LMFDB - Embedded newform 275.2.h.e.26.4

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			26.4
Root			$2.66477 - 1.93607i$ of defining polynomial
Character	$\chi$	$=$	275.26
Dual form			275.2.h.e.201.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.85576 + 1.34829i) q^{2} +(-0.0131041 + 0.0403304i) q^{3} +(1.00792 + 3.10207i) q^{4} +(-0.0786950 + 0.0571753i) q^{6} +(0.352180 + 1.08390i) q^{7} +(-0.894346 + 2.75251i) q^{8} +(2.42560 + 1.76230i) q^{9} +O(q^{10})$	\(q+(1.85576 + 1.34829i) q^{2} +(-0.0131041 + 0.0403304i) q^{3} +(1.00792 + 3.10207i) q^{4} +(-0.0786950 + 0.0571753i) q^{6} +(0.352180 + 1.08390i) q^{7} +(-0.894346 + 2.75251i) q^{8} +(2.42560 + 1.76230i) q^{9} +(-1.53020 - 2.94253i) q^{11} -0.138316 q^{12} +(-2.27310 - 1.65150i) q^{13} +(-0.807845 + 2.48629i) q^{14} +(-0.0933071 + 0.0677915i) q^{16} +(-6.25988 + 4.54807i) q^{17} +(2.12523 + 6.54080i) q^{18} +(1.01450 - 3.12232i) q^{19} -0.0483291 q^{21} +(1.12769 - 7.52377i) q^{22} +5.54471 q^{23} +(-0.0992903 - 0.0721386i) q^{24} +(-1.99162 - 6.12957i) q^{26} +(-0.205781 + 0.149508i) q^{27} +(-3.00736 + 2.18497i) q^{28} +(-2.15164 - 6.62208i) q^{29} +(0.604302 + 0.439051i) q^{31} +5.52377 q^{32} +(0.138725 - 0.0231542i) q^{33} -17.7489 q^{34} +(-3.02196 + 9.30063i) q^{36} +(-1.48775 - 4.57883i) q^{37} +(6.09245 - 4.42643i) q^{38} +(0.0963927 - 0.0700334i) q^{39} +(2.05928 - 6.33782i) q^{41} +(-0.0896870 - 0.0651614i) q^{42} -0.698596 q^{43} +(7.58561 - 7.71264i) q^{44} +(10.2896 + 7.47586i) q^{46} +(-2.67259 + 8.22539i) q^{47} +(-0.00151135 - 0.00465146i) q^{48} +(4.61231 - 3.35104i) q^{49} +(-0.101395 - 0.312062i) q^{51} +(2.83197 - 8.71589i) q^{52} +(-7.08882 - 5.15033i) q^{53} -0.583459 q^{54} -3.29842 q^{56} +(0.112630 + 0.0818306i) q^{57} +(4.93553 - 15.1900i) q^{58} +(3.28551 + 10.1118i) q^{59} +(-7.48769 + 5.44012i) q^{61} +(0.529471 + 1.62954i) q^{62} +(-1.05591 + 3.24975i) q^{63} +(10.4374 + 7.58321i) q^{64} +(0.288659 + 0.144073i) q^{66} -6.69671 q^{67} +(-20.4179 - 14.8345i) q^{68} +(-0.0726587 + 0.223620i) q^{69} +(-6.03555 + 4.38508i) q^{71} +(-7.02007 + 5.10038i) q^{72} +(0.472132 + 1.45307i) q^{73} +(3.41267 - 10.5031i) q^{74} +10.7082 q^{76} +(2.65050 - 2.69488i) q^{77} +0.273306 q^{78} +(8.11356 + 5.89485i) q^{79} +(2.77615 + 8.54412i) q^{81} +(12.3667 - 8.98495i) q^{82} +(-3.96171 + 2.87835i) q^{83} +(-0.0487120 - 0.149920i) q^{84} +(-1.29642 - 0.941908i) q^{86} +0.295266 q^{87} +(9.46788 - 1.58026i) q^{88} -9.00636 q^{89} +(0.989521 - 3.04543i) q^{91} +(5.58865 + 17.2001i) q^{92} +(-0.0256259 + 0.0186183i) q^{93} +(-16.0499 + 11.6609i) q^{94} +(-0.0723842 + 0.222776i) q^{96} +(4.79130 + 3.48108i) q^{97} +13.0775 q^{98} +(1.47397 - 9.83406i) 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 $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.85576	+	1.34829i	1.31222	+	0.953382i	0.999994	+	0.00337397i	$0.00107397\pi$
$2$	1.85576	+	1.34829i	1.31222	+	0.953382i	0.312224	+	0.950008i	$0.398926\pi$
$3$	−0.0131041	+	0.0403304i	−0.00756568	+	0.0232848i	−0.954768	−	0.297351i	$-0.903897\pi$
$3$	−0.0131041	+	0.0403304i	−0.00756568	+	0.0232848i	0.947202	+	0.320636i	$0.103897\pi$
$4$	1.00792	+	3.10207i	0.503962	+	1.55104i
$5$		0			0
$5$		0			0
$6$	−0.0786950	+	0.0571753i	−0.0321271	+	0.0233417i
$7$	0.352180	+	1.08390i	0.133112	+	0.409675i	0.995291	−	0.0969270i	$-0.0309013\pi$
$7$	0.352180	+	1.08390i	0.133112	+	0.409675i	−0.862180	+	0.506602i	$0.830901\pi$
$8$	−0.894346	+	2.75251i	−0.316199	+	0.973161i
$9$	2.42560	+	1.76230i	0.808532	+	0.587433i
$10$		0			0
$11$	−1.53020	−	2.94253i	−0.461373	−	0.887206i
$11$	−1.53020	−	2.94253i	−0.461373	−	0.887206i
$12$	−0.138316			−0.0399283
$13$	−2.27310	−	1.65150i	−0.630444	−	0.458044i	0.226110	−	0.974102i	$-0.427399\pi$
$13$	−2.27310	−	1.65150i	−0.630444	−	0.458044i	−0.856554	+	0.516058i	$0.827399\pi$
$14$	−0.807845	+	2.48629i	−0.215906	+	0.664489i
$15$		0			0
$16$	−0.0933071	+	0.0677915i	−0.0233268	+	0.0169479i
$17$	−6.25988	+	4.54807i	−1.51824	+	1.10307i	−0.555894	+	0.831253i	$0.687624\pi$
$17$	−6.25988	+	4.54807i	−1.51824	+	1.10307i	−0.962349	+	0.271816i	$0.912376\pi$
$18$	2.12523	+	6.54080i	0.500922	+	1.54168i
$19$	1.01450	−	3.12232i	0.232743	−	0.716309i	−0.764670	−	0.644422i	$-0.777098\pi$
$19$	1.01450	−	3.12232i	0.232743	−	0.716309i	0.997413	−	0.0718870i	$-0.0229021\pi$
$20$		0			0
$21$	−0.0483291			−0.0105463
$22$	1.12769	−	7.52377i	0.240425	−	1.60407i
$23$	5.54471			1.15615			0.578076	−	0.815983i	$-0.303804\pi$
$23$	5.54471			1.15615			0.578076	+	0.815983i	$0.303804\pi$
$24$	−0.0992903	−	0.0721386i	−0.0202675	−	0.0147252i
$25$		0			0
$26$	−1.99162	−	6.12957i	−0.390588	−	1.20211i
$27$	−0.205781	+	0.149508i	−0.0396025	+	0.0287729i
$28$	−3.00736	+	2.18497i	−0.568337	+	0.412921i
$29$	−2.15164	−	6.62208i	−0.399550	−	1.22969i	−0.925361	−	0.379087i	$-0.876238\pi$
$29$	−2.15164	−	6.62208i	−0.399550	−	1.22969i	0.525811	−	0.850602i	$-0.323762\pi$
$30$		0			0
$31$	0.604302	+	0.439051i	0.108536	+	0.0788559i	0.640729	−	0.767767i	$-0.278632\pi$
$31$	0.604302	+	0.439051i	0.108536	+	0.0788559i	−0.532193	+	0.846623i	$0.678632\pi$
$32$	5.52377			0.976474
$33$	0.138725	−	0.0231542i	0.0241490	−	0.00403064i
$34$	−17.7489			−3.04391
$35$		0			0
$36$	−3.02196	+	9.30063i	−0.503660	+	1.55011i
$37$	−1.48775	−	4.57883i	−0.244585	−	0.752755i	−0.995704	−	0.0925885i	$-0.970486\pi$
$37$	−1.48775	−	4.57883i	−0.244585	−	0.752755i	0.751120	−	0.660166i	$-0.229514\pi$
$38$	6.09245	−	4.42643i	0.988326	−	0.718061i
$39$	0.0963927	−	0.0700334i	0.0154352	−	0.0112143i
$40$		0			0
$41$	2.05928	−	6.33782i	0.321606	−	0.989801i	−0.651344	−	0.758783i	$-0.725794\pi$
$41$	2.05928	−	6.33782i	0.321606	−	0.989801i	0.972949	−	0.231018i	$-0.0742056\pi$
$42$	−0.0896870	−	0.0651614i	−0.0138390	−	0.0100546i
$43$	−0.698596			−0.106535			−0.0532674	−	0.998580i	$-0.516964\pi$
$43$	−0.698596			−0.106535			−0.0532674	+	0.998580i	$0.516964\pi$
$44$	7.58561	−	7.71264i	1.14357	−	1.16272i
$45$		0			0
$46$	10.2896	+	7.47586i	1.51712	+	1.10226i
$47$	−2.67259	+	8.22539i	−0.389837	+	1.19980i	0.543073	+	0.839686i	$0.317261\pi$
$47$	−2.67259	+	8.22539i	−0.389837	+	1.19980i	−0.932910	+	0.360110i	$0.882739\pi$
$48$	−0.00151135	−	0.00465146i	−0.000218145	−	0.000671380i
$49$	4.61231	−	3.35104i	0.658902	−	0.478720i
$50$		0			0
$51$	−0.101395	−	0.312062i	−0.0141981	−	0.0436974i
$52$	2.83197	−	8.71589i	0.392723	−	1.20868i
$53$	−7.08882	−	5.15033i	−0.973724	−	0.707452i	−0.0174268	−	0.999848i	$-0.505547\pi$
$53$	−7.08882	−	5.15033i	−0.973724	−	0.707452i	−0.956297	+	0.292396i	$0.905547\pi$
$54$	−0.583459			−0.0793988
$55$		0			0
$56$	−3.29842			−0.440769
$57$	0.112630	+	0.0818306i	0.0149182	+	0.0108387i
$58$	4.93553	−	15.1900i	0.648067	−	1.99454i
$59$	3.28551	+	10.1118i	0.427737	+	1.31644i	0.900349	+	0.435168i	$0.143311\pi$
$59$	3.28551	+	10.1118i	0.427737	+	1.31644i	−0.472613	+	0.881270i	$0.656689\pi$
$60$		0			0
$61$	−7.48769	+	5.44012i	−0.958700	+	0.696536i	−0.952848	−	0.303446i	$-0.901863\pi$
$61$	−7.48769	+	5.44012i	−0.958700	+	0.696536i	−0.00585161	+	0.999983i	$0.501863\pi$
$62$	0.529471	+	1.62954i	0.0672429	+	0.206952i
$63$	−1.05591	+	3.24975i	−0.133032	+	0.409430i
$64$	10.4374	+	7.58321i	1.30467	+	0.947901i
$65$		0			0
$66$	0.288659	+	0.144073i	0.0355315	+	0.0177341i
$67$	−6.69671			−0.818133			−0.409066	−	0.912505i	$-0.634146\pi$
$67$	−6.69671			−0.818133			−0.409066	+	0.912505i	$0.634146\pi$
$68$	−20.4179	−	14.8345i	−2.47604	−	1.79895i
$69$	−0.0726587	+	0.223620i	−0.00874708	+	0.0269207i
$70$		0			0
$71$	−6.03555	+	4.38508i	−0.716288	+	0.520414i	−0.885196	−	0.465218i	$-0.845976\pi$
$71$	−6.03555	+	4.38508i	−0.716288	+	0.520414i	0.168908	+	0.985632i	$0.445976\pi$
$72$	−7.02007	+	5.10038i	−0.827324	+	0.601086i
$73$	0.472132	+	1.45307i	0.0552588	+	0.170069i	0.974877	−	0.222745i	$-0.0715016\pi$
$73$	0.472132	+	1.45307i	0.0552588	+	0.170069i	−0.919618	+	0.392814i	$0.871502\pi$
$74$	3.41267	−	10.5031i	0.396714	−	1.22096i
$75$		0			0
$76$	10.7082			1.22831
$77$	2.65050	−	2.69488i	0.302052	−	0.307110i
$78$	0.273306			0.0309459
