LMFDB - Embedded newform 531.2.i.c.64.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [531,2,Mod(19,531)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 38]))

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

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

chi := DirichletCharacter("531.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	531.i (of order $29$, degree $28$, 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:	$4.24005634733$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$5$ over $\Q(\zeta_{29})$
Twist minimal:	no (minimal twist has level 177)
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			64.3
Character	$\chi$	$=$	531.64
Dual form			531.2.i.c.307.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.288668 - 0.0972636i) q^{2} +(-1.51832 - 1.15419i) q^{4} +(1.30154 - 3.26662i) q^{5} +(-3.34578 + 1.54792i) q^{7} +(0.667919 + 0.985107i) q^{8} +O(q^{10})$	\(q+(-0.288668 - 0.0972636i) q^{2} +(-1.51832 - 1.15419i) q^{4} +(1.30154 - 3.26662i) q^{5} +(-3.34578 + 1.54792i) q^{7} +(0.667919 + 0.985107i) q^{8} +(-0.693437 + 0.816377i) q^{10} +(0.412947 - 1.48730i) q^{11} +(1.27783 - 2.41025i) q^{13} +(1.11638 - 0.121413i) q^{14} +(0.923474 + 3.32605i) q^{16} +(-1.02833 - 0.475754i) q^{17} +(-7.65671 + 1.68537i) q^{19} +(-5.74647 + 3.45753i) q^{20} +(-0.263865 + 0.389171i) q^{22} +(-0.600176 + 3.66091i) q^{23} +(-5.34682 - 5.06478i) q^{25} +(-0.603299 + 0.571476i) q^{26} +(6.86657 + 1.51145i) q^{28} +(-2.49973 + 0.842256i) q^{29} +(-3.44618 - 0.758561i) q^{31} +(0.185798 - 3.42683i) q^{32} +(0.250571 + 0.237354i) q^{34} +(0.701808 + 12.9441i) q^{35} +(0.779638 - 1.14988i) q^{37} +(2.37417 + 0.258207i) q^{38} +(4.08729 - 0.899681i) q^{40} +(-0.0782668 - 0.477406i) q^{41} +(3.12061 + 11.2394i) q^{43} +(-2.34362 + 1.78157i) q^{44} +(0.529325 - 0.998413i) q^{46} +(-4.90708 - 12.3158i) q^{47} +(4.26650 - 5.02291i) q^{49} +(1.05084 + 1.98209i) q^{50} +(-4.72205 + 2.18465i) q^{52} +(-5.82908 - 6.86252i) q^{53} +(-4.32097 - 3.28472i) q^{55} +(-3.75959 - 2.26207i) q^{56} +0.803513 q^{58} +(6.04918 - 4.73365i) q^{59} +(-7.45245 - 2.51102i) q^{61} +(0.921021 + 0.554160i) q^{62} +(2.16840 - 5.44227i) q^{64} +(-6.21022 - 7.31123i) q^{65} +(-5.86524 - 8.65058i) q^{67} +(1.01221 + 1.90923i) q^{68} +(1.05640 - 3.80481i) q^{70} +(4.80372 + 12.0564i) q^{71} +(4.65164 - 0.505896i) q^{73} +(-0.336898 + 0.256103i) q^{74} +(13.5706 + 6.27841i) q^{76} +(0.920597 + 5.61539i) q^{77} +(0.589897 - 0.354930i) q^{79} +(12.0669 + 1.31235i) q^{80} +(-0.0238411 + 0.145425i) q^{82} +(-0.522637 - 9.63947i) q^{83} +(-2.89251 + 2.73993i) q^{85} +(0.192366 - 3.54799i) q^{86} +(1.74096 - 0.586599i) q^{88} +(16.4014 - 5.52628i) q^{89} +(-0.544470 + 10.0422i) q^{91} +(5.13666 - 4.86570i) q^{92} +(0.218634 + 4.03247i) q^{94} +(-4.46006 + 27.2051i) q^{95} +(-2.49438 - 0.271280i) q^{97} +(-1.72015 + 1.03498i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8}+O(q^{10}) $ 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8	$ 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8} + 88 q^{10} + 14 q^{11} - 12 q^{13} + q^{14} - 41 q^{16} + 16 q^{17} - 10 q^{19} + 32 q^{20} - 26 q^{22} + 22 q^{23} + 27 q^{25} + 56 q^{26} - 50 q^{28} + 24 q^{29} - 24 q^{31} - 106 q^{32} - 54 q^{34} + 70 q^{35} - 28 q^{37} + 80 q^{38} - 50 q^{40} + 40 q^{41} + 4 q^{43} + 104 q^{44} - 28 q^{46} - 31 q^{47} - q^{49} - 39 q^{50} + 62 q^{52} - 4 q^{53} + 5 q^{55} - 96 q^{56} + 128 q^{58} + q^{59} - 16 q^{61} - 223 q^{62} + 97 q^{64} - 121 q^{65} - 12 q^{67} - 10 q^{68} - 2 q^{70} + 22 q^{71} + 179 q^{73} + 38 q^{74} + 112 q^{76} + 62 q^{77} - 84 q^{79} - 204 q^{80} - 152 q^{82} + 88 q^{83} - 118 q^{85} + 118 q^{86} + 18 q^{88} + 86 q^{89} + 78 q^{91} + 174 q^{92} - 164 q^{94} - 218 q^{95} - 84 q^{97} - 129 q^{98}+O(q^{100}) $ 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8 + 88 * q^10 + 14 * q^11 - 12 * q^13 + q^14 - 41 * q^16 + 16 * q^17 - 10 * q^19 + 32 * q^20 - 26 * q^22 + 22 * q^23 + 27 * q^25 + 56 * q^26 - 50 * q^28 + 24 * q^29 - 24 * q^31 - 106 * q^32 - 54 * q^34 + 70 * q^35 - 28 * q^37 + 80 * q^38 - 50 * q^40 + 40 * q^41 + 4 * q^43 + 104 * q^44 - 28 * q^46 - 31 * q^47 - q^49 - 39 * q^50 + 62 * q^52 - 4 * q^53 + 5 * q^55 - 96 * q^56 + 128 * q^58 + q^59 - 16 * q^61 - 223 * q^62 + 97 * q^64 - 121 * q^65 - 12 * q^67 - 10 * q^68 - 2 * q^70 + 22 * q^71 + 179 * q^73 + 38 * q^74 + 112 * q^76 + 62 * q^77 - 84 * q^79 - 204 * q^80 - 152 * q^82 + 88 * q^83 - 118 * q^85 + 118 * q^86 + 18 * q^88 + 86 * q^89 + 78 * q^91 + 174 * q^92 - 164 * q^94 - 218 * q^95 - 84 * q^97 - 129 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/531\mathbb{Z}\right)^\times$.

$n$	$119$	$415$
$\chi(n)$	$1$	$e\left(\frac{3}{29}\right)$

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 $

$2$	−0.288668	−	0.0972636i	−0.204119	−	0.0687758i	0.215385	−	0.976529i	$-0.430899\pi$
$2$	−0.288668	−	0.0972636i	−0.204119	−	0.0687758i	−0.419504	+	0.907753i	$0.637796\pi$
$3$		0			0
$3$		0			0
$4$	−1.51832	−	1.15419i	−0.759159	−	0.577097i
$5$	1.30154	−	3.26662i	0.582066	−	1.46088i	−0.282951	−	0.959134i	$-0.591313\pi$
$5$	1.30154	−	3.26662i	0.582066	−	1.46088i	0.865017	−	0.501742i	$-0.167307\pi$
$6$		0			0
$7$	−3.34578	+	1.54792i	−1.26459	+	0.585061i	−0.933513	−	0.358544i	$-0.883273\pi$
$7$	−3.34578	+	1.54792i	−1.26459	+	0.585061i	−0.331075	+	0.943605i	$0.607411\pi$
$8$	0.667919	+	0.985107i	0.236145	+	0.348288i
$9$		0			0
$10$	−0.693437	+	0.816377i	−0.219284	+	0.258161i
$11$	0.412947	−	1.48730i	0.124508	−	0.448438i	−0.874845	−	0.484403i	$-0.839037\pi$
$11$	0.412947	−	1.48730i	0.124508	−	0.448438i	0.999353	+	0.0359655i	$0.0114506\pi$
$12$		0			0
$13$	1.27783	−	2.41025i	0.354407	−	0.668483i	−0.640645	−	0.767837i	$-0.721333\pi$
$13$	1.27783	−	2.41025i	0.354407	−	0.668483i	0.995052	+	0.0993544i	$0.0316777\pi$
$14$	1.11638	−	0.121413i	0.298365	−	0.0324491i
$15$		0			0
$16$	0.923474	+	3.32605i	0.230868	+	0.831513i
$17$	−1.02833	−	0.475754i	−0.249405	−	0.115387i	0.291204	−	0.956661i	$-0.405944\pi$
$17$	−1.02833	−	0.475754i	−0.249405	−	0.115387i	−0.540609	+	0.841274i	$0.681806\pi$
$18$		0			0
$19$	−7.65671	+	1.68537i	−1.75657	+	0.386650i	−0.972294	−	0.233761i	$-0.924897\pi$
$19$	−7.65671	+	1.68537i	−1.75657	+	0.386650i	−0.784277	+	0.620411i	$0.786966\pi$
$20$	−5.74647	+	3.45753i	−1.28495	+	0.773128i
$21$		0			0
$22$	−0.263865	+	0.389171i	−0.0562561	+	0.0829716i
$23$	−0.600176	+	3.66091i	−0.125145	+	0.763352i	0.847455	+	0.530868i	$0.178134\pi$
$23$	−0.600176	+	3.66091i	−0.125145	+	0.763352i	−0.972600	+	0.232485i	$0.925314\pi$
$24$		0			0
$25$	−5.34682	−	5.06478i	−1.06936	−	1.01296i
$26$	−0.603299	+	0.571476i	−0.118317	+	0.112076i
$27$		0			0
$28$	6.86657	+	1.51145i	1.29766	+	0.285636i
$29$	−2.49973	+	0.842256i	−0.464188	+	0.156403i	−0.541671	−	0.840591i	$-0.682208\pi$
$29$	−2.49973	+	0.842256i	−0.464188	+	0.156403i	0.0774832	+	0.996994i	$0.475312\pi$
$30$		0			0
$31$	−3.44618	−	0.758561i	−0.618952	−	0.136242i	−0.105584	−	0.994410i	$-0.533671\pi$
$31$	−3.44618	−	0.758561i	−0.618952	−	0.136242i	−0.513368	+	0.858169i	$0.671602\pi$
$32$	0.185798	−	3.42683i	0.0328447	−	0.605785i
$33$		0			0
$34$	0.250571	+	0.237354i	0.0429726	+	0.0407058i
$35$	0.701808	+	12.9441i	0.118627	+	2.18795i
$36$		0			0
$37$	0.779638	−	1.14988i	0.128172	−	0.189039i	−0.758189	−	0.652035i	$-0.773915\pi$
$37$	0.779638	−	1.14988i	0.128172	−	0.189039i	0.886360	+	0.462996i	$0.153226\pi$
$38$	2.37417	+	0.258207i	0.385142	+	0.0418867i
$39$		0			0
