LMFDB - Embedded newform 625.2.e.a.374.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(124,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("625.124");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.e (of order $10$, degree $4$, not 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:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			374.2
Root			$1.17421 + 0.0566033i$ of defining polynomial
Character	$\chi$	$=$	625.374
Dual form			625.2.e.a.249.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.107666 + 0.148189i) q^{2} +(1.39991 + 0.454857i) q^{3} +(0.607666 - 1.87020i) q^{4} +(0.0833172 + 0.256424i) q^{6} -3.26086i q^{7} +(0.690983 - 0.224514i) q^{8} +(-0.674207 - 0.489840i) q^{9} +O(q^{10})$	\(q+(0.107666 + 0.148189i) q^{2} +(1.39991 + 0.454857i) q^{3} +(0.607666 - 1.87020i) q^{4} +(0.0833172 + 0.256424i) q^{6} -3.26086i q^{7} +(0.690983 - 0.224514i) q^{8} +(-0.674207 - 0.489840i) q^{9} +(-1.61803 + 1.17557i) q^{11} +(1.70135 - 2.34171i) q^{12} +(0.174207 - 0.239775i) q^{13} +(0.483224 - 0.351083i) q^{14} +(-3.07411 - 2.23347i) q^{16} +(4.91027 - 1.59545i) q^{17} -0.152649i q^{18} +(-0.534717 - 1.64569i) q^{19} +(1.48322 - 4.56489i) q^{21} +(-0.348414 - 0.113207i) q^{22} +(0.516776 + 0.711281i) q^{23} +1.06943 q^{24} +0.0542883 q^{26} +(-3.31659 - 4.56489i) q^{27} +(-6.09846 - 1.98151i) q^{28} +(-1.82696 + 5.62280i) q^{29} +(1.88486 + 5.80100i) q^{31} -2.14910i q^{32} +(-2.79981 + 0.909715i) q^{33} +(0.765097 + 0.555875i) q^{34} +(-1.32579 + 0.963245i) q^{36} +(4.75401 - 6.54333i) q^{37} +(0.186303 - 0.256424i) q^{38} +(0.352937 - 0.256424i) q^{39} +(0.821270 + 0.596687i) q^{41} +(0.836161 - 0.271685i) q^{42} +3.24199i q^{43} +(1.21533 + 3.74041i) q^{44} +(-0.0497651 + 0.153161i) q^{46} +(4.01342 + 1.30404i) q^{47} +(-3.28756 - 4.52494i) q^{48} -3.63318 q^{49} +7.59963 q^{51} +(-0.342569 - 0.471506i) q^{52} +(7.70424 + 2.50326i) q^{53} +(0.319385 - 0.982966i) q^{54} +(-0.732108 - 2.25320i) q^{56} -2.54703i q^{57} +(-1.02994 + 0.334648i) q^{58} +(4.80261 + 3.48930i) q^{59} +(-0.740748 + 0.538185i) q^{61} +(-0.656711 + 0.903885i) q^{62} +(-1.59730 + 2.19849i) q^{63} +(-5.82975 + 4.23556i) q^{64} +(-0.436254 - 0.316957i) q^{66} +(-6.55093 + 2.12853i) q^{67} -10.1527i q^{68} +(0.399907 + 1.23079i) q^{69} +(-1.84445 + 5.67664i) q^{71} +(-0.575842 - 0.187102i) q^{72} +(5.19215 + 7.14638i) q^{73} +1.48150 q^{74} -3.40270 q^{76} +(3.83337 + 5.27618i) q^{77} +(0.0759986 + 0.0246934i) q^{78} +(2.39818 - 7.38084i) q^{79} +(-1.79397 - 5.52127i) q^{81} +0.185946i q^{82} +(13.8049 - 4.48550i) q^{83} +(-7.63597 - 5.54786i) q^{84} +(-0.480429 + 0.349052i) q^{86} +(-5.11514 + 7.04039i) q^{87} +(-0.854102 + 1.17557i) q^{88} +(6.08901 - 4.42392i) q^{89} +(-0.781873 - 0.568064i) q^{91} +(1.64427 - 0.534255i) q^{92} +8.97820i q^{93} +(0.238863 + 0.735146i) q^{94} +(0.977536 - 3.00855i) q^{96} +(-6.39727 - 2.07860i) q^{97} +(-0.391169 - 0.538398i) q^{98} +1.66673 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9}+O(q^{10}) $ 8 * q - 5 * q^3 + 4 * q^4 + 6 * q^6 + 10 * q^8 + q^9	$ 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9} - 4 q^{11} + 10 q^{12} - 5 q^{13} - 7 q^{14} - 2 q^{16} + 15 q^{17} + 10 q^{19} + q^{21} + 10 q^{22} + 15 q^{23} - 20 q^{24} + 6 q^{26} - 5 q^{27} - 20 q^{28} + 15 q^{29} + q^{31} + 10 q^{33} - 12 q^{34} - 17 q^{36} - 5 q^{37} + 12 q^{39} - 9 q^{41} + 5 q^{42} + 8 q^{44} + 16 q^{46} - 15 q^{47} - 5 q^{48} + 14 q^{49} - 4 q^{51} - 20 q^{52} + 35 q^{53} - 10 q^{54} - 15 q^{56} - 20 q^{58} + 15 q^{59} + 6 q^{61} + 45 q^{62} - 20 q^{63} - 26 q^{64} - 18 q^{66} - 13 q^{69} - 29 q^{71} + 5 q^{72} + 10 q^{73} - 12 q^{74} - 20 q^{76} + 20 q^{77} - 25 q^{78} - 10 q^{79} - 12 q^{81} + 15 q^{83} - 27 q^{84} + 16 q^{86} - 55 q^{87} + 20 q^{88} + 40 q^{89} + q^{91} - 5 q^{92} - 7 q^{94} + 11 q^{96} - 10 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) $ 8 * q - 5 * q^3 + 4 * q^4 + 6 * q^6 + 10 * q^8 + q^9 - 4 * q^11 + 10 * q^12 - 5 * q^13 - 7 * q^14 - 2 * q^16 + 15 * q^17 + 10 * q^19 + q^21 + 10 * q^22 + 15 * q^23 - 20 * q^24 + 6 * q^26 - 5 * q^27 - 20 * q^28 + 15 * q^29 + q^31 + 10 * q^33 - 12 * q^34 - 17 * q^36 - 5 * q^37 + 12 * q^39 - 9 * q^41 + 5 * q^42 + 8 * q^44 + 16 * q^46 - 15 * q^47 - 5 * q^48 + 14 * q^49 - 4 * q^51 - 20 * q^52 + 35 * q^53 - 10 * q^54 - 15 * q^56 - 20 * q^58 + 15 * q^59 + 6 * q^61 + 45 * q^62 - 20 * q^63 - 26 * q^64 - 18 * q^66 - 13 * q^69 - 29 * q^71 + 5 * q^72 + 10 * q^73 - 12 * q^74 - 20 * q^76 + 20 * q^77 - 25 * q^78 - 10 * q^79 - 12 * q^81 + 15 * q^83 - 27 * q^84 + 16 * q^86 - 55 * q^87 + 20 * q^88 + 40 * q^89 + q^91 - 5 * q^92 - 7 * q^94 + 11 * q^96 - 10 * q^97 - 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	0.107666	+	0.148189i	0.0761313	+	0.104786i	0.845384	−	0.534159i	$-0.179371\pi$
$2$	0.107666	+	0.148189i	0.0761313	+	0.104786i	−0.769253	+	0.638944i	$0.779371\pi$
$3$	1.39991	+	0.454857i	0.808237	+	0.262612i	0.683851	−	0.729622i	$-0.260304\pi$
$3$	1.39991	+	0.454857i	0.808237	+	0.262612i	0.124386	+	0.992234i	$0.460304\pi$
$4$	0.607666	−	1.87020i	0.303833	−	0.935102i
$5$		0			0
$5$		0			0
$6$	0.0833172	+	0.256424i	0.0340141	+	0.104685i
$7$		−	3.26086i		−	1.23249i	−0.787555	−	0.616244i	$-0.788654\pi$
$7$		−	3.26086i		−	1.23249i	0.787555	−	0.616244i	$-0.211346\pi$
$8$	0.690983	−	0.224514i	0.244299	−	0.0793777i
$9$	−0.674207	−	0.489840i	−0.224736	−	0.163280i
$10$		0			0
$11$	−1.61803	+	1.17557i	−0.487856	+	0.354448i	−0.804359	−	0.594144i	$-0.797491\pi$
$11$	−1.61803	+	1.17557i	−0.487856	+	0.354448i	0.316503	+	0.948591i	$0.397491\pi$
$12$	1.70135	−	2.34171i	0.491138	−	0.675993i
$13$	0.174207	−	0.239775i	0.0483163	−	0.0665017i	−0.784175	−	0.620539i	$-0.786914\pi$
$13$	0.174207	−	0.239775i	0.0483163	−	0.0665017i	0.832492	+	0.554038i	$0.186914\pi$
$14$	0.483224	−	0.351083i	0.129147	−	0.0938308i
$15$		0			0
$16$	−3.07411	−	2.23347i	−0.768528	−	0.558369i
$17$	4.91027	−	1.59545i	1.19092	−	0.386952i	0.354505	−	0.935054i	$-0.384649\pi$
$17$	4.91027	−	1.59545i	1.19092	−	0.386952i	0.836412	+	0.548102i	$0.184649\pi$
$18$		−	0.152649i		−	0.0359798i
$19$	−0.534717	−	1.64569i	−0.122672	−	0.377547i	0.870797	−	0.491642i	$-0.163603\pi$
$19$	−0.534717	−	1.64569i	−0.122672	−	0.377547i	−0.993470	+	0.114095i	$0.963603\pi$
$20$		0			0
$21$	1.48322	−	4.56489i	0.323666	−	0.996142i
$22$	−0.348414	−	0.113207i	−0.0742821	−	0.0241357i
$23$	0.516776	+	0.711281i	0.107755	+	0.148312i	0.859489	−	0.511155i	$-0.170782\pi$
$23$	0.516776	+	0.711281i	0.107755	+	0.148312i	−0.751734	+	0.659467i	$0.770782\pi$
$24$	1.06943			0.218297
$25$		0			0
$26$	0.0542883			0.0106468
$27$	−3.31659	−	4.56489i	−0.638278	−	0.878514i
$28$	−6.09846	−	1.98151i	−1.15250	−	0.374470i
$29$	−1.82696	+	5.62280i	−0.339258	+	1.04413i	0.625329	+	0.780361i	$0.284965\pi$
