$
$152$	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	−0.968380	−	0.249481i	$-0.919740\pi$
$157$	−4.15475	−	12.7870i	−0.331585	−	1.02051i	0.636795	−	0.771033i	$-0.280260\pi$
$158$	−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	−0.682677	−	0.730720i	$-0.739184\pi$
$163$	−2.53658	+	1.84293i	−0.198680	+	0.144349i	0.483997	+	0.875070i	$0.339184\pi$
$164$	2.28831			0.178687
$165$		0			0
$166$	14.7035			1.14121
$167$	−2.12672	+	1.54515i	−0.164570	+	0.119567i	−0.667022	−	0.745038i	$-0.732431\pi$
$167$	−2.12672	+	1.54515i	−0.164570	+	0.119567i	0.502452	+	0.864605i	$0.332431\pi$
$168$	−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	0.894343	−	0.447383i	$-0.147644\pi$
$173$	−1.21218	−	3.73072i	−0.0921606	−	0.283641i	−0.986503	+	0.163741i	$0.947644\pi$
$174$	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	0.905448	−	0.424456i	$-0.139535\pi$
$179$	−1.02435	−	3.15264i	−0.0765639	−	0.235639i	−0.982012	+	0.188817i	$0.939535\pi$
$180$		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	$0.916233\pi$
$182$	0.691018	+	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	0.382806	+	0.923829i	$0.374958\pi$
$191$	−6.49420	+	19.9871i	−0.469903	+	1.44621i	−0.852709	+	0.522385i	$0.825042\pi$
$192$	−14.3290	−	10.4106i	−1.03411	−	0.751322i
$193$	−2.68051	−	1.94751i	−0.192947	−	0.140184i	0.487117	−	0.873336i	$-0.338048\pi$
$193$	−2.68051	−	1.94751i	−0.192947	−	0.140184i	−0.680065	+	0.733152i	$0.738048\pi$
$194$	−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	−0.700911	−	0.713249i	$-0.747223\pi$
$211$	−3.47407	+	2.52406i	−0.239165	+	0.173764i	0.461746	+	0.887012i	$0.347223\pi$
$212$	−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	0.998836	+	0.0482295i	$0.0153579\pi$
$223$	3.27200	+	10.0702i	0.219109	+	0.674349i	−0.779727	+	0.626120i	$0.784642\pi$
$224$	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	−0.992650	−	0.121017i	$-0.961384\pi$
$227$	−1.78459	+	5.49240i	−0.118447	+	0.364543i	0.874203	+	0.485560i	$0.161384\pi$
$228$	1.13546	+	3.49459i	0.0751978	+	0.231435i
$229$	4.13124	−	3.00152i	0.273000	−	0.198346i	−0.442858	−	0.896592i	$-0.646036\pi$
$229$	4.13124	−	3.00152i	0.273000	−	0.198346i	0.715858	+	0.698245i	$0.246036\pi$
$230$		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	0.492850	−	0.870115i	$-0.335955\pi$
$233$	22.4794	−	16.3323i	1.47268	−	1.06996i	0.979827	−	0.199848i	$-0.0640447\pi$
$234$	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	0.860701	−	0.509111i	$-0.170026\pi$
$239$	−2.08502	−	6.41702i	−0.134868	−	0.415082i	−0.995570	+	0.0940282i	$0.970026\pi$
$240$		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	0.588650	−	0.808388i	$-0.299660\pi$
$251$	24.3883	−	17.7191i	1.53938	−	1.11842i	0.950726	−	0.310033i	$-0.100340\pi$
$252$	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	−0.947497	−	0.319764i	$-0.896396\pi$
$257$	0.112162	−	0.345199i	0.00699648	−	0.0215329i	0.954494	+	0.298231i	$0.0963965\pi$
$258$	−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	0.728983	−	0.684532i	$-0.239993\pi$
$269$	4.97323	+	3.61326i	0.303223	+	0.220305i	−0.425760	+	0.904836i	$0.639993\pi$
