LMFDB - Embedded newform 520.2.ca.b.101.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(101,520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 5]))

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

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

chi := DirichletCharacter("520.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.ca (of order $6$, degree $2$, 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:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.20
Character	$\chi$	$=$	520.101
Dual form			520.2.ca.b.381.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.837733 + 1.13939i) q^{2} +(0.654624 - 0.377948i) q^{3} +(-0.596406 + 1.90900i) q^{4} +1.00000 q^{5} +(0.979029 + 0.429251i) q^{6} +(0.518819 + 0.299540i) q^{7} +(-2.67472 + 0.919699i) q^{8} +(-1.21431 + 2.10325i) q^{9} +O(q^{10})$	\(q+(0.837733 + 1.13939i) q^{2} +(0.654624 - 0.377948i) q^{3} +(-0.596406 + 1.90900i) q^{4} +1.00000 q^{5} +(0.979029 + 0.429251i) q^{6} +(0.518819 + 0.299540i) q^{7} +(-2.67472 + 0.919699i) q^{8} +(-1.21431 + 2.10325i) q^{9} +(0.837733 + 1.13939i) q^{10} +(0.495825 + 0.858794i) q^{11} +(0.331082 + 1.47509i) q^{12} +(1.20206 + 3.39927i) q^{13} +(0.0933396 + 0.842071i) q^{14} +(0.654624 - 0.377948i) q^{15} +(-3.28860 - 2.27708i) q^{16} +(3.48363 - 6.03382i) q^{17} +(-3.41368 + 0.378391i) q^{18} +(-2.07109 + 3.58723i) q^{19} +(-0.596406 + 1.90900i) q^{20} +0.452842 q^{21} +(-0.563130 + 1.28438i) q^{22} +(2.57315 + 4.45684i) q^{23} +(-1.40334 + 1.61296i) q^{24} +1.00000 q^{25} +(-2.86608 + 4.21729i) q^{26} +4.10347i q^{27} +(-0.881251 + 0.811781i) q^{28} +(3.70124 - 2.13691i) q^{29} +(0.979029 + 0.429251i) q^{30} -10.2309i q^{31} +(-0.160488 - 5.65458i) q^{32} +(0.649158 + 0.374792i) q^{33} +(9.79320 - 1.08553i) q^{34} +(0.518819 + 0.299540i) q^{35} +(-3.29089 - 3.57252i) q^{36} +(3.38708 + 5.86659i) q^{37} +(-5.82226 + 0.645370i) q^{38} +(2.07164 + 1.77093i) q^{39} +(-2.67472 + 0.919699i) q^{40} +(-1.99903 + 1.15414i) q^{41} +(0.379361 + 0.515963i) q^{42} +(-8.49472 - 4.90443i) q^{43} +(-1.93516 + 0.434342i) q^{44} +(-1.21431 + 2.10325i) q^{45} +(-2.92244 + 6.66546i) q^{46} -5.84920i q^{47} +(-3.01342 - 0.247717i) q^{48} +(-3.32055 - 5.75136i) q^{49} +(0.837733 + 1.13939i) q^{50} -5.26651i q^{51} +(-7.20614 + 0.267391i) q^{52} +1.02996i q^{53} +(-4.67544 + 3.43761i) q^{54} +(0.495825 + 0.858794i) q^{55} +(-1.66319 - 0.324031i) q^{56} +3.13105i q^{57} +(5.53542 + 2.42698i) q^{58} +(0.213398 - 0.369616i) q^{59} +(0.331082 + 1.47509i) q^{60} +(7.52376 + 4.34384i) q^{61} +(11.6569 - 8.57075i) q^{62} +(-1.26002 + 0.727471i) q^{63} +(6.30831 - 4.91988i) q^{64} +(1.20206 + 3.39927i) q^{65} +(0.116789 + 1.05362i) q^{66} +(-5.26656 - 9.12195i) q^{67} +(9.44093 + 10.2489i) q^{68} +(3.36890 + 1.94504i) q^{69} +(0.0933396 + 0.842071i) q^{70} +(2.90416 + 1.67672i) q^{71} +(1.31359 - 6.74241i) q^{72} -11.3352i q^{73} +(-3.84685 + 8.77383i) q^{74} +(0.654624 - 0.377948i) q^{75} +(-5.61283 - 6.09316i) q^{76} +0.594079i q^{77} +(-0.282291 + 3.84397i) q^{78} -1.48646 q^{79} +(-3.28860 - 2.27708i) q^{80} +(-2.09204 - 3.62352i) q^{81} +(-2.98967 - 1.31081i) q^{82} -8.05860 q^{83} +(-0.270078 + 0.864478i) q^{84} +(3.48363 - 6.03382i) q^{85} +(-1.52827 - 13.7874i) q^{86} +(1.61528 - 2.79775i) q^{87} +(-2.11603 - 1.84103i) q^{88} +(4.06454 - 2.34667i) q^{89} +(-3.41368 + 0.378391i) q^{90} +(-0.394568 + 2.12367i) q^{91} +(-10.0428 + 2.25408i) q^{92} +(-3.86674 - 6.69738i) q^{93} +(6.66451 - 4.90007i) q^{94} +(-2.07109 + 3.58723i) q^{95} +(-2.24219 - 3.64097i) q^{96} +(12.6350 + 7.29481i) q^{97} +(3.77129 - 8.60150i) q^{98} -2.40834 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9}+O(q^{10}) $ 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9	$ 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9} - 8 q^{11} + 6 q^{12} - 4 q^{14} + 14 q^{16} + 18 q^{18} - 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 22 q^{24} + 56 q^{25} - 37 q^{26} - 12 q^{28} - 13 q^{30} - 30 q^{32} - 16 q^{34} + 15 q^{36} + 4 q^{37} - 24 q^{39} - 61 q^{42} + 24 q^{44} + 28 q^{45} - 19 q^{46} - 51 q^{48} + 20 q^{49} - 64 q^{52} - 5 q^{54} - 8 q^{55} - 23 q^{56} - q^{58} - 16 q^{59} + 6 q^{60} + 10 q^{62} - 30 q^{64} + 14 q^{66} - 36 q^{67} - 51 q^{68} - 4 q^{70} - 81 q^{72} + 70 q^{74} - 60 q^{76} + 143 q^{78} + 14 q^{80} - 28 q^{81} + 21 q^{82} + 40 q^{83} + 31 q^{84} - 28 q^{86} - 36 q^{87} - 19 q^{88} + 18 q^{90} + 16 q^{91} - 18 q^{92} + 43 q^{94} - 16 q^{95} - 48 q^{96} + 24 q^{97} + 56 q^{98} - 48 q^{99}+O(q^{100}) $ 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9 - 8 * q^11 + 6 * q^12 - 4 * q^14 + 14 * q^16 + 18 * q^18 - 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 22 * q^24 + 56 * q^25 - 37 * q^26 - 12 * q^28 - 13 * q^30 - 30 * q^32 - 16 * q^34 + 15 * q^36 + 4 * q^37 - 24 * q^39 - 61 * q^42 + 24 * q^44 + 28 * q^45 - 19 * q^46 - 51 * q^48 + 20 * q^49 - 64 * q^52 - 5 * q^54 - 8 * q^55 - 23 * q^56 - q^58 - 16 * q^59 + 6 * q^60 + 10 * q^62 - 30 * q^64 + 14 * q^66 - 36 * q^67 - 51 * q^68 - 4 * q^70 - 81 * q^72 + 70 * q^74 - 60 * q^76 + 143 * q^78 + 14 * q^80 - 28 * q^81 + 21 * q^82 + 40 * q^83 + 31 * q^84 - 28 * q^86 - 36 * q^87 - 19 * q^88 + 18 * q^90 + 16 * q^91 - 18 * q^92 + 43 * q^94 - 16 * q^95 - 48 * q^96 + 24 * q^97 + 56 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	0.837733	+	1.13939i	0.592367	+	0.805668i
$2$	0.837733	+	1.13939i	0.592367	+	0.805668i
$3$	0.654624	−	0.377948i	0.377948	−	0.218208i	−0.298977	−	0.954260i	$-0.596646\pi$
$3$	0.654624	−	0.377948i	0.377948	−	0.218208i	0.676925	+	0.736052i	$0.263312\pi$
$4$	−0.596406	+	1.90900i	−0.298203	+	0.954502i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	0.979029	+	0.429251i	0.399687	+	0.175241i
$7$	0.518819	+	0.299540i	0.196095	+	0.113216i	0.594833	−	0.803849i	$-0.297218\pi$
$7$	0.518819	+	0.299540i	0.196095	+	0.113216i	−0.398738	+	0.917065i	$0.630552\pi$
$8$	−2.67472	+	0.919699i	−0.945658	+	0.325163i
$9$	−1.21431	+	2.10325i	−0.404770	+	0.701083i
$10$	0.837733	+	1.13939i	0.264914	+	0.360306i
$11$	0.495825	+	0.858794i	0.149497	+	0.258936i	0.931042	−	0.364913i	$-0.118901\pi$
$11$	0.495825	+	0.858794i	0.149497	+	0.258936i	−0.781545	+	0.623849i	$0.785568\pi$
$12$	0.331082	+	1.47509i	0.0955750	+	0.425822i
$13$	1.20206	+	3.39927i	0.333391	+	0.942789i
$13$	1.20206	+	3.39927i	0.333391	+	0.942789i
$14$	0.0933396	+	0.842071i	0.0249460	+	0.225053i
$15$	0.654624	−	0.377948i	0.169023	−	0.0975856i
$16$	−3.28860	−	2.27708i	−0.822150	−	0.569271i
$17$	3.48363	−	6.03382i	0.844903	−	1.46342i	−0.0408019	−	0.999167i	$-0.512991\pi$
$17$	3.48363	−	6.03382i	0.844903	−	1.46342i	0.885705	−	0.464248i	$-0.153675\pi$
$18$	−3.41368	+	0.378391i	−0.804613	+	0.0891875i
$19$	−2.07109	+	3.58723i	−0.475140	+	0.822967i	−0.999595	−	0.0284718i	$-0.990936\pi$
$19$	−2.07109	+	3.58723i	−0.475140	+	0.822967i	0.524455	+	0.851438i	$0.324269\pi$
$20$	−0.596406	+	1.90900i	−0.133360	+	0.426866i
$21$	0.452842			0.0988183
$22$	−0.563130	+	1.28438i	−0.120060	+	0.273830i
$23$	2.57315	+	4.45684i	0.536540	+	0.929314i	0.999087	+	0.0427197i	$0.0136022\pi$
$23$	2.57315	+	4.45684i	0.536540	+	0.929314i	−0.462547	+	0.886595i	$0.653064\pi$
$24$	−1.40334	+	1.61296i	−0.286456	+	0.329245i
$25$	1.00000			0.200000
$26$	−2.86608	+	4.21729i	−0.562085	+	0.827080i
$27$			4.10347i			0.789713i
$28$	−0.881251	+	0.811781i	−0.166541	+	0.153412i
$29$	3.70124	−	2.13691i	0.687303	−	0.396815i	−0.115298	−	0.993331i	$-0.536782\pi$
$29$	3.70124	−	2.13691i	0.687303	−	0.396815i	0.802601	+	0.596516i	$0.203449\pi$