$40$	4.08729	−	0.899681i	0.646258	−	0.142252i
$41$	−0.0782668	−	0.477406i	−0.0122232	−	0.0745583i	0.980011	−	0.198946i	$-0.0637517\pi$
$41$	−0.0782668	−	0.477406i	−0.0122232	−	0.0745583i	−0.992234	+	0.124387i	$0.960303\pi$
$42$		0			0
$43$	3.12061	+	11.2394i	0.475889	+	1.71400i	0.678378	+	0.734713i	$0.262683\pi$
$43$	3.12061	+	11.2394i	0.475889	+	1.71400i	−0.202489	+	0.979285i	$0.564903\pi$
$44$	−2.34362	+	1.78157i	−0.353313	+	0.268582i
$45$		0			0
$46$	0.529325	−	0.998413i	0.0780447	−	0.147208i
$47$	−4.90708	−	12.3158i	−0.715771	−	1.79645i	−0.594930	−	0.803777i	$-0.702820\pi$
$47$	−4.90708	−	12.3158i	−0.715771	−	1.79645i	−0.120840	−	0.992672i	$-0.538559\pi$
$48$		0			0
$49$	4.26650	−	5.02291i	0.609500	−	0.717559i
$50$	1.05084	+	1.98209i	0.148611	+	0.280310i
$51$		0			0
$52$	−4.72205	+	2.18465i	−0.654831	+	0.302957i
$53$	−5.82908	−	6.86252i	−0.800686	−	0.942640i	0.198613	−	0.980078i	$-0.436356\pi$
$53$	−5.82908	−	6.86252i	−0.800686	−	0.942640i	−0.999299	+	0.0374378i	$0.988080\pi$
$54$		0			0
$55$	−4.32097	−	3.28472i	−0.582640	−	0.442911i
$56$	−3.75959	−	2.26207i	−0.502396	−	0.302281i
$57$		0			0
$58$	0.803513			0.105506
$59$	6.04918	−	4.73365i	0.787536	−	0.616269i
$59$	6.04918	−	4.73365i	0.787536	−	0.616269i
$60$		0			0
$61$	−7.45245	−	2.51102i	−0.954188	−	0.321503i	−0.201209	−	0.979548i	$-0.564487\pi$
$61$	−7.45245	−	2.51102i	−0.954188	−	0.321503i	−0.752979	+	0.658045i	$0.771384\pi$
$62$	0.921021	+	0.554160i	0.116970	+	0.0703784i
$63$		0			0
$64$	2.16840	−	5.44227i	0.271050	−	0.680284i
$65$	−6.21022	−	7.31123i	−0.770283	−	0.906847i
$66$		0			0
$67$	−5.86524	−	8.65058i	−0.716553	−	1.05684i	−0.995335	−	0.0964821i	$-0.969241\pi$
$67$	−5.86524	−	8.65058i	−0.716553	−	1.05684i	0.278782	−	0.960354i	$-0.410069\pi$
$68$	1.01221	+	1.90923i	0.122749	+	0.231528i
$69$		0			0
$70$	1.05640	−	3.80481i	0.126264	−	0.454761i
$71$	4.80372	+	12.0564i	0.570097	+	1.43083i	0.877649	+	0.479303i	$0.159111\pi$
$71$	4.80372	+	12.0564i	0.570097	+	1.43083i	−0.307553	+	0.951531i	$0.599510\pi$
$72$		0			0
$73$	4.65164	−	0.505896i	0.544433	−	0.0592107i	0.168230	−	0.985748i	$-0.446195\pi$
$73$	4.65164	−	0.505896i	0.544433	−	0.0592107i	0.376203	+	0.926537i	$0.377229\pi$
$74$	−0.336898	+	0.256103i	−0.0391636	+	0.0297714i
$75$		0			0
$76$	13.5706	+	6.27841i	1.55665	+	0.720183i
$77$	0.920597	+	5.61539i	0.104912	+	0.639933i
$78$		0			0
$79$	0.589897	−	0.354930i	0.0663686	−	0.0399327i	−0.481983	−	0.876181i	$-0.660083\pi$
$79$	0.589897	−	0.354930i	0.0663686	−	0.0399327i	0.548351	+	0.836248i	$0.315256\pi$
$80$	12.0669	+	1.31235i	1.34912	+	0.146725i
$81$		0			0
$82$	−0.0238411	+	0.145425i	−0.00263281	+	0.0160594i
$83$	−0.522637	−	9.63947i	−0.0573668	−	1.05807i	−0.875555	−	0.483118i	$-0.839504\pi$
$83$	−0.522637	−	9.63947i	−0.0573668	−	1.05807i	0.818188	−	0.574950i	$-0.194979\pi$
$84$		0			0
$85$	−2.89251	+	2.73993i	−0.313737	+	0.297188i
$86$	0.192366	−	3.54799i	0.0207434	−	0.382590i
$87$		0			0
$88$	1.74096	−	0.586599i	0.185587	−	0.0625317i
$89$	16.4014	−	5.52628i	1.73855	−	0.585784i	0.742120	−	0.670267i	$-0.233820\pi$
$89$	16.4014	−	5.52628i	1.73855	−	0.585784i	0.996425	+	0.0844828i	$0.0269238\pi$
$90$		0			0
$91$	−0.544470	+	10.0422i	−0.0570760	+	1.05270i
$92$	5.13666	−	4.86570i	0.535534	−	0.507284i
$93$		0			0
$94$	0.218634	+	4.03247i	0.0225504	+	0.415918i
$95$	−4.46006	+	27.2051i	−0.457592	+	2.79119i
$96$		0			0
$97$	−2.49438	−	0.271280i	−0.253266	−	0.0275443i	−0.0193945	−	0.999812i	$-0.506174\pi$
$97$	−2.49438	−	0.271280i	−0.253266	−	0.0275443i	−0.233871	+	0.972268i	$0.575139\pi$
$98$	−1.72015	+	1.03498i	−0.173761	+	0.104549i
$99$		0			0
$100$	2.27243	+	13.8612i	0.227243	+	1.38612i
$101$	−5.58022	−	2.58168i	−0.555253	−	0.256887i	0.122135	−	0.992514i	$-0.461026\pi$
$101$	−5.58022	−	2.58168i	−0.555253	−	0.256887i	−0.677388	+	0.735626i	$0.736888\pi$
$102$		0			0
$103$	6.15829	−	4.68141i	0.606794	−	0.461273i	−0.256105	−	0.966649i	$-0.582439\pi$
$103$	6.15829	−	4.68141i	0.606794	−	0.461273i	0.862899	+	0.505376i	$0.168646\pi$
$104$	3.22784	−	0.351049i	0.316516	−	0.0344232i
$105$		0			0
$106$	1.01520	+	2.54795i	0.0986045	+	0.247479i
$107$	1.51987	−	5.47409i	0.146932	−	0.529200i	−0.853041	−	0.521843i	$-0.825245\pi$
$107$	1.51987	−	5.47409i	0.146932	−	0.529200i	0.999973	−	0.00735661i	$-0.00234170\pi$
$108$		0			0
$109$	2.16175	+	4.07750i	0.207059	+	0.390554i	0.965191	−	0.261547i	$-0.0842327\pi$
$109$	2.16175	+	4.07750i	0.207059	+	0.390554i	−0.758132	+	0.652101i	$0.773888\pi$
$110$	0.927844	+	1.36847i	0.0884665	+	0.130478i
$111$		0			0
$112$	−8.23822	−	9.69878i	−0.778439	−	0.916449i
$113$	2.94716	−	7.39682i	0.277246	−	0.695834i	−0.722743	−	0.691117i	$-0.757119\pi$
$113$	2.94716	−	7.39682i	0.277246	−	0.695834i	0.999989	−	0.00471742i	$-0.00150161\pi$
$114$		0			0
$115$	11.1776	+	6.72537i	1.04232	+	0.627144i
$116$	4.76751	+	1.60636i	0.442652	+	0.149147i
$117$		0			0
$118$	−2.20662	+	0.778089i	−0.203136	+	0.0716289i
$119$	4.17699			0.382904
$120$		0			0
$121$	7.38389	+	4.44274i	0.671263	+	0.403886i
$122$	1.90705	+	1.44970i	0.172657	+	0.131250i
$123$		0			0
$124$	4.35686	+	5.12930i	0.391258	+	0.460624i
$125$	−7.54697	+	3.49160i	−0.675022	+	0.312298i
$126$		0			0
$127$	−4.20944	−	7.93985i	−0.373527	−	0.704547i	0.623481	−	0.781838i	$-0.285718\pi$
$127$	−4.20944	−	7.93985i	−0.373527	−	0.704547i	−0.997009	+	0.0772909i	$0.975373\pi$
$128$	−5.59877	+	6.59138i	−0.494866	+	0.582601i
$129$		0			0
$130$	1.08157	+	2.71455i	0.0948604	+	0.238082i
$131$	−3.78827	+	7.14543i	−0.330982	+	0.624299i	−0.992024	−	0.126050i	$-0.959770\pi$
$131$	−3.78827	+	7.14543i	−0.330982	+	0.624299i	0.661042	+	0.750349i	$0.270115\pi$
$132$		0			0
$133$	23.0089	−	17.4909i	1.99512	−	1.51665i
$134$	0.851721	+	3.06762i	0.0735775	+	0.265002i
$135$		0			0
$136$	−0.218170	−	1.33078i	−0.0187079	−	0.114113i
$137$	12.9787	−	2.85682i	1.10884	−	0.244075i	0.377449	−	0.926030i	$-0.376801\pi$
$137$	12.9787	−	2.85682i	1.10884	−	0.244075i	0.731394	+	0.681955i	$0.238870\pi$
$138$		0			0
$139$	−21.3503	−	2.32198i	−1.81091	−	0.196948i	−0.860816	−	0.508917i	$-0.830046\pi$
$139$	−21.3503	−	2.32198i	−1.81091	−	0.196948i	−0.950092	+	0.311969i	$0.899012\pi$
$140$	13.8744	−	20.4633i	1.17260	−	1.72946i
$141$		0			0
$142$	−0.214029	−	3.94753i	−0.0179609	−	0.331270i
$143$	−3.05709	−	2.89582i	−0.255646	−	0.242161i
$144$		0			0
$145$	−0.502165	+	9.26189i	−0.0417025	+	0.769158i
$146$	−1.39199	−	0.306399i	−0.115202	−	0.0253578i
$147$		0			0
$148$	−2.51092	+	0.846028i	−0.206397	+	0.0695431i
$149$	−1.79773	−	0.395711i	−0.147276	−	0.0324179i	0.140721	−	0.990049i	$-0.455058\pi$
$149$	−1.79773	−	0.395711i	−0.147276	−	0.0324179i	−0.287996	+	0.957631i	$0.592989\pi$
$150$		0			0
$151$	13.8995	−	13.1663i	1.13112	−	1.07146i	0.134370	−	0.990931i	$-0.457099\pi$
$151$	13.8995	−	13.1663i	1.13112	−	1.07146i	0.996753	−	0.0805253i	$-0.0256598\pi$
$152$	−6.77434	−	6.41699i	−0.549471	−	0.520487i
$153$		0			0
$154$	0.280426	−	1.71053i	0.0225974	−	0.137838i
$155$	−6.96327	+	10.2701i	−0.559303	+	0.824911i
$156$		0			0
$157$	−9.90064	+	5.95702i	−0.790157	+	0.475422i	−0.852560	−	0.522629i	$-0.824951\pi$
$157$	−9.90064	+	5.95702i	−0.790157	+	0.475422i	0.0624029	+	0.998051i	$0.480124\pi$
$158$	−0.204806	+	0.0450813i	−0.0162935	+	0.00358647i
$159$		0			0
$160$	−10.9523	−	5.06709i	−0.865859	−	0.400589i
$161$	−3.65875	−	13.1776i	−0.288350	−	1.03854i
$162$		0			0
$163$	7.22140	−	0.785374i	0.565623	−	0.0615153i	0.179160	−	0.983820i	$-0.442662\pi$
$163$	7.22140	−	0.785374i	0.565623	−	0.0615153i	0.386464	+	0.922305i	$0.373697\pi$