$270$		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	$-0.0692858\pi$
$272$	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	−0.978622	−	0.205665i	$-0.934064\pi$
$277$	−18.0652	+	13.1252i	−1.08543	+	0.788614i	−0.106812	+	0.994279i	$0.534064\pi$
$278$	−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	−0.162640	−	0.986685i	$-0.552001\pi$
$281$	−19.2992	−	14.0217i	−1.15129	−	0.836463i	−0.988652	+	0.150223i	$0.952001\pi$
$282$	6.01000	−	18.4969i	0.357891	−	1.10147i
$283$	−0.0450824	−	0.138749i	−0.00267987	−	0.00824779i	0.949708	−	0.313138i	$-0.101380\pi$
$283$	−0.0450824	−	0.138749i	−0.00267987	−	0.00824779i	−0.952388	+	0.304890i	$0.901380\pi$
$284$	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	−0.857573	−	0.514363i	$-0.828029\pi$
$293$	2.37164	−	7.29917i	0.138553	−	0.426422i	0.996126	+	0.0879405i	$0.0280285\pi$
$294$	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	0.886978	+	0.461811i	$0.152800\pi$
$311$	7.77436	+	23.9270i	0.440844	+	1.35678i	−0.446135	+	0.894966i	$0.647200\pi$
$312$	−3.46071	+	10.6510i	−0.195924	+	0.602992i
$313$	8.79698	+	6.39138i	0.497235	+	0.361262i	0.807960	−	0.589238i	$-0.200572\pi$
$313$	8.79698	+	6.39138i	0.497235	+	0.361262i	−0.310725	+	0.950500i	$0.600572\pi$
$314$	−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	−0.989230	−	0.146373i	$-0.953240\pi$
$317$	−20.5768	+	14.9499i	−1.15571	+	0.839672i	−0.166480	+	0.986045i	$0.553240\pi$
$318$	−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	−0.929790	−	0.368091i	$-0.880012\pi$
$337$	0.711987	−	2.19127i	0.0387844	−	0.119366i	0.968574	+	0.248725i	$0.0800115\pi$
$338$	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	0.938642	−	0.344892i	$-0.112085\pi$
$347$	16.7779	+	12.1899i	0.900686	+	0.654387i	−0.0379558	+	0.999279i	$0.512085\pi$
$348$	−0.920138	+	2.83189i	−0.0493246	+	0.151806i
$349$	1.14723	+	3.53080i	0.0614097	+	0.189000i	0.977055	−	0.212988i	$-0.0683195\pi$
$349$	1.14723	+	3.53080i	0.0614097	+	0.189000i	−0.915645	+	0.401988i	$0.868320\pi$
$350$		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	0.575371	+	0.817893i	$0.304858\pi$
$359$	−7.02678	+	21.6262i	−0.370859	+	1.14139i	−0.946230	+	0.323494i	$0.895142\pi$
$360$		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	−0.780426	−	0.625248i	$-0.784998\pi$
$367$	4.18516	−	12.8806i	0.218464	−	0.672362i	0.998890	−	0.0471138i	$-0.0150024\pi$
$368$	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	0.452374	−	0.891829i	$-0.350577\pi$
$379$	−4.98407	−	3.62114i	−0.256015	−	0.186005i	−0.708388	+	0.705823i	$0.750577\pi$
$380$		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	−0.580243	−	0.814443i	$-0.697042\pi$
$383$	0.294214	−	0.213759i	0.0150337	−	0.0109226i	0.595277	+	0.803521i	$0.297042\pi$
$384$	−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	−0.964622	−	0.263636i	$-0.915078\pi$
$389$	−0.577201	+	1.77644i	−0.0292653	+	0.0900693i	0.935357	+	0.353705i	$0.115078\pi$
$390$		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	0.942326	−	0.334696i	$-0.108634\pi$