$79$	8.11356	+	5.89485i	0.912847	+	0.663222i	0.941733	−	0.336360i	$-0.109196\pi$
$79$	8.11356	+	5.89485i	0.912847	+	0.663222i	−0.0288861	+	0.999583i	$0.509196\pi$
$80$		0			0
$81$	2.77615	+	8.54412i	0.308461	+	0.949347i
$82$	12.3667	−	8.98495i	1.36568	−	0.992222i
$83$	−3.96171	+	2.87835i	−0.434854	+	0.315940i	−0.783587	−	0.621282i	$-0.786612\pi$
$83$	−3.96171	+	2.87835i	−0.434854	+	0.315940i	0.348733	+	0.937222i	$0.386612\pi$
$84$	−0.0487120	−	0.149920i	−0.00531492	−	0.0163576i
$85$		0			0
$86$	−1.29642	−	0.941908i	−0.139797	−	0.101569i
$87$	0.295266			0.0316559
$88$	9.46788	−	1.58026i	1.00928	−	0.168456i
$89$	−9.00636			−0.954672			−0.477336	−	0.878721i	$-0.658398\pi$
$89$	−9.00636			−0.954672			−0.477336	+	0.878721i	$0.658398\pi$
$90$		0			0
$91$	0.989521	−	3.04543i	0.103730	−	0.319248i
$92$	5.58865	+	17.2001i	0.582657	+	1.79323i
$93$	−0.0256259	+	0.0186183i	−0.00265729	+	0.00193063i
$94$	−16.0499	+	11.6609i	−1.65542	+	1.20273i
$95$		0			0
$96$	−0.0723842	+	0.222776i	−0.00738769	+	0.0227370i
$97$	4.79130	+	3.48108i	0.486482	+	0.353450i	0.803830	−	0.594859i	$-0.202792\pi$
$97$	4.79130	+	3.48108i	0.486482	+	0.353450i	−0.317348	+	0.948309i	$0.602792\pi$
$98$	13.0775			1.32103
$99$	1.47397	−	9.83406i	0.148140	−	0.988360i
$100$		0			0
$101$	7.55718	+	5.49062i	0.751968	+	0.546337i	0.896436	−	0.443173i	$-0.146147\pi$
$101$	7.55718	+	5.49062i	0.751968	+	0.546337i	−0.144468	+	0.989509i	$0.546147\pi$
$102$	0.232584	−	0.715821i	0.0230293	−	0.0708768i
$103$	3.21686	+	9.90047i	0.316966	+	0.975522i	0.974937	+	0.222479i	$0.0714149\pi$
$103$	3.21686	+	9.90047i	0.316966	+	0.975522i	−0.657971	+	0.753043i	$0.728585\pi$
$104$	6.57871	−	4.77972i	0.645096	−	0.468690i
$105$		0			0
$106$	−6.21101	−	19.1155i	−0.603266	−	1.85666i
$107$	1.36747	−	4.20865i	0.132199	−	0.406866i	−0.862945	−	0.505298i	$-0.831383\pi$
$107$	1.36747	−	4.20865i	0.132199	−	0.406866i	0.995144	+	0.0984318i	$0.0313826\pi$
$108$	−0.671197	−	0.487653i	−0.0645860	−	0.0469245i
$109$	−3.22523			−0.308921			−0.154460	−	0.987999i	$-0.549364\pi$
$109$	−3.22523			−0.308921			−0.154460	+	0.987999i	$0.549364\pi$
$110$		0			0
$111$	0.204162			0.0193782
$112$	−0.106340	−	0.0772606i	−0.0100482	−	0.00730044i
$113$	1.50030	−	4.61746i	0.141137	−	0.434374i	−0.855357	−	0.518039i	$-0.826662\pi$
$113$	1.50030	−	4.61746i	0.141137	−	0.434374i	0.996494	+	0.0836643i	$0.0266623\pi$
$114$	0.0986831	+	0.303716i	0.00924252	+	0.0284456i
$115$		0			0
$116$	18.3735	−	13.3491i	1.70593	−	1.23943i
$117$	−2.60318	−	8.01175i	−0.240664	−	0.740687i
$118$	−7.53644	+	23.1948i	−0.693785	+	2.13525i
$119$	−7.13425	−	5.18333i	−0.653995	−	0.475156i
$120$		0			0
$121$	−6.31697	+	9.00532i	−0.574270	+	0.818666i
$122$	−21.2302			−1.92209
$123$	0.228622	+	0.166103i	0.0206141	+	0.0149770i
$124$	−0.752877	+	2.31712i	−0.0676103	+	0.208083i
$125$		0			0
$126$	−6.34109	+	4.60707i	−0.564910	+	0.410431i
$127$	12.6642	−	9.20111i	1.12377	−	0.816467i	0.138994	−	0.990293i	$-0.455613\pi$
$127$	12.6642	−	9.20111i	1.12377	−	0.816467i	0.984776	+	0.173827i	$0.0556132\pi$
$128$	5.73105	+	17.6383i	0.506558	+	1.55902i
$129$	0.00915450	−	0.0281746i	0.000806009	−	0.00248064i
$130$		0			0
$131$	−21.8905			−1.91258			−0.956291	−	0.292415i	$-0.905541\pi$
$131$	−21.8905			−1.91258			−0.956291	+	0.292415i	$0.905541\pi$
$132$	0.211651	+	0.406998i	0.0184218	+	0.0354246i
$133$	3.74157			0.324435
$134$	−12.4275	−	9.02908i	−1.07357	−	0.779994i
$135$		0			0
$136$	−6.92012	−	21.2979i	−0.593396	−	1.82628i
$137$	−7.74963	+	5.63043i	−0.662095	+	0.481040i	−0.867370	−	0.497664i	$-0.834191\pi$
$137$	−7.74963	+	5.63043i	−0.662095	+	0.481040i	0.205275	+	0.978704i	$0.434191\pi$
$138$	−0.436341	+	0.317020i	−0.0371438	+	0.0269866i
$139$	3.86417	+	11.8927i	0.327755	+	1.00872i	0.970182	+	0.242378i	$0.0779275\pi$
$139$	3.86417	+	11.8927i	0.327755	+	1.00872i	−0.642427	+	0.766347i	$0.722073\pi$
$140$		0			0
$141$	−0.296711	−	0.215573i	−0.0249876	−	0.0181545i
$142$	−17.1129			−1.43608
$143$	−1.38130	+	9.21578i	−0.115510	+	0.770663i
$144$	−0.345794			−0.0288162
$145$		0			0
$146$	−1.08300	+	3.33312i	−0.0896294	+	0.275851i
$147$	0.0747084	+	0.229929i	0.00616185	+	0.0189642i
$148$	12.7043	−	9.23022i	1.04429	−	0.758719i
$149$	−6.72017	+	4.88249i	−0.550538	+	0.399989i	−0.827984	−	0.560752i	$-0.810512\pi$
$149$	−6.72017	+	4.88249i	−0.550538	+	0.399989i	0.277446	+	0.960741i	$0.410512\pi$
$150$		0			0
$151$	3.99542	−	12.2966i	0.325143	−	1.00069i	−0.646233	−	0.763140i	$-0.723657\pi$
$151$	3.99542	−	12.2966i	0.325143	−	1.00069i	0.971376	−	0.237547i	$-0.0763434\pi$
$152$	7.68691	+	5.58487i	0.623491	+	0.452993i
$153$	−23.1990			−1.87553
$154$	8.55215	−	1.42741i	0.689152	−	0.115024i
$155$		0			0
$156$	0.314405	+	0.228429i	0.0251725	+	0.0182889i
$157$	2.38088	−	7.32758i	0.190015	−	0.584805i	−0.809984	−	0.586452i	$-0.800524\pi$
$157$	2.38088	−	7.32758i	0.190015	−	0.584805i	0.999999	+	0.00164706i	$0.000524275\pi$
$158$	7.10886	+	21.8788i	0.565550	+	1.74059i
$159$	0.300608	−	0.218404i	0.0238397	−	0.0173206i
$160$		0			0
$161$	1.95274	+	6.00990i	0.153897	+	0.473647i
$162$	−6.36806	+	19.5989i	−0.500322	+	1.53983i
$163$	17.5390	+	12.7428i	1.37376	+	0.998093i	0.997433	+	0.0716050i	$0.0228121\pi$
$163$	17.5390	+	12.7428i	1.37376	+	0.998093i	0.376324	+	0.926488i	$0.377188\pi$
$164$	21.7360			1.69729
$165$		0			0
$166$	−11.2328			−0.871835
$167$	−11.4995	−	8.35490i	−0.889861	−	0.646522i	0.0459807	−	0.998942i	$-0.485359\pi$
$167$	−11.4995	−	8.35490i	−0.889861	−	0.646522i	−0.935842	+	0.352420i	$0.885359\pi$
$168$	0.0432229	−	0.133026i	0.00333472	−	0.0102632i
$169$	−1.57771	−	4.85569i	−0.121362	−	0.373515i
$170$		0			0
$171$	7.96324	−	5.78563i	0.608964	−	0.442438i
$172$	−0.704132	−	2.16709i	−0.0536895	−	0.165239i
$173$	5.88217	−	18.1034i	0.447213	−	1.37638i	−0.432826	−	0.901478i	$-0.642483\pi$
$173$	5.88217	−	18.1034i	0.447213	−	1.37638i	0.880039	−	0.474902i	$-0.157517\pi$
$174$	0.547943	+	0.398104i	0.0415394	+	0.0301802i
$175$		0			0
$176$	0.342257	+	0.170824i	0.0257986	+	0.0128764i
$177$	−0.450865			−0.0338891
$178$	−16.7136	−	12.1431i	−1.25274	−	0.910168i
$179$	−3.28731	+	10.1173i	−0.245705	+	0.756202i	0.749815	+	0.661648i	$0.230143\pi$
$179$	−3.28731	+	10.1173i	−0.245705	+	0.756202i	−0.995520	+	0.0945541i	$0.969857\pi$
$180$		0			0
$181$	12.4293	−	9.03045i	0.923866	−	0.671228i	−0.0206172	−	0.999787i	$-0.506563\pi$
$181$	12.4293	−	9.03045i	0.923866	−	0.671228i	0.944483	+	0.328559i	$0.106563\pi$
$182$	5.94242	−	4.31742i	0.440482	−	0.320029i
$183$	−0.121283	−	0.373269i	−0.00896547	−	0.0275929i
$184$	−4.95889	+	15.2619i	−0.365574	+	1.12512i
$185$		0			0
$186$	−0.0726584			−0.00532757
$187$	22.9617	+	11.4604i	1.67913	+	0.838070i
$188$	−28.2095			−2.05739
$189$	−0.234524	−	0.170392i	−0.0170591	−	0.0123942i
$190$		0			0
$191$	4.60845	+	14.1834i	0.333456	+	1.02627i	0.967478	+	0.252956i	$0.0814029\pi$
$191$	4.60845	+	14.1834i	0.333456	+	1.02627i	−0.634022	+	0.773315i	$0.718597\pi$
$192$	−0.442607	+	0.321573i	−0.0319424	+	0.0232075i
$193$	−5.40812	+	3.92923i	−0.389285	+	0.282832i	−0.765162	−	0.643837i	$-0.777341\pi$
$193$	−5.40812	+	3.92923i	−0.389285	+	0.282832i	0.375878	+	0.926669i	$0.377341\pi$
$194$	4.19799	+	12.9201i	0.301398	+	0.927607i
$195$		0			0
$196$	15.0440	+	10.9301i	1.07457	+	0.780724i
$197$	8.96183			0.638504			0.319252	−	0.947670i	$-0.396568\pi$
$197$	8.96183			0.638504			0.319252	+	0.947670i	$0.396568\pi$
$198$	15.9945	−	16.2623i	1.13668	−	1.15571i
$199$	13.7830			0.977053			0.488527	−	0.872549i	$-0.337534\pi$
$199$	13.7830			0.977053			0.488527	+	0.872549i	$0.337534\pi$
$200$		0			0
$201$	0.0877546	−	0.270081i	0.00618973	−	0.0190500i
$202$	6.62137	+	20.3785i	0.465878	+	1.43383i
$203$	6.41989	−	4.66433i	0.450588	−	0.327371i
$204$	0.865840	−	0.629069i	0.0606209	−	0.0440437i
$205$		0			0
$206$	−7.37896	+	22.7101i	−0.514117	+	1.58229i
$207$	13.4492	+	9.77144i	0.934786	+	0.679162i
$208$	0.324054			0.0224691
$209$	−10.7399	+	1.79257i	−0.742896	+	0.123994i
$210$		0			0
$211$	−7.10704	−	5.16357i	−0.489269	−	0.355475i	0.315634	−	0.948881i	$-0.397783\pi$