$30$	0.979029	+	0.429251i	0.178745	+	0.0783702i
$31$		−	10.2309i		−	1.83752i	−0.394816	−	0.918760i	$-0.629192\pi$
$31$		−	10.2309i		−	1.83752i	0.394816	−	0.918760i	$-0.370808\pi$
$32$	−0.160488	−	5.65458i	−0.0283705	−	0.999597i
$33$	0.649158	+	0.374792i	0.113004	+	0.0652429i
$34$	9.79320	−	1.08553i	1.67952	−	0.186167i
$35$	0.518819	+	0.299540i	0.0876964	+	0.0506316i
$36$	−3.29089	−	3.57252i	−0.548482	−	0.595420i
$37$	3.38708	+	5.86659i	0.556832	+	0.964461i	0.997758	+	0.0669179i	$0.0213166\pi$
$37$	3.38708	+	5.86659i	0.556832	+	0.964461i	−0.440927	+	0.897543i	$0.645350\pi$
$38$	−5.82226	+	0.645370i	−0.944495	+	0.104693i
$39$	2.07164	+	1.77093i	0.331729	+	0.283576i
$40$	−2.67472	+	0.919699i	−0.422911	+	0.145417i
$41$	−1.99903	+	1.15414i	−0.312196	+	0.180246i	−0.647909	−	0.761718i	$-0.724356\pi$
$41$	−1.99903	+	1.15414i	−0.312196	+	0.180246i	0.335713	+	0.941964i	$0.391023\pi$
$42$	0.379361	+	0.515963i	0.0585367	+	0.0796148i
$43$	−8.49472	−	4.90443i	−1.29543	−	0.747919i	−0.315822	−	0.948819i	$-0.602280\pi$
$43$	−8.49472	−	4.90443i	−1.29543	−	0.747919i	−0.979612	+	0.200900i	$0.935613\pi$
$44$	−1.93516	+	0.434342i	−0.291736	+	0.0654796i
$45$	−1.21431	+	2.10325i	−0.181019	+	0.313534i
$46$	−2.92244	+	6.66546i	−0.430891	+	0.982768i
$47$		−	5.84920i		−	0.853194i	−0.904442	−	0.426597i	$-0.859712\pi$
$47$		−	5.84920i		−	0.853194i	0.904442	−	0.426597i	$-0.140288\pi$
$48$	−3.01342	−	0.247717i	−0.434949	−	0.0357549i
$49$	−3.32055	−	5.75136i	−0.474364	−	0.821623i
$50$	0.837733	+	1.13939i	0.118473	+	0.161134i
$51$		−	5.26651i		−	0.737459i
$52$	−7.20614	+	0.267391i	−0.999312	+	0.0370804i
$53$			1.02996i			0.141476i	0.997495	+	0.0707381i	$0.0225355\pi$
$53$			1.02996i			0.141476i	−0.997495	+	0.0707381i	$0.977465\pi$
$54$	−4.67544	+	3.43761i	−0.636247	+	0.467800i
$55$	0.495825	+	0.858794i	0.0668570	+	0.115800i
$56$	−1.66319	−	0.324031i	−0.222253	−	0.0433004i
$57$			3.13105i			0.414718i
$58$	5.53542	+	2.42698i	0.726837	+	0.318679i
$59$	0.213398	−	0.369616i	0.0277820	−	0.0481198i	−0.851800	−	0.523867i	$-0.824489\pi$
$59$	0.213398	−	0.369616i	0.0277820	−	0.0481198i	0.879582	+	0.475747i	$0.157822\pi$
$60$	0.331082	+	1.47509i	0.0427425	+	0.190433i
$61$	7.52376	+	4.34384i	0.963318	+	0.556172i	0.897193	−	0.441639i	$-0.145603\pi$
$61$	7.52376	+	4.34384i	0.963318	+	0.556172i	0.0661256	+	0.997811i	$0.478936\pi$
$62$	11.6569	−	8.57075i	1.48043	−	1.08849i
$63$	−1.26002	+	0.727471i	−0.158747	+	0.0916527i
$64$	6.30831	−	4.91988i	0.788538	−	0.614986i
$65$	1.20206	+	3.39927i	0.149097	+	0.421628i
$66$	0.116789	+	1.05362i	0.0143757	+	0.129691i
$67$	−5.26656	−	9.12195i	−0.643413	−	1.11442i	−0.984666	−	0.174452i	$-0.944185\pi$
$67$	−5.26656	−	9.12195i	−0.643413	−	1.11442i	0.341253	−	0.939971i	$-0.389149\pi$
$68$	9.44093	+	10.2489i	1.14488	+	1.24286i
$69$	3.36890	+	1.94504i	0.405568	+	0.234155i
$70$	0.0933396	+	0.842071i	0.0111562	+	0.100647i
$71$	2.90416	+	1.67672i	0.344660	+	0.198990i	0.662331	−	0.749211i	$-0.269567\pi$
$71$	2.90416	+	1.67672i	0.344660	+	0.198990i	−0.317671	+	0.948201i	$0.602901\pi$
$72$	1.31359	−	6.74241i	0.154808	−	0.794601i
$73$		−	11.3352i		−	1.32669i	−0.748315	−	0.663344i	$-0.769137\pi$
$73$		−	11.3352i		−	1.32669i	0.748315	−	0.663344i	$-0.230863\pi$
$74$	−3.84685	+	8.77383i	−0.447187	+	1.01994i
$75$	0.654624	−	0.377948i	0.0755895	−	0.0436416i
$76$	−5.61283	−	6.09316i	−0.643835	−	0.698933i
$77$			0.594079i			0.0677015i
$78$	−0.282291	+	3.84397i	−0.0319631	+	0.435244i
$79$	−1.48646			−0.167240			−0.0836199	−	0.996498i	$-0.526648\pi$
$79$	−1.48646			−0.167240			−0.0836199	+	0.996498i	$0.526648\pi$
$80$	−3.28860	−	2.27708i	−0.367677	−	0.254586i
$81$	−2.09204	−	3.62352i	−0.232449	−	0.402613i
$82$	−2.98967	−	1.31081i	−0.330153	−	0.144754i
$83$	−8.05860			−0.884547			−0.442273	−	0.896880i	$-0.645828\pi$
$83$	−8.05860			−0.884547			−0.442273	+	0.896880i	$0.645828\pi$
$84$	−0.270078	+	0.864478i	−0.0294679	+	0.0943223i
$85$	3.48363	−	6.03382i	0.377852	−	0.654459i
$86$	−1.52827	−	13.7874i	−0.164797	−	1.48673i
$87$	1.61528	−	2.79775i	0.173176	−	0.299950i
$88$	−2.11603	−	1.84103i	−0.225569	−	0.196254i
$89$	4.06454	−	2.34667i	0.430841	−	0.248746i	−0.268864	−	0.963178i	$-0.586648\pi$
$89$	4.06454	−	2.34667i	0.430841	−	0.248746i	0.699705	+	0.714432i	$0.253315\pi$
$90$	−3.41368	+	0.378391i	−0.359834	+	0.0398859i
$91$	−0.394568	+	2.12367i	−0.0413619	+	0.222621i
$92$	−10.0428	+	2.25408i	−1.04703	+	0.235004i
$93$	−3.86674	−	6.69738i	−0.400962	−	0.694486i
$94$	6.66451	−	4.90007i	0.687391	−	0.505404i
$95$	−2.07109	+	3.58723i	−0.212489	+	0.368042i
$96$	−2.24219	−	3.64097i	−0.228843	−	0.371605i
$97$	12.6350	+	7.29481i	1.28289	+	0.740675i	0.977375	−	0.211513i	$-0.0678390\pi$
$97$	12.6350	+	7.29481i	1.28289	+	0.740675i	0.305512	+	0.952188i	$0.401172\pi$
$98$	3.77129	−	8.60150i	0.380958	−	0.868883i
$99$	−2.40834			−0.242048
$100$	−0.596406	+	1.90900i	−0.0596406	+	0.190900i
$101$	12.6762	−	7.31860i	1.26133	−	0.728228i	0.287996	−	0.957632i	$-0.407011\pi$
$101$	12.6762	−	7.31860i	1.26133	−	0.728228i	0.973331	+	0.229404i	$0.0736776\pi$
$102$	6.00059	−	4.41193i	0.594147	−	0.436846i
$103$	10.7862			1.06280			0.531400	−	0.847121i	$-0.321666\pi$
$103$	10.7862			1.06280			0.531400	+	0.847121i	$0.321666\pi$
$104$	−6.34149	−	7.98659i	−0.621834	−	0.783149i
$105$	0.452842			0.0441929
$106$	−1.17353	+	0.862834i	−0.113983	+	0.0838058i
$107$	−9.93426	+	5.73555i	−0.960381	+	0.554476i	−0.896290	−	0.443468i	$-0.853748\pi$
$107$	−9.93426	+	5.73555i	−0.960381	+	0.554476i	−0.0640910	+	0.997944i	$0.520415\pi$
$108$	−7.83354	−	2.44733i	−0.753783	−	0.235495i
$109$	2.97887			0.285324			0.142662	−	0.989771i	$-0.454434\pi$
$109$	2.97887			0.285324			0.142662	+	0.989771i	$0.454434\pi$
$110$	−0.563130	+	1.28438i	−0.0536923	+	0.122461i
$111$	4.43452	+	2.56027i	0.420906	+	0.243010i
$112$	−1.02411	−	2.16646i	−0.0967692	−	0.204712i
$113$	−9.38881	+	16.2619i	−0.883225	+	1.52979i	−0.0354897	+	0.999370i	$0.511299\pi$
$113$	−9.38881	+	16.2619i	−0.883225	+	1.52979i	−0.847735	+	0.530420i	$0.822034\pi$
$114$	−3.56748	+	2.62298i	−0.334125	+	0.245665i
$115$	2.57315	+	4.45684i	0.239948	+	0.415602i
$116$	1.87193	+	8.34016i	0.173805	+	0.774364i
$117$	−8.60919	−	1.59954i	−0.795920	−	0.147878i
$118$	0.599905	−	0.0664967i	0.0552258	−	0.00612152i
$119$	3.61474	−	2.08697i	0.331363	−	0.191313i
$120$	−1.40334	+	1.61296i	−0.128107	+	0.147243i
$121$	5.00831	−	8.67466i	0.455301	−	0.788605i
$122$	1.35358	+	12.2115i	0.122548	+	1.10557i
$123$	−0.872409	+	1.51106i	−0.0786624	+	0.136247i
$124$	19.5308	+	6.10176i	1.75392	+	0.547954i
$125$	1.00000			0.0894427
$126$	−1.88443	−	0.826220i	−0.167878	−	0.0736055i
$127$	−8.35088	−	14.4641i	−0.741020	−	1.28348i	−0.952031	−	0.306001i	$-0.901009\pi$
$127$	−8.35088	−	14.4641i	−0.741020	−	1.28348i	0.211011	−	0.977484i	$-0.432324\pi$
$128$	10.8903	+	3.06605i	0.962578	+	0.271003i
$129$	−7.41447			−0.652808
$130$	−2.86608	+	4.21729i	−0.251372	+	0.369881i
$131$		−	17.0053i		−	1.48576i	−0.669426	−	0.742879i	$-0.733460\pi$
$131$		−	17.0053i		−	1.48576i	0.669426	−	0.742879i	$-0.266540\pi$
$132$	−1.10264	+	1.01572i	−0.0959726	+	0.0884069i
$133$	−2.14904	+	1.24075i	−0.186345	+	0.107587i
$134$	5.98146	−	13.6424i	0.516719	−	1.17852i
$135$			4.10347i			0.353170i
$136$	−3.76844	+	19.3427i	−0.323141	+	1.65862i
$137$	−1.14959	−	0.663718i	−0.0982165	−	0.0567053i	0.450087	−	0.892985i	$-0.351393\pi$
$137$	−1.14959	−	0.663718i	−0.0982165	−	0.0567053i	−0.548304	+	0.836279i	$0.684726\pi$
$138$	0.606091	+	5.46790i	0.0515939	+	0.465459i
$139$	6.77015	+	3.90875i	0.574237	+	0.331536i	0.758840	−	0.651277i	$-0.225767\pi$