$29$	−1.82696	+	5.62280i	−0.339258	+	1.04413i	−0.964587	+	0.263766i	$0.915035\pi$
$30$		0			0
$31$	1.88486	+	5.80100i	0.338531	+	1.04189i	0.964957	+	0.262409i	$0.0845170\pi$
$31$	1.88486	+	5.80100i	0.338531	+	1.04189i	−0.626426	+	0.779481i	$0.715483\pi$
$32$		−	2.14910i		−	0.379912i
$33$	−2.79981	+	0.909715i	−0.487385	+	0.158361i
$34$	0.765097	+	0.555875i	0.131213	+	0.0953318i
$35$		0			0
$36$	−1.32579	+	0.963245i	−0.220965	+	0.160541i
$37$	4.75401	−	6.54333i	0.781554	−	1.07572i	−0.213554	−	0.976931i	$-0.568504\pi$
$37$	4.75401	−	6.54333i	0.781554	−	1.07572i	0.995109	−	0.0987860i	$-0.0314959\pi$
$38$	0.186303	−	0.256424i	0.0302223	−	0.0415974i
$39$	0.352937	−	0.256424i	0.0565152	−	0.0410607i
$40$		0			0
$41$	0.821270	+	0.596687i	0.128261	+	0.0931869i	0.650066	−	0.759878i	$-0.274741\pi$
$41$	0.821270	+	0.596687i	0.128261	+	0.0931869i	−0.521805	+	0.853065i	$0.674741\pi$
$42$	0.836161	−	0.271685i	0.129022	−	0.0419219i
$43$			3.24199i			0.494399i	0.968965	+	0.247200i	$0.0795103\pi$
$43$			3.24199i			0.494399i	−0.968965	+	0.247200i	$0.920490\pi$
$44$	1.21533	+	3.74041i	0.183218	+	0.563887i
$45$		0			0
$46$	−0.0497651	+	0.153161i	−0.00733747	+	0.0225824i
$47$	4.01342	+	1.30404i	0.585417	+	0.190214i	0.586726	−	0.809786i	$-0.300417\pi$
$47$	4.01342	+	1.30404i	0.585417	+	0.190214i	−0.00130878	+	0.999999i	$0.500417\pi$
$48$	−3.28756	−	4.52494i	−0.474519	−	0.653119i
$49$	−3.63318			−0.519026
$50$		0			0
$51$	7.59963			1.06416
$52$	−0.342569	−	0.471506i	−0.0475058	−	0.0653861i
$53$	7.70424	+	2.50326i	1.05826	+	0.343849i	0.785905	−	0.618348i	$-0.212198\pi$
$53$	7.70424	+	2.50326i	1.05826	+	0.343849i	0.272355	+	0.962197i	$0.412198\pi$
$54$	0.319385	−	0.982966i	0.0434628	−	0.133765i
$55$		0			0
$56$	−0.732108	−	2.25320i	−0.0978320	−	0.301096i
$57$		−	2.54703i		−	0.337363i
$58$	−1.02994	+	0.334648i	−0.135238	+	0.0439414i
$59$	4.80261	+	3.48930i	0.625246	+	0.454268i	0.854750	−	0.519040i	$-0.173710\pi$
$59$	4.80261	+	3.48930i	0.625246	+	0.454268i	−0.229504	+	0.973308i	$0.573710\pi$
$60$		0			0
$61$	−0.740748	+	0.538185i	−0.0948431	+	0.0689075i	−0.634196	−	0.773172i	$-0.718669\pi$
$61$	−0.740748	+	0.538185i	−0.0948431	+	0.0689075i	0.539353	+	0.842080i	$0.318669\pi$
$62$	−0.656711	+	0.903885i	−0.0834024	+	0.114794i
$63$	−1.59730	+	2.19849i	−0.201241	+	0.276984i
$64$	−5.82975	+	4.23556i	−0.728719	+	0.529445i
$65$		0			0
$66$	−0.436254	−	0.316957i	−0.0536992	−	0.0390147i
$67$	−6.55093	+	2.12853i	−0.800323	+	0.260041i	−0.680494	−	0.732754i	$-0.738235\pi$
$67$	−6.55093	+	2.12853i	−0.800323	+	0.260041i	−0.119829	+	0.992794i	$0.538235\pi$
$68$		−	10.1527i		−	1.23120i
$69$	0.399907	+	1.23079i	0.0481431	+	0.148169i
$70$		0			0
$71$	−1.84445	+	5.67664i	−0.218896	+	0.673694i	0.779958	+	0.625832i	$0.215241\pi$
$71$	−1.84445	+	5.67664i	−0.218896	+	0.673694i	−0.998854	+	0.0478614i	$0.984759\pi$
$72$	−0.575842	−	0.187102i	−0.0678636	−	0.0220502i
$73$	5.19215	+	7.14638i	0.607695	+	0.836420i	0.996385	−	0.0849481i	$-0.0270724\pi$
$73$	5.19215	+	7.14638i	0.607695	+	0.836420i	−0.388690	+	0.921368i	$0.627072\pi$
$74$	1.48150			0.172220
$75$		0			0
$76$	−3.40270			−0.390317
$77$	3.83337	+	5.27618i	0.436853	+	0.601276i
$78$	0.0759986	+	0.0246934i	0.00860514	+	0.00279598i
$79$	2.39818	−	7.38084i	0.269816	−	0.830409i	−0.720728	−	0.693218i	$-0.756192\pi$
$79$	2.39818	−	7.38084i	0.269816	−	0.830409i	0.990545	−	0.137191i	$-0.0438075\pi$
$80$		0			0
$81$	−1.79397	−	5.52127i	−0.199330	−	0.613474i
$82$			0.185946i			0.0205343i
$83$	13.8049	−	4.48550i	1.51529	−	0.492347i	0.570856	−	0.821050i	$-0.306612\pi$
$83$	13.8049	−	4.48550i	1.51529	−	0.492347i	0.944433	+	0.328703i	$0.106612\pi$
$84$	−7.63597	−	5.54786i	−0.833153	−	0.605321i
$85$		0			0
$86$	−0.480429	+	0.349052i	−0.0518059	+	0.0376392i
$87$	−5.11514	+	7.04039i	−0.548401	+	0.754809i
$88$	−0.854102	+	1.17557i	−0.0910476	+	0.125316i
$89$	6.08901	−	4.42392i	0.645433	−	0.468935i	−0.216279	−	0.976332i	$-0.569392\pi$
$89$	6.08901	−	4.42392i	0.645433	−	0.468935i	0.861713	+	0.507397i	$0.169392\pi$
$90$		0			0
$91$	−0.781873	−	0.568064i	−0.0819625	−	0.0595493i
$92$	1.64427	−	0.534255i	0.171427	−	0.0556999i
$93$			8.97820i			0.930996i
$94$	0.238863	+	0.735146i	0.0246369	+	0.0758245i
$95$		0			0
$96$	0.977536	−	3.00855i	0.0997694	−	0.307058i
$97$	−6.39727	−	2.07860i	−0.649544	−	0.211050i	−0.0343310	−	0.999411i	$-0.510930\pi$
$97$	−6.39727	−	2.07860i	−0.649544	−	0.211050i	−0.615213	+	0.788361i	$0.710930\pi$
$98$	−0.391169	−	0.538398i	−0.0395141	−	0.0543865i
$99$	1.66673			0.167513
$100$		0			0
$101$	−12.1955			−1.21350			−0.606748	−	0.794894i	$-0.707526\pi$
$101$	−12.1955			−1.21350			−0.606748	+	0.794894i	$0.707526\pi$
$102$	0.818220	+	1.12618i	0.0810159	+	0.111509i
$103$	−1.31379	−	0.426878i	−0.129452	−	0.0420615i	0.243575	−	0.969882i	$-0.421680\pi$
$103$	−1.31379	−	0.426878i	−0.129452	−	0.0420615i	−0.373027	+	0.927821i	$0.621680\pi$
$104$	0.0665412	−	0.204793i	0.00652490	−	0.0200816i
$105$		0			0
$106$	0.458527	+	1.41120i	0.0445361	+	0.137068i
$107$			15.8285i			1.53020i	0.643911	+	0.765101i	$0.277311\pi$
$107$			15.8285i			1.53020i	−0.643911	+	0.765101i	$0.722689\pi$
$108$	−10.5527	+	3.42877i	−1.01543	+	0.329933i
$109$	−1.62108	−	1.17779i	−0.155272	−	0.112811i	0.507437	−	0.861689i	$-0.330593\pi$
$109$	−1.62108	−	1.17779i	−0.155272	−	0.112811i	−0.662708	+	0.748878i	$0.730593\pi$
$110$		0			0
$111$	9.63145	−	6.99766i	0.914177	−	0.664188i
$112$	−7.28304	+	10.0242i	−0.688182	+	0.947202i
$113$	6.12912	−	8.43601i	0.576579	−	0.793593i	−0.416736	−	0.909028i	$-0.636826\pi$
$113$	6.12912	−	8.43601i	0.576579	−	0.793593i	0.993315	+	0.115434i	$0.0368260\pi$
$114$	0.377443	−	0.274228i	0.0353508	−	0.0256838i
$115$		0			0
$116$	9.40559	+	6.83356i	0.873288	+	0.634481i
$117$	−0.234903	+	0.0763247i	−0.0217168	+	0.00705622i
$118$			1.08737i			0.100101i
$119$	−5.20252	−	16.0117i	−0.476914	−	1.46779i
$120$		0			0
$121$	−2.16312	+	6.65740i	−0.196647	+	0.605218i
$122$	−0.159507	−	0.0518268i	−0.0144410	−	0.00469218i
$123$	0.878294	+	1.20887i	0.0791931	+	0.109000i
$124$	11.9944			1.07713
$125$		0			0
$126$	−0.497767			−0.0443446
$127$	3.43858	+	4.73280i	0.305125	+	0.419969i	0.933853	−	0.357657i	$-0.116424\pi$
$127$	3.43858	+	4.73280i	0.305125	+	0.419969i	−0.628728	+	0.777625i	$0.716424\pi$
$128$	−5.34317	−	1.73610i	−0.472274	−	0.153451i
$129$	−1.47464	+	4.53849i	−0.129835	+	0.399591i
$130$		0			0
$131$	−0.462488	−	1.42339i	−0.0404077	−	0.124362i	0.928818	−	0.370537i	$-0.120826\pi$
$131$	−0.462488	−	1.42339i	−0.0404077	−	0.124362i	−0.969225	+	0.246175i	$0.920826\pi$
$132$			5.78902i			0.503870i
$133$	−5.36635	+	1.74363i	−0.465322	+	0.151192i
$134$	−1.02074	−	0.741608i	−0.0881782	−	0.0640652i
$135$		0			0
$136$	3.03472	−	2.20485i	0.260225	−	0.189064i
$137$	−4.61345	+	6.34987i	−0.394154	+	0.542506i	−0.959265	−	0.282509i	$-0.908833\pi$
$137$	−4.61345	+	6.34987i	−0.394154	+	0.542506i	0.565111	+	0.825015i	$0.308833\pi$