$164$	−0.432186	+	0.815189i	−0.0337481	+	0.0636556i
$165$		0			0
$166$	−0.786701	+	2.83344i	−0.0610598	+	0.219918i
$167$	−12.0152	+	14.1454i	−0.929768	+	1.09461i	0.0655405	+	0.997850i	$0.479123\pi$
$167$	−12.0152	+	14.1454i	−0.929768	+	1.09461i	−0.995308	+	0.0967571i	$0.969153\pi$
$168$		0			0
$169$	3.11899	+	4.60016i	0.239922	+	0.353859i
$170$	1.10147	−	0.509595i	0.0844791	−	0.0390842i
$171$		0			0
$172$	8.23441	−	20.6668i	0.627868	−	1.57583i
$173$	−11.1940	−	8.50944i	−0.851063	−	0.646961i	0.0859334	−	0.996301i	$-0.472613\pi$
$173$	−11.1940	−	8.50944i	−0.851063	−	0.646961i	−0.936996	+	0.349340i	$0.886406\pi$
$174$		0			0
$175$	25.7292	+	8.66917i	1.94494	+	0.655328i
$176$	5.32818			0.401627
$177$		0			0
$178$	−5.27207			−0.395158
$179$	−17.5527	−	5.91421i	−1.31195	−	0.442049i	−0.425539	−	0.904940i	$-0.639915\pi$
$179$	−17.5527	−	5.91421i	−1.31195	−	0.442049i	−0.886415	+	0.462892i	$0.846812\pi$
$180$		0			0
$181$	−3.40459	−	2.58810i	−0.253061	−	0.192372i	0.470951	−	0.882159i	$-0.343911\pi$
$181$	−3.40459	−	2.58810i	−0.253061	−	0.192372i	−0.724012	+	0.689787i	$0.757704\pi$
$182$	1.13391	−	2.84590i	0.0840509	−	0.210952i
$183$		0			0
$184$	−4.00726	+	1.85395i	−0.295419	+	0.136675i
$185$	−2.74149	−	4.04339i	−0.201558	−	0.297276i
$186$		0			0
$187$	−1.13223	+	1.33297i	−0.0827970	+	0.0974761i
$188$	−6.76437	+	24.3631i	−0.493342	+	1.77686i
$189$		0			0
$190$	3.93355	−	7.41946i	0.285370	−	0.538264i
$191$	10.3485	−	1.12546i	0.748789	−	0.0814358i	0.274236	−	0.961662i	$-0.411575\pi$
$191$	10.3485	−	1.12546i	0.748789	−	0.0814358i	0.474553	+	0.880227i	$0.342610\pi$
$192$		0			0
$193$	−1.26088	−	4.54128i	−0.0907601	−	0.326888i	0.904207	−	0.427096i	$-0.140463\pi$
$193$	−1.26088	−	4.54128i	−0.0907601	−	0.326888i	−0.994967	+	0.100207i	$0.968049\pi$
$194$	0.693661	+	0.320922i	0.0498020	+	0.0230409i
$195$		0			0
$196$	−12.2753	+	2.70200i	−0.876808	+	0.193000i
$197$	−6.94517	+	4.17877i	−0.494823	+	0.297725i	−0.741006	−	0.671498i	$-0.765651\pi$
$197$	−6.94517	+	4.17877i	−0.494823	+	0.297725i	0.246183	+	0.969223i	$0.420824\pi$
$198$		0			0
$199$	3.48945	−	5.14655i	0.247360	−	0.364829i	−0.683657	−	0.729803i	$-0.739612\pi$
$199$	3.48945	−	5.14655i	0.247360	−	0.364829i	0.931018	+	0.364974i	$0.118922\pi$
$200$	1.41810	−	8.65005i	0.100275	−	0.611651i
$201$		0			0
$202$	1.35973	+	1.28800i	0.0956701	+	0.0906236i
$203$	7.05980	−	6.68740i	0.495501	−	0.469363i
$204$		0			0
$205$	−1.66137	−	0.365696i	−0.116035	−	0.0255413i
$206$	−2.23303	+	0.752396i	−0.155583	+	0.0524219i
$207$		0			0
$208$	9.19666	+	2.02434i	0.637674	+	0.140363i
$209$	−0.655164	+	12.0838i	−0.0453187	+	0.835853i
$210$		0			0
$211$	−5.79839	−	5.49253i	−0.399178	−	0.378121i	0.461612	−	0.887082i	$-0.347271\pi$
$211$	−5.79839	−	5.49253i	−0.399178	−	0.378121i	−0.860790	+	0.508961i	$0.830030\pi$
$212$	0.929704	+	17.1474i	0.0638523	+	1.17769i
$213$		0			0
$214$	−0.971169	+	1.43237i	−0.0663877	+	0.0979146i
$215$	40.7766	+	4.43472i	2.78094	+	0.302445i
$216$		0			0
$217$	12.7044	−	2.79644i	0.862428	−	0.189835i
$218$	−0.227437	−	1.38731i	−0.0154040	−	0.0939602i
$219$		0			0
$220$	2.76940	+	9.97449i	0.186713	+	0.672480i
$221$	−2.46071	+	1.87059i	−0.165526	+	0.125829i
$222$		0			0
$223$	2.66757	−	5.03156i	0.178633	−	0.336938i	−0.777985	−	0.628283i	$-0.783758\pi$
$223$	2.66757	−	5.03156i	0.178633	−	0.336938i	0.956618	+	0.291345i	$0.0941027\pi$
$224$	4.68284	+	11.7531i	0.312886	+	0.785284i
$225$		0			0
$226$	−1.57019	+	1.84857i	−0.104448	+	0.122965i
$227$	−11.0567	−	20.8552i	−0.733860	−	1.38421i	−0.916099	−	0.400952i	$-0.868679\pi$
$227$	−11.0567	−	20.8552i	−0.733860	−	1.38421i	0.182239	−	0.983254i	$-0.441665\pi$
$228$		0			0
$229$	−5.63546	+	2.60724i	−0.372401	+	0.172291i	−0.597158	−	0.802124i	$-0.703703\pi$
$229$	−5.63546	+	2.60724i	−0.372401	+	0.172291i	0.224756	+	0.974415i	$0.427841\pi$
$230$	−2.57250	−	3.02858i	−0.169625	−	0.199698i
$231$		0			0
$232$	−2.49933	−	1.89994i	−0.164089	−	0.124737i
$233$	22.6385	+	13.6211i	1.48310	+	0.892349i	0.999858	+	0.0168601i	$0.00536699\pi$
$233$	22.6385	+	13.6211i	1.48310	+	0.892349i	0.483238	+	0.875489i	$0.339461\pi$
$234$		0			0
$235$	−46.6179			−3.04102
$236$	−14.6481	+	0.205251i	−0.953512	+	0.0133607i
$237$		0			0
$238$	−1.20576	−	0.406269i	−0.0781580	−	0.0263345i
$239$	8.26418	+	4.97239i	0.534565	+	0.321637i	0.757112	−	0.653285i	$-0.226609\pi$
$239$	8.26418	+	4.97239i	0.534565	+	0.321637i	−0.222547	+	0.974922i	$0.571437\pi$
$240$		0			0
$241$	−1.58145	+	3.96914i	−0.101870	+	0.255675i	−0.971074	−	0.238779i	$-0.923253\pi$
$241$	−1.58145	+	3.96914i	−0.101870	+	0.255675i	0.869204	+	0.494454i	$0.164632\pi$
$242$	−1.69938	−	2.00066i	−0.109240	−	0.128607i
$243$		0			0
$244$	8.41697	+	12.4141i	0.538841	+	0.794732i
$245$	−10.8549	−	20.4745i	−0.693495	−	1.30807i
$246$		0			0
$247$	−5.72184	+	20.6082i	−0.364072	+	1.31127i
$248$	−1.55450	−	3.90151i	−0.0987111	−	0.247746i
$249$		0			0
$250$	2.51818	−	0.273868i	0.159263	−	0.0173209i
$251$	9.70863	−	7.38031i	0.612803	−	0.465841i	−0.252154	−	0.967687i	$-0.581139\pi$
$251$	9.70863	−	7.38031i	0.612803	−	0.465841i	0.864957	+	0.501846i	$0.167346\pi$
$252$		0			0
$253$	5.19703	+	2.40440i	0.326734	+	0.151163i
$254$	0.442873	+	2.70141i	0.0277883	+	0.169501i
$255$		0			0
$256$	−7.78225	+	4.68243i	−0.486391	+	0.292652i
$257$	−29.3299	−	3.18982i	−1.82955	−	0.198975i	−0.872442	−	0.488717i	$-0.837465\pi$
$257$	−29.3299	−	3.18982i	−1.82955	−	0.198975i	−0.957105	+	0.289742i	$0.906430\pi$
$258$		0			0
$259$	−0.828573	+	5.05407i	−0.0514850	+	0.314045i
$260$	0.990493	+	18.2686i	0.0614278	+	1.13297i
$261$		0			0
$262$	1.78854	−	1.69420i	0.110496	−	0.104668i
$263$	0.334643	−	6.17213i	0.0206350	−	0.380590i	−0.969916	−	0.243442i	$-0.921724\pi$
$263$	0.334643	−	6.17213i	0.0206350	−	0.380590i	0.990551	−	0.137148i	$-0.0437937\pi$
$264$		0			0
$265$	−30.0040	+	10.1095i	−1.84313	+	0.621024i
$266$	−8.34316	+	2.81114i	−0.511552	+	0.172362i
$267$		0			0
$268$	−1.07916	+	19.9039i	−0.0659202	+	1.21583i
$269$	6.77768	−	6.42016i	0.413242	−	0.391444i	−0.452639	−	0.891694i	$-0.649517\pi$
$269$	6.77768	−	6.42016i	0.413242	−	0.391444i	0.865881	+	0.500250i	$0.166759\pi$
$270$		0			0
$271$	0.110065	+	2.03003i	0.00668596	+	0.123315i	0.999971	+	0.00762206i	$0.00242620\pi$
$271$	0.110065	+	2.03003i	0.00668596	+	0.123315i	−0.993285	+	0.115693i	$0.963091\pi$
$272$	0.632751	−	3.85961i	0.0383662	−	0.234023i
$273$		0			0
$274$	−4.02440	−	0.437679i	−0.243123	−	0.0264412i
$275$	−9.74079	+	5.86084i	−0.587392	+	0.353422i
$276$		0			0
$277$	−1.89823	−	11.5787i	−0.114054	−	0.695696i	−0.980514	−	0.196450i	$-0.937059\pi$
$277$	−1.89823	−	11.5787i	−0.114054	−	0.695696i	0.866460	−	0.499246i	$-0.166390\pi$
$278$	5.93731	+	2.74689i	0.356096	+	0.164748i
$279$		0			0
$280$	−12.2826	+	9.33696i	−0.734024	+	0.557990i
$281$	7.35626	−	0.800042i	0.438838	−	0.0477265i	0.113966	−	0.993485i	$-0.463644\pi$
$281$	7.35626	−	0.800042i	0.438838	−	0.0477265i	0.324872	+	0.945758i	$0.394679\pi$
$282$		0			0
$283$	11.6768	+	29.3065i	0.694112	+	1.74209i	0.669979	+	0.742380i	$0.266303\pi$
$283$	11.6768	+	29.3065i	0.694112	+	1.74209i	0.0241324	+	0.999709i	$0.492318\pi$
$284$	6.62189	−	23.8499i	0.392937	−	1.41523i
$285$		0			0
$286$	0.600825	+	1.13328i	0.0355275	+	0.0670120i
$287$	1.00085	+	1.47615i	0.0590785	+	0.0871342i
$288$		0			0
$289$	−10.1745	−	11.9783i	−0.598497	−	0.704606i
$290$	1.04580	−	2.62477i	0.0614117	−	0.154132i
$291$		0			0
$292$	−7.64657	−	4.60079i	−0.447481	−	0.269241i
