LMFDB - Embedded newform 625.2.e.a.249.2

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			249.2
Root			$1.17421 - 0.0566033i$ of defining polynomial
Character	$\chi$	$=$	625.249
Dual form			625.2.e.a.374.2

$q$-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 $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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	−0.769253	−	0.638944i	$-0.779371\pi$
$2$	0.107666	−	0.148189i	0.0761313	−	0.104786i	0.845384	+	0.534159i	$0.179371\pi$
$3$	1.39991	−	0.454857i	0.808237	−	0.262612i	0.124386	−	0.992234i	$-0.460304\pi$
$3$	1.39991	−	0.454857i	0.808237	−	0.262612i	0.683851	+	0.729622i	$0.260304\pi$
$4$	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	$0.211346\pi$
$7$			3.26086i			1.23249i	−0.787555	+	0.616244i	$0.788654\pi$
$8$	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	0.316503	−	0.948591i	$-0.397491\pi$
$11$	−1.61803	−	1.17557i	−0.487856	−	0.354448i	−0.804359	+	0.594144i	$0.797491\pi$
$12$	1.70135	+	2.34171i	0.491138	+	0.675993i
$13$	0.174207	+	0.239775i	0.0483163	+	0.0665017i	0.832492	−	0.554038i	$-0.186914\pi$
$13$	0.174207	+	0.239775i	0.0483163	+	0.0665017i	−0.784175	+	0.620539i	$0.786914\pi$
$14$	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	0.836412	−	0.548102i	$-0.184649\pi$
$17$	4.91027	+	1.59545i	1.19092	+	0.386952i	0.354505	+	0.935054i	$0.384649\pi$
$18$			0.152649i			0.0359798i
$19$	−0.534717	+	1.64569i	−0.122672	+	0.377547i	−0.993470	−	0.114095i	$-0.963603\pi$
$19$	−0.534717	+	1.64569i	−0.122672	+	0.377547i	0.870797	+	0.491642i	$0.163603\pi$
$20$		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	−0.751734	−	0.659467i	$-0.770782\pi$
$23$	0.516776	−	0.711281i	0.107755	−	0.148312i	0.859489	+	0.511155i	$0.170782\pi$
$24$	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	−0.964587	−	0.263766i	$-0.915035\pi$
$29$	−1.82696	−	5.62280i	−0.339258	−	1.04413i	0.625329	−	0.780361i	$-0.284965\pi$
$30$		0			0
$31$	1.88486	−	5.80100i	0.338531	−	1.04189i	−0.626426	−	0.779481i	$-0.715483\pi$
$31$	1.88486	−	5.80100i	0.338531	−	1.04189i	0.964957	−	0.262409i	$-0.0845170\pi$
$32$			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	0.995109	+	0.0987860i	$0.0314959\pi$
$37$	4.75401	+	6.54333i	0.781554	+	1.07572i	−0.213554	+	0.976931i	$0.568504\pi$
$38$	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	−0.521805	−	0.853065i	$-0.674741\pi$
$41$	0.821270	−	0.596687i	0.128261	−	0.0931869i	0.650066	+	0.759878i	$0.274741\pi$
$42$	0.836161	+	0.271685i	0.129022	+	0.0419219i
$43$		−	3.24199i		−	0.494399i	−0.968965	−	0.247200i	$-0.920490\pi$
$43$		−	3.24199i		−	0.494399i	0.968965	−	0.247200i	$-0.0795103\pi$
$44$	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	−0.00130878	−	0.999999i	$-0.500417\pi$
$47$	4.01342	−	1.30404i	0.585417	−	0.190214i	0.586726	+	0.809786i	$0.300417\pi$
$48$	−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	0.272355	−	0.962197i	$-0.412198\pi$
$53$	7.70424	−	2.50326i	1.05826	−	0.343849i	0.785905	+	0.618348i	$0.212198\pi$
$54$	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	−0.229504	−	0.973308i	$-0.573710\pi$
$59$	4.80261	−	3.48930i	0.625246	−	0.454268i	0.854750	+	0.519040i	$0.173710\pi$
$60$		0			0