$138$	−0.139333	+	0.191776i	−0.0118608	+	0.0163250i
$139$	4.36183	−	3.16906i	0.369966	−	0.268796i	−0.387231	−	0.921983i	$-0.626568\pi$
$139$	4.36183	−	3.16906i	0.369966	−	0.268796i	0.757197	+	0.653187i	$0.226568\pi$
$140$		0			0
$141$	5.02526	+	3.65106i	0.423203	+	0.307475i
$142$	−1.03980	+	0.337852i	−0.0872583	+	0.0283519i
$143$			0.592757i			0.0495689i
$144$	0.978544	+	3.01165i	0.0815453	+	0.250971i
$145$		0			0
$146$	−0.500000	+	1.53884i	−0.0413803	+	0.127355i
$147$	−5.08611	−	1.65258i	−0.419495	−	0.136302i
$148$	−9.34851	−	12.8671i	−0.768443	−	1.05767i
$149$	−18.8229			−1.54203			−0.771015	−	0.636817i	$-0.780251\pi$
$149$	−18.8229			−1.54203			−0.771015	+	0.636817i	$0.780251\pi$
$150$		0			0
$151$	−3.88797			−0.316398			−0.158199	−	0.987407i	$-0.550569\pi$
$151$	−3.88797			−0.316398			−0.158199	+	0.987407i	$0.550569\pi$
$152$	−0.738960	−	1.01709i	−0.0599376	−	0.0824970i
$153$	−4.09205	−	1.32959i	−0.330823	−	0.107491i
$154$	−0.369150	+	1.13613i	−0.0297470	+	0.0915518i
$155$		0			0
$156$	−0.265097	−	0.815884i	−0.0212247	−	0.0653230i
$157$			4.28378i			0.341883i	0.985281	+	0.170941i	$0.0546808\pi$
$157$			4.28378i			0.341883i	−0.985281	+	0.170941i	$0.945319\pi$
$158$	1.35196	−	0.439279i	0.107556	−	0.0349472i
$159$	9.64660	+	7.00866i	0.765025	+	0.555823i
$160$		0			0
$161$	2.31939	−	1.68513i	0.182793	−	0.132807i
$162$	0.625044	−	0.860299i	0.0491081	−	0.0675915i
$163$	−9.24370	+	12.7229i	−0.724023	+	0.996531i	0.275358	+	0.961342i	$0.411204\pi$
$163$	−9.24370	+	12.7229i	−0.724023	+	0.996531i	−0.999381	+	0.0351898i	$0.988796\pi$
$164$	1.61498	−	1.17335i	0.126109	−	0.0916236i
$165$		0			0
$166$	2.15102	+	1.56281i	0.166952	+	0.121298i
$167$	−20.0036	+	6.49956i	−1.54792	+	0.502951i	−0.953549	−	0.301237i	$-0.902601\pi$
$167$	−20.0036	+	6.49956i	−1.54792	+	0.502951i	−0.594375	+	0.804188i	$0.702601\pi$
$168$		−	3.48727i		−	0.269049i
$169$	3.99008	+	12.2802i	0.306929	+	0.944630i
$170$		0			0
$171$	−0.445615	+	1.37146i	−0.0340770	+	0.104878i
$172$	6.06318	+	1.97005i	0.462313	+	0.150215i
$173$	4.21244	+	5.79793i	0.320266	+	0.440808i	0.938548	−	0.345148i	$-0.112171\pi$
$173$	4.21244	+	5.79793i	0.320266	+	0.440808i	−0.618283	+	0.785956i	$0.712171\pi$
$174$	−1.59404			−0.120844
$175$		0			0
$176$	7.59963			0.572843
$177$	5.13607	+	7.06920i	0.386051	+	0.531353i
$178$	1.31116	+	0.426020i	0.0982753	+	0.0319316i
$179$	−2.48429	+	7.64586i	−0.185685	+	0.571479i	−0.999959	−	0.00900088i	$-0.997135\pi$
$179$	−2.48429	+	7.64586i	−0.185685	+	0.571479i	0.814275	+	0.580480i	$0.197135\pi$
$180$		0			0
$181$	−6.37104	−	19.6080i	−0.473555	−	1.45745i	−0.847896	−	0.530162i	$-0.822131\pi$
$181$	−6.37104	−	19.6080i	−0.473555	−	1.45745i	0.374341	−	0.927291i	$-0.377869\pi$
$182$		−	0.177026i		−	0.0131221i
$183$	−1.28178	+	0.416474i	−0.0947516	+	0.0307867i
$184$	0.516776	+	0.375460i	0.0380972	+	0.0276793i
$185$		0			0
$186$	−1.33047	+	0.966645i	−0.0975550	+	0.0708779i
$187$	−6.06943	+	8.35386i	−0.443841	+	0.610895i
$188$	4.87763	−	6.71349i	0.355738	−	0.489631i
$189$	−14.8855	+	10.8149i	−1.08276	+	0.786670i
$190$		0			0
$191$	−14.5868	−	10.5979i	−1.05546	−	0.766840i	−0.0822207	−	0.996614i	$-0.526201\pi$
$191$	−14.5868	−	10.5979i	−1.05546	−	0.766840i	−0.973244	+	0.229774i	$0.926201\pi$
$192$	−10.0877	+	3.27769i	−0.728016	+	0.236547i
$193$		−	6.78859i		−	0.488653i	−0.969693	−	0.244327i	$-0.921433\pi$
$193$		−	6.78859i		−	0.488653i	0.969693	−	0.244327i	$-0.0785669\pi$
$194$	−0.380741	−	1.17180i	−0.0273356	−	0.0841304i
$195$		0			0
$196$	−2.20776	+	6.79478i	−0.157697	+	0.485342i
$197$	7.60405	+	2.47071i	0.541766	+	0.176031i	0.567101	−	0.823648i	$-0.308065\pi$
$197$	7.60405	+	2.47071i	0.541766	+	0.176031i	−0.0253343	+	0.999679i	$0.508065\pi$
$198$	0.179450	+	0.246992i	0.0127530	+	0.0175529i
$199$	5.20485			0.368962			0.184481	−	0.982836i	$-0.440940\pi$
$199$	5.20485			0.368962			0.184481	+	0.982836i	$0.440940\pi$
$200$		0			0
$201$	−10.1389			−0.715141
$202$	−1.31304	−	1.80724i	−0.0923850	−	0.127157i
$203$	18.3351	+	5.95745i	1.28687	+	0.418131i
$204$	4.61803	−	14.2128i	0.323327	−	0.995098i
$205$		0			0
$206$	−0.0781921	−	0.240650i	−0.00544790	−	0.0167669i
$207$		−	0.732688i		−	0.0509254i
$208$	−1.07106	+	0.348010i	−0.0742649	+	0.0241301i
$209$	2.79981	+	2.03418i	0.193667	+	0.140707i
$210$		0			0
$211$	−13.4313	+	9.75839i	−0.924646	+	0.671795i	−0.944676	−	0.328004i	$-0.893624\pi$
$211$	−13.4313	+	9.75839i	−0.924646	+	0.671795i	0.0200297	+	0.999799i	$0.493624\pi$
$212$	9.36321	−	12.8874i	0.643068	−	0.885107i
$213$	−5.16413	+	7.10781i	−0.353840	+	0.487019i
$214$	−2.34562	+	1.70419i	−0.160343	+	0.116496i
$215$		0			0
$216$	−3.31659	−	2.40964i	−0.225665	−	0.163955i
$217$	18.9162	−	6.14625i	1.28412	−	0.417235i
$218$		−	0.367035i		−	0.0248587i
$219$	4.01794	+	12.3660i	0.271507	+	0.835613i
$220$		0			0
$221$	0.472856	−	1.45530i	0.0318077	−	0.0978941i
$222$	2.07396	+	0.673869i	0.139195	+	0.0452272i
$223$	3.89589	+	5.36223i	0.260888	+	0.359082i	0.919287	−	0.393587i	$-0.128766\pi$
$223$	3.89589	+	5.36223i	0.260888	+	0.359082i	−0.658399	+	0.752669i	$0.728766\pi$
$224$	−7.00792			−0.468236
$225$		0			0
$226$	1.91002			0.127053
$227$	−7.87158	−	10.8343i	−0.522455	−	0.719097i	0.463502	−	0.886096i	$-0.346593\pi$
$227$	−7.87158	−	10.8343i	−0.522455	−	0.719097i	−0.985957	+	0.166998i	$0.946593\pi$
$228$	−4.76347	−	1.54774i	−0.315468	−	0.102502i
$229$	−3.11697	+	9.59304i	−0.205975	+	0.633926i	0.793697	+	0.608313i	$0.208154\pi$
$229$	−3.11697	+	9.59304i	−0.205975	+	0.633926i	−0.999672	+	0.0256124i	$0.991846\pi$
$230$		0			0
$231$	2.96645	+	9.12979i	0.195178	+	0.600696i
$232$			4.29544i			0.282009i
$233$	20.9285	−	6.80007i	1.37107	−	0.445488i	0.471346	−	0.881948i	$-0.343768\pi$
$233$	20.9285	−	6.80007i	1.37107	−	0.445488i	0.899723	+	0.436461i	$0.143768\pi$
$234$	−0.0366015	−	0.0265926i	−0.00239272	−	0.00173841i
$235$		0			0
$236$	9.44408	−	6.86153i	0.614757	−	0.446647i
$237$	6.71445	−	9.24165i	0.436151	−	0.600310i
$238$	1.81263	−	2.49487i	0.117495	−	0.161718i
$239$	6.11640	−	4.44383i	0.395637	−	0.287447i	−0.372124	−	0.928183i	$-0.621371\pi$
$239$	6.11640	−	4.44383i	0.395637	−	0.287447i	0.767762	+	0.640736i	$0.221371\pi$
$240$		0			0
$241$	16.4995	+	11.9876i	1.06283	+	0.772190i	0.974610	−	0.223911i	$-0.0718825\pi$
$241$	16.4995	+	11.9876i	1.06283	+	0.772190i	0.0882188	+	0.996101i	$0.471883\pi$
$242$	−1.21945	+	0.396223i	−0.0783892	+	0.0254702i
$243$			8.38230i			0.537725i
$244$	0.556388	+	1.71239i	0.0356191	+	0.109624i
$245$		0			0
$246$	−0.0845790	+	0.260307i	−0.00539256	+	0.0165966i
$247$	−0.487747	−	0.158479i	−0.0310346	−	0.0100838i
$248$	2.60481	+	3.58521i	0.165406	+	0.227661i
$249$	21.3659			1.35401
$250$		0			0
$251$	10.5717			0.667278			0.333639	−	0.942701i	$-0.391723\pi$
$251$	10.5717			0.667278			0.333639	+	0.942701i	$0.391723\pi$