$401$	18.3270	+	13.3153i	0.915206	+	0.664936i	−0.0271201	+	0.999632i	$0.508634\pi$
$402$	−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	0.177816	−	0.984064i	$-0.443097\pi$
$409$	23.6348	−	17.1717i	1.16866	−	0.849085i	0.990848	+	0.134979i	$0.0430967\pi$
$410$		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	−0.957003	−	0.290078i	$-0.906319\pi$
$421$	−7.24859	−	22.3089i	−0.353275	−	1.08727i	0.603728	−	0.797190i	$-0.293681\pi$
$422$	−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	−0.658608	−	0.752486i	$-0.728854\pi$
$431$	−3.04083	+	2.20930i	−0.146472	+	0.106418i	0.512136	+	0.858904i	$0.328854\pi$
$432$	4.06627	+	12.5147i	0.195639	+	0.602114i
$433$	−4.20476	+	12.9409i	−0.202068	+	0.621901i	0.797753	+	0.602984i	$0.206022\pi$
$433$	−4.20476	+	12.9409i	−0.202068	+	0.621901i	−0.999821	+	0.0189169i	$0.993978\pi$
$434$	−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	0.940125	−	0.340830i	$-0.110708\pi$
$443$	−0.437512	−	1.34652i	−0.0207868	−	0.0639753i	−0.960912	+	0.276855i	$0.910708\pi$
$444$	−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	−0.711812	−	0.702370i	$-0.752125\pi$
$449$	−5.58939	+	4.06093i	−0.263780	+	0.191647i	0.448032	+	0.894017i	$0.352125\pi$
$450$		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	0.881776	+	0.471669i	$0.156348\pi$
$457$	34.2649	+	24.8949i	1.60284	+	1.16453i	0.721068	+	0.692865i	$0.243652\pi$
$458$	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	0.845136	−	0.534551i	$-0.179519\pi$
$467$	12.9209	+	9.38761i	0.597909	+	0.434407i	−0.247227	+	0.968958i	$0.579519\pi$
$468$	−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	0.289788	−	0.957091i	$-0.406415\pi$
$479$	−11.6195	−	8.44209i	−0.530910	−	0.385729i	−0.820698	+	0.571362i	$0.806415\pi$
$480$		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	0.803868	+	0.594808i	$0.202772\pi$
$487$	11.1034	+	34.1729i	0.503145	+	1.54852i	−0.300723	+	0.953712i	$0.597228\pi$
$488$	−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	−0.331760	−	0.943364i	$-0.607642\pi$
$491$	10.8828	−	33.4939i	0.491135	−	1.51156i	0.822895	−	0.568194i	$-0.192358\pi$
$492$	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	−0.582569	−	0.812781i	$-0.697952\pi$
$499$	8.18654	−	25.1956i	0.366480	−	1.12791i	0.949049	−	0.315128i	$-0.102048\pi$
$500$		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	−0.995722	−	0.0924004i	$-0.970546\pi$
$503$	−5.48306	−	16.8751i	−0.244478	−	0.752424i	0.751244	−	0.660024i	$-0.229454\pi$
$504$	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	0.811604	−	0.584208i	$-0.198595\pi$
$509$	−4.25018	−	13.0807i	−0.188386	−	0.579793i	−0.999990	+	0.00441502i	$0.998595\pi$
$510$		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	−0.829087	−	0.559120i	$-0.811139\pi$
$521$	3.88720	−	11.9636i	0.170301	−	0.524133i	0.999388	+	0.0349870i	$0.0111390\pi$
$522$	6.86203	+	4.98555i	0.300343	+	0.218212i
$523$	−33.0052	−	23.9797i	−1.44322	−	1.04856i	−0.987358	−	0.158508i	$-0.949331\pi$
$523$	−33.0052	−	23.9797i	−1.44322	−	1.04856i	−0.455861	−	0.890051i	$-0.650669\pi$