$61$	−0.740748	−	0.538185i	−0.0948431	−	0.0689075i	0.539353	−	0.842080i	$-0.318669\pi$
$61$	−0.740748	−	0.538185i	−0.0948431	−	0.0689075i	−0.634196	+	0.773172i	$0.718669\pi$
$62$	−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	−0.119829	−	0.992794i	$-0.538235\pi$
$67$	−6.55093	−	2.12853i	−0.800323	−	0.260041i	−0.680494	+	0.732754i	$0.738235\pi$
$68$			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	−0.998854	−	0.0478614i	$-0.984759\pi$
$71$	−1.84445	−	5.67664i	−0.218896	−	0.673694i	0.779958	−	0.625832i	$-0.215241\pi$
$72$	−0.575842	+	0.187102i	−0.0678636	+	0.0220502i
$73$	5.19215	−	7.14638i	0.607695	−	0.836420i	−0.388690	−	0.921368i	$-0.627072\pi$
$73$	5.19215	−	7.14638i	0.607695	−	0.836420i	0.996385	+	0.0849481i	$0.0270724\pi$
$74$	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	0.990545	+	0.137191i	$0.0438075\pi$
$79$	2.39818	+	7.38084i	0.269816	+	0.830409i	−0.720728	+	0.693218i	$0.756192\pi$
$80$		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	0.944433	−	0.328703i	$-0.106612\pi$
$83$	13.8049	+	4.48550i	1.51529	+	0.492347i	0.570856	+	0.821050i	$0.306612\pi$
$84$	−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	0.861713	−	0.507397i	$-0.169392\pi$
$89$	6.08901	+	4.42392i	0.645433	+	0.468935i	−0.216279	+	0.976332i	$0.569392\pi$
$90$		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	−0.615213	−	0.788361i	$-0.710930\pi$
$97$	−6.39727	+	2.07860i	−0.649544	+	0.211050i	−0.0343310	+	0.999411i	$0.510930\pi$
$98$	−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	−0.373027	−	0.927821i	$-0.621680\pi$
$103$	−1.31379	+	0.426878i	−0.129452	+	0.0420615i	0.243575	+	0.969882i	$0.421680\pi$
$104$	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	$-0.722689\pi$
$107$		−	15.8285i		−	1.53020i	0.643911	−	0.765101i	$-0.277311\pi$
$108$	−10.5527	−	3.42877i	−1.01543	−	0.329933i
$109$	−1.62108	+	1.17779i	−0.155272	+	0.112811i	−0.662708	−	0.748878i	$-0.730593\pi$
$109$	−1.62108	+	1.17779i	−0.155272	+	0.112811i	0.507437	+	0.861689i	$0.330593\pi$
$110$		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	0.993315	−	0.115434i	$-0.0368260\pi$
$113$	6.12912	+	8.43601i	0.576579	+	0.793593i	−0.416736	+	0.909028i	$0.636826\pi$
$114$	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	−0.628728	−	0.777625i	$-0.716424\pi$
$127$	3.43858	−	4.73280i	0.305125	−	0.419969i	0.933853	+	0.357657i	$0.116424\pi$
$128$	−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	−0.969225	−	0.246175i	$-0.920826\pi$
$131$	−0.462488	+	1.42339i	−0.0404077	+	0.124362i	0.928818	+	0.370537i	$0.120826\pi$
$132$		−	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	0.565111	−	0.825015i	$-0.308833\pi$
$137$	−4.61345	−	6.34987i	−0.394154	−	0.542506i	−0.959265	+	0.282509i	$0.908833\pi$
$138$	−0.139333	−	0.191776i	−0.0118608	−	0.0163250i
$139$	4.36183	+	3.16906i	0.369966	+	0.268796i	0.757197	−	0.653187i	$-0.226568\pi$
$139$	4.36183	+	3.16906i	0.369966	+	0.268796i	−0.387231	+	0.921983i	$0.626568\pi$
$140$		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	$-0.945319\pi$
$157$		−	4.28378i		−	0.341883i	0.985281	−	0.170941i	$-0.0546808\pi$
$158$	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	−0.999381	−	0.0351898i	$-0.988796\pi$
$163$	−9.24370	−	12.7229i	−0.724023	−	0.996531i	0.275358	−	0.961342i	$-0.411204\pi$