$252$	3.14100	+	4.32322i	0.197865	+	0.272337i
$253$	−1.67232	−	0.543370i	−0.105138	−	0.0341614i
$254$	−0.331133	+	1.01912i	−0.0207771	+	0.0639455i
$255$		0			0
$256$	4.13553	+	12.7279i	0.258471	+	0.795491i
$257$		−	20.2700i		−	1.26441i	−0.774801	−	0.632205i	$-0.782150\pi$
$257$		−	20.2700i		−	1.26441i	0.774801	−	0.632205i	$-0.217850\pi$
$258$	−0.831324	+	0.270114i	−0.0517560	+	0.0168165i
$259$	−21.3369	−	15.5021i	−1.32581	−	0.963256i
$260$		0			0
$261$	3.98602	−	2.89601i	0.246728	−	0.179259i
$262$	0.161137	−	0.221786i	0.00995509	−	0.0137020i
$263$	16.5114	−	22.7260i	1.01814	−	1.40135i	0.104636	−	0.994511i	$-0.466632\pi$
$263$	16.5114	−	22.7260i	1.01814	−	1.40135i	0.913501	−	0.406835i	$-0.133368\pi$
$264$	−1.73038	+	1.25719i	−0.106498	+	0.0773750i
$265$		0			0
$266$	−0.836161	−	0.607507i	−0.0512683	−	0.0372486i
$267$	10.5363	−	3.42345i	0.644811	−	0.209512i
$268$			13.5450i			0.827393i
$269$	−6.28015	−	19.3283i	−0.382907	−	1.17847i	−0.937987	−	0.346670i	$-0.887312\pi$
$269$	−6.28015	−	19.3283i	−0.382907	−	1.17847i	0.555080	−	0.831797i	$-0.312688\pi$
$270$		0			0
$271$	9.71756	−	29.9076i	0.590300	−	1.81676i	0.0134456	−	0.999910i	$-0.495720\pi$
$271$	9.71756	−	29.9076i	0.590300	−	1.81676i	0.576854	−	0.816847i	$-0.304280\pi$
$272$	−18.6581	−	6.06239i	−1.13132	−	0.367587i
$273$	−0.836161	−	1.15088i	−0.0506068	−	0.0696542i
$274$	−1.43769			−0.0868543
$275$		0			0
$276$	2.54483			0.153181
$277$	−8.18813	−	11.2700i	−0.491977	−	0.677148i	0.488774	−	0.872410i	$-0.337444\pi$
$277$	−8.18813	−	11.2700i	−0.491977	−	0.677148i	−0.980751	+	0.195262i	$0.937444\pi$
$278$	0.939241	+	0.305178i	0.0563319	+	0.0183033i
$279$	1.57078	−	4.83435i	0.0940399	−	0.289425i
$280$		0			0
$281$	7.99664	+	24.6111i	0.477040	+	1.46818i	0.843187	+	0.537620i	$0.180677\pi$
$281$	7.99664	+	24.6111i	0.477040	+	1.46818i	−0.366147	+	0.930557i	$0.619323\pi$
$282$			1.13778i			0.0677541i
$283$	−22.5701	+	7.33348i	−1.34166	+	0.435930i	−0.889877	−	0.456200i	$-0.849210\pi$
$283$	−22.5701	+	7.33348i	−1.34166	+	0.435930i	−0.451778	+	0.892130i	$0.649210\pi$
$284$	9.49567	+	6.89901i	0.563464	+	0.409381i
$285$		0			0
$286$	−0.0878403	+	0.0638197i	−0.00519411	+	0.00377374i
$287$	1.94571	−	2.67804i	0.114852	−	0.158080i
$288$	−1.05272	+	1.44894i	−0.0620320	+	0.0853797i
$289$	7.81207	−	5.67580i	0.459533	−	0.333871i
$290$		0			0
$291$	−8.01011	−	5.81969i	−0.469561	−	0.341156i
$292$	16.5203	−	5.36776i	0.966776	−	0.314124i
$293$		−	12.3029i		−	0.718742i	−0.933195	−	0.359371i	$-0.882991\pi$
$293$		−	12.3029i		−	0.718742i	0.933195	−	0.359371i	$-0.117009\pi$
$294$	−0.302706	−	0.931634i	−0.0176542	−	0.0543340i
$295$		0			0
$296$	1.81587	−	5.58867i	0.105545	−	0.324835i
$297$	10.7327	+	3.48727i	0.622775	+	0.202352i
$298$	−2.02658	−	2.78935i	−0.117397	−	0.161583i
$299$	0.260574			0.0150694
$300$		0			0
$301$	10.5717			0.609341
$302$	−0.418601	−	0.576155i	−0.0240878	−	0.0331540i
$303$	−17.0725	−	5.54721i	−0.980792	−	0.318679i
$304$	−2.03182	+	6.25331i	−0.116533	+	0.358652i
$305$		0			0
$306$	−0.243544	−	0.749550i	−0.0139225	−	0.0428489i
$307$		−	4.28249i		−	0.244415i	−0.992505	−	0.122207i	$-0.961003\pi$
$307$		−	4.28249i		−	0.244415i	0.992505	−	0.122207i	$-0.0389973\pi$
$308$	12.1969	−	3.96302i	0.694984	−	0.225814i
$309$	−1.64502	−	1.19518i	−0.0935820	−	0.0679913i
$310$		0			0
$311$	−20.7486	+	15.0747i	−1.17655	+	0.854810i	−0.991778	−	0.127972i	$-0.959153\pi$
$311$	−20.7486	+	15.0747i	−1.17655	+	0.854810i	−0.184768	+	0.982782i	$0.559153\pi$
$312$	0.186303	−	0.256424i	0.0105473	−	0.0145171i
$313$	−13.1377	+	18.0825i	−0.742589	+	1.02209i	0.255876	+	0.966709i	$0.417636\pi$
$313$	−13.1377	+	18.0825i	−0.742589	+	1.02209i	−0.998466	+	0.0553767i	$0.982364\pi$
$314$	−0.634810	+	0.461216i	−0.0358244	+	0.0260280i
$315$		0			0
$316$	−12.3464	−	8.97016i	−0.694538	−	0.504611i
$317$	20.8499	−	6.77453i	1.17105	−	0.380496i	0.342012	−	0.939695i	$-0.388892\pi$
$317$	20.8499	−	6.77453i	1.17105	−	0.380496i	0.829033	+	0.559200i	$0.188892\pi$
$318$			2.18412i			0.122479i
$319$	−3.65392	−	11.2456i	−0.204580	−	0.629632i
$320$		0			0
$321$	−7.19972	+	22.1585i	−0.401849	+	1.23676i
$322$	0.499437	+	0.162277i	0.0278325	+	0.00904334i
$323$	−5.25121	−	7.22768i	−0.292185	−	0.402159i
$324$	−11.4160			−0.634224
$325$		0			0
$326$	−2.88062			−0.159543
$327$	−1.73364	−	2.38615i	−0.0958706	−	0.131955i
$328$	0.701448	+	0.227914i	0.0387310	+	0.0125845i
$329$	4.25228	−	13.0872i	0.234436	−	0.721519i
$330$		0			0
$331$	−2.76972	−	8.52431i	−0.152237	−	0.468539i	0.845633	−	0.533765i	$-0.179223\pi$
$331$	−2.76972	−	8.52431i	−0.152237	−	0.468539i	−0.997871	+	0.0652260i	$0.979223\pi$
$332$		−	28.5437i		−	1.56654i
$333$	−6.41037	+	2.08286i	−0.351286	+	0.114140i
$334$	−3.11687	−	2.26454i	−0.170547	−	0.123910i
$335$		0			0
$336$	−14.7552	+	10.7203i	−0.804961	+	0.584838i
$337$	17.0949	−	23.5291i	0.931218	−	1.28171i	−0.0281648	−	0.999603i	$-0.508966\pi$
$337$	17.0949	−	23.5291i	0.931218	−	1.28171i	0.959383	−	0.282108i	$-0.0910337\pi$
$338$	−1.39020	+	1.91344i	−0.0756168	+	0.104078i
$339$	12.4174	−	9.02176i	0.674420	−	0.489995i
$340$		0			0
$341$	−9.86925	−	7.17043i	−0.534450	−	0.388300i
$342$	−0.251213	+	0.0816242i	−0.0135841	+	0.00441373i
$343$		−	10.9787i		−	0.592795i
$344$	0.727872	+	2.24016i	0.0392443	+	0.120781i
$345$		0			0
$346$	−0.405655	+	1.24848i	−0.0218081	+	0.0671185i
$347$	−13.5974	−	4.41807i	−0.729948	−	0.237175i	−0.0796174	−	0.996825i	$-0.525370\pi$
$347$	−13.5974	−	4.41807i	−0.729948	−	0.237175i	−0.650331	+	0.759651i	$0.725370\pi$
$348$	10.0587	+	13.8446i	0.539201	+	0.742146i
$349$	−5.62382			−0.301036			−0.150518	−	0.988607i	$-0.548094\pi$
$349$	−5.62382			−0.301036			−0.150518	+	0.988607i	$0.548094\pi$
$350$		0			0
$351$	−1.67232			−0.0892620
$352$	2.52642	+	3.47732i	0.134659	+	0.185342i
$353$	1.81649	+	0.590214i	0.0966821	+	0.0314139i	0.356959	−	0.934120i	$-0.383814\pi$
$353$	1.81649	+	0.590214i	0.0966821	+	0.0314139i	−0.260276	+	0.965534i	$0.583814\pi$
$354$	−0.494600	+	1.52222i	−0.0262877	+	0.0809052i
$355$		0			0
$356$	−4.57355	−	14.0759i	−0.242398	−	0.746023i
$357$		−	24.7813i		−	1.31156i
$358$	−1.40051	+	0.455053i	−0.0740192	+	0.0240503i
$359$	17.9639	+	13.0516i	0.948101	+	0.688835i	0.950357	−	0.311162i	$-0.100718\pi$
$359$	17.9639	+	13.0516i	0.948101	+	0.688835i	−0.00225634	+	0.999997i	$0.500718\pi$
$360$		0			0
$361$	12.9490	−	9.40796i	0.681524	−	0.495156i
$362$	2.21976	−	3.05523i	0.116668	−	0.160580i
$363$	−6.05633	+	8.33582i	−0.317875	+	0.437517i
$364$	−1.53751	+	1.11707i	−0.0805875	+	0.0585503i
$365$		0			0
$366$	−0.199721	−	0.145105i	−0.0104396	−	0.00758478i
$367$	−20.3954	+	6.62686i	−1.06463	+	0.345919i	−0.788394	−	0.615170i	$-0.789087\pi$
$367$	−20.3954	+	6.62686i	−1.06463	+	0.345919i	−0.276236	+	0.961090i	$0.589087\pi$
$368$		−	3.34077i		−	0.174149i
$369$	−0.261424	−	0.804582i	−0.0136092	−	0.0418849i
$370$		0			0