$293$	−20.2471	−	6.82204i	−1.18285	−	0.398548i	−0.341938	−	0.939723i	$-0.611083\pi$
$293$	−20.2471	−	6.82204i	−1.18285	−	0.398548i	−0.840910	+	0.541175i	$0.817980\pi$
$294$		0			0
$295$	−7.58978	−	25.9214i	−0.441894	−	1.50920i
$296$	1.65349			0.0961071
$297$		0			0
$298$	0.480459	+	0.289083i	0.0278323	+	0.0167461i
$299$	8.05678	+	6.12460i	0.465936	+	0.354195i
$300$		0			0
$301$	−27.8387	−	32.7742i	−1.60460	−	1.88908i
$302$	−5.29293	+	2.44877i	−0.304574	+	0.140911i
$303$		0			0
$304$	−12.6764	−	23.9102i	−0.727042	−	1.37135i
$305$	−17.9022	+	21.0761i	−1.02508	+	1.20681i
$306$		0			0
$307$	1.32512	+	3.32579i	0.0756284	+	0.189813i	0.961930	−	0.273295i	$-0.0881135\pi$
$307$	1.32512	+	3.32579i	0.0756284	+	0.189813i	−0.886302	+	0.463108i	$0.846734\pi$
$308$	5.08350	−	9.58849i	0.289659	−	0.546355i
$309$		0			0
$310$	3.00898	−	2.28736i	0.170898	−	0.129914i
$311$	−5.67625	−	20.4440i	−0.321871	−	1.15927i	−0.930643	−	0.365929i	$-0.880751\pi$
$311$	−5.67625	−	20.4440i	−0.321871	−	1.15927i	0.608772	−	0.793345i	$-0.291662\pi$
$312$		0			0
$313$	−2.84236	−	17.3376i	−0.160660	−	0.979980i	−0.936914	−	0.349560i	$-0.886331\pi$
$313$	−2.84236	−	17.3376i	−0.160660	−	0.979980i	0.776254	−	0.630420i	$-0.217117\pi$
$314$	3.43740	−	0.756629i	0.193984	−	0.0426991i
$315$		0			0
$316$	−1.30531	−	0.141961i	−0.0734294	−	0.00798593i
$317$	4.04722	−	5.96921i	0.227315	−	0.335264i	−0.696879	−	0.717189i	$-0.745428\pi$
$317$	4.04722	−	5.96921i	0.227315	−	0.335264i	0.924193	+	0.381925i	$0.124739\pi$
$318$		0			0
$319$	0.220433	+	4.06565i	0.0123419	+	0.227633i
$320$	−14.9556	−	14.1667i	−0.836042	−	0.791941i
$321$		0			0
$322$	−0.225539	+	4.15983i	−0.0125688	+	0.231818i
$323$	8.67541	+	1.90960i	0.482713	+	0.106253i
$324$		0			0
$325$	−19.0397	+	6.41523i	−1.05613	+	0.355853i
$326$	−2.16098	−	0.475667i	−0.119685	−	0.0263447i
$327$		0			0
$328$	0.418020	−	0.395970i	0.0230813	−	0.0218638i
$329$	35.4820	+	33.6103i	1.95619	+	1.85300i
$330$		0			0
$331$	−4.25122	+	25.9313i	−0.233668	+	1.42531i	0.565769	+	0.824564i	$0.308580\pi$
$331$	−4.25122	+	25.9313i	−0.233668	+	1.42531i	−0.799437	+	0.600750i	$0.794869\pi$
$332$	−10.3323	+	15.2390i	−0.567058	+	0.836348i
$333$		0			0
$334$	4.84426	−	2.91469i	0.265066	−	0.159485i
$335$	−35.8920	+	7.90043i	−1.96099	+	0.431646i
$336$		0			0
$337$	−10.6774	−	4.93989i	−0.581635	−	0.269093i	0.106931	−	0.994266i	$-0.465898\pi$
$337$	−10.6774	−	4.93989i	−0.581635	−	0.269093i	−0.688566	+	0.725173i	$0.741760\pi$
$338$	−0.452924	−	1.63128i	−0.0246358	−	0.0887302i
$339$		0			0
$340$	7.55417	−	0.821565i	0.409682	−	0.0445556i
$341$	−2.55129	+	4.81225i	−0.138160	+	0.260598i
$342$		0			0
$343$	0.404022	−	1.45516i	0.0218151	−	0.0785710i
$344$	−8.98773	+	10.5812i	−0.484586	+	0.570499i
$345$		0			0
$346$	2.40369	+	3.54517i	0.129223	+	0.190590i
$347$	−5.27436	+	2.44018i	−0.283143	+	0.130996i	−0.556320	−	0.830968i	$-0.687787\pi$
$347$	−5.27436	+	2.44018i	−0.283143	+	0.130996i	0.273178	+	0.961964i	$0.411925\pi$
$348$		0			0
$349$	−12.5870	+	31.5910i	−0.673767	+	1.69103i	0.0479594	+	0.998849i	$0.484728\pi$
$349$	−12.5870	+	31.5910i	−0.673767	+	1.69103i	−0.721726	+	0.692178i	$0.756651\pi$
$350$	−6.58400	−	5.00503i	−0.351930	−	0.267530i
$351$		0			0
$352$	−5.02000	−	1.69144i	−0.267567	−	0.0901539i
$353$	−2.11925			−0.112796			−0.0563980	−	0.998408i	$-0.517962\pi$
$353$	−2.11925			−0.112796			−0.0563980	+	0.998408i	$0.517962\pi$
$354$		0			0
$355$	45.6360			2.42211
$356$	−31.2809	−	10.5398i	−1.65789	−	0.558607i
$357$		0			0
$358$	4.49168	+	3.41449i	0.237393	+	0.180461i
$359$	10.6579	−	26.7492i	0.562501	−	1.41177i	−0.322673	−	0.946511i	$-0.604581\pi$
$359$	10.6579	−	26.7492i	0.562501	−	1.41177i	0.885174	−	0.465260i	$-0.154039\pi$
$360$		0			0
$361$	38.5409	−	17.8309i	2.02847	−	0.938469i
$362$	0.731069	+	1.07825i	0.0384241	+	0.0566714i
$363$		0			0
$364$	12.4173	−	14.6188i	0.650843	−	0.766231i
$365$	4.40172	−	15.8536i	0.230397	−	0.829814i
$366$		0			0
$367$	7.68537	−	14.4961i	0.401173	−	0.756693i	−0.597817	−	0.801633i	$-0.703965\pi$
$367$	7.68537	−	14.4961i	0.401173	−	0.756693i	0.998990	+	0.0449402i	$0.0143097\pi$
$368$	−12.7306	+	1.38454i	−0.663629	+	0.0721741i
$369$		0			0
$370$	0.398106	+	1.43385i	0.0206965	+	0.0745421i
$371$	30.1255	+	13.9375i	1.56404	+	0.723601i
$372$		0			0
$373$	9.44869	−	2.07981i	0.489235	−	0.107689i	0.0364994	−	0.999334i	$-0.488379\pi$
$373$	9.44869	−	2.07981i	0.489235	−	0.107689i	0.452735	+	0.891645i	$0.350448\pi$
$374$	0.456488	−	0.274660i	0.0236045	−	0.0142023i
$375$		0			0
$376$	8.85489	−	13.0600i	0.456656	−	0.673517i
$377$	−1.16419	+	7.10123i	−0.0599587	+	0.365732i
$378$		0			0
$379$	19.3140	+	18.2952i	0.992092	+	0.939760i	0.998185	−	0.0602217i	$-0.0191808\pi$
$379$	19.3140	+	18.2952i	0.992092	+	0.939760i	−0.00609272	+	0.999981i	$0.501939\pi$
$380$	38.1718	−	36.1583i	1.95817	−	1.85488i
$381$		0			0
$382$	−3.09674	−	0.681645i	−0.158443	−	0.0348760i
$383$	14.2530	−	4.80239i	0.728294	−	0.245391i	0.0693600	−	0.997592i	$-0.477904\pi$
$383$	14.2530	−	4.80239i	0.728294	−	0.245391i	0.658934	+	0.752201i	$0.271008\pi$
$384$		0			0
$385$	19.5415	+	4.30142i	0.995929	+	0.219221i
$386$	−0.0777254	+	1.43356i	−0.00395612	+	0.0729663i
$387$		0			0
$388$	3.47414	+	3.29088i	0.176373	+	0.167069i
$389$	1.15692	+	21.3381i	0.0586580	+	1.08188i	0.868645	+	0.495435i	$0.164991\pi$
$389$	1.15692	+	21.3381i	0.0586580	+	1.08188i	−0.809987	+	0.586448i	$0.800526\pi$
$390$		0			0
$391$	2.35887	−	3.47907i	0.119293	−	0.175944i
$392$	7.79778	+	0.848060i	0.393847	+	0.0428335i
$393$		0			0
$394$	2.41129	−	0.530766i	0.121479	−	0.0267396i
$395$	−0.391644	−	2.38893i	−0.0197058	−	0.120200i
$396$		0			0
$397$	4.19128	+	15.0956i	0.210355	+	0.757629i	0.991139	+	0.132828i	$0.0424059\pi$
$397$	4.19128	+	15.0956i	0.210355	+	0.757629i	−0.780785	+	0.624800i	$0.785180\pi$
$398$	−1.50786	+	1.14625i	−0.0755824	+	0.0574563i
$399$		0			0
$400$	11.9081	−	22.4610i	0.595403	−	1.12305i
$401$	12.4325	+	31.2033i	0.620852	+	1.55822i	0.816375	+	0.577521i	$0.195980\pi$
$401$	12.4325	+	31.2033i	0.620852	+	1.55822i	−0.195524	+	0.980699i	$0.562641\pi$
$402$		0			0
$403$	−6.23196	+	7.33683i	−0.310436	+	0.365474i
$404$	5.49278	+	10.3605i	0.273276	+	0.515453i
$405$		0			0
$406$	−2.68838	+	1.24378i	−0.133422	+	0.0617276i
$407$	−1.38827	−	1.63439i	−0.0688138	−	0.0810139i
$408$		0			0
$409$	19.1955	+	14.5921i	0.949158	+	0.721531i	0.960464	−	0.278405i	$-0.0898056\pi$
$409$	19.1955	+	14.5921i	0.949158	+	0.721531i	−0.0113055	+	0.999936i	$0.503599\pi$
$410$	0.444016	+	0.267156i	0.0219284	+	0.0131939i
$411$		0			0
$412$	−14.7535			−0.726852
$413$	−12.9119	+	25.2014i	−0.635354	+	1.24008i
$414$		0			0
$415$	−32.1687	−	10.8389i	−1.57910	−	0.532061i
$416$	−8.02211	−	4.82674i	−0.393316	−	0.236651i
$417$		0			0
$418$	1.36444	−	3.42448i	0.0667369	−	0.167497i
$419$	6.46698	+	7.61351i	0.315932	+	0.371944i	0.897091	−	0.441846i	$-0.145676\pi$
$419$	6.46698	+	7.61351i	0.315932	+	0.371944i	−0.581158	+	0.813790i	$0.697400\pi$
$420$		0			0
$421$	4.36202	+	6.43350i	0.212592	+	0.313550i	0.919002	−	0.394253i	$-0.128997\pi$
$421$	4.36202	+	6.43350i	0.212592	+	0.313550i	−0.706410	+	0.707803i	$0.749686\pi$
$422$	1.13959	+	2.14949i	0.0554743	+	0.104636i
$423$		0			0
$424$	2.86697	−	10.3259i	0.139232	−	0.501469i
$425$	3.08868	+	7.75201i	0.149823	+	0.376028i
$426$		0			0
$427$	28.8212	−	3.13449i	1.39475	−	0.151689i
$428$	−8.62581	+	6.55717i	−0.416944	+	0.316953i
$429$		0			0
$430$	−11.3396	−	5.24624i	−0.546842	−	0.252996i