$164$	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	−0.594375	−	0.804188i	$-0.702601\pi$
$167$	−20.0036	−	6.49956i	−1.54792	−	0.502951i	−0.953549	+	0.301237i	$0.902601\pi$
$168$			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	−0.618283	−	0.785956i	$-0.712171\pi$
$173$	4.21244	−	5.79793i	0.320266	−	0.440808i	0.938548	+	0.345148i	$0.112171\pi$
$174$	−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	0.814275	−	0.580480i	$-0.197135\pi$
$179$	−2.48429	−	7.64586i	−0.185685	−	0.571479i	−0.999959	+	0.00900088i	$0.997135\pi$
$180$		0			0
$181$	−6.37104	+	19.6080i	−0.473555	+	1.45745i	0.374341	+	0.927291i	$0.377869\pi$
$181$	−6.37104	+	19.6080i	−0.473555	+	1.45745i	−0.847896	+	0.530162i	$0.822131\pi$
$182$			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	−0.973244	−	0.229774i	$-0.926201\pi$
$191$	−14.5868	+	10.5979i	−1.05546	+	0.766840i	−0.0822207	+	0.996614i	$0.526201\pi$
$192$	−10.0877	−	3.27769i	−0.728016	−	0.236547i
$193$			6.78859i			0.488653i	0.969693	+	0.244327i	$0.0785669\pi$
$193$			6.78859i			0.488653i	−0.969693	+	0.244327i	$0.921433\pi$
$194$	−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	−0.0253343	−	0.999679i	$-0.508065\pi$
$197$	7.60405	−	2.47071i	0.541766	−	0.176031i	0.567101	+	0.823648i	$0.308065\pi$
$198$	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	0.0200297	−	0.999799i	$-0.493624\pi$
$211$	−13.4313	−	9.75839i	−0.924646	−	0.671795i	−0.944676	+	0.328004i	$0.893624\pi$
$212$	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	−0.658399	−	0.752669i	$-0.728766\pi$
$223$	3.89589	−	5.36223i	0.260888	−	0.359082i	0.919287	+	0.393587i	$0.128766\pi$
$224$	−7.00792			−0.468236
$225$		0			0
$226$	1.91002			0.127053
$227$	−7.87158	+	10.8343i	−0.522455	+	0.719097i	−0.985957	−	0.166998i	$-0.946593\pi$
$227$	−7.87158	+	10.8343i	−0.522455	+	0.719097i	0.463502	+	0.886096i	$0.346593\pi$
$228$	−4.76347	+	1.54774i	−0.315468	+	0.102502i
$229$	−3.11697	−	9.59304i	−0.205975	−	0.633926i	−0.999672	−	0.0256124i	$-0.991846\pi$
$229$	−3.11697	−	9.59304i	−0.205975	−	0.633926i	0.793697	−	0.608313i	$-0.208154\pi$
$230$		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	0.899723	−	0.436461i	$-0.143768\pi$
$233$	20.9285	+	6.80007i	1.37107	+	0.445488i	0.471346	+	0.881948i	$0.343768\pi$
$234$	−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	0.767762	−	0.640736i	$-0.221371\pi$
$239$	6.11640	+	4.44383i	0.395637	+	0.287447i	−0.372124	+	0.928183i	$0.621371\pi$
$240$		0			0
$241$	16.4995	−	11.9876i	1.06283	−	0.772190i	0.0882188	−	0.996101i	$-0.471883\pi$
$241$	16.4995	−	11.9876i	1.06283	−	0.772190i	0.974610	+	0.223911i	$0.0718825\pi$
$242$	−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	$0.217850\pi$
$257$			20.2700i			1.26441i	−0.774801	+	0.632205i	$0.782150\pi$
$258$	−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	0.913501	+	0.406835i	$0.133368\pi$
$263$	16.5114	+	22.7260i	1.01814	+	1.40135i	0.104636	+	0.994511i	$0.466632\pi$
$264$	−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	0.555080	+	0.831797i	$0.312688\pi$
$269$	−6.28015	+	19.3283i	−0.382907	+	1.17847i	−0.937987	+	0.346670i	$0.887312\pi$
$270$		0			0
$271$	9.71756	+	29.9076i	0.590300	+	1.81676i	0.576854	+	0.816847i	$0.304280\pi$