$371$	8.16277	−	25.1224i	0.423790	−	1.30429i
$372$	16.7911	+	5.45574i	0.870576	+	0.282867i
$373$	−13.6013	−	18.7206i	−0.704248	−	0.969315i	−0.999902	−	0.0140195i	$-0.995537\pi$
$373$	−13.6013	−	18.7206i	−0.704248	−	0.969315i	0.295653	−	0.955295i	$-0.404463\pi$
$374$	−1.89142			−0.0978032
$375$		0			0
$376$	3.06598			0.158116
$377$	1.02994	+	1.41759i	0.0530446	+	0.0730096i
$378$	−3.20531	−	1.04147i	−0.164863	−	0.0535674i
$379$	6.69026	−	20.5905i	0.343656	−	1.05766i	−0.618644	−	0.785672i	$-0.712318\pi$
$379$	6.69026	−	20.5905i	0.343656	−	1.05766i	0.962300	−	0.271992i	$-0.0876824\pi$
$380$		0			0
$381$	2.66095	+	8.18955i	0.136324	+	0.419563i
$382$		−	3.30265i		−	0.168978i
$383$	−5.37804	+	1.74743i	−0.274805	+	0.0892896i	−0.443178	−	0.896434i	$-0.646149\pi$
$383$	−5.37804	+	1.74743i	−0.274805	+	0.0892896i	0.168372	+	0.985723i	$0.446149\pi$
$384$	−6.69026	−	4.86076i	−0.341411	−	0.248050i
$385$		0			0
$386$	1.00600	−	0.730899i	0.0512039	−	0.0372018i
$387$	1.58806	−	2.18577i	0.0807255	−	0.111109i
$388$	−7.77480	+	10.7011i	−0.394706	+	0.543266i
$389$	−6.57411	+	4.77637i	−0.333321	+	0.242172i	−0.741838	−	0.670579i	$-0.766046\pi$
$389$	−6.57411	+	4.77637i	−0.333321	+	0.242172i	0.408518	+	0.912750i	$0.366046\pi$
$390$		0			0
$391$	3.67232	+	2.66810i	0.185717	+	0.134932i
$392$	−2.51047	+	0.815700i	−0.126798	+	0.0411991i
$393$		−	2.20298i		−	0.111126i
$394$	0.452564	+	1.39285i	0.0227999	+	0.0701708i
$395$		0			0
$396$	1.01282	−	3.11713i	0.0508959	−	0.156641i
$397$	19.7524	+	6.41794i	0.991343	+	0.322107i	0.759401	−	0.650623i	$-0.225492\pi$
$397$	19.7524	+	6.41794i	0.991343	+	0.322107i	0.231942	+	0.972730i	$0.425492\pi$
$398$	0.560384	+	0.771303i	0.0280895	+	0.0386619i
$399$	−8.30550			−0.415795
$400$		0			0
$401$	30.1195			1.50410			0.752049	−	0.659107i	$-0.229066\pi$
$401$	30.1195			1.50410			0.752049	+	0.659107i	$0.229066\pi$
$402$	−1.09161	−	1.50247i	−0.0544445	−	0.0749365i
$403$	1.71929	+	0.558632i	0.0856440	+	0.0278274i
$404$	−7.41078	+	22.8080i	−0.368700	+	1.13474i
$405$		0			0
$406$	1.09124	+	3.35848i	0.0541572	+	0.166679i
$407$			16.1760i			0.801815i
$408$	5.25121	−	1.70622i	0.259974	−	0.0844706i
$409$	8.93579	+	6.49223i	0.441846	+	0.321020i	0.786368	−	0.617758i	$-0.211959\pi$
$409$	8.93579	+	6.49223i	0.441846	+	0.321020i	−0.344522	+	0.938778i	$0.611959\pi$
$410$		0			0
$411$	−9.34669	+	6.79077i	−0.461038	+	0.334964i
$412$	−1.59670	+	2.19766i	−0.0786636	+	0.108271i
$413$	11.3781	−	15.6606i	0.559880	−	0.770608i
$414$	0.108577	−	0.0788855i	0.00533625	−	0.00387701i
$415$		0			0
$416$	−0.515302	−	0.374389i	−0.0252648	−	0.0183559i
$417$	7.54763	−	2.45237i	0.369609	−	0.120093i
$418$			0.633915i			0.0310058i
$419$	10.1732	+	31.3099i	0.496993	+	1.52959i	0.813827	+	0.581107i	$0.197380\pi$
$419$	10.1732	+	31.3099i	0.496993	+	1.52959i	−0.316834	+	0.948481i	$0.602620\pi$
$420$		0			0
$421$	−6.26214	+	19.2729i	−0.305198	+	0.939304i	0.674405	+	0.738362i	$0.264400\pi$
$421$	−6.26214	+	19.2729i	−0.305198	+	0.939304i	−0.979603	+	0.200942i	$0.935600\pi$
$422$	−2.89218	−	0.939725i	−0.140789	−	0.0457451i
$423$	−2.06710	−	2.84512i	−0.100506	−	0.138335i
$424$	5.88552			0.285826
$425$		0			0
$426$	−1.60930			−0.0779709
$427$	1.75494	+	2.41547i	0.0849277	+	0.116893i
$428$	29.6026	+	9.61845i	1.43089	+	0.464926i
$429$	−0.269620	+	0.829805i	−0.0130174	+	0.0400634i
$430$		0			0
$431$	2.21110	+	6.80506i	0.106505	+	0.327788i	0.990081	−	0.140500i	$-0.0448710\pi$
$431$	2.21110	+	6.80506i	0.106505	+	0.327788i	−0.883576	+	0.468288i	$0.844871\pi$
$432$			21.4405i			1.03156i
$433$	5.21430	−	1.69423i	0.250583	−	0.0814195i	−0.181032	−	0.983477i	$-0.557944\pi$
$433$	5.21430	−	1.69423i	0.250583	−	0.0814195i	0.431615	+	0.902058i	$0.357944\pi$
$434$	2.94744	+	2.14144i	0.141482	+	0.102792i
$435$		0			0
$436$	−3.18778	+	2.31606i	−0.152667	+	0.110919i
$437$	0.894219	−	1.23079i	0.0427763	−	0.0588765i
$438$	−1.39991	+	1.92681i	−0.0668901	+	0.0920664i
$439$	−24.8822	+	18.0780i	−1.18756	+	0.862815i	−0.993005	−	0.118076i	$-0.962327\pi$
$439$	−24.8822	+	18.0780i	−1.18756	+	0.862815i	−0.194558	+	0.980891i	$0.562327\pi$
$440$		0			0
$441$	2.44951	+	1.77968i	0.116644	+	0.0847465i
$442$	0.266570	−	0.0866140i	0.0126795	−	0.00411981i
$443$			11.3527i			0.539381i	0.962947	+	0.269691i	$0.0869214\pi$
$443$			11.3527i			0.539381i	−0.962947	+	0.269691i	$0.913079\pi$
$444$	−7.23434	−	22.2650i	−0.343327	−	1.05665i
$445$		0			0
$446$	−0.375171	+	1.15466i	−0.0177649	+	0.0546747i
$447$	−26.3503	−	8.56172i	−1.24633	−	0.404956i
$448$	13.8116	+	19.0100i	0.652535	+	0.898137i
$449$	15.7661			0.744050			0.372025	−	0.928223i	$-0.378664\pi$
$449$	15.7661			0.744050			0.372025	+	0.928223i	$0.378664\pi$
$450$		0			0
$451$	−2.03029			−0.0956027
$452$	−12.0526	−	16.5890i	−0.566907	−	0.780280i
$453$	−5.44279	−	1.76847i	−0.255725	−	0.0830900i
$454$	0.758027	−	2.33297i	0.0355760	−	0.109492i
$455$		0			0
$456$	−0.571844	−	1.75996i	−0.0267791	−	0.0824175i
$457$			4.16714i			0.194931i	0.995239	+	0.0974653i	$0.0310735\pi$
$457$			4.16714i			0.194931i	−0.995239	+	0.0974653i	$0.968926\pi$
$458$	−1.75718	+	0.570941i	−0.0821075	+	0.0266783i
$459$	−23.5684	−	17.1234i	−1.10008	−	0.799254i
$460$		0			0
$461$	19.3933	−	14.0900i	0.903235	−	0.656239i	−0.0360595	−	0.999350i	$-0.511481\pi$
$461$	19.3933	−	14.0900i	0.903235	−	0.656239i	0.939295	+	0.343111i	$0.111481\pi$
$462$	−1.03355	+	1.42256i	−0.0480852	+	0.0661836i
$463$	24.2900	−	33.4324i	1.12885	−	1.55373i	0.338624	−	0.940922i	$-0.390038\pi$
$463$	24.2900	−	33.4324i	1.12885	−	1.55373i	0.790229	−	0.612812i	$-0.209962\pi$
$464$	18.1747	−	13.2047i	0.843737	−	0.613011i
$465$		0			0
$466$	3.26098	+	2.36924i	0.151062	+	0.109753i
$467$	−9.88775	+	3.21272i	−0.457550	+	0.148667i	−0.528719	−	0.848797i	$-0.677327\pi$
$467$	−9.88775	+	3.21272i	−0.457550	+	0.148667i	0.0711682	+	0.997464i	$0.477327\pi$
$468$			0.485697i			0.0224513i
$469$	6.94082	+	21.3616i	0.320497	+	0.986389i
$470$		0			0
$471$	−1.94851	+	5.99689i	−0.0897825	+	0.276322i
$472$	4.10192	+	1.33279i	0.188806	+	0.0613468i
$473$	−3.81119	−	5.24565i	−0.175239	−	0.241195i
$474$	2.09243			0.0961086
$475$		0			0
$476$	−33.1065			−1.51743
$477$	−3.96806	−	5.46156i	−0.181685	−	0.250068i
$478$	1.31706	+	0.427937i	0.0602407	+	0.0195734i
$479$	−11.1271	+	34.2458i	−0.508411	+	1.56473i	0.286548	+	0.958066i	$0.407492\pi$
$479$	−11.1271	+	34.2458i	−0.508411	+	1.56473i	−0.794959	+	0.606663i	$0.792508\pi$
$480$		0			0
$481$	−0.740748	−	2.27979i	−0.0337752	−	0.103949i
$482$			3.73571i			0.170157i
$483$	4.01342	−	1.30404i	0.182617	−	0.0593358i
$484$	11.1362	+	8.09094i	0.506192	+	0.367770i
$485$		0			0
$486$	−1.24217	+	0.902487i	−0.0563458	+	0.0409377i
$487$	−6.25275	+	8.60617i	−0.283339	+	0.389983i	−0.926836	−	0.375466i	$-0.877483\pi$
$487$	−6.25275	+	8.60617i	−0.283339	+	0.389983i	0.643497	+	0.765448i	$0.277483\pi$