$211$	−7.10704	−	5.16357i	−0.489269	−	0.355475i	−0.804903	+	0.593406i	$0.797783\pi$
$212$	8.83169	−	27.1812i	0.606563	−	1.86681i
$213$	−0.0977614	−	0.300879i	−0.00669850	−	0.0206159i
$214$	8.21217	−	5.96649i	0.561373	−	0.407861i
$215$		0			0
$216$	−0.227485	−	0.700127i	−0.0154784	−	0.0476376i
$217$	−0.263064	+	0.809627i	−0.0178579	+	0.0549610i
$218$	−5.98524	−	4.34853i	−0.405372	−	0.294520i
$219$	−0.0647899			−0.00437809
$220$		0			0
$221$	21.7405			1.46242
$222$	0.378874	+	0.275268i	0.0254284	+	0.0184748i
$223$	2.79247	−	8.59432i	0.186997	−	0.575519i	−0.812980	−	0.582292i	$-0.802156\pi$
$223$	2.79247	−	8.59432i	0.186997	−	0.575519i	0.999977	+	0.00677342i	$0.00215606\pi$
$224$	1.94536	+	5.98721i	0.129980	+	0.400037i
$225$		0			0
$226$	9.00986	−	6.54605i	0.599327	−	0.435437i
$227$	1.75583	+	5.40389i	0.116539	+	0.358669i	0.992265	−	0.124139i	$-0.0396169\pi$
$227$	1.75583	+	5.40389i	0.116539	+	0.358669i	−0.875726	+	0.482808i	$0.839617\pi$
$228$	−0.140322	+	0.431866i	−0.00929303	+	0.0286010i
$229$	−4.76848	−	3.46450i	−0.315110	−	0.228941i	0.418976	−	0.907997i	$-0.362389\pi$
$229$	−4.76848	−	3.46450i	−0.315110	−	0.228941i	−0.734086	+	0.679057i	$0.762389\pi$
$230$		0			0
$231$	0.0739531	+	0.142210i	0.00486576	+	0.00935671i
$232$	20.1517			1.32302
$233$	0.0331172	+	0.0240610i	0.00216958	+	0.00157629i	0.588870	−	0.808228i	$-0.299573\pi$
$233$	0.0331172	+	0.0240610i	0.00216958	+	0.00157629i	−0.586700	+	0.809804i	$0.699573\pi$
$234$	5.97127	−	18.3777i	0.390354	−	1.20139i
$235$		0			0
$236$	−28.0558	+	20.3838i	−1.82628	+	1.32687i
$237$	−0.344063	+	0.249976i	−0.0223493	+	0.0162377i
$238$	−6.25081	−	19.2380i	−0.405180	−	1.24702i
$239$	−2.32818	+	7.16539i	−0.150597	+	0.463491i	−0.997688	−	0.0679571i	$-0.978352\pi$
$239$	−2.32818	+	7.16539i	−0.150597	+	0.463491i	0.847091	+	0.531448i	$0.178352\pi$
$240$		0			0
$241$	−0.718212			−0.0462641			−0.0231321	−	0.999732i	$-0.507364\pi$
$241$	−0.718212			−0.0462641			−0.0231321	+	0.999732i	$0.507364\pi$
$242$	−23.8645	+	8.19460i	−1.53407	+	0.526769i
$243$	−1.14404			−0.0733904
$244$	−24.4227	−	17.7441i	−1.56350	−	1.13595i
$245$		0			0
$246$	0.200311	+	0.616495i	0.0127714	+	0.0393063i
$247$	−7.46258	+	5.42188i	−0.474833	+	0.344986i
$248$	−1.74895	+	1.27069i	−0.111058	+	0.0806886i
$249$	−0.0641702	−	0.197496i	−0.00406662	−	0.0125158i
$250$		0			0
$251$	5.22156	+	3.79369i	0.329582	+	0.239455i	0.740253	−	0.672328i	$-0.234706\pi$
$251$	5.22156	+	3.79369i	0.329582	+	0.239455i	−0.410671	+	0.911783i	$0.634706\pi$
$252$	−11.1452			−0.702083
$253$	−8.48452	−	16.3155i	−0.533417	−	1.02575i
$254$	35.9075			2.25304
$255$		0			0
$256$	−5.17266	+	15.9198i	−0.323291	+	0.994988i
$257$	−7.24342	−	22.2930i	−0.451832	−	1.39060i	−0.874814	−	0.484459i	$-0.839017\pi$
$257$	−7.24342	−	22.2930i	−0.451832	−	1.39060i	0.422982	−	0.906138i	$-0.360983\pi$
$258$	0.0549760	−	0.0399424i	0.00342266	−	0.00248671i
$259$	4.43903	−	3.22514i	0.275828	−	0.200401i
$260$		0			0
$261$	6.45106	−	19.8543i	0.399311	−	1.22895i
$262$	−40.6235	−	29.5147i	−2.50973	−	1.82342i
$263$	20.1226			1.24081			0.620405	−	0.784281i	$-0.286968\pi$
$263$	20.1226			1.24081			0.620405	+	0.784281i	$0.286968\pi$
$264$	−0.0603361	+	0.402551i	−0.00371343	+	0.0247753i
$265$		0			0
$266$	6.94344	+	5.04470i	0.425729	+	0.309311i
$267$	0.118021	−	0.363230i	0.00722274	−	0.0222293i
$268$	−6.74977	−	20.7737i	−0.412308	−	1.26895i
$269$	−0.570215	+	0.414286i	−0.0347666	+	0.0252594i	−0.605033	−	0.796200i	$-0.706840\pi$
$269$	−0.570215	+	0.414286i	−0.0347666	+	0.0252594i	0.570266	+	0.821460i	$0.306840\pi$
$270$		0			0
$271$	−6.31438	−	19.4337i	−0.383571	−	1.18051i	−0.937512	−	0.347954i	$-0.886876\pi$
$271$	−6.31438	−	19.4337i	−0.383571	−	1.18051i	0.553940	−	0.832556i	$-0.313124\pi$
$272$	0.275770	−	0.848734i	0.0167210	−	0.0514620i
$273$	0.109857	+	0.0798155i	0.00664883	+	0.00483065i
$274$	−21.9729			−1.32743
$275$		0			0
$276$	−0.766921			−0.0461632
$277$	−12.4119	−	9.01780i	−0.745761	−	0.541827i	0.148749	−	0.988875i	$-0.452475\pi$
$277$	−12.4119	−	9.01780i	−0.745761	−	0.541827i	−0.894510	+	0.447048i	$0.852475\pi$
$278$	−8.86379	+	27.2800i	−0.531615	+	1.63614i
$279$	0.692053	+	2.12992i	0.0414321	+	0.127515i
$280$		0			0
$281$	−11.1904	+	8.13034i	−0.667566	+	0.485015i	−0.869210	−	0.494444i	$-0.835372\pi$
$281$	−11.1904	+	8.13034i	−0.667566	+	0.485015i	0.201644	+	0.979459i	$0.435372\pi$
$282$	−0.259969	−	0.800103i	−0.0154809	−	0.0476454i
$283$	5.25199	−	16.1640i	0.312199	−	0.960848i	−0.664694	−	0.747116i	$-0.731438\pi$
$283$	5.25199	−	16.1640i	0.312199	−	0.960848i	0.976892	−	0.213732i	$-0.0685620\pi$
$284$	−19.6862	−	14.3029i	−1.16816	−	0.848719i
$285$		0			0
$286$	−14.9889	+	15.2399i	−0.886311	+	0.901152i
$287$	7.59479			0.448306
$288$	13.3984	+	9.73453i	0.789510	+	0.573613i
$289$	13.2479	−	40.7728i	0.779287	−	2.39840i
$290$		0			0
$291$	−0.203179	+	0.147618i	−0.0119106	+	0.00865353i
$292$	−4.03166	+	2.92917i	−0.235935	+	0.171417i
$293$	0.259404	+	0.798364i	0.0151546	+	0.0466409i	0.958348	−	0.285604i	$-0.0921941\pi$
$293$	0.259404	+	0.798364i	0.0151546	+	0.0466409i	−0.943193	+	0.332245i	$0.892194\pi$
$294$	−0.171369	+	0.527421i	−0.00999446	+	0.0307598i
$295$		0			0
$296$	13.9338			0.809889
$297$	0.754819	+	0.376738i	0.0437990	+	0.0218606i
$298$	−19.0540			−1.10377
$299$	−12.6037	−	9.15710i	−0.728889	−	0.529569i
$300$		0			0
$301$	−0.246032	−	0.757207i	−0.0141810	−	0.0436447i
$302$	23.9939	−	17.4326i	1.38070	−	1.00313i
$303$	−0.320469	+	0.232834i	−0.0184105	+	0.0133760i
$304$	0.117007	+	0.360109i	0.00671079	+	0.0206537i
$305$		0			0
$306$	−43.0517	−	31.2789i	−2.46110	−	1.78810i
$307$	6.41496			0.366121			0.183060	−	0.983102i	$-0.441400\pi$
$307$	6.41496			0.366121			0.183060	+	0.983102i	$0.441400\pi$
$308$	11.0312	+	5.50580i	0.628562	+	0.313722i
$309$	−0.441444			−0.0251129
$310$		0			0
$311$	9.38914	−	28.8968i	0.532410	−	1.63859i	−0.216771	−	0.976222i	$-0.569553\pi$
$311$	9.38914	−	28.8968i	0.532410	−	1.63859i	0.749181	−	0.662366i	$-0.230447\pi$
$312$	0.106559	+	0.327956i	0.00603274	+	0.0185669i
$313$	1.90239	−	1.38217i	0.107529	−	0.0781247i	−0.532721	−	0.846291i	$-0.678831\pi$
$313$	1.90239	−	1.38217i	0.107529	−	0.0781247i	0.640251	+	0.768166i	$0.278831\pi$
$314$	14.2980	−	10.3881i	0.806883	−	0.586235i
$315$		0			0
$316$	−10.1084	+	31.1104i	−0.568641	+	1.75010i
$317$	0.650112	+	0.472334i	0.0365139	+	0.0265289i	0.605893	−	0.795547i	$-0.292816\pi$
$317$	0.650112	+	0.472334i	0.0365139	+	0.0265289i	−0.569379	+	0.822075i	$0.692816\pi$
$318$	0.852326			0.0477961
$319$	−16.1932	+	16.4644i	−0.906646	+	0.921828i
$320$		0			0
$321$	0.151817	+	0.110302i	0.00847360	+	0.00615643i
$322$	−4.47927	+	13.7858i	−0.249620	+	0.768251i
$323$	7.84986	+	24.1594i	0.436778	+	1.34426i
$324$	−23.7063	+	17.2236i	−1.31702	+	0.956869i
$325$		0			0
$326$	15.3671	+	47.2951i	0.851105	+	2.61943i
$327$	0.0422638	−	0.130075i	0.00233720	−	0.00719315i
$328$	15.6032	+	11.3364i	0.861544	+	0.625948i
$329$	−9.85672			−0.543418
$330$		0			0
$331$	29.5735			1.62551			0.812753	−	0.582608i	$-0.197968\pi$
$331$	29.5735			1.62551			0.812753	+	0.582608i	$0.197968\pi$
$332$	−12.9220	−	9.38835i	−0.709184	−	0.515253i
$333$	4.46058	−	13.7282i	0.244438	−	0.752303i
$334$	−10.0755	−	31.0093i	−0.551309	−	1.69676i
$335$		0			0
$336$	0.00450944	−	0.00327630i	0.000246010	−	0.000178737i
$337$	8.80022	+	27.0843i	0.479378	+	1.47537i	0.839961	+	0.542648i	$0.182578\pi$
$337$	8.80022	+	27.0843i	0.479378	+	1.47537i	−0.360582	+	0.932727i	$0.617422\pi$
$338$	3.61902	−	11.1382i	0.196848	−	0.605837i
$339$	0.166564	+	0.121016i	0.00904651	+	0.00657267i
$340$		0			0
$341$	0.367218	−	2.45001i	0.0198860	−	0.132676i
$342$	22.5785			1.22091
$343$	11.7107	+	8.50831i	0.632318	+	0.459406i
$344$	0.624786	−	1.92290i	0.0336862	−	0.103676i
$345$		0			0
$346$	35.3245	−	25.6648i	1.89906	−	1.37975i
$347$	−6.53075	+	4.74487i	−0.350589	+	0.254718i	−0.749116	−	0.662439i	$-0.769522\pi$
$347$	−6.53075	+	4.74487i	−0.350589	+	0.254718i	0.398527	+	0.917157i	$0.369522\pi$
$348$	0.297606	+	0.915937i	0.0159534	+	0.0490994i
$349$	−9.27242	+	28.5376i	−0.496341	+	1.52758i	0.318514	+	0.947918i	$0.396816\pi$