$271$	9.71756	+	29.9076i	0.590300	+	1.81676i	0.0134456	+	0.999910i	$0.495720\pi$
$272$	−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	−0.980751	−	0.195262i	$-0.937444\pi$
$277$	−8.18813	+	11.2700i	−0.491977	+	0.677148i	0.488774	+	0.872410i	$0.337444\pi$
$278$	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	−0.366147	−	0.930557i	$-0.619323\pi$
$281$	7.99664	−	24.6111i	0.477040	−	1.46818i	0.843187	−	0.537620i	$-0.180677\pi$
$282$		−	1.13778i		−	0.0677541i
$283$	−22.5701	−	7.33348i	−1.34166	−	0.435930i	−0.451778	−	0.892130i	$-0.649210\pi$
$283$	−22.5701	−	7.33348i	−1.34166	−	0.435930i	−0.889877	+	0.456200i	$0.849210\pi$
$284$	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	$0.117009\pi$
$293$			12.3029i			0.718742i	−0.933195	+	0.359371i	$0.882991\pi$
$294$	−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	$0.0389973\pi$
$307$			4.28249i			0.244415i	−0.992505	+	0.122207i	$0.961003\pi$
$308$	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	−0.184768	−	0.982782i	$-0.559153\pi$
$311$	−20.7486	−	15.0747i	−1.17655	−	0.854810i	−0.991778	+	0.127972i	$0.959153\pi$
$312$	0.186303	+	0.256424i	0.0105473	+	0.0145171i
$313$	−13.1377	−	18.0825i	−0.742589	−	1.02209i	−0.998466	−	0.0553767i	$-0.982364\pi$
$313$	−13.1377	−	18.0825i	−0.742589	−	1.02209i	0.255876	−	0.966709i	$-0.417636\pi$
$314$	−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	0.829033	−	0.559200i	$-0.188892\pi$
$317$	20.8499	+	6.77453i	1.17105	+	0.380496i	0.342012	+	0.939695i	$0.388892\pi$
$318$		−	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	−0.997871	−	0.0652260i	$-0.979223\pi$
$331$	−2.76972	+	8.52431i	−0.152237	+	0.468539i	0.845633	+	0.533765i	$0.179223\pi$
$332$			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	0.959383	+	0.282108i	$0.0910337\pi$
$337$	17.0949	+	23.5291i	0.931218	+	1.28171i	−0.0281648	+	0.999603i	$0.508966\pi$
$338$	−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	−0.650331	−	0.759651i	$-0.725370\pi$
$347$	−13.5974	+	4.41807i	−0.729948	+	0.237175i	−0.0796174	+	0.996825i	$0.525370\pi$
$348$	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	−0.260276	−	0.965534i	$-0.583814\pi$
$353$	1.81649	−	0.590214i	0.0966821	−	0.0314139i	0.356959	+	0.934120i	$0.383814\pi$
$354$	−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	−0.00225634	−	0.999997i	$-0.500718\pi$
$359$	17.9639	−	13.0516i	0.948101	−	0.688835i	0.950357	+	0.311162i	$0.100718\pi$
$360$		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	−0.276236	−	0.961090i	$-0.589087\pi$
$367$	−20.3954	−	6.62686i	−1.06463	−	0.345919i	−0.788394	+	0.615170i	$0.789087\pi$
$368$			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	0.295653	+	0.955295i	$0.404463\pi$
$373$	−13.6013	+	18.7206i	−0.704248	+	0.969315i	−0.999902	+	0.0140195i	$0.995537\pi$
$374$	−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	0.962300	+	0.271992i	$0.0876824\pi$
$379$	6.69026	+	20.5905i	0.343656	+	1.05766i	−0.618644	+	0.785672i	$0.712318\pi$
$380$		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	0.168372	−	0.985723i	$-0.446149\pi$
$383$	−5.37804	−	1.74743i	−0.274805	−	0.0892896i	−0.443178	+	0.896434i	$0.646149\pi$
$384$	−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	0.408518	−	0.912750i	$-0.366046\pi$