$139$	6.77015	+	3.90875i	0.574237	+	0.331536i	−0.184603	+	0.982813i	$0.559100\pi$
$140$	−0.881251	+	0.811781i	−0.0744793	+	0.0686080i
$141$	−2.21069	−	3.82903i	−0.186174	−	0.322463i
$142$	0.522480	+	4.71360i	0.0438456	+	0.395557i
$143$	−2.32326	+	2.71777i	−0.194281	+	0.227271i
$144$	8.78266	−	4.15165i	0.731888	−	0.345971i
$145$	3.70124	−	2.13691i	0.307371	−	0.177461i
$146$	12.9152	−	9.49589i	1.06887	−	0.785886i
$147$	−4.34743	−	2.50999i	−0.358570	−	0.207020i
$148$	−13.2194	+	2.96708i	−1.08663	+	0.243892i
$149$	−3.16075	+	5.47457i	−0.258939	+	0.448495i	−0.965958	−	0.258700i	$-0.916706\pi$
$149$	−3.16075	+	5.47457i	−0.258939	+	0.448495i	0.707019	+	0.707194i	$0.250039\pi$
$150$	0.979029	+	0.429251i	0.0799374	+	0.0350482i
$151$			0.928828i			0.0755869i	0.999286	+	0.0377935i	$0.0120329\pi$
$151$			0.928828i			0.0755869i	−0.999286	+	0.0377935i	$0.987967\pi$
$152$	2.24042	−	11.4996i	0.181722	−	0.932743i
$153$	8.46041	+	14.6539i	0.683984	+	1.18469i
$154$	−0.676885	+	0.497679i	−0.0545450	+	0.0401041i
$155$		−	10.2309i		−	0.821764i
$156$	−4.61626	+	2.89858i	−0.369596	+	0.232072i
$157$			9.31053i			0.743061i	0.928421	+	0.371531i	$0.121167\pi$
$157$			9.31053i			0.743061i	−0.928421	+	0.371531i	$0.878833\pi$
$158$	−1.24526	−	1.69365i	−0.0990673	−	0.134740i
$159$	0.389272	+	0.674239i	0.0308713	+	0.0534706i
$160$	−0.160488	−	5.65458i	−0.0126877	−	0.447034i
$161$			3.08306i			0.242979i
$162$	2.37602	−	5.41918i	0.186678	−	0.425771i
$163$	−3.78241	+	6.55133i	−0.296261	+	0.513140i	−0.975278	−	0.220984i	$-0.929073\pi$
$163$	−3.78241	+	6.55133i	−0.296261	+	0.513140i	0.679016	+	0.734123i	$0.262407\pi$
$164$	−1.01103	−	4.50449i	−0.0789478	−	0.351742i
$165$	0.649158	+	0.374792i	0.0505369	+	0.0291775i
$166$	−6.75096	−	9.18187i	−0.523976	−	0.712651i
$167$	−17.1080	+	9.87729i	−1.32385	+	0.764328i	−0.984341	−	0.176273i	$-0.943596\pi$
$167$	−17.1080	+	9.87729i	−1.32385	+	0.764328i	−0.339514	+	0.940601i	$0.610262\pi$
$168$	−1.21123	+	0.416479i	−0.0934483	+	0.0321320i
$169$	−10.1101	+	8.17226i	−0.777700	+	0.628635i
$170$	9.79320	−	1.08553i	0.751104	−	0.0832563i
$171$	−5.02989	−	8.71202i	−0.384645	−	0.666225i
$172$	14.4289	−	13.2914i	1.10019	−	1.01346i
$173$	17.2600	+	9.96506i	1.31225	+	0.757630i	0.982469	−	0.186426i	$-0.0596906\pi$
$173$	17.2600	+	9.96506i	1.31225	+	0.757630i	0.329784	+	0.944056i	$0.393024\pi$
$174$	4.54090	−	0.503337i	0.344244	−	0.0381579i
$175$	0.518819	+	0.299540i	0.0392190	+	0.0226431i
$176$	0.324977	−	3.95327i	0.0244961	−	0.297989i
$177$		−	0.322612i		−	0.0242490i
$178$	6.07876	+	2.66521i	0.455623	+	0.199766i
$179$	−3.23782	+	1.86936i	−0.242006	+	0.139722i	−0.616099	−	0.787669i	$-0.711288\pi$
$179$	−3.23782	+	1.86936i	−0.242006	+	0.139722i	0.374092	+	0.927392i	$0.377954\pi$
$180$	−3.29089	−	3.57252i	−0.245288	−	0.266280i
$181$		−	18.1723i		−	1.35074i	−0.737480	−	0.675369i	$-0.763984\pi$
$181$		−	18.1723i		−	1.35074i	0.737480	−	0.675369i	$-0.236016\pi$
$182$	−2.75023	+	1.32951i	−0.203860	+	0.0985495i
$183$	6.56698			0.485445
$184$	−10.9814	−	9.55428i	−0.809562	−	0.704351i
$185$	3.38708	+	5.86659i	0.249023	+	0.431320i
$186$	4.39162	−	10.0163i	0.322009	−	0.734433i
$187$	6.90908			0.505242
$188$	11.1662	+	3.48850i	0.814376	+	0.254425i
$189$	−1.22915	+	2.12896i	−0.0894078	+	0.154859i
$190$	−5.82226	+	0.645370i	−0.422391	+	0.0468201i
$191$	−0.252672	+	0.437640i	−0.0182827	+	0.0316665i	−0.875022	−	0.484083i	$-0.839153\pi$
$191$	−0.252672	+	0.437640i	−0.0182827	+	0.0316665i	0.856739	+	0.515750i	$0.172487\pi$
$192$	2.27011	−	5.60488i	0.163831	−	0.404498i
$193$	2.77201	−	1.60042i	0.199534	−	0.115201i	−0.396904	−	0.917860i	$-0.629915\pi$
$193$	2.77201	−	1.60042i	0.199534	−	0.115201i	0.596438	+	0.802659i	$0.296582\pi$
$194$	2.27313	+	20.5072i	0.163201	+	1.47233i
$195$	2.07164	+	1.77093i	0.148354	+	0.126819i
$196$	12.9598	−	2.90880i	0.925698	−	0.207771i
$197$	4.00968	+	6.94498i	0.285678	+	0.494809i	0.972773	−	0.231758i	$-0.0744478\pi$
$197$	4.00968	+	6.94498i	0.285678	+	0.494809i	−0.687095	+	0.726567i	$0.741115\pi$
$198$	−2.01755	−	2.74404i	−0.143381	−	0.195010i
$199$	7.24444	−	12.5477i	0.513544	−	0.889485i	−0.486332	−	0.873774i	$-0.661665\pi$
$199$	7.24444	−	12.5477i	0.513544	−	0.889485i	0.999877	−	0.0157111i	$-0.00500120\pi$
$200$	−2.67472	+	0.919699i	−0.189132	+	0.0650325i
$201$	−6.89524	−	3.98097i	−0.486352	−	0.280796i
$202$	18.9580	+	8.31205i	1.33388	+	0.584834i
$203$	2.56037			0.179703
$204$	10.0538	+	3.14098i	0.703906	+	0.219913i
$205$	−1.99903	+	1.15414i	−0.139618	+	0.0806086i
$206$	9.03600	+	12.2897i	0.629568	+	0.856265i
$207$	−12.4984			−0.868702
$208$	3.78734	−	13.9160i	0.262605	−	0.964904i
$209$	−4.10759			−0.284128
$210$	0.379361	+	0.515963i	0.0261784	+	0.0356048i
$211$	9.85182	−	5.68795i	0.678227	−	0.391575i	−0.120959	−	0.992657i	$-0.538597\pi$
$211$	9.85182	−	5.68795i	0.678227	−	0.391575i	0.799187	+	0.601083i	$0.205264\pi$
$212$	−1.96620	−	0.614276i	−0.135039	−	0.0421887i
$213$	2.53484			0.173685
$214$	−14.8573	−	6.51411i	−1.01562	−	0.445295i
$215$	−8.49472	−	4.90443i	−0.579335	−	0.334479i
$216$	−3.77396	−	10.9757i	−0.256785	−	0.746798i
$217$	3.06456	−	5.30798i	0.208036	−	0.360329i
$218$	2.49550	+	3.39409i	0.169017	+	0.229877i
$219$	−4.28412	−	7.42031i	−0.289494	−	0.501418i
$220$	−1.93516	+	0.434342i	−0.130468	+	0.0292834i
$221$	24.6981	+	4.58878i	1.66137	+	0.308675i
$222$	0.797805	+	7.19747i	0.0535452	+	0.483062i
$223$	−21.0816	+	12.1715i	−1.41173	+	0.815062i	−0.995551	−	0.0942207i	$-0.969964\pi$
$223$	−21.0816	+	12.1715i	−1.41173	+	0.815062i	−0.416178	+	0.909283i	$0.636631\pi$
$224$	1.61051	−	2.98178i	0.107607	−	0.199228i
$225$	−1.21431	+	2.10325i	−0.0809541	+	0.140217i
$226$	−26.3939	+	2.92564i	−1.75570	+	0.194611i
$227$	−13.2058	+	22.8730i	−0.876497	+	1.51814i	−0.0213366	+	0.999772i	$0.506792\pi$
$227$	−13.2058	+	22.8730i	−0.876497	+	1.51814i	−0.855160	+	0.518364i	$0.826541\pi$
$228$	−5.97719	−	1.86738i	−0.395849	−	0.123670i
$229$	−29.1285			−1.92487			−0.962434	−	0.271517i	$-0.912475\pi$
$229$	−29.1285			−1.92487			−0.962434	+	0.271517i	$0.912475\pi$
$230$	−2.92244	+	6.66546i	−0.192700	+	0.439507i
$231$	0.224531	+	0.388898i	0.0147730	+	0.0255876i
$232$	−7.93449	+	9.11968i	−0.520925	+	0.598737i
$233$	−15.3090			−1.00292			−0.501462	−	0.865180i	$-0.667204\pi$
$233$	−15.3090			−1.00292			−0.501462	+	0.865180i	$0.667204\pi$
$234$	−5.38970	−	11.1492i	−0.352336	−	0.728846i
$235$		−	5.84920i		−	0.381560i
$236$	0.578326	+	0.627818i	0.0376458	+	0.0408675i
$237$	−0.973073	+	0.561804i	−0.0632079	+	0.0364931i
$238$	5.40606	+	2.37027i	0.350423	+	0.153641i
$239$			18.7350i			1.21186i	0.795516	+	0.605932i	$0.207200\pi$
$239$			18.7350i			1.21186i	−0.795516	+	0.605932i	$0.792800\pi$
$240$	−3.01342	−	0.247717i	−0.194515	−	0.0159901i
$241$	−2.21984	−	1.28163i	−0.142992	−	0.0825567i	0.426797	−	0.904347i	$-0.359642\pi$
$241$	−2.21984	−	1.28163i	−0.142992	−	0.0825567i	−0.569789	+	0.821791i	$0.692975\pi$
$242$	14.0794	−	1.56064i	0.905060	−	0.100322i
$243$	−13.4001	−	7.73656i	−0.859618	−	0.496301i
$244$	−12.7796	+	11.7722i	−0.818132	+	0.753637i
$245$	−3.32055	−	5.75136i	−0.212142	−	0.367441i
$246$	−2.45252	+	0.271851i	−0.156367	+	0.0173326i
$247$	−14.6835	−	2.72813i	−0.934291	−	0.173587i
$248$	9.40933	+	27.3648i	0.597493	+	1.73767i
$249$	−5.27536	+	3.04573i	−0.334312	+	0.193015i
$250$	0.837733	+	1.13939i	0.0529829	+	0.0720612i
$251$	23.8918	+	13.7940i	1.50804	+	0.870667i	0.999956	+	0.00935859i	$0.00297897\pi$
$251$	23.8918	+	13.7940i	1.50804	+	0.870667i	0.508083	+	0.861308i	$0.330354\pi$