$349$	−9.27242	+	28.5376i	−0.496341	+	1.52758i	−0.814856	+	0.579664i	$0.803184\pi$
$350$		0			0
$351$	0.714673			0.0381464
$352$	−8.45247	−	16.2539i	−0.450518	−	0.866334i
$353$	3.17893			0.169197			0.0845987	−	0.996415i	$-0.473039\pi$
$353$	3.17893			0.169197			0.0845987	+	0.996415i	$0.473039\pi$
$354$	−0.836695	−	0.607895i	−0.0444699	−	0.0323092i
$355$		0			0
$356$	−9.07772	−	27.9384i	−0.481118	−	1.48073i
$357$	0.302534	−	0.219804i	0.0160118	−	0.0116333i
$358$	−19.7414	+	14.3430i	−1.04337	+	0.758051i
$359$	−0.905888	−	2.78804i	−0.0478110	−	0.147147i	0.924301	−	0.381664i	$-0.124649\pi$
$359$	−0.905888	−	2.78804i	−0.0478110	−	0.147147i	−0.972112	+	0.234517i	$0.924649\pi$
$360$		0			0
$361$	6.65166	+	4.83271i	0.350087	+	0.254353i
$362$	35.2415			1.85225
$363$	−0.280410	−	0.372773i	−0.0147177	−	0.0195655i
$364$	10.4445			0.547441
$365$		0			0
$366$	0.278203	−	0.856221i	0.0145419	−	0.0447554i
$367$	−5.65439	−	17.4024i	−0.295157	−	0.908399i	−0.983169	−	0.182700i	$-0.941516\pi$
$367$	−5.65439	−	17.4024i	−0.295157	−	0.908399i	0.688012	−	0.725699i	$-0.258484\pi$
$368$	−0.517361	+	0.375885i	−0.0269693	+	0.0195943i
$369$	16.1641	−	11.7439i	0.841470	−	0.611364i
$370$		0			0
$371$	3.08589	−	9.49740i	0.160212	−	0.493081i
$372$	−0.0835844	−	0.0607276i	−0.00433365	−	0.00314858i
$373$	−8.37860			−0.433827			−0.216914	−	0.976191i	$-0.569599\pi$
$373$	−8.37860			−0.433827			−0.216914	+	0.976191i	$0.569599\pi$
$374$	27.1594	+	52.2267i	1.40438	+	2.70058i
$375$		0			0
$376$	−20.2503	−	14.7127i	−1.04433	−	0.758749i
$377$	−6.04548	+	18.6061i	−0.311358	+	0.958261i
$378$	−0.205483	−	0.632411i	−0.0105689	−	0.0325277i
$379$	11.6010	−	8.42861i	0.595903	−	0.432949i	−0.248519	−	0.968627i	$-0.579944\pi$
$379$	11.6010	−	8.42861i	0.595903	−	0.432949i	0.844422	+	0.535678i	$0.179944\pi$
$380$		0			0
$381$	0.205130	+	0.631327i	0.0105091	+	0.0323438i
$382$	−10.5711	+	32.5344i	−0.540862	+	1.66460i
$383$	−22.0030	−	15.9861i	−1.12430	−	0.816852i	−0.139445	−	0.990230i	$-0.544532\pi$
$383$	−22.0030	−	15.9861i	−1.12430	−	0.816852i	−0.984855	+	0.173378i	$0.944532\pi$
$384$	−0.786462			−0.0401340
$385$		0			0
$386$	−15.3339			−0.780473
$387$	−1.69451	−	1.23113i	−0.0861369	−	0.0625821i
$388$	−5.96929	+	18.3716i	−0.303045	+	0.932677i
$389$	6.19659	+	19.0711i	0.314180	+	0.966945i	0.976091	+	0.217363i	$0.0697456\pi$
$389$	6.19659	+	19.0711i	0.314180	+	0.966945i	−0.661911	+	0.749582i	$0.730254\pi$
$390$		0			0
$391$	−34.7092	+	25.2177i	−1.75532	+	1.27532i
$392$	5.09879	+	15.6924i	0.257528	+	0.792588i
$393$	0.286856	−	0.882853i	0.0144700	−	0.0445340i
$394$	16.6310	+	12.0831i	0.837856	+	0.608738i
$395$		0			0
$396$	31.9916	−	5.33962i	1.60764	−	0.268326i
$397$	29.4343			1.47727			0.738633	−	0.674108i	$-0.235472\pi$
$397$	29.4343			1.47727			0.738633	+	0.674108i	$0.235472\pi$
$398$	25.5780	+	18.5835i	1.28211	+	0.931506i
$399$	−0.0490300	+	0.150899i	−0.00245457	+	0.00755439i
$400$		0			0
$401$	−15.5521	+	11.2993i	−0.776637	+	0.564260i	−0.903968	−	0.427601i	$-0.859359\pi$
$401$	−15.5521	+	11.2993i	−0.776637	+	0.564260i	0.127331	+	0.991860i	$0.459359\pi$
$402$	0.526997	−	0.382886i	0.0262842	−	0.0190966i
$403$	−0.648543	−	1.99601i	−0.0323062	−	0.0994283i
$404$	−9.41521	+	28.9770i	−0.468424	+	1.44166i
$405$		0			0
$406$	18.2026			0.903380
$407$	−11.1968	+	11.3843i	−0.555004	+	0.564298i
$408$	0.949637			0.0470140
$409$	10.3483	+	7.51846i	0.511689	+	0.371764i	0.813464	−	0.581615i	$-0.197579\pi$
$409$	10.3483	+	7.51846i	0.511689	+	0.371764i	−0.301775	+	0.953379i	$0.597579\pi$
$410$		0			0
$411$	−0.125525	−	0.386327i	−0.00619171	−	0.0190561i
$412$	−27.4696	+	19.9578i	−1.35333	+	0.983252i
$413$	−9.80302	+	7.12231i	−0.482375	+	0.350466i
$414$	11.7838	+	36.2668i	0.579143	+	1.78242i
$415$		0			0
$416$	−12.5561	−	9.12251i	−0.615612	−	0.447268i
$417$	−0.530273			−0.0259676
$418$	−22.3476	−	11.1539i	−1.09306	−	0.545556i
$419$	4.22237			0.206276			0.103138	−	0.994667i	$-0.467112\pi$
$419$	4.22237			0.206276			0.103138	+	0.994667i	$0.467112\pi$
$420$		0			0
$421$	0.252842	−	0.778168i	0.0123228	−	0.0379256i	−0.944706	−	0.327918i	$-0.893653\pi$
$421$	0.252842	−	0.778168i	0.0123228	−	0.0379256i	0.957029	+	0.289993i	$0.0936529\pi$
$422$	−6.22697	−	19.1646i	−0.303124	−	0.932920i
$423$	−20.9782	+	15.2416i	−1.02000	+	0.741070i
$424$	20.5162	−	14.9059i	0.996355	−	0.723894i
$425$		0			0
$426$	0.224249	−	0.690168i	0.0108649	−	0.0334388i
$427$	−8.53355	−	6.19999i	−0.412968	−	0.300039i
$428$	14.4339			0.697687
$429$	−0.353575	−	0.176473i	−0.0170708	−	0.00852021i
$430$		0			0
$431$	4.70010	+	3.41482i	0.226396	+	0.164486i	0.695201	−	0.718815i	$-0.255315\pi$
$431$	4.70010	+	3.41482i	0.226396	+	0.164486i	−0.468805	+	0.883302i	$0.655315\pi$
$432$	0.00906539	−	0.0279004i	0.000436159	−	0.00134236i
$433$	−4.82611	−	14.8532i	−0.231928	−	0.713801i	−0.997514	−	0.0704677i	$-0.977551\pi$
$433$	−4.82611	−	14.8532i	−0.231928	−	0.713801i	0.765586	−	0.643334i	$-0.222449\pi$
$434$	−1.57979	+	1.14779i	−0.0758324	+	0.0550954i
$435$		0			0
$436$	−3.25079	−	10.0049i	−0.155684	−	0.479147i
$437$	5.62513	−	17.3124i	0.269086	−	0.828163i
$438$	−0.120234	−	0.0873553i	−0.00574501	−	0.00417400i
$439$	21.6614			1.03384			0.516922	−	0.856032i	$-0.327078\pi$
$439$	21.6614			1.03384			0.516922	+	0.856032i	$0.327078\pi$
$440$		0			0
$441$	17.0931			0.813959
$442$	40.3450	+	29.3124i	1.91902	+	1.39425i
$443$	−8.87659	+	27.3193i	−0.421739	+	1.29798i	0.484343	+	0.874878i	$0.339059\pi$
$443$	−8.87659	+	27.3193i	−0.421739	+	1.29798i	−0.906082	+	0.423102i	$0.860941\pi$
$444$	0.205779	+	0.633324i	0.00976586	+	0.0300562i
$445$		0			0
$446$	16.7697	−	12.1839i	0.794071	−	0.576926i
$447$	−0.108851	−	0.335008i	−0.00514846	−	0.0158453i
$448$	−4.54359	+	13.9837i	−0.214664	+	0.660669i
$449$	−14.1841	−	10.3053i	−0.669389	−	0.486339i	0.200432	−	0.979708i	$-0.435766\pi$
$449$	−14.1841	−	10.3053i	−0.669389	−	0.486339i	−0.869821	+	0.493368i	$0.835766\pi$
$450$		0			0
$451$	−21.8003	+	3.63863i	−1.02654	+	0.171336i
$452$	15.8359			0.744858
$453$	0.443572	+	0.322274i	0.0208408	+	0.0151417i
$454$	−4.02760	+	12.3957i	−0.189024	+	0.581757i
$455$		0			0
$456$	−0.325970	+	0.236831i	−0.0152650	+	0.0110906i
$457$	−15.9851	+	11.6139i	−0.747753	+	0.543275i	−0.895130	−	0.445806i	$-0.852917\pi$
$457$	−15.9851	+	11.6139i	−0.747753	+	0.543275i	0.147376	+	0.989080i	$0.452917\pi$
$458$	−4.17800	−	12.8585i	−0.195225	−	0.600840i
$459$	0.608188	−	1.87181i	0.0283878	−	0.0873686i
$460$		0			0
$461$	−12.9859			−0.604812			−0.302406	−	0.953179i	$-0.597790\pi$
$461$	−12.9859			−0.604812			−0.302406	+	0.953179i	$0.597790\pi$
$462$	−0.0545004	+	0.363617i	−0.00253559	+	0.0169170i
$463$	9.66418			0.449133			0.224566	−	0.974459i	$-0.427903\pi$
$463$	9.66418			0.449133			0.224566	+	0.974459i	$0.427903\pi$
$464$	0.649684	+	0.472023i	0.0301608	+	0.0219131i
$465$		0			0
$466$	0.0290163	+	0.0893029i	0.00134415	+	0.00413688i
$467$	−7.84274	+	5.69808i	−0.362919	+	0.263676i	−0.754268	−	0.656566i	$-0.772008\pi$
$467$	−7.84274	+	5.69808i	−0.362919	+	0.263676i	0.391350	+	0.920242i	$0.372008\pi$
$468$	22.2292	−	16.1505i	1.02755	−	0.746556i
$469$	−2.35845	−	7.25855i	−0.108903	−	0.335169i
$470$		0			0
$471$	0.264325	+	0.192043i	0.0121795	+	0.00884889i
$472$	−30.7711			−1.41636
$473$	1.06899	+	2.05564i	0.0491523	+	0.0945184i
$474$	−0.975537			−0.0448079
$475$		0			0
$476$	8.88829	−	27.3554i	0.407394	−	1.25383i
$477$	−8.11819	−	24.9852i	−0.371707	−	1.14400i
$478$	−13.9815	+	10.1582i	−0.639501	+	0.464624i
$479$	−4.23099	+	3.07400i	−0.193319	+	0.140454i	−0.680234	−	0.732995i	$-0.738122\pi$
$479$	−4.23099	+	3.07400i	−0.193319	+	0.140454i	0.486915	+	0.873449i	$0.338122\pi$
$480$		0			0
$481$	−4.18014	+	12.8651i	−0.190598	+	0.586600i
$482$	−1.33283	−	0.968356i	−0.0607086	−	0.0441074i
$483$	−0.267971			−0.0121931
$484$	−34.3022	−	10.5190i	−1.55919	−	0.478137i
$485$		0			0
$486$	−2.12307	−	1.54250i	−0.0963043	−	0.0699692i
$487$	1.68511	−	5.18624i	0.0763597	−	0.235011i	−0.905590	−	0.424155i	$-0.860571\pi$
$487$	1.68511	−	5.18624i	0.0763597	−	0.235011i	0.981949	+	0.189144i	$0.0605713\pi$