$389$	−6.57411	−	4.77637i	−0.333321	−	0.242172i	−0.741838	+	0.670579i	$0.766046\pi$
$390$		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	0.231942	−	0.972730i	$-0.425492\pi$
$397$	19.7524	−	6.41794i	0.991343	−	0.322107i	0.759401	+	0.650623i	$0.225492\pi$
$398$	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	−0.344522	−	0.938778i	$-0.611959\pi$
$409$	8.93579	−	6.49223i	0.441846	−	0.321020i	0.786368	+	0.617758i	$0.211959\pi$
$410$		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	−0.316834	−	0.948481i	$-0.602620\pi$
$419$	10.1732	−	31.3099i	0.496993	−	1.52959i	0.813827	−	0.581107i	$-0.197380\pi$
$420$		0			0
$421$	−6.26214	−	19.2729i	−0.305198	−	0.939304i	−0.979603	−	0.200942i	$-0.935600\pi$
$421$	−6.26214	−	19.2729i	−0.305198	−	0.939304i	0.674405	−	0.738362i	$-0.264400\pi$
$422$	−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	−0.883576	−	0.468288i	$-0.844871\pi$
$431$	2.21110	−	6.80506i	0.106505	−	0.327788i	0.990081	+	0.140500i	$0.0448710\pi$
$432$		−	21.4405i		−	1.03156i
$433$	5.21430	+	1.69423i	0.250583	+	0.0814195i	0.431615	−	0.902058i	$-0.357944\pi$
$433$	5.21430	+	1.69423i	0.250583	+	0.0814195i	−0.181032	+	0.983477i	$0.557944\pi$
$434$	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	−0.194558	−	0.980891i	$-0.562327\pi$
$439$	−24.8822	−	18.0780i	−1.18756	−	0.862815i	−0.993005	+	0.118076i	$0.962327\pi$
$440$		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	$-0.913079\pi$
$443$		−	11.3527i		−	0.539381i	0.962947	−	0.269691i	$-0.0869214\pi$
$444$	−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	$-0.968926\pi$
$457$		−	4.16714i		−	0.194931i	0.995239	−	0.0974653i	$-0.0310735\pi$
$458$	−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	0.939295	−	0.343111i	$-0.111481\pi$
$461$	19.3933	+	14.0900i	0.903235	+	0.656239i	−0.0360595	+	0.999350i	$0.511481\pi$
$462$	−1.03355	−	1.42256i	−0.0480852	−	0.0661836i
$463$	24.2900	+	33.4324i	1.12885	+	1.55373i	0.790229	+	0.612812i	$0.209962\pi$
$463$	24.2900	+	33.4324i	1.12885	+	1.55373i	0.338624	+	0.940922i	$0.390038\pi$
$464$	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	0.0711682	−	0.997464i	$-0.477327\pi$
$467$	−9.88775	−	3.21272i	−0.457550	−	0.148667i	−0.528719	+	0.848797i	$0.677327\pi$
$468$		−	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	−0.794959	−	0.606663i	$-0.792508\pi$
$479$	−11.1271	−	34.2458i	−0.508411	−	1.56473i	0.286548	−	0.958066i	$-0.407492\pi$
$480$		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	0.643497	−	0.765448i	$-0.277483\pi$
$487$	−6.25275	−	8.60617i	−0.283339	−	0.389983i	−0.926836	+	0.375466i	$0.877483\pi$
$488$	−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	−0.216491	−	0.976285i	$-0.569461\pi$
$491$	14.2947	−	10.3857i	0.645112	−	0.468701i	0.861603	+	0.507583i	$0.169461\pi$
$492$	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	−0.664935	−	0.746901i	$-0.731541\pi$
$503$	−17.1316	+	5.56641i	−0.763862	+	0.248194i	−0.0989268	+	0.995095i	$0.531541\pi$
$504$	−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	−0.837093	−	0.547060i	$-0.815747\pi$
$509$	−12.9835	+	9.43307i	−0.575484	+	0.418114i	0.261609	+	0.965174i	$0.415747\pi$
$510$		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	0.935054	−	0.354505i	$-0.115351\pi$