$488$	−0.391014	+	0.538185i	−0.0177004	+	0.0243625i
$489$	−18.7274	+	13.6063i	−0.846883	+	0.615296i
$490$		0			0
$491$	14.2947	+	10.3857i	0.645112	+	0.468701i	0.861603	−	0.507583i	$-0.169461\pi$
$491$	14.2947	+	10.3857i	0.645112	+	0.468701i	−0.216491	+	0.976285i	$0.569461\pi$
$492$	2.79454	−	0.908000i	0.125987	−	0.0409358i
$493$			30.5243i			1.37475i
$494$	−0.0290289	−	0.0893417i	−0.00130607	−	0.00401967i
$495$		0			0
$496$	7.16211	−	22.0427i	0.321588	−	0.989747i
$497$	18.5107	+	6.01450i	0.830319	+	0.269787i
$498$	2.30038	+	3.16620i	0.103082	+	0.141881i
$499$	9.41734			0.421578			0.210789	−	0.977532i	$-0.432397\pi$
$499$	9.41734			0.421578			0.210789	+	0.977532i	$0.432397\pi$
$500$		0			0
$501$	−30.9595			−1.38317
$502$	1.13821	+	1.56661i	0.0508007	+	0.0699211i
$503$	−17.1316	−	5.56641i	−0.763862	−	0.248194i	−0.0989268	−	0.995095i	$-0.531541\pi$
$503$	−17.1316	−	5.56641i	−0.763862	−	0.248194i	−0.664935	+	0.746901i	$0.731541\pi$
$504$	−0.610113	+	1.87774i	−0.0271766	+	0.0836410i
$505$		0			0
$506$	−0.0995303	−	0.306323i	−0.00442466	−	0.0136177i
$507$			19.0060i			0.844088i
$508$	10.9408	−	3.55489i	0.485420	−	0.157723i
$509$	−12.9835	−	9.43307i	−0.575484	−	0.418114i	0.261609	−	0.965174i	$-0.415747\pi$
$509$	−12.9835	−	9.43307i	−0.575484	−	0.418114i	−0.837093	+	0.547060i	$0.815747\pi$
$510$		0			0
$511$	23.3033	−	16.9308i	1.03088	−	0.748976i
$512$	−8.04540	+	11.0735i	−0.355560	+	0.489386i
$513$	−5.73896	+	7.89900i	−0.253381	+	0.348749i
$514$	3.00380	−	2.18239i	0.132492	−	0.0962611i
$515$		0			0
$516$	7.59180	+	5.51577i	0.334210	+	0.242818i
$517$	−8.02684	+	2.60808i	−0.353020	+	0.114703i
$518$		−	4.83095i		−	0.212260i
$519$	3.25979	+	10.0326i	0.143089	+	0.440383i
$520$		0			0
$521$	−0.680052	+	2.09298i	−0.0297936	+	0.0916953i	−0.964848	−	0.262810i	$-0.915351\pi$
$521$	−0.680052	+	2.09298i	−0.0297936	+	0.0916953i	0.935054	+	0.354505i	$0.115351\pi$
$522$	0.858316	+	0.278884i	0.0375675	+	0.0122064i
$523$	4.37070	+	6.01575i	0.191117	+	0.263050i	0.893813	−	0.448440i	$-0.148020\pi$
$523$	4.37070	+	6.01575i	0.191117	+	0.263050i	−0.702695	+	0.711491i	$0.748020\pi$
$524$	−2.94307			−0.128569
$525$		0			0
$526$	5.14547			0.224353
$527$	18.5103	+	25.4773i	0.806323	+	1.10981i
$528$	10.6388	+	3.45675i	0.462993	+	0.150436i
$529$	6.86853	−	21.1392i	0.298632	−	0.919094i
$530$		0			0
$531$	−1.52875	−	4.70502i	−0.0663423	−	0.204181i
$532$			11.0957i			0.481061i
$533$	0.286142	−	0.0929731i	0.0123942	−	0.00402711i
$534$	1.64172	+	1.19278i	0.0710441	+	0.0516165i
$535$		0			0
$536$	−4.04870	+	2.94155i	−0.174877	+	0.127056i
$537$	−6.95555	+	9.57350i	−0.300154	+	0.413127i
$538$	2.18809	−	3.01165i	0.0943353	−	0.129841i
$539$	5.87861	−	4.27106i	0.253210	−	0.183968i
$540$		0			0
$541$	−16.7041	−	12.1362i	−0.718165	−	0.521777i	0.167632	−	0.985850i	$-0.446388\pi$
$541$	−16.7041	−	12.1362i	−0.718165	−	0.521777i	−0.885797	+	0.464072i	$0.846388\pi$
$542$	5.47824	−	1.77999i	0.235310	−	0.0764570i
$543$		−	30.3473i		−	1.30233i
$544$	−3.42878	−	10.5527i	−0.147008	−	0.452443i
$545$		0			0
$546$	0.0805217	−	0.247820i	0.00344601	−	0.0106057i
$547$	−29.8405	−	9.69577i	−1.27589	−	0.414561i	−0.408758	−	0.912643i	$-0.634038\pi$
$547$	−29.8405	−	9.69577i	−1.27589	−	0.414561i	−0.867130	+	0.498082i	$0.834038\pi$
$548$	9.07211	+	12.4867i	0.387541	+	0.533405i
$549$	0.763042			0.0325658
$550$		0			0
$551$	10.2303			0.435825
$552$	0.552658	+	0.760668i	0.0235227	+	0.0323762i
$553$	−24.0678	−	7.82012i	−1.02347	−	0.332545i
$554$	0.788511	−	2.42679i	0.0335006	−	0.103104i
$555$		0			0
$556$	−3.27624	−	10.0832i	−0.138944	−	0.427625i
$557$			22.3515i			0.947064i	0.880776	+	0.473532i	$0.157021\pi$
$557$			22.3515i			0.947064i	−0.880776	+	0.473532i	$0.842979\pi$
$558$	0.885518	−	0.287722i	0.0374870	−	0.0121803i
$559$	0.777350	+	0.564778i	0.0328784	+	0.0238875i
$560$		0			0
$561$	−12.2965	+	8.93390i	−0.519157	+	0.377189i
$562$	−2.78614	+	3.83480i	−0.117526	+	0.161761i
$563$	−20.2000	+	27.8029i	−0.851329	+	1.17175i	0.132240	+	0.991218i	$0.457783\pi$
$563$	−20.2000	+	27.8029i	−0.851329	+	1.17175i	−0.983568	+	0.180536i	$0.942217\pi$
$564$	9.88191	−	7.17963i	0.416104	−	0.302317i
$565$		0			0
$566$	−3.51678	−	2.55509i	−0.147821	−	0.107398i
$567$	−18.0041	+	5.84987i	−0.756099	+	0.245672i
$568$			4.33657i			0.181958i
$569$	−9.93991	−	30.5919i	−0.416703	−	1.28248i	−0.910719	−	0.413026i	$-0.864472\pi$
$569$	−9.93991	−	30.5919i	−0.416703	−	1.28248i	0.494017	−	0.869452i	$-0.335528\pi$
$570$		0			0
$571$	−8.39501	+	25.8372i	−0.351320	+	1.08125i	0.606792	+	0.794861i	$0.292456\pi$
$571$	−8.39501	+	25.8372i	−0.351320	+	1.08125i	−0.958112	+	0.286392i	$0.907544\pi$
$572$	1.10858	+	0.360198i	0.0463519	+	0.0150607i
$573$	−15.5996	−	21.4710i	−0.651684	−	0.896966i
$574$	0.606344			0.0253083
$575$		0			0
$576$	6.00521			0.250217
$577$	8.14100	+	11.2051i	0.338914	+	0.466476i	0.944124	−	0.329591i	$-0.106911\pi$
$577$	8.14100	+	11.2051i	0.338914	+	0.466476i	−0.605210	+	0.796066i	$0.706911\pi$
$578$	1.68219	+	0.546575i	0.0699697	+	0.0227345i
$579$	3.08784	−	9.50340i	0.128326	−	0.394948i
$580$		0			0
$581$	−14.6266	−	45.0159i	−0.606812	−	1.86757i
$582$		−	1.81360i		−	0.0751759i
$583$	−15.4085	+	5.00652i	−0.638154	+	0.207349i
$584$	5.19215	+	3.77232i	0.214853	+	0.156100i
$585$		0			0
$586$	1.82315	−	1.32460i	0.0753138	−	0.0547187i
$587$	−25.9507	+	35.7180i	−1.07110	+	1.47424i	−0.202139	+	0.979357i	$0.564789\pi$
$587$	−25.9507	+	35.7180i	−1.07110	+	1.47424i	−0.868959	+	0.494884i	$0.835211\pi$
$588$	−6.18131	+	8.50785i	−0.254913	+	0.350858i
$589$	8.53877	−	6.20378i	0.351834	−	0.255622i
$590$		0			0
$591$	9.52115	+	6.91752i	0.391648	+	0.284549i
$592$	−29.2287	+	9.49699i	−1.20129	+	0.390324i
$593$		−	16.2531i		−	0.667437i	−0.942673	−	0.333718i	$-0.891697\pi$
$593$		−	16.2531i		−	0.667437i	0.942673	−	0.333718i	$-0.108303\pi$
$594$	0.638770	+	1.96593i	0.0262091	+	0.0806632i
$595$		0			0
$596$	−11.4380	+	35.2026i	−0.468520	+	1.44196i
$597$	7.28630	+	2.36746i	0.298208	+	0.0968938i
$598$	0.0280549	+	0.0386142i	0.00114725	+	0.00157905i
$599$	−30.4822			−1.24547			−0.622734	−	0.782433i	$-0.713978\pi$
$599$	−30.4822			−1.24547			−0.622734	+	0.782433i	$0.713978\pi$
$600$		0			0
$601$	−28.9162			−1.17952			−0.589758	−	0.807580i	$-0.700777\pi$
$601$	−28.9162			−1.17952			−0.589758	+	0.807580i	$0.700777\pi$
$602$	1.13821	+	1.56661i	0.0463899	+	0.0638502i
$603$	5.45932	+	1.77384i	0.222321	+	0.0722364i
$604$	−2.36259	+	7.27129i	−0.0961322	+	0.295865i
$605$		0			0
$606$	−1.01609	−	3.12721i	−0.0412760	−	0.127034i
$607$		−	8.23276i		−	0.334157i	−0.985944	−	0.167079i	$-0.946567\pi$
$607$		−	8.23276i		−	0.334157i	0.985944	−	0.167079i	$-0.0534334\pi$
$608$	−3.53676	+	1.14916i	−0.143435	+	0.0466047i
$609$	22.9577	+	16.6797i	0.930293	+	0.675897i
$610$		0			0
$611$	1.01184	−	0.735146i	0.0409347	−	0.0297408i
$612$	−4.97320	+	6.84503i	−0.201030	+	0.276694i