$252$	−0.637263	−	2.83924i	−0.0401438	−	0.178856i
$253$	−2.55167	+	4.41962i	−0.160422	+	0.277859i
$254$	9.48445	−	21.6320i	0.595107	−	1.35731i
$255$		−	5.26651i		−	0.329802i
$256$	5.62977	+	14.9768i	0.351861	+	0.936052i
$257$	3.03249	+	5.25242i	0.189161	+	0.327637i	0.944971	−	0.327155i	$-0.106090\pi$
$257$	3.03249	+	5.25242i	0.189161	+	0.327637i	−0.755810	+	0.654792i	$0.772756\pi$
$258$	−6.21135	−	8.44795i	−0.386702	−	0.525947i
$259$			4.05826i			0.252168i
$260$	−7.20614	+	0.267391i	−0.446906	+	0.0165829i
$261$			10.3795i			0.642476i
$262$	19.3756	−	14.2459i	1.19703	−	0.880113i
$263$	2.49677	+	4.32454i	0.153958	+	0.266662i	0.932679	−	0.360708i	$-0.117465\pi$
$263$	2.49677	+	4.32454i	0.153958	+	0.266662i	−0.778721	+	0.627370i	$0.784131\pi$
$264$	−2.08102	−	0.405434i	−0.128078	−	0.0249528i
$265$			1.02996i			0.0632701i
$266$	−3.21401	−	1.40917i	−0.197064	−	0.0864019i
$267$	1.77383	−	3.07237i	0.108557	−	0.188026i
$268$	20.5549	−	4.61350i	1.25559	−	0.281814i
$269$	−12.0862	−	6.97794i	−0.736906	−	0.425453i	0.0840375	−	0.996463i	$-0.473218\pi$
$269$	−12.0862	−	6.97794i	−0.736906	−	0.425453i	−0.820943	+	0.571010i	$0.806552\pi$
$270$	−4.67544	+	3.43761i	−0.284538	+	0.209206i
$271$	−22.1003	+	12.7596i	−1.34250	+	0.775091i	−0.987173	−	0.159652i	$-0.948963\pi$
$271$	−22.1003	+	12.7596i	−1.34250	+	0.775091i	−0.355324	+	0.934743i	$0.615630\pi$
$272$	−25.1958	+	11.9103i	−1.52772	+	0.722168i
$273$	0.544343	+	1.53933i	0.0329452	+	0.0931647i
$274$	−0.206821	−	1.86585i	−0.0124945	−	0.112720i
$275$	0.495825	+	0.858794i	0.0298994	+	0.0517872i
$276$	−5.72231	+	5.27121i	−0.344443	+	0.317290i
$277$	−6.59518	−	3.80773i	−0.396266	−	0.228784i	0.288606	−	0.957448i	$-0.406808\pi$
$277$	−6.59518	−	3.80773i	−0.396266	−	0.228784i	−0.684872	+	0.728664i	$0.740142\pi$
$278$	1.21800	+	10.9883i	0.0730509	+	0.659035i
$279$	21.5181	+	12.4235i	1.28825	+	0.743774i
$280$	−1.66319	−	0.324031i	−0.0993944	−	0.0193645i
$281$			13.0983i			0.781377i	0.920523	+	0.390689i	$0.127763\pi$
$281$			13.0983i			0.781377i	−0.920523	+	0.390689i	$0.872237\pi$
$282$	2.51078	−	5.72654i	0.149515	−	0.341010i
$283$	12.7407	−	7.35583i	0.757354	−	0.437258i	−0.0709910	−	0.997477i	$-0.522616\pi$
$283$	12.7407	−	7.35583i	0.757354	−	0.437258i	0.828345	+	0.560218i	$0.189283\pi$
$284$	−4.93292	+	4.54405i	−0.292715	+	0.269640i
$285$			3.13105i			0.185467i
$286$	−5.04286	−	0.370334i	−0.298191	−	0.0218983i
$287$	−1.38285			−0.0816268
$288$	12.0879	+	6.52887i	0.712284	+	0.384717i
$289$	−15.7713	−	27.3167i	−0.927723	−	1.60686i
$290$	5.53542	+	2.42698i	0.325051	+	0.142517i
$291$	11.0282			0.646485
$292$	21.6390	+	6.76040i	1.26633	+	0.395622i
$293$	−0.811966	+	1.40637i	−0.0474356	+	0.0821608i	−0.888768	−	0.458357i	$-0.848438\pi$
$293$	−0.811966	+	1.40637i	−0.0474356	+	0.0821608i	0.841333	+	0.540518i	$0.181772\pi$
$294$	−0.782136	−	7.05610i	−0.0456151	−	0.411520i
$295$	0.213398	−	0.369616i	0.0124245	−	0.0215198i
$296$	−14.4550	−	12.5764i	−0.840179	−	0.730989i
$297$	−3.52404	+	2.03460i	−0.204485	+	0.118060i
$298$	−8.88552	+	0.984918i	−0.514725	+	0.0570548i
$299$	−12.0569	+	14.1042i	−0.697269	+	0.815669i
$300$	0.331082	+	1.47509i	0.0191150	+	0.0851644i
$301$	−2.93815	−	5.08903i	−0.169352	−	0.293327i
$302$	−1.05829	+	0.778110i	−0.0608980	+	0.0447752i
$303$	5.53209	−	9.58186i	0.317810	−	0.550464i
$304$	14.9794	−	7.08092i	0.859127	−	0.406118i
$305$	7.52376	+	4.34384i	0.430809	+	0.248728i
$306$	−9.60886	+	21.9157i	−0.549302	+	1.25284i
$307$	−15.4593			−0.882310			−0.441155	−	0.897431i	$-0.645431\pi$
$307$	−15.4593			−0.882310			−0.441155	+	0.897431i	$0.645431\pi$
$308$	−1.13410	−	0.354312i	−0.0646213	−	0.0201888i
$309$	7.06094	−	4.07663i	0.401683	−	0.231912i
$310$	11.6569	−	8.57075i	0.662069	−	0.486786i
$311$	9.94170			0.563742			0.281871	−	0.959452i	$-0.409045\pi$
$311$	9.94170			0.563742			0.281871	+	0.959452i	$0.409045\pi$
$312$	−7.16980	−	2.83146i	−0.405910	−	0.160300i
$313$	−10.7805			−0.609350			−0.304675	−	0.952456i	$-0.598548\pi$
$313$	−10.7805			−0.609350			−0.304675	+	0.952456i	$0.598548\pi$
$314$	−10.6083	+	7.79974i	−0.598661	+	0.440165i
$315$	−1.26002	+	0.727471i	−0.0709939	+	0.0409883i
$316$	0.886534	−	2.83766i	0.0498714	−	0.159631i
$317$	−8.70514			−0.488929			−0.244465	−	0.969658i	$-0.578612\pi$
$317$	−8.70514			−0.488929			−0.244465	+	0.969658i	$0.578612\pi$
$318$	−0.442113	+	1.00836i	−0.0247925	+	0.0565462i
$319$	3.67034	+	2.11907i	0.205499	+	0.118645i
$320$	6.30831	−	4.91988i	0.352645	−	0.275030i
$321$	−4.33547	+	7.50926i	−0.241983	+	0.419126i
$322$	−3.51279	+	2.58278i	−0.195760	+	0.143933i
$323$	14.4298	+	24.9931i	0.802895	+	1.39065i
$324$	8.16501	−	1.83262i	0.453612	−	0.101812i
$325$	1.20206	+	3.39927i	0.0666783	+	0.188558i
$326$	−10.6332	+	1.17863i	−0.588916	+	0.0652785i
$327$	1.95004	−	1.12586i	0.107838	−	0.0622600i
$328$	4.28539	−	4.92551i	0.236621	−	0.271966i
$329$	1.75207	−	3.03468i	0.0965949	−	0.167307i
$330$	0.116789	+	1.05362i	0.00642900	+	0.0579998i
$331$	−0.941747	+	1.63115i	−0.0517631	+	0.0896563i	−0.890746	−	0.454502i	$-0.849817\pi$
$331$	−0.941747	+	1.63115i	−0.0517631	+	0.0896563i	0.838983	+	0.544158i	$0.183151\pi$
$332$	4.80620	−	15.3839i	0.263775	−	0.844302i
$333$	−16.4519			−0.901556
$334$	−25.5860	−	11.2181i	−1.40000	−	0.613826i
$335$	−5.26656	−	9.12195i	−0.287743	−	0.498385i
$336$	−1.48922	−	1.03116i	−0.0812434	−	0.0562544i
$337$	5.17568			0.281937			0.140969	−	0.990014i	$-0.454978\pi$
$337$	5.17568			0.281937			0.140969	+	0.990014i	$0.454978\pi$
$338$	−17.7809	−	4.67315i	−0.967155	−	0.254186i
$339$			14.1939i			0.770907i
$340$	9.44093	+	10.2489i	0.512006	+	0.555823i
$341$	8.78622	−	5.07273i	0.475801	−	0.274704i
$342$	5.71266	−	13.0293i	0.308905	−	0.704546i
$343$		−	8.17212i		−	0.441253i
$344$	27.2317	+	5.30541i	1.46823	+	0.286049i
$345$	3.36890	+	1.94504i	0.181375	+	0.104717i
$346$	3.10521	+	28.0139i	0.166937	+	1.50604i
$347$	15.6650	+	9.04422i	0.840944	+	0.485519i	0.857585	−	0.514342i	$-0.171964\pi$
$347$	15.6650	+	9.04422i	0.840944	+	0.485519i	−0.0166411	+	0.999862i	$0.505297\pi$
$348$	4.37756	+	4.75218i	0.234662	+	0.254743i
$349$	0.595137	+	1.03081i	0.0318570	+	0.0551779i	0.881514	−	0.472157i	$-0.156525\pi$
$349$	0.595137	+	1.03081i	0.0318570	+	0.0551779i	−0.849657	+	0.527335i	$0.823191\pi$
$350$	0.0933396	+	0.842071i	0.00498921	+	0.0450106i
$351$	−13.9488	+	4.93261i	−0.744532	+	0.263283i
$352$	4.77654	−	2.94151i	0.254591	−	0.156783i
$353$	−7.33282	+	4.23360i	−0.390287	+	0.225332i	−0.682284	−	0.731087i	$-0.739013\pi$
$353$	−7.33282	+	4.23360i	−0.390287	+	0.225332i	0.291998	+	0.956419i	$0.405680\pi$
$354$	0.367580	−	0.270263i	0.0195367	−	0.0143643i
$355$	2.90416	+	1.67672i	0.154137	+	0.0889909i
$356$	2.05568	+	9.15880i	0.108951	+	0.485416i
$357$	1.57753	−	2.73237i	0.0834919	−	0.144612i
$358$	−4.84236	−	2.12311i	−0.255926	−	0.112210i
$359$		−	13.9662i		−	0.737109i	−0.929606	−	0.368555i	$-0.879853\pi$
$359$		−	13.9662i		−	0.737109i	0.929606	−	0.368555i	$-0.120147\pi$
$360$	1.31359	−	6.74241i	0.0692324	−	0.355356i
$361$	0.921195	+	1.59556i	0.0484840	+	0.0839767i
$362$	20.7053	−	15.2236i	1.08825	−	0.800133i
$363$		−	7.57152i		−	0.397402i
$364$	−3.81878	−	2.01980i	−0.200158	−	0.105866i
$365$		−	11.3352i		−	0.593313i
$366$	5.50138	+	7.48233i	0.287562	+	0.391108i
$367$	0.887977	+	1.53802i	0.0463520	+	0.0802840i	0.888271	−	0.459321i	$-0.151907\pi$
$367$	0.887977	+	1.53802i	0.0463520	+	0.0802840i	−0.841919	+	0.539605i	$0.818574\pi$
$368$	1.68652	−	20.5160i	0.0879157	−	1.06947i
$369$		−	5.60594i		−	0.291834i
$370$	−3.84685	+	8.77383i	−0.199988	+	0.456130i