$431$	−0.0898386	−	0.547991i	−0.00432737	−	0.0263958i	0.984575	−	0.174965i	$-0.0559814\pi$
$431$	−0.0898386	−	0.547991i	−0.00432737	−	0.0263958i	−0.988902	+	0.148570i	$0.952533\pi$
$432$		0			0
$433$	−16.5785	+	9.97493i	−0.796710	+	0.479365i	−0.854807	−	0.518946i	$-0.826324\pi$
$433$	−16.5785	+	9.97493i	−0.796710	+	0.479365i	0.0580965	+	0.998311i	$0.481497\pi$
$434$	−3.93934	−	0.428429i	−0.189094	−	0.0205652i
$435$		0			0
$436$	1.42400	−	8.68603i	0.0681973	−	0.415985i
$437$	−1.57461	−	29.0421i	−0.0753240	−	1.38927i
$438$		0			0
$439$	2.01613	−	1.90978i	0.0962246	−	0.0911488i	−0.638075	−	0.769974i	$-0.720269\pi$
$439$	2.01613	−	1.90978i	0.0962246	−	0.0911488i	0.734300	+	0.678825i	$0.237511\pi$
$440$	0.349739	−	6.45055i	0.0166731	−	0.307518i
$441$		0			0
$442$	0.892270	−	0.300641i	0.0424409	−	0.0143000i
$443$	5.83442	−	1.96584i	0.277202	−	0.0934001i	−0.177267	−	0.984163i	$-0.556726\pi$
$443$	5.83442	−	1.96584i	0.277202	−	0.0934001i	0.454469	+	0.890763i	$0.349829\pi$
$444$		0			0
$445$	3.29484	−	60.7698i	0.156191	−	2.88077i
$446$	−1.25943	+	1.19299i	−0.0596357	+	0.0564899i
$447$		0			0
$448$	1.16923	+	21.5652i	0.0552409	+	1.01886i
$449$	1.59964	−	9.75736i	0.0754916	−	0.460478i	−0.921846	−	0.387556i	$-0.873319\pi$
$449$	1.59964	−	9.75736i	0.0754916	−	0.460478i	0.997338	−	0.0729220i	$-0.0232324\pi$
$450$		0			0
$451$	−0.742366	−	0.0807372i	−0.0349566	−	0.00380176i
$452$	−13.0121	+	7.82912i	−0.612037	+	0.368251i
$453$		0			0
$454$	1.16327	+	7.09564i	0.0545950	+	0.333015i
$455$	32.0953	+	14.8489i	1.50465	+	0.696125i
$456$		0			0
$457$	−29.7186	+	22.5915i	−1.39018	+	1.05678i	−0.400067	+	0.916486i	$0.631013\pi$
$457$	−29.7186	+	22.5915i	−1.39018	+	1.05678i	−0.990109	+	0.140299i	$0.955194\pi$
$458$	1.88037	−	0.204502i	0.0878637	−	0.00955576i
$459$		0			0
$460$	−9.20883	−	23.1124i	−0.429364	−	1.07762i
$461$	2.19006	−	7.88788i	0.102001	−	0.367375i	−0.894879	−	0.446310i	$-0.852738\pi$
$461$	2.19006	−	7.88788i	0.102001	−	0.367375i	0.996880	+	0.0789344i	$0.0251517\pi$
$462$		0			0
$463$	−3.70194	−	6.98261i	−0.172044	−	0.324509i	0.782463	−	0.622697i	$-0.213963\pi$
$463$	−3.70194	−	6.98261i	−0.172044	−	0.324509i	−0.954507	+	0.298187i	$0.903618\pi$
$464$	−5.10982	−	7.53642i	−0.237217	−	0.349870i
$465$		0			0
$466$	−5.21017	−	6.13388i	−0.241356	−	0.284147i
$467$	−4.92723	+	12.3664i	−0.228005	+	0.572249i	−0.997818	−	0.0660197i	$-0.978970\pi$
$467$	−4.92723	+	12.3664i	−0.228005	+	0.572249i	0.769813	+	0.638269i	$0.220349\pi$
$468$		0			0
$469$	33.0143	+	19.8640i	1.52446	+	0.917236i
$470$	13.4571	+	4.53423i	0.620730	+	0.209148i
$471$		0			0
$472$	8.70351	+	2.79739i	0.400612	+	0.128761i
$473$	18.0050			0.827873
$474$		0			0
$475$	49.4751	+	29.7682i	2.27007	+	1.36586i
$476$	−6.34199	−	4.82105i	−0.290685	−	0.220973i
$477$		0			0
$478$	−1.90197	−	2.23918i	−0.0869942	−	0.102418i
$479$	−17.7086	+	8.19288i	−0.809128	+	0.374342i	−0.780428	−	0.625246i	$-0.784999\pi$
$479$	−17.7086	+	8.19288i	−0.809128	+	0.374342i	−0.0286997	+	0.999588i	$0.509137\pi$
$480$		0			0
$481$	−1.77525	−	3.34848i	−0.0809444	−	0.152677i
$482$	0.842568	−	0.991948i	0.0383779	−	0.0451820i
$483$		0			0
$484$	−6.08330	−	15.2679i	−0.276514	−	0.693997i
$485$	−4.13270	+	7.79510i	−0.187656	+	0.353957i
$486$		0			0
$487$	4.54402	−	3.45427i	0.205909	−	0.156528i	−0.497138	−	0.867672i	$-0.665616\pi$
$487$	4.54402	−	3.45427i	0.205909	−	0.156528i	0.703047	+	0.711144i	$0.251822\pi$
$488$	−2.50401	−	9.01862i	−0.113351	−	0.408254i
$489$		0			0
$490$	1.14204	+	6.96614i	0.0515921	+	0.314698i
$491$	−12.6647	+	2.78771i	−0.571550	+	0.125808i	−0.491336	−	0.870970i	$-0.663491\pi$
$491$	−12.6647	+	2.78771i	−0.571550	+	0.125808i	−0.0802136	+	0.996778i	$0.525560\pi$
$492$		0			0
$493$	2.97124	+	0.323142i	0.133818	+	0.0145536i
$494$	3.65614	−	5.39241i	0.164498	−	0.242616i
$495$		0			0
$496$	−0.659441	−	12.1627i	−0.0296098	−	0.546120i
$497$	−34.7346	−	32.9024i	−1.55806	−	1.47587i
$498$		0			0
$499$	−1.78751	+	32.9687i	−0.0800201	+	1.47588i	0.632679	+	0.774414i	$0.281955\pi$
$499$	−1.78751	+	32.9687i	−0.0800201	+	1.47588i	−0.712699	+	0.701470i	$0.752528\pi$
$500$	15.4887	+	3.40932i	0.692675	+	0.152469i
$501$		0			0
$502$	−3.52041	+	1.18616i	−0.157124	+	0.0529411i
$503$	19.4450	+	4.28017i	0.867010	+	0.190843i	0.626137	−	0.779713i	$-0.284635\pi$
$503$	19.4450	+	4.28017i	0.867010	+	0.190843i	0.240873	+	0.970557i	$0.422566\pi$
$504$		0			0
$505$	−15.6963	+	14.8683i	−0.698475	+	0.661630i
$506$	−1.26636	−	1.19956i	−0.0562964	−	0.0533268i
$507$		0			0
$508$	−2.77286	+	16.9137i	−0.123026	+	0.750425i
$509$	11.5082	−	16.9733i	0.510092	−	0.752330i	−0.482225	−	0.876047i	$-0.660171\pi$
$509$	11.5082	−	16.9733i	0.510092	−	0.752330i	0.992317	+	0.123717i	$0.0394816\pi$
$510$		0			0
$511$	−14.7803	+	8.89301i	−0.653842	+	0.393403i
$512$	19.5941	−	4.31298i	0.865944	−	0.190609i
$513$		0			0
$514$	8.15635	+	3.77353i	0.359761	+	0.166443i
$515$	−7.27712	−	26.2098i	−0.320668	−	1.15494i
$516$		0			0
$517$	−20.3437	+	2.21251i	−0.894715	+	0.0973061i
$518$	0.730760	−	1.37836i	0.0321077	−	0.0605616i
$519$		0			0
$520$	3.05442	−	11.0010i	0.133945	−	0.482428i
$521$	−4.32295	+	5.08937i	−0.189392	+	0.222969i	−0.848660	−	0.528938i	$-0.822590\pi$
$521$	−4.32295	+	5.08937i	−0.189392	+	0.222969i	0.659268	+	0.751908i	$0.270866\pi$
$522$		0			0
$523$	0.781161	+	1.15213i	0.0341578	+	0.0503789i	0.844384	−	0.535738i	$-0.179966\pi$
$523$	0.781161	+	1.15213i	0.0341578	+	0.0503789i	−0.810227	+	0.586117i	$0.800656\pi$
$524$	13.9990	−	6.47663i	0.611549	−	0.282933i
$525$		0			0
$526$	−0.696925	+	1.74915i	−0.0303874	+	0.0762666i
$527$	3.18290	+	2.41958i	0.138649	+	0.105399i
$528$		0			0
$529$	8.75398	+	2.94956i	0.380608	+	0.128242i
$530$	9.64450			0.418930
$531$		0			0
$532$	−55.1227			−2.38987
$533$	−1.25068	−	0.421403i	−0.0541730	−	0.0182530i
$534$		0			0
$535$	−15.9036	−	12.0896i	−0.687572	−	0.522679i
$536$	4.60424	−	11.5558i	0.198873	−	0.499134i
$537$		0			0
$538$	−2.58095	+	1.19407i	−0.111273	+	0.0514802i
$539$	−5.70873	−	8.41975i	−0.245893	−	0.362664i
$540$		0			0
$541$	14.4081	−	16.9625i	0.619452	−	0.729275i	−0.359550	−	0.933126i	$-0.617070\pi$
$541$	14.4081	−	16.9625i	0.619452	−	0.729275i	0.979002	+	0.203851i	$0.0653458\pi$
$542$	0.165676	−	0.596709i	0.00711637	−	0.0256309i
$543$		0			0
$544$	−1.82139	+	3.43551i	−0.0780915	+	0.147296i
$545$	16.1333	−	1.75460i	0.691073	−	0.0751587i
$546$		0			0
$547$	0.711730	+	2.56342i	0.0304314	+	0.109604i	0.977206	−	0.212293i	$-0.0680932\pi$
$547$	0.711730	+	2.56342i	0.0304314	+	0.109604i	−0.946775	+	0.321897i	$0.895679\pi$
$548$	−23.0031	−	10.6424i	−0.982643	−	0.454619i
$549$		0			0
$550$	3.38190	−	0.744413i	0.144205	−	0.0317419i
$551$	17.7202	−	10.6619i	0.754905	−	0.454211i
$552$		0			0
$553$	−1.42427	+	2.10063i	−0.0605659	+	0.0893281i
$554$	−0.578227	+	3.52703i	−0.0245665	+	0.149849i
$555$		0			0
$556$	29.7365	+	28.1679i	1.26111	+	1.19459i
$557$	0.787244	−	0.745717i	0.0333566	−	0.0315970i	−0.670840	−	0.741602i	$-0.734066\pi$
$557$	0.787244	−	0.745717i	0.0333566	−	0.0315970i	0.704196	+	0.710005i	$0.251308\pi$
$558$		0			0
$559$	31.0775	+	6.84067i	1.31444	+	0.289329i
$560$	−42.4046	+	14.2878i	−1.79192	+	0.603769i
$561$		0			0
$562$	−2.20133	−	0.484550i	−0.0928577	−	0.0204395i
$563$	0.264711	−	4.88231i	0.0111563	−	0.205765i	−0.987641	−	0.156733i	$-0.949904\pi$
$563$	0.264711	−	4.88231i	0.0111563	−	0.205765i	0.998797	−	0.0490317i	$-0.0156135\pi$
$564$		0			0
$565$	−20.3267	−	19.2545i	−0.855152	−	0.810043i
$566$	−0.520257	−	9.59557i	−0.0218680	−	0.403332i
$567$		0			0