$521$	−0.680052	−	2.09298i	−0.0297936	−	0.0916953i	−0.964848	+	0.262810i	$0.915351\pi$
$522$	0.858316	−	0.278884i	0.0375675	−	0.0122064i
$523$	4.37070	−	6.01575i	0.191117	−	0.263050i	−0.702695	−	0.711491i	$-0.748020\pi$
$523$	4.37070	−	6.01575i	0.191117	−	0.263050i	0.893813	+	0.448440i	$0.148020\pi$
$524$	−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	−0.885797	−	0.464072i	$-0.846388\pi$
$541$	−16.7041	+	12.1362i	−0.718165	+	0.521777i	0.167632	+	0.985850i	$0.446388\pi$
$542$	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	−0.867130	−	0.498082i	$-0.834038\pi$
$547$	−29.8405	+	9.69577i	−1.27589	+	0.414561i	−0.408758	+	0.912643i	$0.634038\pi$
$548$	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	$-0.842979\pi$
$557$		−	22.3515i		−	0.947064i	0.880776	−	0.473532i	$-0.157021\pi$
$558$	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	−0.983568	−	0.180536i	$-0.942217\pi$
$563$	−20.2000	−	27.8029i	−0.851329	−	1.17175i	0.132240	−	0.991218i	$-0.457783\pi$
$564$	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	0.494017	+	0.869452i	$0.335528\pi$
$569$	−9.93991	+	30.5919i	−0.416703	+	1.28248i	−0.910719	+	0.413026i	$0.864472\pi$
$570$		0			0
$571$	−8.39501	−	25.8372i	−0.351320	−	1.08125i	−0.958112	−	0.286392i	$-0.907544\pi$
$571$	−8.39501	−	25.8372i	−0.351320	−	1.08125i	0.606792	−	0.794861i	$-0.292456\pi$
$572$	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	−0.605210	−	0.796066i	$-0.706911\pi$
$577$	8.14100	−	11.2051i	0.338914	−	0.466476i	0.944124	+	0.329591i	$0.106911\pi$
$578$	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	−0.868959	−	0.494884i	$-0.835211\pi$
$587$	−25.9507	−	35.7180i	−1.07110	−	1.47424i	−0.202139	−	0.979357i	$-0.564789\pi$
$588$	−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	$0.108303\pi$
$593$			16.2531i			0.667437i	−0.942673	+	0.333718i	$0.891697\pi$
$594$	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	$0.0534334\pi$
$607$			8.23276i			0.334157i	−0.985944	+	0.167079i	$0.946567\pi$
$608$	−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	0.862165	−	0.506628i	$-0.169108\pi$
$613$	2.82026	+	3.88175i	0.113909	+	0.156783i	−0.748256	+	0.663411i	$0.769108\pi$
$614$	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	0.269861	−	0.962899i	$-0.413022\pi$
$617$	−1.93239	−	0.627872i	−0.0777951	−	0.0252772i	−0.347656	+	0.937622i	$0.613022\pi$
$618$			0.372454i			0.0149823i
$619$	−2.51571	+	7.74255i	−0.101115	+	0.311200i	−0.988799	−	0.149253i	$-0.952313\pi$
$619$	−2.51571	+	7.74255i	−0.101115	+	0.311200i	0.887684	+	0.460453i	$0.152313\pi$
$620$		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	−0.507651	−	0.861563i	$-0.669486\pi$
$631$	10.2855	−	31.6557i	0.409461	−	1.26019i	0.917112	−	0.398629i	$-0.130514\pi$
$632$			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	0.280162	−	0.959953i	$-0.409612\pi$
$641$	32.3996	−	23.5397i	1.27971	−	0.929761i	0.999544	+	0.0301916i	$0.00961174\pi$
$642$	−4.05881	−	1.31879i	−0.160189	−	0.0520484i
$643$			11.6870i			0.460890i	0.973085	+	0.230445i	$0.0740182\pi$
$643$			11.6870i			0.460890i	−0.973085	+	0.230445i	$0.925982\pi$
$644$	−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	−0.156608	−	0.987661i	$-0.550056\pi$