$524$	−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	−0.986340	−	0.164720i	$-0.947328\pi$
$541$	−26.3873	+	19.1715i	−1.13448	+	0.824247i	−0.148138	+	0.988967i	$0.547328\pi$
$542$	−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	0.906041	−	0.423190i	$-0.139090\pi$
$547$	−1.77062	−	5.44942i	−0.0757064	−	0.233000i	−0.981747	+	0.190190i	$0.939090\pi$
$548$	−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	0.218064	+	0.975935i	$0.430026\pi$
$557$	−12.5555	+	38.6418i	−0.531993	+	1.63731i	−0.750057	+	0.661373i	$0.769974\pi$
$558$	−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	−0.809318	−	0.587371i	$-0.800163\pi$
$563$	−11.8825	+	8.63316i	−0.500788	+	0.363844i	0.308530	+	0.951215i	$0.400163\pi$
$564$	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	−0.974239	−	0.225518i	$-0.927593\pi$
$569$	−7.60025	−	23.3912i	−0.318619	−	0.980609i	0.655620	−	0.755091i	$-0.272407\pi$
$570$		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	0.998952	−	0.0457674i	$-0.0145733\pi$
$577$	30.3652	+	22.0616i	1.26412	+	0.918435i	0.265166	+	0.964203i	$0.414573\pi$
$578$	−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	−0.597434	−	0.801918i	$-0.703813\pi$
$587$	8.65563	−	26.6393i	0.357256	−	1.09952i	0.954690	−	0.297603i	$-0.0961871\pi$
$588$	−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	0.913061	−	0.407824i	$-0.133712\pi$
$599$	19.7594	+	14.3561i	0.807348	+	0.586573i	−0.105713	+	0.994397i	$0.533712\pi$
$600$		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	$0.128341\pi$
$602$	−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	0.300971	−	0.953633i	$-0.402689\pi$
$607$	32.0516	−	23.2869i	1.30094	−	0.945185i	0.999964	+	0.00844827i	$0.00268920\pi$
$608$	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	0.966018	−	0.258474i	$-0.0832197\pi$
$613$	0.806291	+	2.48151i	0.0325658	+	0.100227i	−0.933452	+	0.358701i	$0.883220\pi$
$614$	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	0.906552	−	0.422093i	$-0.138705\pi$
$619$	−1.86509	−	5.74014i	−0.0749641	−	0.230716i	−0.981517	+	0.191377i	$0.938705\pi$
$620$		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	−0.944194	−	0.329391i	$-0.893157\pi$
$631$	0.333740	−	1.02714i	0.0132860	−	0.0408900i	0.957480	+	0.288501i	$0.0931567\pi$
$632$	−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	0.993084	−	0.117402i	$-0.0374566\pi$
$641$	3.05474	+	9.40153i	0.120655	+	0.371338i	−0.872429	+	0.488740i	$0.837457\pi$
$642$	0.249425	−	0.767650i	0.00984400	−	0.0302967i
$643$	23.2999	+	16.9284i	0.918858	+	0.667589i	0.943240	−	0.332113i	$-0.107762\pi$
$643$	23.2999	+	16.9284i	0.918858	+	0.667589i	−0.0243814	+	0.999703i	$0.507762\pi$
$644$	−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	−0.257245	−	0.966346i	$-0.582815\pi$
$647$	14.8118	−	10.7614i	0.582311	−	0.423074i	0.839557	+	0.543272i	$0.182815\pi$
$648$	−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	−0.549315	−	0.835616i	$-0.685111\pi$
$653$	9.87025	−	30.3775i	0.386253	−	1.18876i	0.935567	−	0.353148i	$-0.114889\pi$
$654$	−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	−0.992305	−	0.123821i	$-0.960485\pi$