$568$	−8.66837	+	12.7849i	−0.363717	+	0.536442i
$569$	−10.9736	−	1.19345i	−0.460036	−	0.0500319i	−0.124833	−	0.992178i	$-0.539839\pi$
$569$	−10.9736	−	1.19345i	−0.460036	−	0.0500319i	−0.335203	+	0.942146i	$0.608805\pi$
$570$		0			0
$571$	26.4647	−	5.82532i	1.10751	−	0.243782i	0.376684	−	0.926342i	$-0.377064\pi$
$571$	26.4647	−	5.82532i	1.10751	−	0.243782i	0.730830	+	0.682560i	$0.239133\pi$
$572$	1.29928	+	7.92525i	0.0543256	+	0.331371i
$573$		0			0
$574$	−0.145339	−	0.523463i	−0.00606633	−	0.0218489i
$575$	21.7507	−	16.5345i	0.907067	−	0.689535i
$576$		0			0
$577$	9.57728	−	18.0647i	0.398707	−	0.752042i	−0.600147	−	0.799889i	$-0.704891\pi$
$577$	9.57728	−	18.0647i	0.398707	−	0.752042i	0.998855	+	0.0478477i	$0.0152362\pi$
$578$	1.77199	+	4.44736i	0.0737050	+	0.184986i
$579$		0			0
$580$	11.4525	−	13.4829i	0.475538	−	0.559846i
$581$	16.6698	+	31.4426i	0.691580	+	1.30446i
$582$		0			0
$583$	−12.6137	+	5.83573i	−0.522407	+	0.241691i
$584$	3.60528	+	4.24447i	0.149188	+	0.175637i
$585$		0			0
$586$	5.18116	+	3.93861i	0.214032	+	0.162703i
$587$	34.4159	+	20.7073i	1.42049	+	0.854683i	0.998648	−	0.0519844i	$-0.0165546\pi$
$587$	34.4159	+	20.7073i	1.42049	+	0.854683i	0.421846	+	0.906667i	$0.361382\pi$
$588$		0			0
$589$	27.6649			1.13991
$590$	−0.330281	+	8.22089i	−0.0135975	+	0.338449i
$591$		0			0
$592$	4.54453	+	1.53123i	0.186779	+	0.0629332i
$593$	11.5791	+	6.96689i	0.475495	+	0.286096i	0.733059	−	0.680165i	$-0.238092\pi$
$593$	11.5791	+	6.96689i	0.475495	+	0.286096i	−0.257563	+	0.966261i	$0.582920\pi$
$594$		0			0
$595$	5.43651	−	13.6446i	0.222875	−	0.559375i
$596$	2.27280	+	2.67575i	0.0930975	+	0.109603i
$597$		0			0
$598$	−1.73003	−	2.55161i	−0.0707464	−	0.104343i
$599$	−2.31412	−	4.36490i	−0.0945525	−	0.178345i	0.831724	−	0.555189i	$-0.187354\pi$
$599$	−2.31412	−	4.36490i	−0.0945525	−	0.178345i	−0.926277	+	0.376844i	$0.877009\pi$
$600$		0			0
$601$	0.789759	−	2.84446i	0.0322150	−	0.116028i	−0.945694	−	0.325057i	$-0.894617\pi$
$601$	0.789759	−	2.84446i	0.0322150	−	0.116028i	0.977909	+	0.209029i	$0.0670303\pi$
$602$	4.84840	+	12.1686i	0.197606	+	0.495954i
$603$		0			0
$604$	−36.3002	+	3.94789i	−1.47704	+	0.160637i
$605$	24.1232	−	18.3380i	0.980747	−	0.745544i
$606$		0			0
$607$	21.8968	+	10.1305i	0.888762	+	0.411185i	0.810494	−	0.585747i	$-0.199199\pi$
$607$	21.8968	+	10.1305i	0.888762	+	0.411185i	0.0782682	+	0.996932i	$0.475061\pi$
$608$	4.35289	+	26.5514i	0.176533	+	1.07680i
$609$		0			0
$610$	7.21774	−	4.34277i	0.292238	−	0.175834i
$611$	−35.9547	−	3.91031i	−1.45457	−	0.158194i
$612$		0			0
$613$	3.78863	−	23.1096i	0.153021	−	0.933389i	−0.792985	−	0.609241i	$-0.791474\pi$
$613$	3.78863	−	23.1096i	0.153021	−	0.933389i	0.946006	−	0.324148i	$-0.105078\pi$
$614$	−0.0590404	−	1.08894i	−0.00238268	−	0.0439459i
$615$		0			0
$616$	−4.91688	+	4.65752i	−0.198107	+	0.187657i
$617$	1.02925	−	18.9834i	0.0414361	−	0.764244i	−0.901807	−	0.432140i	$-0.857759\pi$
$617$	1.02925	−	18.9834i	0.0414361	−	0.764244i	0.943243	−	0.332104i	$-0.107759\pi$
$618$		0			0
$619$	−5.87259	+	1.97871i	−0.236039	+	0.0795310i	−0.434835	−	0.900510i	$-0.643193\pi$
$619$	−5.87259	+	1.97871i	−0.236039	+	0.0795310i	0.198796	+	0.980041i	$0.436297\pi$
$620$	22.4261	−	7.55623i	0.900653	−	0.303465i
$621$		0			0
$622$	−0.349906	+	6.45363i	−0.0140299	+	0.258767i
$623$	−46.3213	+	43.8779i	−1.85582	+	1.75793i
$624$		0			0
$625$	−0.410569	−	7.57250i	−0.0164228	−	0.302900i
$626$	−0.865821	+	5.28128i	−0.0346052	+	0.211082i
$627$		0			0
$628$	21.9079	+	2.38262i	0.874219	+	0.0950771i
$629$	−1.34878	+	0.811535i	−0.0537794	+	0.0323580i
$630$		0			0
$631$	4.89817	+	29.8775i	0.194993	+	1.18940i	0.884996	+	0.465598i	$0.154161\pi$
$631$	4.89817	+	29.8775i	0.194993	+	1.18940i	−0.690003	+	0.723806i	$0.742391\pi$
$632$	0.743647	+	0.344048i	0.0295807	+	0.0136855i
$633$		0			0
$634$	−1.74889	+	1.32947i	−0.0694573	+	0.0528001i
$635$	−31.4152	+	3.41661i	−1.24667	+	0.135584i
$636$		0			0
$637$	−6.65459	−	16.7018i	−0.263665	−	0.661748i
$638$	0.331808	−	1.19506i	0.0131364	−	0.0473130i
$639$		0			0
$640$	14.2445	+	26.8680i	0.563064	+	1.06205i
$641$	14.0805	+	20.7671i	0.556145	+	0.820252i	0.997006	−	0.0773233i	$-0.0246374\pi$
$641$	14.0805	+	20.7671i	0.556145	+	0.820252i	−0.440862	+	0.897575i	$0.645327\pi$
$642$		0			0
$643$	−14.2356	−	16.7594i	−0.561397	−	0.660927i	0.406095	−	0.913831i	$-0.366890\pi$
$643$	−14.2356	−	16.7594i	−0.561397	−	0.660927i	−0.967491	+	0.252904i	$0.918614\pi$
$644$	−9.65441	+	24.2307i	−0.380437	+	0.954825i
$645$		0			0
$646$	−2.31858	−	1.39504i	−0.0912233	−	0.0548873i
$647$	−6.98096	−	2.35216i	−0.274450	−	0.0924729i	0.178711	−	0.983902i	$-0.442807\pi$
$647$	−6.98096	−	2.35216i	−0.274450	−	0.0924729i	−0.453161	+	0.891429i	$0.649704\pi$
$648$		0			0
$649$	−4.54236	−	10.9517i	−0.178303	−	0.429891i
$650$	6.12013			0.240051
$651$		0			0
$652$	−11.8708	−	7.14245i	−0.464898	−	0.279720i
$653$	−21.3805	−	16.2530i	−0.836684	−	0.636030i	0.0965389	−	0.995329i	$-0.469223\pi$
$653$	−21.3805	−	16.2530i	−0.836684	−	0.636030i	−0.933223	+	0.359299i	$0.883016\pi$
$654$		0			0
$655$	18.4108	+	21.6749i	0.719370	+	0.846908i
$656$	1.51560	−	0.701192i	0.0591743	−	0.0273769i
$657$		0			0
$658$	−6.97346	−	13.1533i	−0.271854	−	0.512771i
$659$	−20.5498	+	24.1931i	−0.800507	+	0.942430i	−0.999292	−	0.0376129i	$-0.988025\pi$
$659$	−20.5498	+	24.1931i	−0.800507	+	0.942430i	0.198785	+	0.980043i	$0.436300\pi$
$660$		0			0
$661$	4.49720	+	11.2871i	0.174921	+	0.439018i	0.990131	−	0.140148i	$-0.0447577\pi$
$661$	4.49720	+	11.2871i	0.174921	+	0.439018i	−0.815210	+	0.579166i	$0.803378\pi$
$662$	3.74937	−	7.07206i	0.145723	−	0.274863i
$663$		0			0
$664$	9.14683	−	6.95324i	0.354966	−	0.269838i
$665$	−27.1891	−	97.9264i	−1.05435	−	3.79742i
$666$		0			0
$667$	−1.58315	−	9.65678i	−0.0612997	−	0.373912i
$668$	34.5695	−	7.60933i	1.33754	−	0.294414i
$669$		0			0
$670$	11.1293	+	1.21038i	0.429962	+	0.0467612i
$671$	−6.81210	+	10.0471i	−0.262978	+	0.387864i
$672$		0			0
$673$	0.171210	+	3.15778i	0.00659965	+	0.121723i	0.999977	+	0.00682346i	$0.00217199\pi$
$673$	0.171210	+	3.15778i	0.00659965	+	0.121723i	−0.993377	+	0.114900i	$0.963345\pi$
$674$	2.60176	+	2.46451i	0.100216	+	0.0949295i
$675$		0			0
$676$	0.573871	−	10.5844i	0.0220720	−	0.407093i
$677$	29.1955	+	6.42641i	1.12207	+	0.246987i	0.736996	−	0.675897i	$-0.236244\pi$
$677$	29.1955	+	6.42641i	1.12207	+	0.246987i	0.385078	+	0.922884i	$0.374175\pi$
$678$		0			0
$679$	8.76557	−	2.95346i	0.336392	−	0.113344i
$680$	−4.63109	−	1.01938i	−0.177594	−	0.0390915i
$681$		0			0
$682$	1.20453	−	1.14100i	0.0461240	−	0.0436910i
$683$	−18.1084	−	17.1532i	−0.692899	−	0.656349i	0.257895	−	0.966173i	$-0.416971\pi$
$683$	−18.1084	−	17.1532i	−0.692899	−	0.656349i	−0.950794	+	0.309824i	$0.899730\pi$
$684$		0			0
$685$	7.56012	−	46.1147i	0.288857	−	1.76195i
$686$	−0.258162	+	0.380760i	−0.00985667	+	0.0145375i
$687$		0			0
$688$	−34.5011	+	20.7586i	−1.31534	+	0.791416i
$689$	−23.9890	+	5.28038i	−0.913908	+	0.201166i
$690$		0			0
$691$	−15.7054	−	7.26610i	−0.597463	−	0.276416i	0.0977602	−	0.995210i	$-0.468832\pi$
$691$	−15.7054	−	7.26610i	−0.597463	−	0.276416i	−0.695223	+	0.718794i	$0.744694\pi$
$692$	7.17446	+	25.8401i	0.272732	+	0.982292i
$693$		0			0
$694$	1.75988	−	0.191399i	0.0668042	−	0.00726539i
$695$	−35.3733	+	66.7211i	−1.34179	+	2.53088i
$696$		0			0
$697$	−0.146644	+	0.528165i	−0.00555454	+	0.0200057i
$698$	6.70612	−	7.89506i	0.253831	−	0.298832i
$699$		0			0
$700$	−29.0592	−	42.8591i	−1.09833	−	1.61992i