$371$	−0.308515	+	0.534364i	−0.0160173	+	0.0277428i
$372$	15.0915	−	3.38726i	0.782457	−	0.175621i
$373$	1.84160	+	1.06325i	0.0953543	+	0.0550528i	0.546919	−	0.837186i	$-0.315801\pi$
$373$	1.84160	+	1.06325i	0.0953543	+	0.0550528i	−0.451565	+	0.892238i	$0.649134\pi$
$374$	5.78796	+	7.87211i	0.299288	+	0.407057i
$375$	0.654624	−	0.377948i	0.0338047	−	0.0195171i
$376$	5.37951	+	15.6450i	0.277427	+	0.806830i
$377$	11.7131	+	10.0128i	0.603253	+	0.515687i
$378$	−3.45541	+	0.383016i	−0.177727	+	0.0197002i
$379$	−12.8653	−	22.2834i	−0.660848	−	1.14462i	−0.980393	−	0.197051i	$-0.936863\pi$
$379$	−12.8653	−	22.2834i	−0.660848	−	1.14462i	0.319545	−	0.947571i	$-0.396470\pi$
$380$	−5.61283	−	6.09316i	−0.287932	−	0.312573i
$381$	−10.9334	−	6.31239i	−0.560134	−	0.323393i
$382$	−0.710313	+	0.0787348i	−0.0363428	+	0.00402842i
$383$	23.3475	+	13.4797i	1.19300	+	0.688780i	0.958986	−	0.283453i	$-0.0914800\pi$
$383$	23.3475	+	13.4797i	1.19300	+	0.688780i	0.234016	+	0.972233i	$0.424813\pi$
$384$	8.28788	−	2.10886i	0.422939	−	0.107617i
$385$			0.594079i			0.0302770i
$386$	4.14571	+	1.81767i	0.211011	+	0.0925170i
$387$	20.6305	−	11.9110i	1.04871	−	0.605471i
$388$	−21.4614	+	19.7696i	−1.08954	+	1.00365i
$389$		−	12.7571i		−	0.646810i	−0.946261	−	0.323405i	$-0.895172\pi$
$389$		−	12.7571i		−	0.646810i	0.946261	−	0.323405i	$-0.104828\pi$
$390$	−0.282291	+	3.84397i	−0.0142944	+	0.194647i
$391$	35.8556			1.81330
$392$	14.1711	+	12.3294i	0.715748	+	0.622729i
$393$	−6.42710	−	11.1321i	−0.324204	−	0.561538i
$394$	−4.55397	+	10.3866i	−0.229426	+	0.523270i
$395$	−1.48646			−0.0747919
$396$	1.43635	−	4.59754i	0.0721794	−	0.231035i
$397$	−14.0076	+	24.2618i	−0.703020	+	1.21767i	0.264382	+	0.964418i	$0.414832\pi$
$397$	−14.0076	+	24.2618i	−0.703020	+	1.21767i	−0.967401	+	0.253248i	$0.918501\pi$
$398$	20.3656	−	2.25743i	1.02084	−	0.113155i
$399$	−0.937876	+	1.62445i	−0.0469525	+	0.0813241i
$400$	−3.28860	−	2.27708i	−0.164430	−	0.113854i
$401$	10.1181	−	5.84166i	0.505272	−	0.291719i	−0.225616	−	0.974216i	$-0.572440\pi$
$401$	10.1181	−	5.84166i	0.505272	−	0.291719i	0.730888	+	0.682497i	$0.239106\pi$
$402$	−1.24051	−	11.1913i	−0.0618708	−	0.558173i
$403$	34.7775	−	12.2981i	1.73239	−	0.612613i
$404$	6.41108	+	28.5638i	0.318963	+	1.42110i
$405$	−2.09204	−	3.62352i	−0.103954	−	0.180054i
$406$	2.14490	+	2.91725i	0.106450	+	0.144781i
$407$	−3.35879	+	5.81760i	−0.166489	+	0.288368i
$408$	4.84360	+	14.0865i	0.239794	+	0.697384i
$409$	−23.2368	−	13.4158i	−1.14898	−	0.663367i	−0.200345	−	0.979725i	$-0.564206\pi$
$409$	−23.2368	−	13.4158i	−1.14898	−	0.663367i	−0.948640	+	0.316359i	$0.897540\pi$
$410$	−2.98967	−	1.31081i	−0.147649	−	0.0647361i
$411$	−1.00340			−0.0494942
$412$	−6.43298	+	20.5910i	−0.316930	+	1.01445i
$413$	0.221430	−	0.127842i	0.0108958	−	0.00629071i
$414$	−10.4704	−	14.2406i	−0.514590	−	0.699886i
$415$	−8.05860			−0.395581
$416$	19.0285	−	7.34268i	0.932951	−	0.360005i
$417$	5.90921			0.289375
$418$	−3.44106	−	4.68013i	−0.168308	−	0.228913i
$419$	−11.1022	+	6.40987i	−0.542379	+	0.313143i	−0.746043	−	0.665898i	$-0.768049\pi$
$419$	−11.1022	+	6.40987i	−0.542379	+	0.313143i	0.203663	+	0.979041i	$0.434715\pi$
$420$	−0.270078	+	0.864478i	−0.0131785	+	0.0421822i
$421$	−29.3648			−1.43115			−0.715577	−	0.698534i	$-0.753836\pi$
$421$	−29.3648			−1.43115			−0.715577	+	0.698534i	$0.753836\pi$
$422$	14.7340	+	6.46005i	0.717239	+	0.314470i
$423$	12.3023	+	7.10275i	0.598160	+	0.345348i
$424$	−0.947256	−	2.75487i	−0.0460028	−	0.133788i
$425$	3.48363	−	6.03382i	0.168981	−	0.292683i
$426$	2.12352	+	2.88817i	0.102885	+	0.139932i
$427$	2.60231	+	4.50734i	0.125935	+	0.218125i
$428$	−5.02434	−	22.3853i	−0.242860	−	1.08203i
$429$	−0.493692	+	2.65719i	−0.0238357	+	0.128290i
$430$	−1.52827	−	13.7874i	−0.0736995	−	0.664887i
$431$	5.07218	−	2.92842i	0.244318	−	0.141057i	−0.372842	−	0.927895i	$-0.621617\pi$
$431$	5.07218	−	2.92842i	0.244318	−	0.141057i	0.617160	+	0.786838i	$0.288283\pi$
$432$	9.34395	−	13.4947i	0.449561	−	0.649262i
$433$	15.8656	−	27.4800i	0.762451	−	1.32060i	−0.179132	−	0.983825i	$-0.557329\pi$
$433$	15.8656	−	27.4800i	0.762451	−	1.32060i	0.941584	−	0.336779i	$-0.109338\pi$
$434$	8.61513	−	0.954946i	0.413539	−	0.0458389i
$435$	1.61528	−	2.79775i	0.0774468	−	0.134142i
$436$	−1.77662	+	5.68668i	−0.0850845	+	0.272343i
$437$	−21.3169			−1.01973
$438$	4.86566	−	11.0975i	0.232490	−	0.530260i
$439$	13.1428	+	22.7640i	0.627272	+	1.08647i	0.988097	+	0.153833i	$0.0491619\pi$
$439$	13.1428	+	22.7640i	0.627272	+	1.08647i	−0.360825	+	0.932634i	$0.617505\pi$
$440$	−2.11603	−	1.84103i	−0.100878	−	0.0877676i
$441$	16.1287			0.768035
$442$	15.4620	+	31.9849i	0.735454	+	1.52137i
$443$			14.0541i			0.667730i	0.942621	+	0.333865i	$0.108353\pi$
$443$			14.0541i			0.667730i	−0.942621	+	0.333865i	$0.891647\pi$
$444$	−7.53235	+	6.93857i	−0.357470	+	0.329290i
$445$	4.06454	−	2.34667i	0.192678	−	0.111243i
$446$	−31.5288	−	13.8237i	−1.49293	−	0.654570i
$447$			4.77839i			0.226010i
$448$	4.74657	−	0.662938i	0.224255	−	0.0313209i
$449$	10.6220	+	6.13259i	0.501281	+	0.289415i	0.729243	−	0.684255i	$-0.239873\pi$
$449$	10.6220	+	6.13259i	0.501281	+	0.289415i	−0.227961	+	0.973670i	$0.573206\pi$
$450$	−3.41368	+	0.378391i	−0.160923	+	0.0178375i
$451$	−1.98234	−	1.14450i	−0.0933446	−	0.0538925i
$452$	−25.4445	−	27.6220i	−1.19681	−	1.29923i
$453$	0.351048	+	0.608033i	0.0164937	+	0.0285679i
$454$	−37.1241	+	4.11503i	−1.74232	+	0.193128i
$455$	−0.394568	+	2.12367i	−0.0184976	+	0.0995593i
$456$	−2.87962	−	8.37470i	−0.134851	−	0.392181i
$457$	33.1389	−	19.1327i	1.55017	−	0.894991i	0.552043	−	0.833815i	$-0.313848\pi$
$457$	33.1389	−	19.1327i	1.55017	−	0.894991i	0.998127	−	0.0611760i	$-0.0194851\pi$
$458$	−24.4019	−	33.1887i	−1.14023	−	1.55080i
$459$	24.7596	+	14.2949i	1.15568	+	0.667231i
$460$	−10.0428	+	2.25408i	−0.468246	+	0.105097i
$461$	7.29249	−	12.6310i	0.339645	−	0.588283i	−0.644721	−	0.764418i	$-0.723026\pi$
$461$	7.29249	−	12.6310i	0.339645	−	0.588283i	0.984366	+	0.176135i	$0.0563597\pi$
$462$	−0.255009	+	0.581620i	−0.0118641	+	0.0270594i
$463$		−	29.0145i		−	1.34842i	−0.738540	−	0.674210i	$-0.764484\pi$
$463$		−	29.0145i		−	1.34842i	0.738540	−	0.674210i	$-0.235516\pi$
$464$	−17.0378	−	1.40059i	−0.790962	−	0.0650208i
$465$	−3.86674	−	6.69738i	−0.179316	−	0.310584i
$466$	−12.8248	−	17.4428i	−0.594099	−	0.808024i
$467$		−	12.3366i		−	0.570868i	−0.958398	−	0.285434i	$-0.907862\pi$
$467$		−	12.3366i		−	0.570868i	0.958398	−	0.285434i	$-0.0921377\pi$
$468$	8.18811	−	15.4810i	0.378496	−	0.715610i
$469$		−	6.31019i		−	0.291377i
$470$	6.66451	−	4.90007i	0.307411	−	0.226023i
$471$	3.51889	+	6.09490i	0.162142	+	0.280838i
$472$	−0.230845	+	1.18488i	−0.0106255	+	0.0545386i
$473$		−	9.72696i		−	0.447246i
$474$	−1.45529	−	0.638065i	−0.0668436	−	0.0293073i
$475$	−2.07109	+	3.58723i	−0.0950280	+	0.164593i
$476$	1.82819	+	8.14525i	0.0837948	+	0.373337i
$477$	−2.16627	−	1.25070i	−0.0991866	−	0.0572654i
$478$	−21.3464	+	15.6949i	−0.976361	+	0.717868i
$479$	2.36253	−	1.36401i	0.107947	−	0.0623231i	−0.445055	−	0.895503i	$-0.646816\pi$
$479$	2.36253	−	1.36401i	0.107947	−	0.0623231i	0.553001	+	0.833180i	$0.313482\pi$
$480$	−2.24219	−	3.64097i	−0.102342	−	0.166187i
$481$	−15.8707	+	18.5656i	−0.723640	+	0.846518i
$482$	−0.399366	−	3.60292i	−0.0181906	−	0.164108i
$483$	1.16523	+	2.01824i	0.0530199	+	0.0918332i
$484$	13.5730	+	14.7345i	0.616953	+	0.669751i
$485$	12.6350	+	7.29481i	0.573725	+	0.331240i
$486$	−2.41079	−	21.7491i	−0.109355	−	0.986559i
$487$	6.48966	+	3.74681i	0.294074	+	0.169784i	0.639778	−	0.768560i	$-0.279026\pi$