$647$	7.56029	−	2.45649i	0.297226	−	0.0965745i	0.453834	+	0.891086i	$0.350056\pi$
$648$	−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	−0.246253	−	0.969206i	$-0.579199\pi$
$653$	3.17402	−	1.03130i	0.124209	−	0.0403579i	0.370462	+	0.928848i	$0.379199\pi$
$654$	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	−0.950106	−	0.311926i	$-0.899026\pi$
$659$	−24.3116	+	17.6634i	−0.947046	+	0.688069i	0.00306074	+	0.999995i	$0.499026\pi$
$660$		0			0
$661$	5.32670	+	3.87008i	0.207185	+	0.150529i	0.686539	−	0.727093i	$-0.259129\pi$
$661$	5.32670	+	3.87008i	0.207185	+	0.150529i	−0.479354	+	0.877621i	$0.659129\pi$
$662$	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	−0.878438	−	0.477857i	$-0.841414\pi$
$673$	−3.95662	+	5.44582i	−0.152516	+	0.209921i	0.725921	+	0.687778i	$0.241414\pi$
$674$	5.32730			0.205200
$675$		0			0
$676$	25.3911			0.976580
$677$	8.02200	−	11.0413i	0.308310	−	0.424353i	−0.626543	−	0.779387i	$-0.715531\pi$
$677$	8.02200	−	11.0413i	0.308310	−	0.424353i	0.934853	+	0.355034i	$0.115531\pi$
$678$	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	0.287610	−	0.957747i	$-0.407139\pi$
$683$	−1.11483	−	0.362229i	−0.0426577	−	0.0138603i	−0.330268	+	0.943887i	$0.607139\pi$
$684$	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	−0.760333	−	0.649533i	$-0.774964\pi$
$691$	−9.92451	+	7.21058i	−0.377546	+	0.274303i	0.382787	+	0.923837i	$0.374964\pi$
$692$	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	−0.652549	−	0.757747i	$-0.726300\pi$
$709$	−3.55571	+	2.58337i	−0.133537	+	0.0970206i	0.519011	+	0.854767i	$0.326300\pi$
$710$		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	−0.868129	−	0.496338i	$-0.834678\pi$
$719$	3.37704	−	10.3934i	0.125942	−	0.387610i	0.994072	+	0.108728i	$0.0346777\pi$
$720$		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	0.282328	+	0.959318i	$0.408893\pi$
$727$	−19.3400	+	26.6193i	−0.717282	+	0.987254i	−0.999610	+	0.0279359i	$0.991107\pi$
$728$	−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	0.540389	−	0.841415i	$-0.318277\pi$
$733$	13.0768	+	4.24891i	0.483002	+	0.156937i	−0.0573871	+	0.998352i	$0.518277\pi$
$734$	−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	−0.285621	−	0.958343i	$-0.592200\pi$
$739$	−34.9409	−	25.3860i	−1.28532	−	0.933840i	−0.999700	+	0.0245030i	$0.992200\pi$
$740$		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	$0.198589\pi$
$743$			31.8479i			1.16838i	−0.811615	+	0.584192i	$0.801411\pi$
$744$	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	$0.000569435\pi$
$757$			0.0984401i			0.00357786i	−0.999998	+	0.00178893i	$0.999431\pi$
$758$	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	0.638539	−	0.769590i	$-0.279539\pi$
$761$	2.86717	+	2.08312i	0.103935	+	0.0755131i	−0.534604	+	0.845103i	$0.679539\pi$
$762$	−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	−0.958696	−	0.284434i	$-0.908194\pi$
$769$	−0.441149	+	1.35772i	−0.0159083	+	0.0489606i	0.942787	+	0.333395i	$0.108194\pi$
$770$		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	−0.285534	−	0.958369i	$-0.592171\pi$
$773$	19.8558	−	27.3292i	0.714163	−	0.982962i	0.999698	−	0.0245930i	$-0.00782898\pi$
$774$	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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