$673$	−30.6425	+	22.2631i	−1.18118	+	0.858179i	−0.188878	+	0.982001i	$0.560485\pi$
$674$	−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	−0.0811701	−	0.996700i	$-0.525866\pi$
$677$	−27.4287	−	19.9281i	−1.05417	−	0.765900i	−0.973001	+	0.230800i	$0.925866\pi$
$678$	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	−0.914330	−	0.404971i	$-0.867282\pi$
$691$	−21.3377	+	15.5027i	−0.811723	+	0.589751i	0.102607	+	0.994722i	$0.467282\pi$
$692$	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	0.999013	+	0.0444171i	$0.0141430\pi$
$701$	5.74279	+	17.6745i	0.216902	+	0.667556i	−0.782111	+	0.623139i	$0.785857\pi$
$702$	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	0.166194	−	0.986093i	$-0.446852\pi$
$709$	−19.1789	−	13.9343i	−0.720280	−	0.523314i	−0.886474	+	0.462779i	$0.846852\pi$
$710$		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	0.600115	+	0.799914i	$0.295121\pi$
$719$	−9.53420	+	29.3432i	−0.355566	+	1.09432i	−0.955681	+	0.294405i	$0.904879\pi$
$720$		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	−0.998458	−	0.0555200i	$-0.982318\pi$
$733$	−4.27917	+	13.1699i	−0.158055	+	0.486442i	0.840403	+	0.541962i	$0.182318\pi$
$734$	−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	−0.916329	−	0.400427i	$-0.868862\pi$
$739$	−22.2549	+	16.1692i	−0.818661	+	0.594792i	0.0976674	+	0.995219i	$0.468862\pi$
$740$		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	0.627065	−	0.778967i	$-0.284256\pi$
$743$	2.18058	+	1.58429i	0.0799979	+	0.0581218i	−0.547067	+	0.837089i	$0.684256\pi$
$744$	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	0.992978	+	0.118300i	$0.0377443\pi$
$751$	7.10258	+	21.8595i	0.259177	+	0.797664i	−0.733801	+	0.679364i	$0.762256\pi$
$752$	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	−0.967878	−	0.251420i	$-0.919103\pi$
$757$	−28.2800	+	20.5466i	−1.02785	+	0.746780i	−0.0599765	+	0.998200i	$0.519103\pi$
$758$	−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	−0.979681	−	0.200564i	$-0.935723\pi$
$761$	−30.1151	+	21.8799i	−1.09167	+	0.793145i	−0.111990	+	0.993709i	$0.535723\pi$
$762$	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	0.962366	+	0.271757i	$0.0876047\pi$
$773$	9.55113	+	29.3954i	0.343530	+	1.05728i	−0.618836	+	0.785521i	$0.712395\pi$
$774$	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	−0.0343320	−	0.999410i	$-0.510930\pi$
$787$	−27.9255	−	20.2891i	−0.995437	−	0.723227i	−0.961105	+	0.276183i	$0.910930\pi$
$788$	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	0.724703	−	0.689061i	$-0.241977\pi$
$797$	8.28055	+	6.01617i	0.293312	+	0.213104i	−0.431391	+	0.902165i	$0.641977\pi$
$798$	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	−0.0537884	−	0.998552i	$-0.517130\pi$
$809$	−29.0143	−	21.0801i	−1.02009	−	0.741139i	−0.966301	+	0.257414i	$0.917130\pi$
$810$		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	$0.794699\pi$
$812$	−0.413999	+	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	0.689275	+	0.724500i	$0.257929\pi$
$821$	−8.43005	+	25.9450i	−0.294211	+	0.905488i	−0.983485	+	0.180987i	$0.942071\pi$