$488$	−8.27743	−	25.4753i	−0.374702	−	1.15321i
$489$	−0.743755	+	0.540370i	−0.0336338	+	0.0244364i
$490$		0			0
$491$	5.00578	+	15.4062i	0.225908	+	0.695272i	0.998198	+	0.0600028i	$0.0191110\pi$
$491$	5.00578	+	15.4062i	0.225908	+	0.695272i	−0.772291	+	0.635269i	$0.780889\pi$
$492$	−0.284831	+	0.876620i	−0.0128412	+	0.0395211i
$493$	43.5867	+	31.6676i	1.96305	+	1.42624i
$494$	−21.1590			−0.951988
$495$		0			0
$496$	−0.0861495			−0.00386823
$497$	−6.87858	−	4.99758i	−0.308547	−	0.224172i
$498$	0.147196	−	0.453024i	0.00659603	−	0.0203005i
$499$	3.63280	+	11.1806i	0.162626	+	0.500513i	0.998854	−	0.0478706i	$-0.0152435\pi$
$499$	3.63280	+	11.1806i	0.162626	+	0.500513i	−0.836227	+	0.548383i	$0.815244\pi$
$500$		0			0
$501$	0.487648	−	0.354297i	0.0217865	−	0.0158288i
$502$	4.57497	+	14.0803i	0.204191	+	0.628435i
$503$	10.0505	−	30.9323i	0.448130	−	1.37920i	−0.430885	−	0.902407i	$-0.641799\pi$
$503$	10.0505	−	30.9323i	0.448130	−	1.37920i	0.879015	−	0.476794i	$-0.158201\pi$
$504$	−8.00062	−	5.81279i	−0.356376	−	0.258922i
$505$		0			0
$506$	6.25274	−	41.7171i	0.277968	−	1.85455i
$507$	0.216506			0.00961539
$508$	41.3071	+	30.0114i	1.83271	+	1.33154i
$509$	−3.94110	+	12.1295i	−0.174686	+	0.537629i	−0.999619	−	0.0276020i	$-0.991213\pi$
$509$	−3.94110	+	12.1295i	−0.174686	+	0.537629i	0.824933	+	0.565231i	$0.191213\pi$
$510$		0			0
$511$	−1.40871	+	1.02349i	−0.0623175	+	0.0452763i
$512$	−1.05550	+	0.766865i	−0.0466469	+	0.0338909i
$513$	0.258048	+	0.794190i	0.0113931	+	0.0350644i
$514$	16.6153	−	51.1365i	0.732868	−	2.25554i
$515$		0			0
$516$	0.0966268			0.00425376
$517$	28.2930	−	4.72231i	1.24433	−	0.207687i
$518$	12.5862			0.553005
$519$	0.653038	+	0.474460i	0.0286652	+	0.0208265i
$520$		0			0
$521$	5.97920	+	18.4021i	0.261954	+	0.806210i	0.992380	+	0.123218i	$0.0393215\pi$
$521$	5.97920	+	18.4021i	0.261954	+	0.806210i	−0.730426	+	0.682992i	$0.760678\pi$
$522$	38.7409	−	28.1469i	1.69564	−	1.23196i
$523$	−12.7358	+	9.25311i	−0.556898	+	0.404610i	−0.830322	−	0.557283i	$-0.811844\pi$
$523$	−12.7358	+	9.25311i	−0.556898	+	0.404610i	0.273424	+	0.961894i	$0.411844\pi$
$524$	−22.0640	−	67.9059i	−0.963869	−	2.96648i
$525$		0			0
$526$	37.3426	+	27.1310i	1.62821	+	1.18297i
$527$	−5.77969			−0.251767
$528$	−0.0113744	+	0.0115649i	−0.000495007	+	0.000503296i
$529$	7.74383			0.336688
$530$		0			0
$531$	−9.85062	+	30.3171i	−0.427480	+	1.31565i
$532$	3.77121	+	11.6066i	0.163503	+	0.503210i
$533$	−15.1479	+	11.0056i	−0.656127	+	0.476704i
$534$	0.708755	−	0.514941i	0.0306708	−	0.0222837i
$535$		0			0
$536$	5.98917	−	18.4328i	0.258693	−	0.796175i
$537$	−0.364957	−	0.265157i	−0.0157491	−	0.0114424i
$538$	−1.61676			−0.0697033
$539$	−16.9183	−	8.44411i	−0.728723	−	0.363714i
$540$		0			0
$541$	−13.8001	−	10.0264i	−0.593312	−	0.431067i	0.250186	−	0.968198i	$-0.419508\pi$
$541$	−13.8001	−	10.0264i	−0.593312	−	0.431067i	−0.843499	+	0.537131i	$0.819508\pi$
$542$	14.4842	−	44.5777i	0.622149	−	1.91478i
$543$	0.201326	+	0.619617i	0.00863971	+	0.0265903i
$544$	−34.5781	+	25.1225i	−1.48253	+	1.07712i
$545$		0			0
$546$	0.0962530	+	0.296236i	0.00411925	+	0.0126777i
$547$	4.71400	−	14.5082i	0.201556	−	0.620326i	−0.798281	−	0.602285i	$-0.794257\pi$
$547$	4.71400	−	14.5082i	0.201556	−	0.620326i	0.999837	−	0.0180408i	$-0.00574287\pi$
$548$	−25.2770	−	18.3648i	−1.07978	−	0.784507i
$549$	−27.7492			−1.18431
$550$		0			0
$551$	−22.8591			−0.973830
$552$	−0.550536	−	0.399988i	−0.0234324	−	0.0170246i
$553$	−3.53198	+	10.8703i	−0.150195	+	0.462253i
$554$	−10.8750	−	33.4697i	−0.462033	−	1.42199i
$555$		0			0
$556$	−32.9972	+	23.9739i	−1.39939	+	1.01672i
$557$	−3.13581	−	9.65102i	−0.132868	−	0.408927i	0.862384	−	0.506255i	$-0.168970\pi$
$557$	−3.13581	−	9.65102i	−0.132868	−	0.408927i	−0.995252	+	0.0973278i	$0.968970\pi$
$558$	−1.58746	+	4.88570i	−0.0672025	+	0.206828i
$559$	1.58798	+	1.15373i	0.0671642	+	0.0487977i
$560$		0			0
$561$	−0.763097	+	0.775875i	−0.0322180	+	0.0327575i
$562$	−31.7288			−1.33840
$563$	−26.5624	−	19.2987i	−1.11947	−	0.813343i	−0.135342	−	0.990799i	$-0.543213\pi$
$563$	−26.5624	−	19.2987i	−1.11947	−	0.813343i	−0.984129	+	0.177456i	$0.943213\pi$
$564$	0.369661	−	1.13770i	0.0155655	−	0.0479058i
$565$		0			0
$566$	31.5401	−	22.9152i	1.32573	−	0.963198i
$567$	−8.28325	+	6.01814i	−0.347864	+	0.252738i
$568$	−6.67213	−	20.5347i	−0.279956	−	0.861617i
$569$	6.96184	−	21.4263i	0.291856	−	0.898239i	−0.692404	−	0.721510i	$-0.743448\pi$
$569$	6.96184	−	21.4263i	0.291856	−	0.898239i	0.984260	−	0.176729i	$-0.0565516\pi$
$570$		0			0
$571$	−25.5317			−1.06847			−0.534234	−	0.845336i	$-0.679400\pi$
$571$	−25.5317			−1.06847			−0.534234	+	0.845336i	$0.679400\pi$
$572$	−29.9803	+	5.00392i	−1.25354	+	0.209224i
$573$	−0.632410			−0.0264193
$574$	14.0941	+	10.2399i	0.588276	+	0.427407i
$575$		0			0
$576$	11.9530	+	36.7876i	0.498042	+	1.53282i
$577$	−34.3605	+	24.9643i	−1.43044	+	1.03928i	−0.440511	+	0.897747i	$0.645203\pi$
$577$	−34.3605	+	24.9643i	−1.43044	+	1.03928i	−0.989934	+	0.141532i	$0.954797\pi$
$578$	79.5582	−	57.8024i	3.30918	−	2.40426i
$579$	−0.0875985	−	0.269601i	−0.00364047	−	0.0112042i
$580$		0			0
$581$	−4.51508	−	3.28039i	−0.187317	−	0.136094i
$582$	−0.576083			−0.0238794
$583$	−4.30769	+	28.7401i	−0.178406	+	1.19029i
$584$	−4.42185			−0.182977
$585$		0			0
$586$	−0.595032	+	1.83132i	−0.0245806	+	0.0756512i
$587$	5.45316	+	16.7831i	0.225076	+	0.692712i	0.998284	+	0.0585597i	$0.0186508\pi$
$587$	5.45316	+	16.7831i	0.225076	+	0.692712i	−0.773208	+	0.634152i	$0.781349\pi$
$588$	−0.637955	+	0.463502i	−0.0263088	+	0.0191145i
$589$	1.98392	−	1.44140i	0.0817461	−	0.0593920i
$590$		0			0
$591$	−0.117437	+	0.361434i	−0.00483071	+	0.0148674i
$592$	0.449223	+	0.326380i	0.0184630	+	0.0134141i
$593$	−16.3570			−0.671700			−0.335850	−	0.941915i	$-0.609024\pi$
$593$	−16.3570			−0.671700			−0.335850	+	0.941915i	$0.609024\pi$
$594$	0.892810	+	1.71685i	0.0366324	+	0.0704431i
$595$		0			0
$596$	−21.9193	−	15.9253i	−0.897848	−	0.652324i
$597$	−0.180615	+	0.555875i	−0.00739207	+	0.0227505i
$598$	−11.0429	−	33.9867i	−0.451580	−	1.38982i
$599$	26.4966	−	19.2509i	1.08262	−	0.786570i	0.104483	−	0.994527i	$-0.466681\pi$
$599$	26.4966	−	19.2509i	1.08262	−	0.786570i	0.978138	+	0.207956i	$0.0666812\pi$
$600$		0			0
$601$	1.53921	+	4.73719i	0.0627855	+	0.193234i	0.977529	−	0.210801i	$-0.0676073\pi$
$601$	1.53921	+	4.73719i	0.0627855	+	0.193234i	−0.914743	+	0.404035i	$0.867607\pi$
$602$	0.564357	−	1.73691i	0.0230015	−	0.0707913i
$603$	−16.2435	−	11.8016i	−0.661487	−	0.480598i
$604$	42.1722			1.71596
$605$		0			0
$606$	−0.908640			−0.0369110
$607$	−8.07212	−	5.86474i	−0.327637	−	0.238042i	0.411790	−	0.911279i	$-0.364904\pi$
$607$	−8.07212	−	5.86474i	−0.327637	−	0.238042i	−0.739427	+	0.673236i	$0.764904\pi$
$608$	5.60388	−	17.2470i	0.227267	−	0.699457i
$609$	0.103987	+	0.320039i	0.00421376	+	0.0129686i
$610$		0			0
$611$	19.6593	−	14.2833i	0.795330	−	0.577841i
$612$	−23.3828	−	71.9649i	−0.945195	−	2.90901i
$613$	−10.6644	+	32.8216i	−0.430730	+	1.32565i	0.466669	+	0.884432i	$0.345454\pi$
$613$	−10.6644	+	32.8216i	−0.430730	+	1.32565i	−0.897399	+	0.441219i	$0.854546\pi$
$614$	11.9046	+	8.64920i	0.480431	+	0.349053i
$615$		0			0
$616$	5.04724	+	9.70569i	0.203359	+	0.391053i
$617$	−34.5830			−1.39226			−0.696129	−	0.717916i	$-0.745096\pi$
$617$	−34.5830			−1.39226			−0.696129	+	0.717916i	$0.745096\pi$
$618$	−0.819213	−	0.595193i	−0.0329536	−	0.0239422i
$619$	−1.25727	+	3.86947i	−0.0505338	+	0.155527i	−0.973139	−	0.230219i	$-0.926056\pi$
$619$	−1.25727	+	3.86947i	−0.0505338	+	0.155527i	0.922605	+	0.385746i	$0.126056\pi$
$620$		0			0
$621$	−1.14100	+	0.828981i	−0.0457866	+	0.0332659i
$622$	56.3852	−	40.9662i	2.26084	−	1.64260i
$623$	−3.17186	−	9.76198i	−0.127078	−	0.391105i
$624$	−0.00424645	+	0.0130692i	−0.000169994	+	0.000523187i
$625$		0			0
$626$	5.39393			0.215585
$627$	0.0684424	−	0.456635i	0.00273333	−	0.0182362i
$628$	25.1304			1.00281
$629$	30.1380	+	21.8965i	1.20168	+	0.873071i
$630$		0			0