$487$	6.48966	+	3.74681i	0.294074	+	0.169784i	−0.345703	+	0.938344i	$0.612360\pi$
$488$	−24.1190	−	4.69899i	−1.09182	−	0.212713i
$489$			5.71821i			0.258587i
$490$	3.77129	−	8.60150i	0.170370	−	0.388576i
$491$	−2.52120	+	1.45562i	−0.113780	+	0.0656910i	−0.555810	−	0.831309i	$-0.687592\pi$
$491$	−2.52120	+	1.45562i	−0.113780	+	0.0656910i	0.442030	+	0.897000i	$0.354259\pi$
$492$	−2.36430	−	2.56664i	−0.106591	−	0.115713i
$493$		−	29.7768i		−	1.34108i
$494$	−9.19249	−	19.0157i	−0.413590	−	0.855556i
$495$	−2.40834			−0.108247
$496$	−23.2966	+	33.6453i	−1.04605	+	1.51072i
$497$	1.00449	+	1.73982i	0.0450575	+	0.0780418i
$498$	−7.88961	−	3.45917i	−0.353542	−	0.155009i
$499$	20.6054			0.922425			0.461212	−	0.887290i	$-0.347415\pi$
$499$	20.6054			0.922425			0.461212	+	0.887290i	$0.347415\pi$
$500$	−0.596406	+	1.90900i	−0.0266721	+	0.0853733i
$501$	−7.46620	+	12.9318i	−0.333565	+	0.577752i
$502$	4.29832	+	38.7777i	0.191844	+	1.73073i
$503$	3.06791	−	5.31377i	0.136791	−	0.236929i	−0.789489	−	0.613765i	$-0.789654\pi$
$503$	3.06791	−	5.31377i	0.136791	−	0.236929i	0.926280	+	0.376835i	$0.122988\pi$
$504$	2.70114	−	3.10462i	0.120318	−	0.138291i
$505$	12.6762	−	7.31860i	0.564083	−	0.325673i
$506$	−7.17328	+	0.795124i	−0.318891	+	0.0353476i
$507$	−3.52964	+	9.17085i	−0.156757	+	0.407292i
$508$	32.5926	−	7.31536i	1.44606	−	0.324567i
$509$	−8.00411	−	13.8635i	−0.354776	−	0.614490i	0.632304	−	0.774721i	$-0.282109\pi$
$509$	−8.00411	−	13.8635i	−0.354776	−	0.614490i	−0.987080	+	0.160231i	$0.948776\pi$
$510$	6.00059	−	4.41193i	0.265711	−	0.195364i
$511$	3.39536	−	5.88093i	0.150202	−	0.260157i
$512$	−12.3482	+	18.9611i	−0.545717	+	0.837969i
$513$	−14.7201	−	8.49864i	−0.649907	−	0.375224i
$514$	−3.44413	+	7.85530i	−0.151914	+	0.346483i
$515$	10.7862			0.475299
$516$	4.42204	−	14.1543i	0.194669	−	0.623107i
$517$	5.02326	−	2.90018i	0.220923	−	0.127550i
$518$	−4.62393	+	3.39974i	−0.203164	+	0.149376i
$519$	15.0651			0.661284
$520$	−6.34149	−	7.98659i	−0.278093	−	0.350235i
$521$	6.62990			0.290461			0.145231	−	0.989398i	$-0.453608\pi$
$521$	6.62990			0.290461			0.145231	+	0.989398i	$0.453608\pi$
$522$	−11.8263	+	8.69526i	−0.517622	+	0.380581i
$523$	−1.39915	+	0.807797i	−0.0611804	+	0.0353225i	−0.530278	−	0.847824i	$-0.677913\pi$
$523$	−1.39915	+	0.807797i	−0.0611804	+	0.0353225i	0.469098	+	0.883146i	$0.344579\pi$
$524$	32.4631	+	10.1420i	1.41816	+	0.443057i
$525$	0.452842			0.0197637
$526$	−2.83569	+	6.46760i	−0.123642	+	0.282001i
$527$	−61.7312	−	35.6406i	−2.68906	−	1.55253i
$528$	−1.28139	−	2.71073i	−0.0557653	−	0.117969i
$529$	−1.74225	+	3.01767i	−0.0757501	+	0.131203i
$530$	−1.17353	+	0.862834i	−0.0509747	+	0.0374791i
$531$	0.518262	+	0.897657i	0.0224907	+	0.0389550i
$532$	−1.08689	−	4.84252i	−0.0471229	−	0.209950i
$533$	−6.32619	−	5.40790i	−0.274018	−	0.234242i
$534$	4.98662	−	0.552743i	0.215792	−	0.0239195i
$535$	−9.93426	+	5.73555i	−0.429496	+	0.247969i
$536$	22.4760	+	19.5551i	0.970817	+	0.844650i
$537$	−1.41304	+	2.44746i	−0.0609771	+	0.105615i
$538$	−2.17439	−	19.6165i	−0.0937447	−	0.845726i
$539$	3.29283	−	5.70334i	0.141832	−	0.245660i
$540$	−7.83354	−	2.44733i	−0.337102	−	0.105317i
$541$	−3.92342			−0.168681			−0.0843405	−	0.996437i	$-0.526878\pi$
$541$	−3.92342			−0.168681			−0.0843405	+	0.996437i	$0.526878\pi$
$542$	−33.0523	−	14.4916i	−1.41972	−	0.622469i
$543$	−6.86819	−	11.8960i	−0.294742	−	0.510508i
$544$	−34.6778	−	18.7301i	−1.48680	−	0.803045i
$545$	2.97887			0.127601
$546$	−1.29788	+	1.90977i	−0.0555443	+	0.0817306i
$547$		−	12.1793i		−	0.520748i	−0.965508	−	0.260374i	$-0.916154\pi$
$547$		−	12.1793i		−	0.520748i	0.965508	−	0.260374i	$-0.0838459\pi$
$548$	1.95267	−	1.79873i	0.0834138	−	0.0768381i
$549$	−18.2724	+	10.5496i	−0.779846	+	0.450244i
$550$	−0.563130	+	1.28438i	−0.0240119	+	0.0547660i
$551$			17.7029i			0.754170i
$552$	−10.7997	−	2.10406i	−0.459667	−	0.0895547i
$553$	−0.771204	−	0.445255i	−0.0327949	−	0.0189342i
$554$	−1.18652	−	10.7043i	−0.0504106	−	0.454783i
$555$	4.43452	+	2.56027i	0.188235	+	0.108678i
$556$	−11.4996	+	10.5931i	−0.487691	+	0.449245i
$557$	−7.09192	−	12.2836i	−0.300494	−	0.520472i	0.675754	−	0.737128i	$-0.263818\pi$
$557$	−7.09192	−	12.2836i	−0.300494	−	0.520472i	−0.976248	+	0.216656i	$0.930485\pi$
$558$	3.87127	+	34.9250i	0.163884	+	1.47849i
$559$	6.46033	−	34.7713i	0.273243	−	1.47067i
$560$	−1.02411	−	2.16646i	−0.0432765	−	0.0915498i
$561$	4.52285	−	2.61127i	0.190955	−	0.110248i
$562$	−14.9240	+	10.9729i	−0.629531	+	0.462862i
$563$	−27.7240	−	16.0065i	−1.16843	−	0.674593i	−0.215120	−	0.976588i	$-0.569014\pi$
$563$	−27.7240	−	16.0065i	−1.16843	−	0.674593i	−0.953310	+	0.301995i	$0.902347\pi$
$564$	8.62811	−	1.93656i	0.363309	−	0.0815440i
$565$	−9.38881	+	16.2619i	−0.394990	+	0.684143i
$566$	19.0544	+	8.35433i	0.800917	+	0.351159i
$567$		−	2.50660i		−	0.105267i
$568$	−9.30990	−	1.81380i	−0.390635	−	0.0761055i
$569$	6.16030	+	10.6700i	0.258253	+	0.447308i	0.965774	−	0.259385i	$-0.0835198\pi$
$569$	6.16030	+	10.6700i	0.258253	+	0.447308i	−0.707521	+	0.706692i	$0.750186\pi$
$570$	−3.56748	+	2.62298i	−0.149425	+	0.109865i
$571$		−	19.7389i		−	0.826047i	−0.910720	−	0.413024i	$-0.864473\pi$
$571$		−	19.7389i		−	0.826047i	0.910720	−	0.413024i	$-0.135527\pi$
$572$	−3.80262	−	6.05602i	−0.158996	−	0.253215i
$573$			0.381986i			0.0159577i
$574$	−1.15846	−	1.57560i	−0.0483530	−	0.0657642i
$575$	2.57315	+	4.45684i	0.107308	+	0.185863i
$576$	2.68749	+	19.2422i	0.111979	+	0.801759i
$577$			39.5967i			1.64843i	0.566276	+	0.824216i	$0.308384\pi$
$577$			39.5967i			1.64843i	−0.566276	+	0.824216i	$0.691616\pi$
$578$	17.9121	−	40.8537i	0.745047	−	1.69929i
$579$	1.20975	−	2.09535i	0.0502756	−	0.0870799i
$580$	1.87193	+	8.34016i	0.0777278	+	0.346306i
$581$	−4.18096	−	2.41388i	−0.173455	−	0.100144i
$582$	9.23870	+	12.5654i	0.382957	+	0.520853i
$583$	−0.884526	+	0.510681i	−0.0366333	+	0.0211503i
$584$	10.4250	+	30.3186i	0.431389	+	1.25459i
$585$	−8.60919	−	1.59954i	−0.355946	−	0.0661330i
$586$	−2.28261	+	0.253016i	−0.0942936	+	0.0104520i
$587$	−3.51186	−	6.08272i	−0.144950	−	0.251061i	0.784404	−	0.620250i	$-0.212969\pi$
$587$	−3.51186	−	6.08272i	−0.144950	−	0.251061i	−0.929354	+	0.369189i	$0.879635\pi$
$588$	7.38441	−	6.80229i	0.304528	−	0.280522i
$589$	36.7005	+	21.1890i	1.51222	+	0.873079i
$590$	0.599905	−	0.0664967i	0.0246977	−	0.00273762i
$591$	5.24967	+	3.03090i	0.215943	+	0.124675i
$592$	2.21998	−	27.0055i	0.0912407	−	1.10992i
$593$		−	9.30743i		−	0.382210i	−0.981570	−	0.191105i	$-0.938793\pi$
$593$		−	9.30743i		−	0.382210i	0.981570	−	0.191105i	$-0.0612071\pi$
$594$	−5.27040	−	2.31079i	−0.216247	−	0.0948127i
$595$	3.61474	−	2.08697i	0.148190	−	0.0855576i
$596$	−8.56590	−	9.29895i	−0.350873	−	0.380900i
$597$		−	10.9521i		−	0.448238i
$598$	−26.1707	−	1.92190i	−1.07020	−	0.0785924i
$599$	45.3221			1.85181			0.925906	−	0.377755i	$-0.123304\pi$
$599$	45.3221			1.85181			0.925906	+	0.377755i	$0.123304\pi$
$600$	−1.40334	+	1.61296i	−0.0572912	+	0.0658489i
$601$	−12.1464	−	21.0382i	−0.495462	−	0.858166i	0.504524	−	0.863398i	$-0.331668\pi$
$601$	−12.1464	−	21.0382i	−0.495462	−	0.858166i	−0.999986	+	0.00523169i	$0.998335\pi$
$602$	3.33698	−	7.61094i	0.136005	−	0.310199i
$603$	25.5810			1.04174
$604$	−1.77314	−	0.553959i	−0.0721479	−	0.0225403i
$605$	5.00831	−	8.67466i	0.203617	−	0.352675i
$606$	15.5519	−	1.72385i	0.631752	−	0.0700267i
$607$	2.64776	−	4.58606i	0.107469	−	0.186143i	−0.807275	−	0.590175i	$-0.799059\pi$
$607$	2.64776	−	4.58606i	0.107469	−	0.186143i	0.914744	+	0.404033i	$0.132392\pi$