$701$	5.08595	−	2.35301i	0.192094	−	0.0888720i	−0.321484	−	0.946915i	$-0.604182\pi$
$701$	5.08595	−	2.35301i	0.192094	−	0.0888720i	0.513578	+	0.858043i	$0.328320\pi$
$702$		0			0
$703$	−4.03149	+	10.1183i	−0.152051	+	0.381618i
$704$	−7.19885	−	5.47243i	−0.271317	−	0.206250i
$705$		0			0
$706$	0.611759	+	0.206126i	0.0230238	+	0.00775764i
$707$	22.6665			0.852460
$708$		0			0
$709$	−2.86141			−0.107462			−0.0537312	−	0.998555i	$-0.517111\pi$
$709$	−2.86141			−0.107462			−0.0537312	+	0.998555i	$0.517111\pi$
$710$	−13.1737	−	4.43872i	−0.494399	−	0.166582i
$711$		0			0
$712$	16.3988	+	12.4660i	0.614570	+	0.467184i
$713$	4.84533	−	12.1609i	0.181459	−	0.455428i
$714$		0			0
$715$	−13.4385	+	6.21730i	−0.502571	+	0.232514i
$716$	19.8245	+	29.2389i	0.740876	+	1.09271i
$717$		0			0
$718$	−5.67832	+	6.68503i	−0.211913	+	0.249483i
$719$	8.86608	−	31.9327i	0.330649	−	1.19089i	−0.592220	−	0.805776i	$-0.701749\pi$
$719$	8.86608	−	31.9327i	0.330649	−	1.19089i	0.922869	−	0.385114i	$-0.125838\pi$
$720$		0			0
$721$	−13.3578	+	25.1956i	−0.497472	+	0.938332i
$722$	−12.8598	+	1.39859i	−0.478593	+	0.0520501i
$723$		0			0
$724$	2.18207	+	7.85912i	0.0810962	+	0.292082i
$725$	17.6314	+	8.15717i	0.654815	+	0.302950i
$726$		0			0
$727$	−15.2669	+	3.36050i	−0.566218	+	0.124634i	−0.488849	−	0.872368i	$-0.662583\pi$
$727$	−15.2669	+	3.36050i	−0.566218	+	0.124634i	−0.0773694	+	0.997002i	$0.524652\pi$
$728$	−10.2563	+	6.17099i	−0.380123	+	0.228712i
$729$		0			0
$730$	−2.81261	+	4.14830i	−0.104100	+	0.153535i
$731$	2.13820	−	13.0424i	0.0790842	−	0.482392i
$732$		0			0
$733$	−15.4823	−	14.6656i	−0.571852	−	0.541687i	0.346193	−	0.938163i	$-0.387474\pi$
$733$	−15.4823	−	14.6656i	−0.571852	−	0.541687i	−0.918045	+	0.396477i	$0.870233\pi$
$734$	−3.62847	+	3.43707i	−0.133929	+	0.126865i
$735$		0			0
$736$	12.4338	+	2.73689i	0.458317	+	0.100883i
$737$	−15.2880	+	5.15114i	−0.563142	+	0.189745i
$738$		0			0
$739$	4.20751	+	0.926144i	0.154776	+	0.0340687i	0.291682	−	0.956515i	$-0.405785\pi$
$739$	4.20751	+	0.926144i	0.154776	+	0.0340687i	−0.136907	+	0.990584i	$0.543716\pi$
$740$	−0.504414	+	9.30337i	−0.0185426	+	0.341999i
$741$		0			0
$742$	−7.34066	−	6.95344i	−0.269484	−	0.255269i
$743$	2.11083	+	38.9319i	0.0774387	+	1.42827i	0.736629	+	0.676297i	$0.236416\pi$
$743$	2.11083	+	38.9319i	0.0774387	+	1.42827i	−0.659190	+	0.751976i	$0.729101\pi$
$744$		0			0
$745$	−3.63245	+	5.35747i	−0.133083	+	0.196283i
$746$	−2.92983	−	0.318638i	−0.107269	−	0.0116662i
$747$		0			0
$748$	3.25759	−	0.717050i	0.119109	−	0.0262179i
$749$	3.38831	+	20.6678i	0.123806	+	0.755184i
$750$		0			0
$751$	0.293741	+	1.05796i	0.0107188	+	0.0386055i	0.968716	−	0.248172i	$-0.0798298\pi$
$751$	0.293741	+	1.05796i	0.0107188	+	0.0386055i	−0.957997	+	0.286777i	$0.907416\pi$
$752$	36.4315	−	27.6945i	1.32852	−	1.00992i
$753$		0			0
$754$	1.02676	−	1.93667i	0.0373922	−	0.0705292i
$755$	−24.9185	−	62.5407i	−0.906877	−	2.27609i
$756$		0			0
$757$	7.27026	−	8.55921i	0.264242	−	0.311090i	−0.614000	−	0.789306i	$-0.710441\pi$
$757$	7.27026	−	8.55921i	0.264242	−	0.311090i	0.878242	+	0.478216i	$0.158716\pi$
$758$	−3.79588	−	7.15978i	−0.137872	−	0.260055i
$759$		0			0
$760$	−29.7789	+	13.7772i	−1.08020	+	0.499752i
$761$	−3.54889	−	4.17807i	−0.128647	−	0.151455i	0.694067	−	0.719910i	$-0.255817\pi$
$761$	−3.54889	−	4.17807i	−0.128647	−	0.151455i	−0.822714	+	0.568455i	$0.807541\pi$
$762$		0			0
$763$	−13.5444	−	10.2962i	−0.490341	−	0.372748i
$764$	−17.0113	−	10.2353i	−0.615446	−	0.370302i
$765$		0			0
$766$	−4.58148			−0.165536
$767$	−3.67943	−	20.6288i	−0.132857	−	0.744864i
$768$		0			0
$769$	28.9910	+	9.76820i	1.04544	+	0.352250i	0.789054	−	0.614324i	$-0.210571\pi$
$769$	28.9910	+	9.76820i	1.04544	+	0.352250i	0.256388	+	0.966574i	$0.417468\pi$
$770$	−5.22265	−	3.14236i	−0.188211	−	0.113243i
$771$		0			0
$772$	−3.32710	+	8.35040i	−0.119745	+	0.300537i
$773$	−12.7405	−	14.9993i	−0.458244	−	0.539486i	0.483710	−	0.875228i	$-0.339289\pi$
$773$	−12.7405	−	14.9993i	−0.458244	−	0.539486i	−0.941954	+	0.335742i	$0.891013\pi$
$774$		0			0
$775$	14.5841	+	21.5100i	0.523878	+	0.772662i
$776$	−1.39880	−	2.63842i	−0.0502141	−	0.0947138i
$777$		0			0
$778$	1.74145	−	6.27215i	0.0624341	−	0.224867i
$779$	1.40387	+	3.52345i	0.0502990	+	0.126241i
$780$		0			0
$781$	19.9152	−	2.16591i	0.712622	−	0.0775023i
$782$	−1.01932	+	0.774865i	−0.0364507	+	0.0277091i
$783$		0			0
$784$	20.6465	+	9.55207i	0.737373	+	0.341145i
$785$	6.57323	+	40.0949i	0.234609	+	1.43105i
$786$		0			0
$787$	25.6419	−	15.4282i	0.914034	−	0.549956i	0.0209173	−	0.999781i	$-0.493341\pi$
$787$	25.6419	−	15.4282i	0.914034	−	0.549956i	0.893117	+	0.449825i	$0.148514\pi$
$788$	15.3681	+	1.67138i	0.547466	+	0.0595405i
$789$		0			0
$790$	−0.119300	+	0.727700i	−0.00424451	+	0.0258904i
$791$	1.58915	+	29.3101i	0.0565037	+	1.04215i
$792$		0			0
$793$	−15.5752	+	14.7536i	−0.553091	+	0.523915i
$794$	0.258367	−	4.76529i	0.00916909	−	0.169114i
$795$		0			0
$796$	−11.2382	+	3.78659i	−0.398328	+	0.134212i
$797$	−33.1424	+	11.1670i	−1.17396	+	0.395554i	−0.837656	−	0.546198i	$-0.816075\pi$
$797$	−33.1424	+	11.1670i	−1.17396	+	0.395554i	−0.336307	+	0.941752i	$0.609178\pi$
$798$		0			0
$799$	−0.813235	+	14.9992i	−0.0287702	+	0.530635i
$800$	−18.3496	+	17.3816i	−0.648755	+	0.614534i
$801$		0			0
$802$	−0.553930	−	10.2166i	−0.0195600	−	0.360762i
$803$	1.16846	−	7.12729i	0.0412340	−	0.251517i
$804$		0			0
$805$	−47.8083	−	5.19947i	−1.68502	−	0.183257i
$806$	2.51258	−	1.51177i	0.0885017	−	0.0532497i
$807$		0			0
$808$	−1.18390	−	7.22147i	−0.0416495	−	0.254050i
$809$	−3.51302	−	1.62530i	−0.123511	−	0.0571424i	0.357160	−	0.934043i	$-0.383745\pi$
$809$	−3.51302	−	1.62530i	−0.123511	−	0.0571424i	−0.480672	+	0.876901i	$0.659607\pi$
$810$		0			0
$811$	2.51578	−	1.91245i	0.0883410	−	0.0671551i	−0.560071	−	0.828444i	$-0.689226\pi$
$811$	2.51578	−	1.91245i	0.0883410	−	0.0671551i	0.648412	+	0.761289i	$0.275433\pi$
$812$	−18.4376	+	2.00521i	−0.647032	+	0.0703690i
$813$		0			0
$814$	0.241781	+	0.606825i	0.00847443	+	0.0212692i
$815$	6.83342	−	24.6118i	0.239364	−	0.862112i
$816$		0			0
$817$	−42.8363	−	80.7978i	−1.49865	−	2.82676i
$818$	−4.12186	−	6.07929i	−0.144118	−	0.212558i
$819$		0			0
$820$	2.10041	+	2.47279i	0.0733493	+	0.0863535i
$821$	10.1097	−	25.3735i	0.352831	−	0.885540i	−0.640256	−	0.768162i	$-0.721172\pi$
$821$	10.1097	−	25.3735i	0.352831	−	0.885540i	0.993087	−	0.117378i	$-0.0374489\pi$
$822$		0			0
$823$	32.1374	+	19.3365i	1.12024	+	0.674027i	0.950271	−	0.311423i	$-0.100806\pi$
$823$	32.1374	+	19.3365i	1.12024	+	0.674027i	0.169969	+	0.985449i	$0.445633\pi$
$824$	8.72493	+	2.93977i	0.303947	+	0.102412i
$825$		0			0
$826$	6.17844	−	6.01899i	0.214976	−	0.209428i
$827$	−37.6501			−1.30922			−0.654612	−	0.755965i	$-0.727168\pi$
$827$	−37.6501			−1.30922			−0.654612	+	0.755965i	$0.727168\pi$
$828$		0			0
$829$	−33.5673	−	20.1968i	−1.16584	−	0.701463i	−0.205054	−	0.978751i	$-0.565737\pi$
$829$	−33.5673	−	20.1968i	−1.16584	−	0.701463i	−0.960787	+	0.277287i	$0.910565\pi$
$830$	8.23185	+	6.25769i	0.285732	+	0.217208i
$831$		0			0
$832$	−10.3464	−	12.1807i	−0.358696	−	0.422290i
$833$	−6.77702	+	3.13538i	−0.234810	+	0.108635i
$834$		0			0
$835$	30.5694	+	57.6601i	1.05790	+	1.99541i
$836$	14.9418	−	17.5908i	0.516773	−	0.608392i
$837$		0			0
$838$	−1.12629	−	2.82678i	−0.0389071	−	0.0976495i
$839$	−12.3341	+	23.2646i	−0.425821	+	0.803183i	−0.999878	−	0.0156321i	$-0.995024\pi$
$839$	−12.3341	+	23.2646i	−0.425821	+	0.803183i	0.574057	+	0.818815i	$0.305369\pi$