$631$	−2.02749	−	6.23999i	−0.0807133	−	0.248410i	0.902555	−	0.430575i	$-0.141689\pi$
$631$	−2.02749	−	6.23999i	−0.0807133	−	0.248410i	−0.983268	+	0.182165i	$0.941689\pi$
$632$	−23.4820	+	17.0607i	−0.934063	+	0.678637i
$633$	0.301380	−	0.218966i	0.0119788	−	0.00870310i
$634$	0.569608	+	1.75307i	0.0226220	+	0.0696235i
$635$		0			0
$636$	0.980495	+	0.712371i	0.0388792	+	0.0282474i
$637$	−16.0185			−0.634676
$638$	−52.2494	+	8.72079i	−2.06857	+	0.345259i
$639$	−22.3676			−0.884850
$640$		0			0
$641$	−2.04709	+	6.30031i	−0.0808553	+	0.248847i	−0.983310	−	0.181938i	$-0.941763\pi$
$641$	−2.04709	+	6.30031i	−0.0808553	+	0.248847i	0.902455	+	0.430785i	$0.141763\pi$
$642$	0.133018	+	0.409386i	0.00524978	+	0.0161572i
$643$	37.7911	−	27.4568i	1.49033	−	1.08279i	0.516295	−	0.856411i	$-0.327311\pi$
$643$	37.7911	−	27.4568i	1.49033	−	1.08279i	0.974039	−	0.226380i	$-0.0726892\pi$
$644$	−16.6749	+	12.1151i	−0.657085	+	0.477400i
$645$		0			0
$646$	−18.0063	+	55.4178i	−0.708450	+	2.18038i
$647$	34.7847	+	25.2725i	1.36753	+	0.993566i	0.997926	+	0.0643747i	$0.0205053\pi$
$647$	34.7847	+	25.2725i	1.36753	+	0.993566i	0.369600	+	0.929191i	$0.379495\pi$
$648$	−26.0006			−1.02140
$649$	24.7267	−	25.1407i	0.970606	−	0.986859i
$650$		0			0
$651$	−0.0292053	−	0.0212189i	−0.00114465	−	0.000831635i
$652$	−21.8511	+	67.2509i	−0.855756	+	2.63375i
$653$	−5.68176	−	17.4867i	−0.222345	−	0.684306i	−0.998550	−	0.0538266i	$-0.982858\pi$
$653$	−5.68176	−	17.4867i	−0.222345	−	0.684306i	0.776206	−	0.630480i	$-0.217142\pi$
$654$	0.253809	−	0.184403i	0.00992473	−	0.00721074i
$655$		0			0
$656$	0.237505	+	0.730965i	0.00927301	+	0.0285394i
$657$	−1.41555	+	4.35660i	−0.0552257	+	0.169967i
$658$	−18.2917	−	13.2897i	−0.713084	−	0.518085i
$659$	13.6816			0.532959			0.266480	−	0.963841i	$-0.414140\pi$
$659$	13.6816			0.532959			0.266480	+	0.963841i	$0.414140\pi$
$660$		0			0
$661$	−35.5389			−1.38230			−0.691151	−	0.722710i	$-0.742896\pi$
$661$	−35.5389			−1.38230			−0.691151	+	0.722710i	$0.742896\pi$
$662$	54.8812	+	39.8736i	2.13302	+	1.54973i
$663$	−0.284890	+	0.876801i	−0.0110642	+	0.0340521i
$664$	−4.37956	−	13.4789i	−0.169960	−	0.523083i
$665$		0			0
$666$	26.7874	−	19.4622i	1.03799	−	0.754143i
$667$	−11.9302	−	36.7175i	−0.461941	−	1.42171i
$668$	14.3268	−	44.0935i	0.554322	−	1.70603i
$669$	0.310020	+	0.225242i	0.0119861	+	0.00870838i
$670$		0			0
$671$	27.4654	+	13.7083i	1.06029	+	0.529202i
$672$	−0.266959			−0.0102982
$673$	13.3679	+	9.71235i	0.515295	+	0.374384i	0.814828	−	0.579702i	$-0.196831\pi$
$673$	13.3679	+	9.71235i	0.515295	+	0.374384i	−0.299534	+	0.954086i	$0.596831\pi$
$674$	−20.1863	+	62.1271i	−0.777547	+	2.39305i
$675$		0			0
$676$	13.4725	−	9.78833i	0.518172	−	0.376474i
$677$	23.0500	−	16.7468i	0.885882	−	0.643631i	−0.0489193	−	0.998803i	$-0.515578\pi$
$677$	23.0500	−	16.7468i	0.885882	−	0.643631i	0.934801	+	0.355172i	$0.115578\pi$
$678$	0.145938	+	0.449152i	0.00560472	+	0.0172496i
$679$	−2.08574	+	6.41924i	−0.0800433	+	0.246348i
$680$		0			0
$681$	−0.240950			−0.00923321
$682$	3.98479	−	4.05151i	0.152585	−	0.155140i
$683$	−3.48712			−0.133431			−0.0667156	−	0.997772i	$-0.521252\pi$
$683$	−3.48712			−0.133431			−0.0667156	+	0.997772i	$0.521252\pi$
$684$	25.9738	+	18.8710i	0.993132	+	0.721553i
$685$		0			0
$686$	10.2605	+	31.5787i	0.391750	+	1.20568i
$687$	0.202211	−	0.146915i	0.00771485	−	0.00560517i
$688$	0.0651839	−	0.0473589i	0.00248511	−	0.00180554i
$689$	7.60780	+	23.4144i	0.289834	+	0.892017i
$690$		0			0
$691$	29.1311	+	21.1650i	1.10820	+	0.805153i	0.982379	−	0.186900i	$-0.0598442\pi$
$691$	29.1311	+	21.1650i	1.10820	+	0.805153i	0.125819	+	0.992053i	$0.459844\pi$
$692$	62.0870			2.36019
$693$	11.1782	−	1.86572i	0.424626	−	0.0708730i
$694$	−18.5169			−0.702893
$695$		0			0
$696$	−0.264070	+	0.812725i	−0.0100096	+	0.0308063i
$697$	15.9340	+	49.0397i	0.603542	+	1.85751i
$698$	−55.6842	+	40.4569i	−2.10768	+	1.53132i
$699$	−0.00140436	+	0.00102033i	−5.31179e−5	+	3.85924e-5i
$700$		0			0
$701$	15.6182	−	48.0679i	0.589891	−	1.81550i	0.0112198	−	0.999937i	$-0.496429\pi$
$701$	15.6182	−	48.0679i	0.589891	−	1.81550i	0.578671	−	0.815561i	$-0.303571\pi$
$702$	1.32626	+	0.963584i	0.0500564	+	0.0363681i
$703$	−15.8059			−0.596131
$704$	6.34253	−	42.3162i	0.239043	−	1.59485i
$705$		0			0
$706$	5.89932	+	4.28611i	0.222024	+	0.161310i
$707$	−3.28978	+	10.1249i	−0.123725	+	0.380786i
$708$	−0.454437	−	1.39861i	−0.0170788	−	0.0525631i
$709$	−20.8602	+	15.1559i	−0.783423	+	0.569190i	−0.906004	−	0.423269i	$-0.860883\pi$
$709$	−20.8602	+	15.1559i	−0.783423	+	0.569190i	0.122582	+	0.992458i	$0.460883\pi$
$710$		0			0
$711$	9.29174	+	28.5970i	0.348468	+	1.07247i
$712$	8.05480	−	24.7901i	0.301866	−	0.929049i
$713$	3.35068	+	2.43441i	0.125484	+	0.0911694i
$714$	0.857788			0.0321019
$715$		0			0
$716$	−34.6979			−1.29672
$717$	−0.258474	−	0.187793i	−0.00965290	−	0.00701324i
$718$	2.07796	−	6.39532i	0.0775490	−	0.238671i
$719$	−8.30636	−	25.5643i	−0.309775	−	0.953389i	−0.977852	−	0.209297i	$-0.932882\pi$
$719$	−8.30636	−	25.5643i	−0.309775	−	0.953389i	0.668077	−	0.744092i	$-0.267118\pi$
$720$		0			0
$721$	−9.59819	+	6.97349i	−0.357455	+	0.259706i
$722$	5.82798	+	17.9367i	0.216895	+	0.667534i
$723$	0.00941155	−	0.0289658i	0.000350019	−	0.00107725i
$724$	40.5409	+	29.4547i	1.50669	+	1.09468i
$725$		0			0
$726$	−0.0177673	−	1.06985i	−0.000659408	−	0.0397058i
$727$	−6.40984			−0.237728			−0.118864	−	0.992911i	$-0.537925\pi$
$727$	−6.40984			−0.237728			−0.118864	+	0.992911i	$0.537925\pi$
$728$	7.49762	+	5.44734i	0.277880	+	0.201892i
$729$	−8.31347	+	25.5862i	−0.307906	+	0.947638i
$730$		0			0
$731$	4.37313	−	3.17726i	0.161746	−	0.117515i
$732$	1.03566	−	0.752454i	0.0382793	−	0.0278115i
$733$	−3.18009	−	9.78732i	−0.117459	−	0.361503i	0.874993	−	0.484136i	$-0.160866\pi$
$733$	−3.18009	−	9.78732i	−0.117459	−	0.361503i	−0.992452	+	0.122633i	$0.960866\pi$
$734$	12.9703	−	39.9184i	0.478742	−	1.47342i
$735$		0			0
$736$	30.6277			1.12895
$737$	10.2473	+	19.7053i	0.377464	+	0.725853i
$738$	45.8308			1.68706
$739$	19.2572	+	13.9912i	0.708387	+	0.514673i	0.882653	−	0.470026i	$-0.155755\pi$
$739$	19.2572	+	13.9912i	0.708387	+	0.514673i	−0.174266	+	0.984699i	$0.555755\pi$
$740$		0			0
$741$	−0.120876	−	0.372018i	−0.00444049	−	0.0136664i
$742$	18.5319	−	13.4642i	0.680327	−	0.494286i
$743$	9.61970	−	6.98912i	0.352913	−	0.256406i	−0.397177	−	0.917742i	$-0.630010\pi$
$743$	9.61970	−	6.98912i	0.352913	−	0.256406i	0.750090	+	0.661336i	$0.230010\pi$
$744$	−0.0283288	−	0.0871870i	−0.00103858	−	0.00319643i
$745$		0			0
$746$	−15.5486	−	11.2968i	−0.569276	−	0.413603i
$747$	−14.6820			−0.537187
$748$	−12.4074	+	82.7801i	−0.453660	+	3.02674i
$749$	5.04335			0.184280
$750$		0			0
$751$	13.4213	−	41.3065i	0.489750	−	1.50730i	−0.335232	−	0.942136i	$-0.608815\pi$
$751$	13.4213	−	41.3065i	0.489750	−	1.50730i	0.824982	−	0.565159i	$-0.191185\pi$
$752$	−0.308240	−	0.948666i	−0.0112404	−	0.0345943i
$753$	−0.221425	+	0.160875i	−0.00806917	+	0.00586260i
$754$	−36.3052	+	26.3773i	−1.32216	+	0.960605i
$755$		0			0
$756$	0.292184	−	0.899251i	0.0106266	−	0.0327055i
$757$	9.71204	+	7.05621i	0.352990	+	0.256462i	0.750122	−	0.661299i	$-0.229995\pi$
$757$	9.71204	+	7.05621i	0.352990	+	0.256462i	−0.397132	+	0.917761i	$0.629995\pi$
$758$	32.8928			1.19472
$759$	0.769192	−	0.128384i	0.0279199	−	0.00466003i
$760$		0			0
$761$	−21.8907	−	15.9045i	−0.793536	−	0.576537i	0.115475	−	0.993310i	$-0.463161\pi$
$761$	−21.8907	−	15.9045i	−0.793536	−	0.576537i	−0.909011	+	0.416773i	$0.863161\pi$
$762$	−0.470537	+	1.44816i	−0.0170457	+	0.0524614i
$763$	−1.13586	−	3.49582i	−0.0411209	−	0.126557i
$764$	−39.3528	+	28.5915i	−1.42373	+	1.03440i
$765$		0			0
$766$	−19.2784	−	59.3327i	−0.696555	−	2.14378i
$767$	9.23130	−	28.4110i	0.333323	−	1.02586i
$768$	−0.574269	−	0.417231i	−0.0207221	−	0.0150555i
$769$	22.0504			0.795158			0.397579	−	0.917568i	$-0.369850\pi$
$769$	22.0504			0.795158			0.397579	+	0.917568i	$0.369850\pi$
$770$		0			0
$771$	0.994003			0.0357981
$772$	−17.6397	−	12.8160i	−0.634867	−	0.461258i