$613$	2.82026	−	3.88175i	0.113909	−	0.156783i	−0.748256	−	0.663411i	$-0.769108\pi$
$613$	2.82026	−	3.88175i	0.113909	−	0.156783i	0.862165	+	0.506628i	$0.169108\pi$
$614$	0.634619	−	0.461078i	0.0256111	−	0.0186076i
$615$		0			0
$616$	3.83337	+	2.78510i	0.154451	+	0.112215i
$617$	−1.93239	+	0.627872i	−0.0777951	+	0.0252772i	−0.347656	−	0.937622i	$-0.613022\pi$
$617$	−1.93239	+	0.627872i	−0.0777951	+	0.0252772i	0.269861	+	0.962899i	$0.413022\pi$
$618$		−	0.372454i		−	0.0149823i
$619$	−2.51571	−	7.74255i	−0.101115	−	0.311200i	0.887684	−	0.460453i	$-0.152313\pi$
$619$	−2.51571	−	7.74255i	−0.101115	−	0.311200i	−0.988799	+	0.149253i	$0.952313\pi$
$620$		0			0
$621$	1.53299	−	4.71806i	0.0615167	−	0.189329i
$622$	−4.46783	−	1.45169i	−0.179144	−	0.0582073i
$623$	−14.4258	−	19.8554i	−0.577956	−	0.795488i
$624$	−1.65769			−0.0663605
$625$		0			0
$626$	−4.09413			−0.163634
$627$	2.99421	+	4.12118i	0.119577	+	0.164584i
$628$	8.01153	+	2.60310i	0.319695	+	0.103875i
$629$	12.9040	−	39.7143i	0.514515	−	1.58351i
$630$		0			0
$631$	10.2855	+	31.6557i	0.409461	+	1.26019i	0.917112	+	0.398629i	$0.130514\pi$
$631$	10.2855	+	31.6557i	0.409461	+	1.26019i	−0.507651	+	0.861563i	$0.669486\pi$
$632$		−	5.63846i		−	0.224286i
$633$	−23.2412	+	7.55152i	−0.923754	+	0.300146i
$634$	3.24873	+	2.36034i	0.129024	+	0.0937412i
$635$		0			0
$636$	18.9695	−	13.7822i	0.752191	−	0.546499i
$637$	−0.632925	+	0.871147i	−0.0250774	+	0.0345161i
$638$	1.27308	−	1.75224i	0.0504015	−	0.0693718i
$639$	4.02419	−	2.92375i	0.159195	−	0.115662i
$640$		0			0
$641$	32.3996	+	23.5397i	1.27971	+	0.929761i	0.999544	−	0.0301916i	$-0.00961174\pi$
$641$	32.3996	+	23.5397i	1.27971	+	0.929761i	0.280162	+	0.959953i	$0.409612\pi$
$642$	−4.05881	+	1.31879i	−0.160189	+	0.0520484i
$643$		−	11.6870i		−	0.460890i	−0.973085	−	0.230445i	$-0.925982\pi$
$643$		−	11.6870i		−	0.460890i	0.973085	−	0.230445i	$-0.0740182\pi$
$644$	−1.74213	−	5.36172i	−0.0686495	−	0.211281i
$645$		0			0
$646$	0.505688	−	1.55635i	0.0198960	−	0.0612337i
$647$	7.56029	+	2.45649i	0.297226	+	0.0965745i	0.453834	−	0.891086i	$-0.350056\pi$
$647$	7.56029	+	2.45649i	0.297226	+	0.0965745i	−0.156608	+	0.987661i	$0.550056\pi$
$648$	−2.47920	−	3.41233i	−0.0973923	−	0.134049i
$649$	−11.8727			−0.466044
$650$		0			0
$651$	29.2766			1.14744
$652$	18.1773	+	25.0188i	0.711876	+	0.979814i
$653$	3.17402	+	1.03130i	0.124209	+	0.0403579i	0.370462	−	0.928848i	$-0.379199\pi$
$653$	3.17402	+	1.03130i	0.124209	+	0.0403579i	−0.246253	+	0.969206i	$0.579199\pi$
$654$	0.166948	−	0.513814i	0.00652820	−	0.0200917i
$655$		0			0
$656$	−1.19199	−	3.66857i	−0.0465394	−	0.143234i
$657$		−	7.36146i		−	0.287198i
$658$	2.39721	−	0.778899i	0.0934528	−	0.0303647i
$659$	−24.3116	−	17.6634i	−0.947046	−	0.688069i	0.00306074	−	0.999995i	$-0.499026\pi$
$659$	−24.3116	−	17.6634i	−0.947046	−	0.688069i	−0.950106	+	0.311926i	$0.899026\pi$
$660$		0			0
$661$	5.32670	−	3.87008i	0.207185	−	0.150529i	−0.479354	−	0.877621i	$-0.659129\pi$
$661$	5.32670	−	3.87008i	0.207185	−	0.150529i	0.686539	+	0.727093i	$0.259129\pi$
$662$	0.965008	−	1.32822i	0.0375061	−	0.0516227i
$663$	1.32391	−	1.82220i	0.0514163	−	0.0707685i
$664$	8.53192	−	6.19880i	0.331103	−	0.240560i
$665$		0			0
$666$	−0.998835	−	0.725696i	−0.0387041	−	0.0281202i
$667$	−4.94352	+	1.60625i	−0.191414	+	0.0621941i
$668$			41.3603i			1.60028i
$669$	3.01483	+	9.27870i	0.116560	+	0.358735i
$670$		0			0
$671$	0.565881	−	1.74160i	0.0218456	−	0.0672339i
$672$	−9.81044	−	3.18760i	−0.378446	−	0.122964i
$673$	−3.95662	−	5.44582i	−0.152516	−	0.209921i	0.725921	−	0.687778i	$-0.241414\pi$
$673$	−3.95662	−	5.44582i	−0.152516	−	0.209921i	−0.878438	+	0.477857i	$0.841414\pi$
$674$	5.32730			0.205200
$675$		0			0
$676$	25.3911			0.976580
$677$	8.02200	+	11.0413i	0.308310	+	0.424353i	0.934853	−	0.355034i	$-0.115531\pi$
$677$	8.02200	+	11.0413i	0.308310	+	0.424353i	−0.626543	+	0.779387i	$0.715531\pi$
$678$	2.67386	+	0.868788i	0.102689	+	0.0333656i
$679$	−6.77801	+	20.8606i	−0.260116	+	0.800555i
$680$		0			0
$681$	−6.09142	−	18.7474i	−0.233424	−	0.718404i
$682$		−	2.23453i		−	0.0855645i
$683$	−1.11483	+	0.362229i	−0.0426577	+	0.0138603i	−0.330268	−	0.943887i	$-0.607139\pi$
$683$	−1.11483	+	0.362229i	−0.0426577	+	0.0138603i	0.287610	+	0.957747i	$0.407139\pi$
$684$	2.29413	+	1.66678i	0.0877181	+	0.0637309i
$685$		0			0
$686$	1.62693	−	1.18203i	0.0621164	−	0.0451302i
$687$	−8.72692	+	12.0116i	−0.332953	+	0.458270i
$688$	7.24091	−	9.96625i	0.276057	−	0.379960i
$689$	1.94235	−	1.41120i	0.0739978	−	0.0537625i
$690$		0			0
$691$	−9.92451	−	7.21058i	−0.377546	−	0.274303i	0.382787	−	0.923837i	$-0.374964\pi$
$691$	−9.92451	−	7.21058i	−0.377546	−	0.274303i	−0.760333	+	0.649533i	$0.774964\pi$
$692$	13.4031	−	4.35492i	0.509508	−	0.165549i
$693$		−	5.43497i		−	0.206457i
$694$	−0.809268	−	2.49067i	−0.0307194	−	0.0945445i
$695$		0			0
$696$	−1.95381	+	6.01321i	−0.0740590	+	0.227930i
$697$	4.98464	+	1.61961i	0.188807	+	0.0613471i
$698$	−0.605493	−	0.833390i	−0.0229183	−	0.0315443i
$699$	32.3910			1.22514
$700$		0			0
$701$	−20.0271			−0.756415			−0.378207	−	0.925721i	$-0.623459\pi$
$701$	−20.0271			−0.756415			−0.378207	+	0.925721i	$0.623459\pi$
$702$	−0.180052	−	0.247820i	−0.00679562	−	0.00935337i
$703$	−13.3103	−	4.32479i	−0.502009	−	0.163113i
$704$	4.45354	−	13.7066i	0.167849	−	0.516586i
$705$		0			0
$706$	0.108111	+	0.332731i	0.00406880	+	0.0125225i
$707$			39.7677i			1.49562i
$708$	16.3418	−	5.30979i	0.614164	−	0.199554i
$709$	−3.55571	−	2.58337i	−0.133537	−	0.0970206i	0.519011	−	0.854767i	$-0.326300\pi$
$709$	−3.55571	−	2.58337i	−0.133537	−	0.0970206i	−0.652549	+	0.757747i	$0.726300\pi$
$710$		0			0
$711$	−5.23230	+	3.80149i	−0.196227	+	0.142567i
$712$	3.21417	−	4.42392i	0.120456	−	0.165793i
$713$	−3.15209	+	4.33848i	−0.118047	+	0.162477i
$714$	3.67232	−	2.66810i	0.137433	−	0.0998511i
$715$		0			0
$716$	12.7897	+	9.29226i	0.477974	+	0.347268i
$717$	10.5837	−	3.43885i	0.395256	−	0.128426i
$718$			4.06727i			0.151789i
$719$	3.37704	+	10.3934i	0.125942	+	0.387610i	0.994072	−	0.108728i	$-0.0346777\pi$
$719$	3.37704	+	10.3934i	0.125942	+	0.387610i	−0.868129	+	0.496338i	$0.834678\pi$
$720$		0			0
$721$	−1.39199	+	4.28409i	−0.0518403	+	0.159548i
$722$	2.78832	+	0.905980i	0.103771	+	0.0337171i
$723$	17.6452	+	24.2865i	0.656230	+	0.903224i
$724$	−40.5425			−1.50675
$725$		0			0
$726$	−1.88734			−0.0700458
$727$	−19.3400	−	26.6193i	−0.717282	−	0.987254i	−0.999610	−	0.0279359i	$-0.991107\pi$
$727$	−19.3400	−	26.6193i	−0.717282	−	0.987254i	0.282328	−	0.959318i	$-0.408893\pi$
$728$	−0.667799	−	0.216981i	−0.0247503	−	0.00804185i
$729$	−9.19466	+	28.2982i	−0.340543	+	1.04808i
$730$		0			0
$731$	5.17242	+	15.9191i	0.191309	+	0.588788i
$732$			2.65026i			0.0979564i
$733$	13.0768	−	4.24891i	0.483002	−	0.156937i	−0.0573871	−	0.998352i	$-0.518277\pi$