$608$	20.6166	+	11.1354i	0.836115	+	0.451601i
$609$	1.67608	−	0.967684i	0.0679181	−	0.0392126i
$610$	1.35358	+	12.2115i	0.0548049	+	0.494427i
$611$	19.8830	−	7.03109i	0.804381	−	0.284448i
$612$	−33.0201	+	7.41131i	−1.33476	+	0.299585i
$613$	−6.59886	−	11.4296i	−0.266526	−	0.461636i	0.701437	−	0.712732i	$-0.252542\pi$
$613$	−6.59886	−	11.4296i	−0.266526	−	0.461636i	−0.967962	+	0.251096i	$0.919209\pi$
$614$	−12.9508	−	17.6142i	−0.522651	−	0.710849i
$615$	−0.872409	+	1.51106i	−0.0351789	+	0.0609317i
$616$	−0.546374	−	1.58900i	−0.0220140	−	0.0640225i
$617$	14.0952	+	8.13787i	0.567452	+	0.327619i	0.756131	−	0.654420i	$-0.227087\pi$
$617$	14.0952	+	8.13787i	0.567452	+	0.327619i	−0.188679	+	0.982039i	$0.560421\pi$
$618$	10.5600	+	4.63001i	0.424787	+	0.186246i
$619$	13.8522			0.556767			0.278384	−	0.960470i	$-0.410201\pi$
$619$	13.8522			0.556767			0.278384	+	0.960470i	$0.410201\pi$
$620$	19.5308	+	6.10176i	0.784376	+	0.245053i
$621$	−18.2885	+	10.5589i	−0.733892	+	0.423713i
$622$	8.32850	+	11.3274i	0.333942	+	0.454189i
$623$	2.81168			0.112648
$624$	−2.78025	−	10.5412i	−0.111299	−	0.421985i
$625$	1.00000			0.0400000
$626$	−9.03118	−	12.2832i	−0.360959	−	0.490934i
$627$	−2.68893	+	1.55245i	−0.107385	+	0.0619990i
$628$	−17.7738	−	5.55286i	−0.709254	−	0.221583i
$629$	47.1972			1.88188
$630$	−1.88443	−	0.826220i	−0.0750774	−	0.0329174i
$631$	−10.7183	−	6.18820i	−0.426688	−	0.246348i	0.271247	−	0.962510i	$-0.412564\pi$
$631$	−10.7183	−	6.18820i	−0.426688	−	0.246348i	−0.697935	+	0.716161i	$0.745897\pi$
$632$	3.97587	−	1.36710i	0.158152	−	0.0543802i
$633$	4.29950	−	7.44694i	0.170890	−	0.295989i
$634$	−7.29259	−	9.91853i	−0.289626	−	0.393915i
$635$	−8.35088	−	14.4641i	−0.331394	−	0.573992i
$636$	−1.51929	+	0.341002i	−0.0602437	+	0.0135216i
$637$	15.5589	−	18.2009i	0.616468	−	0.721147i
$638$	0.660322	+	5.95715i	0.0261424	+	0.235846i
$639$	−7.05310	+	4.07211i	−0.279016	+	0.161090i
$640$	10.8903	+	3.06605i	0.430478	+	0.121196i
$641$	7.47650	−	12.9497i	0.295304	−	0.511481i	−0.679752	−	0.733442i	$-0.737912\pi$
$641$	7.47650	−	12.9497i	0.295304	−	0.511481i	0.975056	+	0.221961i	$0.0712458\pi$
$642$	−12.1879	+	1.35097i	−0.481019	+	0.0533187i
$643$	−2.15763	+	3.73713i	−0.0850887	+	0.147378i	−0.905429	−	0.424498i	$-0.860451\pi$
$643$	−2.15763	+	3.73713i	−0.0850887	+	0.147378i	0.820340	+	0.571876i	$0.193784\pi$
$644$	−5.88557	−	1.83875i	−0.231924	−	0.0724570i
$645$	−7.41447			−0.291945
$646$	−16.3885	+	37.3787i	−0.644798	+	1.47064i
$647$	−11.5479	−	20.0016i	−0.453995	−	0.786343i	0.544634	−	0.838674i	$-0.316668\pi$
$647$	−11.5479	−	20.0016i	−0.453995	−	0.786343i	−0.998630	+	0.0523305i	$0.983335\pi$
$648$	8.92817	+	7.76786i	0.350732	+	0.305151i
$649$	0.423232			0.0166133
$650$	−2.86608	+	4.21729i	−0.112417	+	0.165416i
$651$		−	4.63297i		−	0.181581i
$652$	−10.2507	−	11.1279i	−0.401447	−	0.435802i
$653$	−19.3791	+	11.1885i	−0.758363	+	0.437841i	−0.828708	−	0.559681i	$-0.810923\pi$
$653$	−19.3791	+	11.1885i	−0.758363	+	0.437841i	0.0703444	+	0.997523i	$0.477590\pi$
$654$	2.91640	+	1.27868i	0.114040	+	0.0500005i
$655$		−	17.0053i		−	0.664451i
$656$	9.20208	+	0.756455i	0.359281	+	0.0295346i
$657$	23.8408	+	13.7645i	0.930118	+	0.537004i
$658$	4.92544	−	0.545962i	0.192014	−	0.0212838i
$659$	6.15426	+	3.55316i	0.239736	+	0.138412i	0.615055	−	0.788484i	$-0.289134\pi$
$659$	6.15426	+	3.55316i	0.239736	+	0.138412i	−0.375320	+	0.926895i	$0.622467\pi$
$660$	−1.10264	+	1.01572i	−0.0429203	+	0.0395368i
$661$	8.83848	+	15.3087i	0.343777	+	0.595439i	0.985131	−	0.171806i	$-0.0549602\pi$
$661$	8.83848	+	15.3087i	0.343777	+	0.595439i	−0.641354	+	0.767245i	$0.721627\pi$
$662$	−2.64745	+	0.293457i	−0.102896	+	0.0114055i
$663$	17.9023	−	6.33066i	0.695268	−	0.245862i
$664$	21.5545	−	7.41149i	0.836479	−	0.287622i
$665$	−2.14904	+	1.24075i	−0.0833362	+	0.0481142i
$666$	−13.7823	−	18.7450i	−0.534052	−	0.726355i
$667$	19.0477	+	10.9972i	0.737531	+	0.425814i
$668$	−8.65250	−	38.5501i	−0.334775	−	1.49155i
$669$	−9.20036	+	15.9355i	−0.355706	+	0.616102i
$670$	5.98146	−	13.6424i	0.231084	−	0.527052i
$671$			8.61515i			0.332584i
$672$	−0.0726755	−	2.56063i	−0.00280352	−	0.0987785i
$673$	−17.9948	−	31.1679i	−0.693649	−	1.20143i	−0.970634	−	0.240560i	$-0.922669\pi$
$673$	−17.9948	−	31.1679i	−0.693649	−	1.20143i	0.276986	−	0.960874i	$-0.410665\pi$
$674$	4.33584	+	5.89710i	0.167010	+	0.227148i
$675$			4.10347i			0.157943i
$676$	−9.57115	−	24.1742i	−0.368121	−	0.929778i
$677$		−	9.79680i		−	0.376522i	−0.982119	−	0.188261i	$-0.939715\pi$
$677$		−	9.79680i		−	0.376522i	0.982119	−	0.188261i	$-0.0602850\pi$
$678$	−16.1724	+	11.8907i	−0.621096	+	0.456660i
$679$	4.37018	+	7.56937i	0.167712	+	0.290486i
$680$	−3.76844	+	19.3427i	−0.144513	+	0.741758i
$681$			19.9643i			0.765035i
$682$	13.1403	+	5.76132i	0.503168	+	0.220612i
$683$	−24.3965	+	42.2560i	−0.933507	+	1.61688i	−0.156232	+	0.987720i	$0.549935\pi$
$683$	−24.3965	+	42.2560i	−0.933507	+	1.61688i	−0.777275	+	0.629161i	$0.783399\pi$
$684$	19.6312	−	4.40618i	0.750616	−	0.168474i
$685$	−1.14959	−	0.663718i	−0.0439237	−	0.0253594i
$686$	9.31121	−	6.84606i	0.355504	−	0.261384i
$687$	−19.0682	+	11.0091i	−0.727499	+	0.420022i
$688$	16.7679	+	35.4719i	0.639272	+	1.35235i
$689$	−3.50112	+	1.23808i	−0.133382	+	0.0471670i
$690$	0.606091	+	5.46790i	0.0230735	+	0.208159i
$691$	19.5264	+	33.8207i	0.742819	+	1.28660i	0.951207	+	0.308555i	$0.0998453\pi$
$691$	19.5264	+	33.8207i	0.742819	+	1.28660i	−0.208387	+	0.978046i	$0.566821\pi$
$692$	−29.3173	+	27.0062i	−1.11448	+	1.02662i
$693$	−1.24950	−	0.721396i	−0.0474644	−	0.0274036i
$694$	2.81826	+	25.4252i	0.106980	+	0.965127i
$695$	6.77015	+	3.90875i	0.256806	+	0.148267i
$696$	−1.74735	+	8.96879i	−0.0662330	+	0.339961i
$697$			16.0824i			0.609163i
$698$	−0.675923	+	1.54163i	−0.0255841	+	0.0583517i
$699$	−10.0216	+	5.78599i	−0.379053	+	0.218846i
$700$	−0.881251	+	0.811781i	−0.0333082	+	0.0306824i
$701$		−	25.8238i		−	0.975353i	−0.873024	−	0.487677i	$-0.837845\pi$
$701$		−	25.8238i		−	0.975353i	0.873024	−	0.487677i	$-0.162155\pi$
$702$	−17.3055	−	11.7609i	−0.653155	−	0.443886i
$703$	−28.0597			−1.05829
$704$	7.35299	+	2.97814i	0.277126	+	0.112243i
$705$	−2.21069	−	3.82903i	−0.0832595	−	0.144210i
$706$	−10.9667	−	4.80829i	−0.412736	−	0.180962i
$707$	8.76886			0.329787
$708$	0.615869	+	0.192408i	0.0231458	+	0.00723114i
$709$	1.19551	−	2.07069i	0.0448985	−	0.0777665i	−0.842703	−	0.538379i	$-0.819037\pi$
$709$	1.19551	−	2.07069i	0.0448985	−	0.0777665i	0.887601	+	0.460613i	$0.152370\pi$
$710$	0.522480	+	4.71360i	0.0196083	+	0.176898i
$711$	1.80503	−	3.12640i	0.0676937	−	0.117249i
$712$	−8.71331	+	10.0148i	−0.326545	+	0.375322i
$713$	45.5973	−	26.3256i	1.70763	−	0.985903i
$714$	4.43477	−	0.491574i	0.165967	−	0.0183967i
$715$	−2.32326	+	2.71777i	−0.0868852	+	0.101639i
$716$	−1.63756	−	7.29592i	−0.0611984	−	0.272661i
$717$	7.08083	+	12.2644i	0.264439	+	0.458021i
$718$	15.9129	−	11.7000i	0.593866	−	0.436639i
$719$	−18.4354	+	31.9311i	−0.687524	+	1.19083i	0.285112	+	0.958494i	$0.407969\pi$
$719$	−18.4354	+	31.9311i	−0.687524	+	1.19083i	−0.972636	+	0.232333i	$0.925364\pi$
$720$	8.78266	−	4.15165i	0.327310	−	0.154723i
$721$	5.59611	+	3.23092i	0.208410	+	0.120326i
$722$	−1.04624	+	2.38625i	−0.0389371	+	0.0888070i
$723$	−1.93755			−0.0720582
$724$	34.6911	+	10.8381i	1.28928	+	0.402794i
$725$	3.70124	−	2.13691i	0.137461	−	0.0793630i
$726$	8.62689	−	6.34291i	0.320174	−	0.235408i
$727$	25.8787			0.959789			0.479895	−	0.877326i	$-0.340675\pi$
$727$	25.8787			0.959789			0.479895	+	0.877326i	$0.340675\pi$