$773$	12.3303	−	37.9487i	0.443489	−	1.36492i	−0.440643	−	0.897682i	$-0.645250\pi$
$773$	12.3303	−	37.9487i	0.443489	−	1.36492i	0.884132	−	0.467237i	$-0.154750\pi$
$774$	−1.48468	−	4.56937i	−0.0533657	−	0.164243i
$775$		0			0
$776$	−13.8668	+	10.0748i	−0.497789	+	0.361665i
$777$	0.0719016	+	0.221290i	0.00257946	+	0.00793875i
$778$	−14.2140	+	43.7462i	−0.509597	+	1.56838i
$779$	−17.6995	−	12.8595i	−0.634152	−	0.460738i
$780$		0			0
$781$	22.1388	+	11.0497i	0.792190	+	0.395390i
$782$	−98.4126			−3.51923
$783$	1.43282	+	1.04101i	0.0512049	+	0.0372026i
$784$	−0.203189	+	0.625352i	−0.00725675	+	0.0223340i
$785$		0			0
$786$	1.72267	−	1.25160i	0.0614458	−	0.0446430i
$787$	−19.0068	+	13.8093i	−0.677521	+	0.492247i	−0.872534	−	0.488553i	$-0.837525\pi$
$787$	−19.0068	+	13.8093i	−0.677521	+	0.492247i	0.195014	+	0.980801i	$0.437525\pi$
$788$	9.03284	+	27.8002i	0.321782	+	0.990342i
$789$	−0.263689	+	0.811551i	−0.00938757	+	0.0288920i
$790$		0			0
$791$	5.53324			0.196739
$792$	25.7501	+	12.8522i	0.914992	+	0.456682i
$793$	26.0046			0.923451
$794$	54.6229	+	39.6859i	1.93850	+	1.40840i
$795$		0			0
$796$	13.8922	+	42.7559i	0.492398	+	1.51544i
$797$	4.79548	−	3.48412i	0.169865	−	0.123414i	−0.499605	−	0.866253i	$-0.666521\pi$
$797$	4.79548	−	3.48412i	0.169865	−	0.123414i	0.669470	+	0.742839i	$0.266521\pi$
$798$	−0.294443	+	0.213925i	−0.0104232	+	0.00757286i
$799$	−20.6795	−	63.6450i	−0.731589	−	2.25160i
$800$		0			0
$801$	−21.8458	−	15.8719i	−0.771883	−	0.560806i
$802$	−44.0957			−1.55707
$803$	3.55325	−	3.61275i	0.125392	−	0.127491i
$804$	0.926260			0.0326667
$805$		0			0
$806$	1.48766	−	4.57853i	0.0524004	−	0.161272i
$807$	−0.00923612	−	0.0284259i	−0.000325127	−	0.00100064i
$808$	−21.8717	+	15.8907i	−0.769445	+	0.559034i
$809$	6.82259	−	4.95690i	0.239869	−	0.174275i	−0.461356	−	0.887215i	$-0.652637\pi$
$809$	6.82259	−	4.95690i	0.239869	−	0.174275i	0.701225	+	0.712940i	$0.252637\pi$
$810$		0			0
$811$	2.17579	−	6.69640i	0.0764024	−	0.235143i	−0.905560	−	0.424218i	$-0.860549\pi$
$811$	2.17579	−	6.69640i	0.0764024	−	0.235143i	0.981963	+	0.189075i	$0.0605491\pi$
$812$	20.9398	+	15.2137i	0.734844	+	0.533895i
$813$	0.866511			0.0303899
$814$	−36.1278	+	6.02998i	−1.26628	+	0.211351i
$815$		0			0
$816$	0.0306160	+	0.0222438i	0.00107178	+	0.000778690i
$817$	−0.708728	+	2.18124i	−0.0247953	+	0.0763119i
$818$	9.06684	+	27.9049i	0.317015	+	0.975671i
$819$	7.76714	−	5.64316i	0.271406	−	0.197188i
$820$		0			0
$821$	−12.7675	−	39.2942i	−0.445588	−	1.37138i	−0.881838	−	0.471552i	$-0.843694\pi$
$821$	−12.7675	−	39.2942i	−0.445588	−	1.37138i	0.436251	−	0.899825i	$-0.356306\pi$
$822$	0.287935	−	0.886174i	0.0100429	−	0.0309089i
$823$	−25.1250	−	18.2544i	−0.875804	−	0.636309i	0.0563341	−	0.998412i	$-0.482059\pi$
$823$	−25.1250	−	18.2544i	−0.875804	−	0.636309i	−0.932138	+	0.362103i	$0.882059\pi$
$824$	−30.1282			−1.04956
$825$		0			0
$826$	−27.7949			−0.967110
$827$	−20.9918	−	15.2514i	−0.729957	−	0.530345i	0.159593	−	0.987183i	$-0.448982\pi$
$827$	−20.9918	−	15.2514i	−0.729957	−	0.530345i	−0.889550	+	0.456838i	$0.848982\pi$
$828$	−16.7559	+	51.5693i	−0.582308	+	1.79216i
$829$	−0.0250171	−	0.0769948i	−0.000868881	−	0.00267414i	0.950621	−	0.310354i	$-0.100448\pi$
$829$	−0.0250171	−	0.0769948i	−0.000868881	−	0.00267414i	−0.951490	+	0.307680i	$0.900448\pi$
$830$		0			0
$831$	0.526339	−	0.382408i	0.0182585	−	0.0132656i
$832$	−11.2015	−	34.4747i	−0.388343	−	1.19520i
$833$	−13.6318	+	41.9542i	−0.472312	+	1.45363i
$834$	−0.984059	−	0.714961i	−0.0340752	−	0.0247571i
$835$		0			0
$836$	−16.3857	−	31.5092i	−0.566711	−	1.08977i
$837$	−0.189995			−0.00656720
$838$	7.83570	+	5.69297i	0.270680	+	0.196660i
$839$	−4.54279	+	13.9813i	−0.156835	+	0.482688i	−0.998342	−	0.0575579i	$-0.981669\pi$
$839$	−4.54279	+	13.9813i	−0.156835	+	0.482688i	0.841507	+	0.540245i	$0.181669\pi$
$840$		0			0
$841$	−15.7608	+	11.4509i	−0.543477	+	0.394859i
$842$	1.51841	−	1.10319i	0.0523278	−	0.0380184i
$843$	−0.181258	−	0.557856i	−0.00624287	−	0.0192136i
$844$	8.85439	−	27.2510i	0.304781	−	0.938019i
$845$		0			0
$846$	−59.4805			−2.04498
$847$	−11.9856	−	3.67547i	−0.411829	−	0.126290i
$848$	1.01059			0.0347036
$849$	0.583076	+	0.423630i	0.0200111	+	0.0145389i
$850$		0			0
$851$	−8.24915	−	25.3883i	−0.282777	−	0.870299i
$852$	0.834811	−	0.606526i	0.0286002	−	0.0207792i
$853$	35.6270	−	25.8845i	1.21985	−	0.886270i	0.223759	−	0.974645i	$-0.428167\pi$
$853$	35.6270	−	25.8845i	1.21985	−	0.886270i	0.996087	+	0.0883747i	$0.0281673\pi$
$854$	−7.47684	−	23.0114i	−0.255852	−	0.787432i
$855$		0			0
$856$	10.3614	+	7.52799i	0.354145	+	0.257301i
$857$	−29.9206			−1.02207			−0.511035	−	0.859560i	$-0.670738\pi$
$857$	−29.9206			−1.02207			−0.511035	+	0.859560i	$0.670738\pi$
$858$	−0.418214	−	0.804213i	−0.0142776	−	0.0274554i
$859$	−52.2985			−1.78440			−0.892200	−	0.451640i	$-0.850839\pi$
$859$	−52.2985			−1.78440			−0.892200	+	0.451640i	$0.850839\pi$
$860$		0			0
$861$	−0.0995232	+	0.306301i	−0.00339174	+	0.0104387i
$862$	4.11808	+	12.6742i	0.140262	+	0.431683i
$863$	−29.9594	+	21.7668i	−1.01983	+	0.740949i	−0.966248	−	0.257614i	$-0.917064\pi$
$863$	−29.9594	+	21.7668i	−1.01983	+	0.740949i	−0.0535814	+	0.998563i	$0.517064\pi$
$864$	−1.13669	+	0.825851i	−0.0386708	+	0.0280960i
$865$		0			0
$866$	11.0703	−	34.0710i	0.376185	−	1.15778i
$867$	1.47078	+	1.06858i	0.0499503	+	0.0362910i
$868$	−2.77667			−0.0942462
$869$	4.93040	−	32.8947i	0.167252	−	1.11588i
$870$		0			0
$871$	15.2223	+	11.0596i	0.515787	+	0.374741i
$872$	2.88447	−	8.87749i	0.0976805	−	0.300630i
$873$	5.48704	+	16.8874i	0.185708	+	0.571551i
$874$	33.7809	−	24.5433i	1.14266	−	0.830188i
$875$		0			0
$876$	−0.0653032	−	0.200983i	−0.00220639	−	0.00679058i
$877$	6.69350	−	20.6005i	0.226023	−	0.695629i	−0.772163	−	0.635425i	$-0.780825\pi$
$877$	6.69350	−	20.6005i	0.226023	−	0.695629i	0.998186	−	0.0602037i	$-0.0191750\pi$
$878$	40.1984	+	29.2058i	1.35663	+	0.985649i
$879$	−0.0355976			−0.00120068
$880$		0			0
$881$	−5.86710			−0.197668			−0.0988339	−	0.995104i	$-0.531511\pi$
$881$	−5.86710			−0.197668			−0.0988339	+	0.995104i	$0.531511\pi$
$882$	31.7207	+	23.0465i	1.06809	+	0.776015i
$883$	−0.0940535	+	0.289467i	−0.00316515	+	0.00974134i	−0.952627	−	0.304142i	$-0.901630\pi$
$883$	−0.0940535	+	0.289467i	−0.00316515	+	0.00974134i	0.949461	+	0.313884i	$0.101630\pi$
$884$	21.9127	+	67.4404i	0.737005	+	2.26827i
$885$		0			0
$886$	−53.3071	+	38.7299i	−1.79089	+	1.30115i
$887$	4.49937	+	13.8476i	0.151074	+	0.464959i	0.997742	−	0.0671633i	$-0.0213948\pi$
$887$	4.49937	+	13.8476i	0.151074	+	0.464959i	−0.846668	+	0.532122i	$0.821395\pi$
$888$	−0.182591	+	0.561958i	−0.00612736	+	0.0188581i
$889$	14.4332	+	10.4863i	0.484073	+	0.351699i
$890$		0			0
$891$	20.8933	−	21.2431i	0.699951	−	0.711672i
$892$	29.4748			0.986889
$893$	22.9709	+	16.6894i	0.768693	+	0.558488i
$894$	0.249686	−	0.768455i	0.00835076	−	0.0257010i
$895$		0			0
$896$	−17.0998	+	12.4237i	−0.571265	+	0.415048i
$897$	0.534470	−	0.388315i	0.0178454	−	0.0129655i
$898$	−12.4277	−	38.2484i	−0.414717	−	1.27637i
$899$	1.60719	−	4.94641i	0.0536027	−	0.164972i
$900$		0			0
$901$	67.7992			2.25872
$902$	−45.3620	−	22.6407i	−1.51039	−	0.753852i
$903$	0.0337625			0.00112355
$904$	11.3678	+	8.25922i	0.378089	+	0.274698i
$905$		0			0
$906$	0.388644	+	1.19612i	0.0129118	+	0.0397386i
$907$	−0.277567	+	0.201664i	−0.00921647	+	0.00669615i	−0.592384	−	0.805656i	$-0.701813\pi$
$907$	−0.277567	+	0.201664i	−0.00921647	+	0.00669615i	0.583167	+	0.812352i	$0.301813\pi$
$908$	−14.9935	+	10.8934i	−0.497577	+	0.361511i
$909$	8.65457	+	26.6360i	0.287054	+	0.883461i
$910$		0			0
$911$	23.8975	+	17.3625i	0.791759	+	0.575246i	0.908485	−	0.417918i	$-0.137240\pi$
$911$	23.8975	+	17.3625i	0.791759	+	0.575246i	−0.116726	+	0.993164i	$0.537240\pi$
$912$	−0.0160566			−0.000531688
$913$	14.5318	+	7.25300i	0.480934	+	0.240039i
$914$	−45.3234			−1.49916
$915$		0			0
$916$	5.94087	−	18.2841i	0.196292	−	0.604124i
$917$	−7.70940	−	23.7271i	−0.254587	−	0.783538i
$918$	3.65239	−	2.65361i	0.120547	−	0.0875823i