$733$	13.0768	−	4.24891i	0.483002	−	0.156937i	0.540389	+	0.841415i	$0.318277\pi$
$734$	−3.17792	−	2.30889i	−0.117299	−	0.0852227i
$735$		0			0
$736$	1.52862	−	1.11061i	0.0563456	−	0.0409375i
$737$	8.09739	−	11.1451i	0.298271	−	0.410535i
$738$	0.0910839	−	0.125366i	0.00335285	−	0.00461480i
$739$	−34.9409	+	25.3860i	−1.28532	+	0.933840i	−0.999700	−	0.0245030i	$-0.992200\pi$
$739$	−34.9409	+	25.3860i	−1.28532	+	0.933840i	−0.285621	+	0.958343i	$0.592200\pi$
$740$		0			0
$741$	−0.610715	−	0.443711i	−0.0224352	−	0.0163001i
$742$	4.60173	−	1.49519i	0.168935	−	0.0548902i
$743$		−	31.8479i		−	1.16838i	−0.811615	−	0.584192i	$-0.801411\pi$
$743$		−	31.8479i		−	1.16838i	0.811615	−	0.584192i	$-0.198589\pi$
$744$	2.01573	+	6.20378i	0.0739003	+	0.227442i
$745$		0			0
$746$	1.30979	−	4.03113i	0.0479550	−	0.147590i
$747$	−11.5046	−	3.73806i	−0.420930	−	0.136768i
$748$	11.9352	+	16.4274i	0.436395	+	0.600646i
$749$	51.6145			1.88595
$750$		0			0
$751$	−29.5952			−1.07995			−0.539973	−	0.841682i	$-0.681565\pi$
$751$	−29.5952			−1.07995			−0.539973	+	0.841682i	$0.681565\pi$
$752$	−9.42517	−	12.9726i	−0.343700	−	0.473063i
$753$	14.7993	+	4.80860i	0.539318	+	0.175235i
$754$	−0.0991824	+	0.305252i	−0.00361201	+	0.0111166i
$755$		0			0
$756$	11.1807	+	34.4107i	0.406639	+	1.25150i
$757$		−	0.0984401i		−	0.00357786i	−0.999998	−	0.00178893i	$-0.999431\pi$
$757$		−	0.0984401i		−	0.00357786i	0.999998	−	0.00178893i	$-0.000569435\pi$
$758$	3.77161	−	1.22547i	0.136991	−	0.0445111i
$759$	−2.09394	−	1.52134i	−0.0760052	−	0.0552210i
$760$		0			0
$761$	2.86717	−	2.08312i	0.103935	−	0.0755131i	−0.534604	−	0.845103i	$-0.679539\pi$
$761$	2.86717	−	2.08312i	0.103935	−	0.0755131i	0.638539	+	0.769590i	$0.279539\pi$
$762$	−0.927111	+	1.27606i	−0.0335857	+	0.0462267i
$763$	−3.84059	+	5.28612i	−0.139039	+	0.191370i
$764$	−28.6842	+	20.8403i	−1.03776	+	0.753975i
$765$		0			0
$766$	−0.837983	−	0.608830i	−0.0302775	−	0.0219979i
$767$	1.67330	−	0.543687i	0.0604192	−	0.0196314i
$768$			19.6989i			0.710822i
$769$	−0.441149	−	1.35772i	−0.0159083	−	0.0489606i	0.942787	−	0.333395i	$-0.108194\pi$
$769$	−0.441149	−	1.35772i	−0.0159083	−	0.0489606i	−0.958696	+	0.284434i	$0.908194\pi$
$770$		0			0
$771$	9.21997	−	28.3762i	0.332049	−	1.02194i
$772$	−12.6960	−	4.12520i	−0.456941	−	0.148469i
$773$	19.8558	+	27.3292i	0.714163	+	0.982962i	0.999698	+	0.0245930i	$0.00782898\pi$
$773$	19.8558	+	27.3292i	0.714163	+	0.982962i	−0.285534	+	0.958369i	$0.592171\pi$
$774$	0.494888			0.0177884

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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.107666 + 0.148189i) q^{2} +(1.39991 + 0.454857i) q^{3} +(0.607666 - 1.87020i) q^{4} +(0.0833172 + 0.256424i) q^{6} -3.26086i q^{7} +(0.690983 - 0.224514i) q^{8} +(-0.674207 - 0.489840i) q^{9} +O(q^{10})\)	\(q+(0.107666 + 0.148189i) q^{2} +(1.39991 + 0.454857i) q^{3} +(0.607666 - 1.87020i) q^{4} +(0.0833172 + 0.256424i) q^{6} -3.26086i q^{7} +(0.690983 - 0.224514i) q^{8} +(-0.674207 - 0.489840i) q^{9} +(-1.61803 + 1.17557i) q^{11} +(1.70135 - 2.34171i) q^{12} +(0.174207 - 0.239775i) q^{13} +(0.483224 - 0.351083i) q^{14} +(-3.07411 - 2.23347i) q^{16} +(4.91027 - 1.59545i) q^{17} -0.152649i q^{18} +(-0.534717 - 1.64569i) q^{19} +(1.48322 - 4.56489i) q^{21} +(-0.348414 - 0.113207i) q^{22} +(0.516776 + 0.711281i) q^{23} +1.06943 q^{24} +0.0542883 q^{26} +(-3.31659 - 4.56489i) q^{27} +(-6.09846 - 1.98151i) q^{28} +(-1.82696 + 5.62280i) q^{29} +(1.88486 + 5.80100i) q^{31} -2.14910i q^{32} +(-2.79981 + 0.909715i) q^{33} +(0.765097 + 0.555875i) q^{34} +(-1.32579 + 0.963245i) q^{36} +(4.75401 - 6.54333i) q^{37} +(0.186303 - 0.256424i) q^{38} +(0.352937 - 0.256424i) q^{39} +(0.821270 + 0.596687i) q^{41} +(0.836161 - 0.271685i) q^{42} +3.24199i q^{43} +(1.21533 + 3.74041i) q^{44} +(-0.0497651 + 0.153161i) q^{46} +(4.01342 + 1.30404i) q^{47} +(-3.28756 - 4.52494i) q^{48} -3.63318 q^{49} +7.59963 q^{51} +(-0.342569 - 0.471506i) q^{52} +(7.70424 + 2.50326i) q^{53} +(0.319385 - 0.982966i) q^{54} +(-0.732108 - 2.25320i) q^{56} -2.54703i q^{57} +(-1.02994 + 0.334648i) q^{58} +(4.80261 + 3.48930i) q^{59} +(-0.740748 + 0.538185i) q^{61} +(-0.656711 + 0.903885i) q^{62} +(-1.59730 + 2.19849i) q^{63} +(-5.82975 + 4.23556i) q^{64} +(-0.436254 - 0.316957i) q^{66} +(-6.55093 + 2.12853i) q^{67} -10.1527i q^{68} +(0.399907 + 1.23079i) q^{69} +(-1.84445 + 5.67664i) q^{71} +(-0.575842 - 0.187102i) q^{72} +(5.19215 + 7.14638i) q^{73} +1.48150 q^{74} -3.40270 q^{76} +(3.83337 + 5.27618i) q^{77} +(0.0759986 + 0.0246934i) q^{78} +(2.39818 - 7.38084i) q^{79} +(-1.79397 - 5.52127i) q^{81} +0.185946i q^{82} +(13.8049 - 4.48550i) q^{83} +(-7.63597 - 5.54786i) q^{84} +(-0.480429 + 0.349052i) q^{86} +(-5.11514 + 7.04039i) q^{87} +(-0.854102 + 1.17557i) q^{88} +(6.08901 - 4.42392i) q^{89} +(-0.781873 - 0.568064i) q^{91} +(1.64427 - 0.534255i) q^{92} +8.97820i q^{93} +(0.238863 + 0.735146i) q^{94} +(0.977536 - 3.00855i) q^{96} +(-6.39727 - 2.07860i) q^{97} +(-0.391169 - 0.538398i) q^{98} +1.66673 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9}+O(q^{10}) \) 8 * q - 5 * q^3 + 4 * q^4 + 6 * q^6 + 10 * q^8 + q^9	\( 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9} - 4 q^{11} + 10 q^{12} - 5 q^{13} - 7 q^{14} - 2 q^{16} + 15 q^{17} + 10 q^{19} + q^{21} + 10 q^{22} + 15 q^{23} - 20 q^{24} + 6 q^{26} - 5 q^{27} - 20 q^{28} + 15 q^{29} + q^{31} + 10 q^{33} - 12 q^{34} - 17 q^{36} - 5 q^{37} + 12 q^{39} - 9 q^{41} + 5 q^{42} + 8 q^{44} + 16 q^{46} - 15 q^{47} - 5 q^{48} + 14 q^{49} - 4 q^{51} - 20 q^{52} + 35 q^{53} - 10 q^{54} - 15 q^{56} - 20 q^{58} + 15 q^{59} + 6 q^{61} + 45 q^{62} - 20 q^{63} - 26 q^{64} - 18 q^{66} - 13 q^{69} - 29 q^{71} + 5 q^{72} + 10 q^{73} - 12 q^{74} - 20 q^{76} + 20 q^{77} - 25 q^{78} - 10 q^{79} - 12 q^{81} + 15 q^{83} - 27 q^{84} + 16 q^{86} - 55 q^{87} + 20 q^{88} + 40 q^{89} + q^{91} - 5 q^{92} - 7 q^{94} + 11 q^{96} - 10 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 5 * q^3 + 4 * q^4 + 6 * q^6 + 10 * q^8 + q^9 - 4 * q^11 + 10 * q^12 - 5 * q^13 - 7 * q^14 - 2 * q^16 + 15 * q^17 + 10 * q^19 + q^21 + 10 * q^22 + 15 * q^23 - 20 * q^24 + 6 * q^26 - 5 * q^27 - 20 * q^28 + 15 * q^29 + q^31 + 10 * q^33 - 12 * q^34 - 17 * q^36 - 5 * q^37 + 12 * q^39 - 9 * q^41 + 5 * q^42 + 8 * q^44 + 16 * q^46 - 15 * q^47 - 5 * q^48 + 14 * q^49 - 4 * q^51 - 20 * q^52 + 35 * q^53 - 10 * q^54 - 15 * q^56 - 20 * q^58 + 15 * q^59 + 6 * q^61 + 45 * q^62 - 20 * q^63 - 26 * q^64 - 18 * q^66 - 13 * q^69 - 29 * q^71 + 5 * q^72 + 10 * q^73 - 12 * q^74 - 20 * q^76 + 20 * q^77 - 25 * q^78 - 10 * q^79 - 12 * q^81 + 15 * q^83 - 27 * q^84 + 16 * q^86 - 55 * q^87 + 20 * q^88 + 40 * q^89 + q^91 - 5 * q^92 - 7 * q^94 + 11 * q^96 - 10 * q^97 - 40 * q^98 - 8 * q^99

Introduction

L-functions

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