$822$	7.92900	+	24.4030i	0.276556	+	0.851151i
$823$	−1.60549	+	1.16646i	−0.0559639	+	0.0406602i	−0.615416	−	0.788203i	$-0.711012\pi$
$823$	−1.60549	+	1.16646i	−0.0559639	+	0.0406602i	0.559452	+	0.828863i	$0.311012\pi$
$824$	−58.6135			−2.04190
$825$		0			0
$826$	0.0917386			0.00319199
$827$	−9.97578	+	7.24783i	−0.346892	+	0.252032i	−0.747564	−	0.664190i	$-0.768777\pi$
$827$	−9.97578	+	7.24783i	−0.346892	+	0.252032i	0.400672	+	0.916222i	$0.368777\pi$
$828$	−0.728485	−	2.24205i	−0.0253166	−	0.0779165i
$829$	0.0956826	−	0.294481i	0.00332319	−	0.0102277i	−0.949381	−	0.314126i	$-0.898288\pi$
$829$	0.0956826	−	0.294481i	0.00332319	−	0.0102277i	0.952704	+	0.303899i	$0.0982884\pi$
$830$		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	0.908910	−	0.416993i	$-0.136916\pi$
$839$	−2.07149	−	6.37539i	−0.0715158	−	0.220103i	−0.980426	+	0.196890i	$0.936916\pi$
$840$		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	0.997229	−	0.0743953i	$-0.0237027\pi$
$853$	36.0590	+	26.1984i	1.23464	+	0.897015i	0.237407	+	0.971410i	$0.423703\pi$
$854$	−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	0.695140	−	0.718874i	$-0.255342\pi$
$863$	6.64680	+	4.82918i	0.226260	+	0.164387i	−0.468880	+	0.883262i	$0.655342\pi$
$864$	−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	0.961758	+	0.273901i	$0.0883142\pi$
$877$	10.2073	+	31.4147i	0.344675	+	1.06080i	−0.617083	+	0.786898i	$0.711686\pi$
$878$	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	0.999925	+	0.0122728i	$0.00390665\pi$
$883$	5.88905	+	18.1246i	0.198182	+	0.609943i	−0.801742	+	0.597670i	$0.796093\pi$
$884$	−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	0.765404	+	0.643550i	$0.222539\pi$
$887$	−6.91223	+	21.2737i	−0.232090	+	0.714300i	−0.997494	+	0.0707497i	$0.977461\pi$
$888$	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	−0.158019	−	0.987436i	$-0.550511\pi$
$907$	−34.5121	−	25.0745i	−1.14596	−	0.832586i	−0.987938	+	0.154850i	$0.950511\pi$
$908$	−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	0.0340443	−	0.999420i	$-0.489161\pi$
$911$	30.0340	−	21.8210i	0.995070	−	0.722960i	0.961025	+	0.276460i	$0.0891613\pi$
$912$	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	0.542069	−	0.840334i	$-0.317641\pi$
$919$	−2.71707	−	1.97406i	−0.0896278	−	0.0651184i	−0.631697	+	0.775216i	$0.717641\pi$
$920$		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	0.822058	−	0.569404i	$-0.192826\pi$
$929$	16.2929	+	11.8375i	0.534552	+	0.388375i	−0.287506	+	0.957779i	$0.592826\pi$
$930$		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	−0.439875	−	0.898059i	$-0.644977\pi$
$937$	8.51894	−	6.18937i	0.278302	−	0.202198i	0.718176	+	0.695861i	$0.244977\pi$
$938$	−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	0.813190	−	0.581998i	$-0.197729\pi$
$941$	15.6743	+	11.3880i	0.510966	+	0.371239i	−0.302224	+	0.953237i	$0.597729\pi$
$942$	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	−0.953702	−	0.300752i	$-0.902762\pi$
$953$	−0.165561	+	0.509545i	−0.00536305	+	0.0165058i	0.948339	+	0.317258i	$0.102762\pi$