$919$	−21.6574	+	15.7350i	−0.714413	+	0.519051i	−0.884594	−	0.466362i	$-0.845565\pi$
$919$	−21.6574	+	15.7350i	−0.714413	+	0.519051i	0.170182	+	0.985413i	$0.445565\pi$
$920$		0			0
$921$	−0.0840625	+	0.258718i	−0.00276995	+	0.00852504i
$922$	−24.0986	−	17.5087i	−0.793645	−	0.576617i
$923$	20.9614			0.689951
$924$	−0.366606	+	0.372744i	−0.0120604	+	0.0122624i
$925$		0			0
$926$	17.9344	+	13.0301i	0.589360	+	0.428195i
$927$	−9.64479	+	29.6836i	−0.316776	+	0.974938i
$928$	−11.8852	−	36.5788i	−0.390150	−	1.20076i
$929$	12.2548	−	8.90365i	0.402068	−	0.292119i	−0.368315	−	0.929701i	$-0.620065\pi$
$929$	12.2548	−	8.90365i	0.402068	−	0.292119i	0.770383	+	0.637582i	$0.220065\pi$
$930$		0			0
$931$	−5.78382	−	17.8008i	−0.189557	−	0.583396i
$932$	−0.0412594	+	0.126984i	−0.00135150	+	0.00415948i
$933$	1.04238	+	0.757336i	0.0341261	+	0.0247941i
$934$	−22.2369			−0.727612
$935$		0			0
$936$	24.3806			0.796905
$937$	42.1876	+	30.6510i	1.37821	+	1.00133i	0.997045	+	0.0768179i	$0.0244760\pi$
$937$	42.1876	+	30.6510i	1.37821	+	1.00133i	0.381162	+	0.924508i	$0.375524\pi$
$938$	5.40990	−	16.6500i	0.176640	−	0.543641i
$939$	0.0308142	+	0.0948362i	0.00100558	+	0.00309486i
$940$		0			0
$941$	31.1630	−	22.6412i	1.01588	−	0.738082i	0.0504483	−	0.998727i	$-0.483935\pi$
$941$	31.1630	−	22.6412i	1.01588	−	0.738082i	0.965435	+	0.260644i	$0.0839350\pi$
$942$	0.231594	+	0.712772i	0.00754572	+	0.0232234i
$943$	11.4181	−	35.1414i	0.371825	−	1.14436i
$944$	−0.992052	−	0.720768i	−0.0322886	−	0.0234590i
$945$		0			0
$946$	−0.787803	+	5.25608i	−0.0256137	+	0.170890i
$947$	48.1131			1.56347			0.781733	−	0.623613i	$-0.214336\pi$
$947$	48.1131			1.56347			0.781733	+	0.623613i	$0.214336\pi$
$948$	−1.12223	−	0.815350i	−0.0364484	−	0.0264813i
$949$	1.32655	−	4.08270i	0.0430616	−	0.132530i
$950$		0			0
$951$	−0.0275686	+	0.0200297i	−0.000893972	+	0.000649509i
$952$	20.6477	−	15.0014i	0.669195	−	0.486199i
$953$	12.1252	+	37.3175i	0.392773	+	1.20883i	0.930682	+	0.365829i	$0.119215\pi$
$953$	12.1252	+	37.3175i	0.392773	+	1.20883i	−0.537909	+	0.843003i	$0.680785\pi$
$954$	18.6219	−	57.3122i	0.602905	−	1.85555i
$955$		0			0
$956$	−24.5742			−0.794786
$957$	−0.451817	−	0.868830i	−0.0146052	−	0.0280853i
$958$	−11.9963			−0.387584
$959$	−8.83208	−	6.41688i	−0.285203	−	0.207212i
$960$		0			0
$961$	−9.40711	−	28.9521i	−0.303455	−	0.933939i
$962$	−25.1032	+	18.2386i	−0.809360	+	0.588035i
$963$	10.7338	−	7.79860i	0.345893	−	0.251306i
$964$	−0.723904	−	2.22795i	−0.0233154	−	0.0717573i
$965$		0			0
$966$	−0.497289	−	0.361301i	−0.0160000	−	0.0116247i
$967$	38.7795			1.24706			0.623532	−	0.781798i	$-0.285697\pi$
$967$	38.7795			1.24706			0.623532	+	0.781798i	$0.285697\pi$
$968$	−19.1377	−	25.4414i	−0.615109	−	0.817719i
$969$	−1.07722			−0.0346054
$970$		0			0
$971$	−13.2053	+	40.6418i	−0.423779	+	1.30426i	0.480380	+	0.877060i	$0.340499\pi$
$971$	−13.2053	+	40.6418i	−0.423779	+	1.30426i	−0.904159	+	0.427196i	$0.859501\pi$
$972$	−1.15311	−	3.54891i	−0.0369860	−	0.113831i
$973$	−11.5296	+	8.37674i	−0.369622	+	0.268546i
$974$	10.1197	−	7.35238i	0.324256	−	0.235586i
$975$		0			0
$976$	0.329860	−	1.01520i	0.0105586	−	0.0324959i
$977$	38.9099	+	28.2697i	1.24484	+	0.904427i	0.997911	−	0.0646067i	$-0.0205793\pi$
$977$	38.9099	+	28.2697i	1.24484	+	0.904427i	0.246927	+	0.969034i	$0.420579\pi$
$978$	−2.10880			−0.0674320
$979$	13.7815	+	26.5015i	0.440460	+	0.846991i
$980$		0			0
$981$	−7.82310	−	5.68382i	−0.249772	−	0.181470i
$982$	−11.4825	+	35.3394i	−0.366420	+	1.12773i
$983$	−16.8685	−	51.9158i	−0.538021	−	1.65586i	−0.737030	−	0.675861i	$-0.763772\pi$
$983$	−16.8685	−	51.9158i	−0.538021	−	1.65586i	0.199009	−	0.979998i	$-0.436228\pi$
$984$	−0.661668	+	0.480730i	−0.0210932	+	0.0153251i
$985$		0			0
$986$	38.1893	+	117.535i	1.21620	+	3.74307i
$987$	0.129164	−	0.397525i	0.00411133	−	0.0126534i
$988$	−24.3408	−	17.6846i	−0.774383	−	0.562622i
$989$	−3.87351			−0.123171
$990$		0			0
$991$	1.26477			0.0401766			0.0200883	−	0.999798i	$-0.493605\pi$
$991$	1.26477			0.0401766			0.0200883	+	0.999798i	$0.493605\pi$
$992$	3.33802	+	2.42522i	0.105982	+	0.0770007i
$993$	−0.387535	+	1.19271i	−0.0122981	+	0.0378495i
$994$	−6.02681	−	18.5486i	−0.191159	−	0.588326i
$995$		0			0
$996$	0.547967	−	0.398121i	0.0173630	−	0.0126150i
$997$	1.74655	+	5.37532i	0.0553137	+	0.170238i	0.974897	−	0.222658i	$-0.0714733\pi$
$997$	1.74655	+	5.37532i	0.0553137	+	0.170238i	−0.919583	+	0.392896i	$0.871473\pi$
$998$	−8.33307	+	25.6465i	−0.263779	+	0.811827i
$999$	0.990724	+	0.719803i	0.0313451	+	0.0227736i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.h.e.26.4	yes	16
5.2	odd	4		275.2.z.c.224.2		32
5.3	odd	4		275.2.z.c.224.7		32
5.4	even	2		275.2.h.c.26.1	✓	16
11.3	even	5	inner	275.2.h.e.201.4	yes	16
11.5	even	5		3025.2.a.bn.1.1		8
11.6	odd	10		3025.2.a.bj.1.8		8
55.3	odd	20		275.2.z.c.124.2		32
55.14	even	10		275.2.h.c.201.1	yes	16
55.39	odd	10		3025.2.a.bm.1.1		8
55.47	odd	20		275.2.z.c.124.7		32
55.49	even	10		3025.2.a.bi.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.h.c.26.1	✓	16	5.4	even	2
275.2.h.c.201.1	yes	16	55.14	even	10
275.2.h.e.26.4	yes	16	1.1	even	1	trivial
275.2.h.e.201.4	yes	16	11.3	even	5	inner
275.2.z.c.124.2		32	55.3	odd	20
275.2.z.c.124.7		32	55.47	odd	20
275.2.z.c.224.2		32	5.2	odd	4
275.2.z.c.224.7		32	5.3	odd	4
3025.2.a.bi.1.8		8	55.49	even	10
3025.2.a.bj.1.8		8	11.6	odd	10
3025.2.a.bm.1.1		8	55.39	odd	10
3025.2.a.bn.1.1		8	11.5	even	5

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)

\(f(q)\)	\(=\)	\(q+(1.85576 + 1.34829i) q^{2} +(-0.0131041 + 0.0403304i) q^{3} +(1.00792 + 3.10207i) q^{4} +(-0.0786950 + 0.0571753i) q^{6} +(0.352180 + 1.08390i) q^{7} +(-0.894346 + 2.75251i) q^{8} +(2.42560 + 1.76230i) q^{9} +O(q^{10})\)	\(q+(1.85576 + 1.34829i) q^{2} +(-0.0131041 + 0.0403304i) q^{3} +(1.00792 + 3.10207i) q^{4} +(-0.0786950 + 0.0571753i) q^{6} +(0.352180 + 1.08390i) q^{7} +(-0.894346 + 2.75251i) q^{8} +(2.42560 + 1.76230i) q^{9} +(-1.53020 - 2.94253i) q^{11} -0.138316 q^{12} +(-2.27310 - 1.65150i) q^{13} +(-0.807845 + 2.48629i) q^{14} +(-0.0933071 + 0.0677915i) q^{16} +(-6.25988 + 4.54807i) q^{17} +(2.12523 + 6.54080i) q^{18} +(1.01450 - 3.12232i) q^{19} -0.0483291 q^{21} +(1.12769 - 7.52377i) q^{22} +5.54471 q^{23} +(-0.0992903 - 0.0721386i) q^{24} +(-1.99162 - 6.12957i) q^{26} +(-0.205781 + 0.149508i) q^{27} +(-3.00736 + 2.18497i) q^{28} +(-2.15164 - 6.62208i) q^{29} +(0.604302 + 0.439051i) q^{31} +5.52377 q^{32} +(0.138725 - 0.0231542i) q^{33} -17.7489 q^{34} +(-3.02196 + 9.30063i) q^{36} +(-1.48775 - 4.57883i) q^{37} +(6.09245 - 4.42643i) q^{38} +(0.0963927 - 0.0700334i) q^{39} +(2.05928 - 6.33782i) q^{41} +(-0.0896870 - 0.0651614i) q^{42} -0.698596 q^{43} +(7.58561 - 7.71264i) q^{44} +(10.2896 + 7.47586i) q^{46} +(-2.67259 + 8.22539i) q^{47} +(-0.00151135 - 0.00465146i) q^{48} +(4.61231 - 3.35104i) q^{49} +(-0.101395 - 0.312062i) q^{51} +(2.83197 - 8.71589i) q^{52} +(-7.08882 - 5.15033i) q^{53} -0.583459 q^{54} -3.29842 q^{56} +(0.112630 + 0.0818306i) q^{57} +(4.93553 - 15.1900i) q^{58} +(3.28551 + 10.1118i) q^{59} +(-7.48769 + 5.44012i) q^{61} +(0.529471 + 1.62954i) q^{62} +(-1.05591 + 3.24975i) q^{63} +(10.4374 + 7.58321i) q^{64} +(0.288659 + 0.144073i) q^{66} -6.69671 q^{67} +(-20.4179 - 14.8345i) q^{68} +(-0.0726587 + 0.223620i) q^{69} +(-6.03555 + 4.38508i) q^{71} +(-7.02007 + 5.10038i) q^{72} +(0.472132 + 1.45307i) q^{73} +(3.41267 - 10.5031i) q^{74} +10.7082 q^{76} +(2.65050 - 2.69488i) q^{77} +0.273306 q^{78} +(8.11356 + 5.89485i) q^{79} +(2.77615 + 8.54412i) q^{81} +(12.3667 - 8.98495i) q^{82} +(-3.96171 + 2.87835i) q^{83} +(-0.0487120 - 0.149920i) q^{84} +(-1.29642 - 0.941908i) q^{86} +0.295266 q^{87} +(9.46788 - 1.58026i) q^{88} -9.00636 q^{89} +(0.989521 - 3.04543i) q^{91} +(5.58865 + 17.2001i) q^{92} +(-0.0256259 + 0.0186183i) q^{93} +(-16.0499 + 11.6609i) q^{94} +(-0.0723842 + 0.222776i) q^{96} +(4.79130 + 3.48108i) q^{97} +13.0775 q^{98} +(1.47397 - 9.83406i) 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

L-functions

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