$728$	−0.897780	−	6.04312i	−0.0332739	−	0.223973i
$729$	0.856167			0.0317099
$730$	12.9152	−	9.49589i	0.478013	−	0.351459i
$731$	−59.1849	+	34.1704i	−2.18903	+	1.26384i
$732$	−3.91659	+	12.5364i	−0.144761	+	0.463358i
$733$	−4.42298			−0.163366			−0.0816832	−	0.996658i	$-0.526030\pi$
$733$	−4.42298			−0.163366			−0.0816832	+	0.996658i	$0.526030\pi$
$734$	−1.00851	+	2.30020i	−0.0372249	+	0.0849020i
$735$	−4.34743	−	2.50999i	−0.160357	−	0.0925823i
$736$	24.7886	−	15.2654i	0.913718	−	0.562689i
$737$	5.22258	−	9.04578i	0.192376	−	0.333206i
$738$	6.38734	−	4.69628i	0.235121	−	0.172873i
$739$	5.69026	+	9.85581i	0.209319	+	0.362552i	0.951500	−	0.307648i	$-0.0995418\pi$
$739$	5.69026	+	9.85581i	0.209319	+	0.362552i	−0.742181	+	0.670200i	$0.766208\pi$
$740$	−13.2194	+	2.96708i	−0.485955	+	0.109072i
$741$	−10.6433	+	3.76371i	−0.390991	+	0.138263i
$742$	−0.867302	+	0.0961363i	−0.0318396	+	0.00352927i
$743$	19.7214	−	11.3861i	0.723507	−	0.417717i	−0.0925354	−	0.995709i	$-0.529497\pi$
$743$	19.7214	−	11.3861i	0.723507	−	0.417717i	0.816042	+	0.577993i	$0.196164\pi$
$744$	16.5020	+	14.3574i	0.604994	+	0.526369i
$745$	−3.16075	+	5.47457i	−0.115801	+	0.200573i
$746$	0.331317	+	2.98901i	0.0121304	+	0.109435i
$747$	9.78565	−	16.9492i	0.358038	−	0.620141i
$748$	−4.12062	+	13.1895i	−0.150665	+	0.482254i
$749$	−6.87211			−0.251102
$750$	0.979029	+	0.429251i	0.0357491	+	0.0156740i
$751$	−6.37962	−	11.0498i	−0.232796	−	0.403214i	0.725834	−	0.687870i	$-0.241454\pi$
$751$	−6.37962	−	11.0498i	−0.232796	−	0.403214i	−0.958630	+	0.284656i	$0.908121\pi$
$752$	−13.3191	+	19.2357i	−0.485699	+	0.701453i
$753$	20.8536			0.759946
$754$	−1.59607	+	21.7338i	−0.0581255	+	0.791498i
$755$			0.928828i			0.0338035i
$756$	−3.33112	−	3.61619i	−0.121152	−	0.131519i
$757$	−38.1489	+	22.0253i	−1.38654	+	0.800522i	−0.992924	−	0.118751i	$-0.962111\pi$
$757$	−38.1489	+	22.0253i	−1.38654	+	0.800522i	−0.393620	+	0.919273i	$0.628777\pi$
$758$	14.6117	−	33.3262i	0.530722	−	1.21046i
$759$			3.85759i			0.140022i
$760$	2.24042	−	11.4996i	0.0812685	−	0.417135i
$761$	0.405243	+	0.233967i	0.0146900	+	0.00848130i	0.507327	−	0.861754i	$-0.330634\pi$
$761$	0.405243	+	0.233967i	0.0146900	+	0.00848130i	−0.492637	+	0.870235i	$0.663967\pi$
$762$	−1.96700	−	17.7454i	−0.0712568	−	0.642849i
$763$	1.54550	+	0.892292i	0.0559507	+	0.0323031i
$764$	−0.684762	−	0.743362i	−0.0247738	−	0.0268939i
$765$	8.46041	+	14.6539i	0.305887	+	0.529812i
$766$	4.20040	+	37.8942i	0.151766	+	1.36917i
$767$	1.51294	+	0.281097i	0.0546291	+	0.0101498i
$768$	9.34584	+	7.67645i	0.337239	+	0.277000i
$769$	−45.7185	+	26.3956i	−1.64865	+

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:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.ca (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.837733 + 1.13939i) q^{2} +(0.654624 - 0.377948i) q^{3} +(-0.596406 + 1.90900i) q^{4} +1.00000 q^{5} +(0.979029 + 0.429251i) q^{6} +(0.518819 + 0.299540i) q^{7} +(-2.67472 + 0.919699i) q^{8} +(-1.21431 + 2.10325i) q^{9} +O(q^{10})\)	\(q+(0.837733 + 1.13939i) q^{2} +(0.654624 - 0.377948i) q^{3} +(-0.596406 + 1.90900i) q^{4} +1.00000 q^{5} +(0.979029 + 0.429251i) q^{6} +(0.518819 + 0.299540i) q^{7} +(-2.67472 + 0.919699i) q^{8} +(-1.21431 + 2.10325i) q^{9} +(0.837733 + 1.13939i) q^{10} +(0.495825 + 0.858794i) q^{11} +(0.331082 + 1.47509i) q^{12} +(1.20206 + 3.39927i) q^{13} +(0.0933396 + 0.842071i) q^{14} +(0.654624 - 0.377948i) q^{15} +(-3.28860 - 2.27708i) q^{16} +(3.48363 - 6.03382i) q^{17} +(-3.41368 + 0.378391i) q^{18} +(-2.07109 + 3.58723i) q^{19} +(-0.596406 + 1.90900i) q^{20} +0.452842 q^{21} +(-0.563130 + 1.28438i) q^{22} +(2.57315 + 4.45684i) q^{23} +(-1.40334 + 1.61296i) q^{24} +1.00000 q^{25} +(-2.86608 + 4.21729i) q^{26} +4.10347i q^{27} +(-0.881251 + 0.811781i) q^{28} +(3.70124 - 2.13691i) q^{29} +(0.979029 + 0.429251i) q^{30} -10.2309i q^{31} +(-0.160488 - 5.65458i) q^{32} +(0.649158 + 0.374792i) q^{33} +(9.79320 - 1.08553i) q^{34} +(0.518819 + 0.299540i) q^{35} +(-3.29089 - 3.57252i) q^{36} +(3.38708 + 5.86659i) q^{37} +(-5.82226 + 0.645370i) q^{38} +(2.07164 + 1.77093i) q^{39} +(-2.67472 + 0.919699i) q^{40} +(-1.99903 + 1.15414i) q^{41} +(0.379361 + 0.515963i) q^{42} +(-8.49472 - 4.90443i) q^{43} +(-1.93516 + 0.434342i) q^{44} +(-1.21431 + 2.10325i) q^{45} +(-2.92244 + 6.66546i) q^{46} -5.84920i q^{47} +(-3.01342 - 0.247717i) q^{48} +(-3.32055 - 5.75136i) q^{49} +(0.837733 + 1.13939i) q^{50} -5.26651i q^{51} +(-7.20614 + 0.267391i) q^{52} +1.02996i q^{53} +(-4.67544 + 3.43761i) q^{54} +(0.495825 + 0.858794i) q^{55} +(-1.66319 - 0.324031i) q^{56} +3.13105i q^{57} +(5.53542 + 2.42698i) q^{58} +(0.213398 - 0.369616i) q^{59} +(0.331082 + 1.47509i) q^{60} +(7.52376 + 4.34384i) q^{61} +(11.6569 - 8.57075i) q^{62} +(-1.26002 + 0.727471i) q^{63} +(6.30831 - 4.91988i) q^{64} +(1.20206 + 3.39927i) q^{65} +(0.116789 + 1.05362i) q^{66} +(-5.26656 - 9.12195i) q^{67} +(9.44093 + 10.2489i) q^{68} +(3.36890 + 1.94504i) q^{69} +(0.0933396 + 0.842071i) q^{70} +(2.90416 + 1.67672i) q^{71} +(1.31359 - 6.74241i) q^{72} -11.3352i q^{73} +(-3.84685 + 8.77383i) q^{74} +(0.654624 - 0.377948i) q^{75} +(-5.61283 - 6.09316i) q^{76} +0.594079i q^{77} +(-0.282291 + 3.84397i) q^{78} -1.48646 q^{79} +(-3.28860 - 2.27708i) q^{80} +(-2.09204 - 3.62352i) q^{81} +(-2.98967 - 1.31081i) q^{82} -8.05860 q^{83} +(-0.270078 + 0.864478i) q^{84} +(3.48363 - 6.03382i) q^{85} +(-1.52827 - 13.7874i) q^{86} +(1.61528 - 2.79775i) q^{87} +(-2.11603 - 1.84103i) q^{88} +(4.06454 - 2.34667i) q^{89} +(-3.41368 + 0.378391i) q^{90} +(-0.394568 + 2.12367i) q^{91} +(-10.0428 + 2.25408i) q^{92} +(-3.86674 - 6.69738i) q^{93} +(6.66451 - 4.90007i) q^{94} +(-2.07109 + 3.58723i) q^{95} +(-2.24219 - 3.64097i) q^{96} +(12.6350 + 7.29481i) q^{97} +(3.77129 - 8.60150i) q^{98} -2.40834 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9}+O(q^{10}) \) 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9	\( 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9} - 8 q^{11} + 6 q^{12} - 4 q^{14} + 14 q^{16} + 18 q^{18} - 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 22 q^{24} + 56 q^{25} - 37 q^{26} - 12 q^{28} - 13 q^{30} - 30 q^{32} - 16 q^{34} + 15 q^{36} + 4 q^{37} - 24 q^{39} - 61 q^{42} + 24 q^{44} + 28 q^{45} - 19 q^{46} - 51 q^{48} + 20 q^{49} - 64 q^{52} - 5 q^{54} - 8 q^{55} - 23 q^{56} - q^{58} - 16 q^{59} + 6 q^{60} + 10 q^{62} - 30 q^{64} + 14 q^{66} - 36 q^{67} - 51 q^{68} - 4 q^{70} - 81 q^{72} + 70 q^{74} - 60 q^{76} + 143 q^{78} + 14 q^{80} - 28 q^{81} + 21 q^{82} + 40 q^{83} + 31 q^{84} - 28 q^{86} - 36 q^{87} - 19 q^{88} + 18 q^{90} + 16 q^{91} - 18 q^{92} + 43 q^{94} - 16 q^{95} - 48 q^{96} + 24 q^{97} + 56 q^{98} - 48 q^{99}+O(q^{100}) \) 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9 - 8 * q^11 + 6 * q^12 - 4 * q^14 + 14 * q^16 + 18 * q^18 - 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 22 * q^24 + 56 * q^25 - 37 * q^26 - 12 * q^28 - 13 * q^30 - 30 * q^32 - 16 * q^34 + 15 * q^36 + 4 * q^37 - 24 * q^39 - 61 * q^42 + 24 * q^44 + 28 * q^45 - 19 * q^46 - 51 * q^48 + 20 * q^49 - 64 * q^52 - 5 * q^54 - 8 * q^55 - 23 * q^56 - q^58 - 16 * q^59 + 6 * q^60 + 10 * q^62 - 30 * q^64 + 14 * q^66 - 36 * q^67 - 51 * q^68 - 4 * q^70 - 81 * q^72 + 70 * q^74 - 60 * q^76 + 143 * q^78 + 14 * q^80 - 28 * q^81 + 21 * q^82 + 40 * q^83 + 31 * q^84 - 28 * q^86 - 36 * q^87 - 19 * q^88 + 18 * q^90 + 16 * q^91 - 18 * q^92 + 43 * q^94 - 16 * q^95 - 48 * q^96 + 24 * q^97 + 56 * q^98 - 48 * q^99

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