$954$	−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	0.999731	+	0.0231946i	$0.00738372\pi$
$971$	6.37443	+	19.6185i	0.204565	+	0.629587i	−0.795166	+	0.606392i	$0.792616\pi$
$972$	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	−0.239965	−	0.970781i	$-0.577136\pi$
$977$	19.0402	−	13.8335i	0.609149	−	0.442573i	0.849115	+	0.528209i	$0.177136\pi$
$978$	−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	0.523400	+	0.852087i	$0.324663\pi$
$983$	−12.5688	+	38.6829i	−0.400883	+	1.23379i	−0.924284	+	0.381706i	$0.875337\pi$
$984$	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	−0.921591	−	0.388162i	$-0.873110\pi$
$997$	1.64658	−	5.06765i	0.0521477	−	0.160494i	0.973739	+	0.227668i	$0.0731101\pi$
$998$	−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.201.3	yes	16
5.2	odd	4		275.2.z.c.124.6		32
5.3	odd	4		275.2.z.c.124.3		32
5.4	even	2		275.2.h.e.201.2	yes	16
11.2	odd	10		3025.2.a.bm.1.5		8
11.4	even	5	inner	275.2.h.c.26.3	✓	16
11.9	even	5		3025.2.a.bi.1.4		8
55.4	even	10		275.2.h.e.26.2	yes	16
55.9	even	10		3025.2.a.bn.1.5		8
55.24	odd	10		3025.2.a.bj.1.4		8
55.37	odd	20		275.2.z.c.224.3		32
55.48	odd	20		275.2.z.c.224.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.h.c.26.3	✓	16	11.4	even	5	inner
275.2.h.c.201.3	yes	16	1.1	even	1	trivial
275.2.h.e.26.2	yes	16	55.4	even	10
275.2.h.e.201.2	yes	16	5.4	even	2
275.2.z.c.124.3		32	5.3	odd	4
275.2.z.c.124.6		32	5.2	odd	4
275.2.z.c.224.3		32	55.37	odd	20
275.2.z.c.224.6		32	55.48	odd	20
3025.2.a.bi.1.4		8	11.9	even	5
3025.2.a.bj.1.4		8	55.24	odd	10
3025.2.a.bm.1.5		8	11.2	odd	10
3025.2.a.bn.1.5		8	55.9	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.06921 - 0.776830i) q^{2} +(0.626199 + 1.92724i) q^{3} +(-0.0782786 + 0.240917i) q^{4} +(2.16668 + 1.57419i) q^{6} +(-0.107618 + 0.331213i) q^{7} +(0.920262 + 2.83228i) q^{8} +(-0.895086 + 0.650318i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} - 2 q^{4} - 3 q^{6} + 4 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 - 2 * q^4 - 3 * q^6 + 4 * q^7 + 16 * q^8 + 8 * q^9	\( 16 q - 2 q^{3} - 2 q^{4} - 3 q^{6} + 4 q^{7} + 16 q^{8} + 8 q^{9} - 5 q^{11} - 6 q^{12} + 7 q^{13} + 3 q^{14} - 4 q^{16} + 12 q^{17} + 16 q^{18} - 13 q^{19} + 10 q^{21} + 28 q^{22} - 4 q^{23} - 43 q^{24} - 34 q^{26} - 11 q^{27} + 47 q^{28} - 11 q^{29} - 10 q^{31} - 58 q^{32} - 34 q^{33} + 20 q^{34} + 3 q^{36} - 4 q^{37} - 36 q^{38} + 3 q^{39} + 25 q^{41} + 13 q^{42} - 28 q^{43} - q^{44} + 40 q^{46} + 8 q^{47} - 106 q^{48} + 16 q^{49} + 35 q^{51} + 39 q^{52} - 22 q^{53} + 60 q^{54} - 20 q^{56} + 29 q^{57} + 6 q^{58} + 14 q^{59} + 16 q^{61} - 10 q^{62} + 73 q^{63} + 40 q^{64} - 55 q^{66} - 14 q^{67} + 83 q^{68} + 35 q^{69} - 46 q^{71} + 28 q^{72} + 7 q^{73} - 7 q^{74} - 62 q^{76} - 51 q^{77} + 34 q^{78} - 39 q^{79} - 43 q^{81} - 51 q^{82} + 28 q^{83} - 54 q^{84} + 2 q^{86} - 50 q^{87} - 76 q^{88} - 22 q^{89} - 34 q^{91} + 4 q^{92} + 3 q^{93} - 40 q^{94} + 108 q^{96} - 39 q^{97} - 52 q^{98} - 10 q^{99}+O(q^{100}) \) 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

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