$840$		0			0
$841$	−17.5475	+	13.3392i	−0.605085	+	0.459973i
$842$	−0.633431	−	2.28141i	−0.0218295	−	0.0786227i
$843$		0			0
$844$	2.46435	+	15.0319i	0.0848264	+	0.517418i
$845$	19.0865	−	4.20125i	0.656594	−	0.144527i
$846$		0			0
$847$	−31.5819	−	3.43474i	−1.08517	−	0.118019i
$848$	17.4421	−	25.7252i	0.598964	−	0.883406i
$849$		0			0
$850$	−0.137616	−	2.53817i	−0.00472018	−	0.0870586i
$851$	3.74169	+	3.54431i	0.128263	+	0.121497i
$852$		0			0
$853$	1.66653	−	30.7373i	0.0570608	−	1.05242i	−0.820098	−	0.572224i	$-0.806081\pi$
$853$	1.66653	−	30.7373i	0.0570608	−	1.05242i	0.877158	−	0.480201i	$-0.159436\pi$
$854$	−8.62462	−	1.89842i	−0.295129	−	0.0649627i
$855$		0			0
$856$	6.40772	−	2.15901i	0.219011	−	0.0737935i
$857$	23.4210	+	5.15536i	0.800047	+	0.176104i	0.596134	−	0.802885i	$-0.296703\pi$
$857$	23.4210	+	5.15536i	0.800047	+	0.176104i	0.203914	+	0.978989i	$0.434634\pi$
$858$		0			0
$859$	−30.0421	+	28.4574i	−1.02502	+	0.970953i	−0.999587	−	0.0287237i	$-0.990856\pi$
$859$	−30.0421	+	28.4574i	−1.02502	+	0.970953i	−0.0254350	+	0.999676i	$0.508097\pi$
$860$	−56.7932	−	53.7974i	−1.93663	−	1.83448i
$861$		0			0
$862$	−0.0273661	+	0.166926i	−0.000932092	+	0.00568551i
$863$	10.8187	−	15.9564i	0.368272	−	0.543161i	−0.597729	−	0.801698i	$-0.703930\pi$
$863$	10.8187	−	15.9564i	0.368272	−	0.543161i	0.966001	+	0.258537i	$0.0832406\pi$
$864$		0			0
$865$	−42.3665	+	25.4911i	−1.44051	+	0.866723i
$866$	5.75587	−	1.26696i	0.195593	−	0.0430532i
$867$		0			0
$868$	−22.5169	−	10.4174i	−0.764273	−	0.353590i
$869$	−0.284290	−	1.02392i	−0.00964389	−	0.0347341i
$870$		0			0
$871$	−28.3449	+	3.08269i	−0.960429	+	0.104453i
$872$	−2.57290	+	4.85300i	−0.0871293	+	0.164343i
$873$		0			0
$874$	−2.37019	+	8.53667i	−0.0801730	+	0.288757i
$875$	19.8458	−	23.3643i	0.670911	−	0.789857i
$876$		0			0
$877$	1.42839	+	2.10671i	0.0482332	+	0.0711387i	0.851041	−	0.525099i	$-0.175972\pi$
$877$	1.42839	+	2.10671i	0.0482332	+	0.0711387i	−0.802808	+	0.596238i	$0.796661\pi$
$878$	−0.767745	+	0.355197i	−0.0259101	+	0.0119873i
$879$		0			0
$880$	6.93484	−	17.4051i	0.233773	−	0.586727i
$881$	46.4540	+	35.3134i	1.56507	+	1.18974i	0.893743	+	0.448580i	$0.148070\pi$
$881$	46.4540	+	35.3134i	1.56507	+	1.18974i	0.671331	+	0.741158i	$0.265723\pi$
$882$		0			0
$883$	−22.2346	−	7.49172i	−0.748255	−	0.252116i	−0.0807629	−	0.996733i	$-0.525736\pi$
$883$	−22.2346	−	7.49172i	−0.748255	−	0.252116i	−0.667492	+	0.744617i	$0.732632\pi$
$884$	5.89516			0.198276
$885$		0			0
$886$	−1.87542			−0.0630058
$887$	−21.3162	−	7.18228i	−0.715729	−	0.241157i	−0.0622057	−	0.998063i	$-0.519813\pi$
$887$	−21.3162	−	7.18228i	−0.715729	−	0.241157i	−0.653524	+	0.756906i	$0.726710\pi$
$888$		0			0
$889$	26.3742	+	20.0491i	0.884561	+	0.672426i
$890$	−6.86181	+	17.2218i	−0.230008	+	0.577277i
$891$		0			0
$892$	−9.85761	+	4.56062i	−0.330057	+	0.152701i
$893$	58.3288	+	86.0286i	1.95190	+	2.87884i
$894$		0			0
$895$	−42.1651	+	49.6405i	−1.40942	+	1.65930i
$896$	8.52932	−	30.7198i	0.284944	−	1.02628i
$897$		0			0
$898$	−1.41080	+	2.66105i	−0.0470790	+	0.0888005i
$899$	9.25341	−	1.00637i	0.308618	−	0.0335643i
$900$		0			0
$901$	2.72932	+	9.83011i	0.0909268	+	0.327489i
$902$	0.206445	+	0.0955115i	0.00687385	+	0.00318018i
$903$		0			0
$904$	9.25512	−	2.03721i	0.307821	−	0.0677565i
$905$	−12.8856	+	7.75299i	−0.428331	+	0.257718i
$906$		0			0
$907$	−0.774619	+	1.14248i	−0.0257208	+	0.0379353i	−0.840332	−	0.542072i	$-0.817640\pi$
$907$	−0.774619	+	1.14248i	−0.0257208	+	0.0379353i	0.814611	+	0.580007i	$0.196950\pi$
$908$	−7.28333	+	44.4264i	−0.241706	+	1.47434i
$909$		0			0
$910$	−7.82063	−	7.40810i	−0.259251	−	0.245576i
$911$	17.7064	−	16.7724i	0.586640	−	0.555695i	−0.335752	−	0.941950i	$-0.608990\pi$
$911$	17.7064	−	16.7724i	0.586640	−	0.555695i	0.922392	+	0.386256i	$0.126232\pi$
$912$		0			0
$913$	−14.5526	−	3.20327i	−0.481620	−	0.106013i
$914$	10.7761	−	3.63090i	0.356443	−	0.120100i
$915$		0			0
$916$	11.5657	+	2.54580i	0.382140	+	0.0841155i
$917$	1.61414	−	29.7710i	0.0533035	−	0.983125i
$918$		0			0
$919$	−11.1495	−	10.5613i	−0.367787	−	0.348386i	0.481379	−	0.876512i	$-0.340136\pi$
$919$	−11.1495	−	10.5613i	−0.367787	−	0.348386i	−0.849166	+	0.528127i	$0.822895\pi$
$920$	0.840558	+	15.5032i	0.0277124	+	0.511125i
$921$		0			0
$922$	−1.39941	+	2.06397i	−0.0460870	+	0.0679732i
$923$	35.1973	+	3.82794i	1.15853	+	0.125998i
$924$		0			0
$925$	−9.99246	+	2.19951i	−0.328550	+	0.0723194i
$926$	0.389480	+	2.37572i	0.0127991	+	0.0780711i
$927$		0			0
$928$	2.42183	+	8.72264i	0.0795005	+	0.286335i
$929$	−6.88025	+	5.23023i	−0.225734	+	0.171598i	−0.711928	−	0.702252i	$-0.752178\pi$
$929$	−6.88025	+	5.23023i	−0.225734	+	0.171598i	0.486194	+	0.873851i	$0.338385\pi$
$930$		0			0
$931$	−24.2019	+	45.6496i	−0.793185	+	1.49611i
$932$	−18.6510	−	46.8104i	−0.610933	−	1.53333i
$933$		0			0
$934$	2.62514	−	3.09055i	0.0858971	−	0.101126i
$935$	2.88065	+	5.43348i	0.0942073	+	0.177694i
$936$		0			0
$937$	14.4754	−	6.69702i	0.472890	−	0.218782i	−0.168944	−	0.985626i	$-0.554036\pi$
$937$	14.4754	−	6.69702i	0.472890	−	0.218782i	0.641834	+	0.766844i	$0.278174\pi$
$938$	−7.59812	−	8.94520i	−0.248087	−	0.292071i
$939$		0			0
$940$	70.7808	+	53.8061i	2.30861	+	1.75496i
$941$	39.0222	+	23.4789i	1.27209	+	0.765389i	0.981500	−	0.191460i	$-0.0613222\pi$
$941$	39.0222	+	23.4789i	1.27209	+	0.765389i	0.290586	+	0.956849i	$0.406150\pi$
$942$		0			0
$943$	1.79471			0.0584440
$944$	21.3306	+	15.7485i	0.694253	+	0.512569i
$945$		0			0
$946$	−5.19748	−	1.75124i	−0.168985	−	0.0569376i
$947$	−42.3072	−	25.4554i	−1.37480	−	0.827189i	−0.379609	−	0.925147i	$-0.623941\pi$
$947$	−42.3072	−	25.4554i	−1.37480	−	0.827189i	−0.995191	+	0.0979580i	$0.968769\pi$
$948$		0			0
$949$	4.72468	−	11.8581i	0.153370	−	0.384929i
$950$	−11.3865	−	13.4053i	−0.369428	−	0.434924i
$951$		0			0
$952$	2.78989	+	4.11478i	0.0904208	+	0.133361i
$953$	−14.1522	−	26.6939i	−0.458435	−	0.864700i	−0.999715	−	0.0238579i	$-0.992405\pi$
$953$	−14.1522	−	26.6939i	−0.458435	−	0.864700i	0.541280	−	0.840842i	$-0.317940\pi$
$954$		0			0
$955$	9.79249	−	35.2694i	0.316878	−	1.14129i
$956$	−6.80854	−	17.0881i	−0.220204	−	0.552670i
$957$		0			0
$958$	5.90879	−	0.642619i	0.190904	−	0.0207621i
$959$	−39.0017	+	29.6483i	−1.25943	+	0.957394i
$960$		0			0
$961$	−16.8341	−	7.78829i	−0.543036	−	0.251235i
$962$	0.186773	+	1.13927i	0.00602181	+	0.0367314i
$963$		0			0
$964$	6.98231	−	4.20112i	0.224885	−	0.135309i
$965$	−16.4757	−	1.79184i	−0.530372	−	0.0576814i
$966$		0			0
$967$	3.92700	−	23.9536i	0.126284	−	0.770296i	−0.845422	−	0.534100i	$-0.820651\pi$
$967$	3.92700	−	23.9536i	0.126284	−	0.770296i	0.971705	−	0.236197i	$-0.0759010\pi$
$968$	0.555268	+	10.2413i	0.0178470	+	0.329169i
$969$		0			0
$970$	1.95116	−	1.84824i	0.0626479	−	0.0593433i
$971$	0.835864	−	15.4166i	0.0268241	−	0.494742i	−0.953995	−	0.299822i	$-0.903073\pi$
$971$	0.835864	−	15.4166i	0.0268241	−	0.494742i	0.980819	−	0.194920i	$-0.0624447\pi$
$972$		0			0
$973$	75.0277	−	25.2798i	2.40528	−	0.810433i
$974$	−1.64769	+	0.555171i	−0.0527954	+	0.0177888i
$975$		0			0
$976$	1.46965	−	27.1061i	0.0470423	−	0.867645i
$977$	−4.11198	+	3.89507i	−0.131554	+	0.124614i	−0.750648	−	0.660702i	$-0.770259\pi$
$977$	−4.11198	+	3.89507i	−0.131554	+	0.124614i	0.619094	+	0.785317i	$0.287500\pi$
$978$		0			0
$979$	−1.44632	−	26.6758i	−0.0462247	−	0.852564i
$980$	−7.15040	+	43.6155i	−0.228411	+	1.39325i
$981$		0			0
$982$	3.92704	+	0.427091i	0.125317	+	0.0136290i
$983$	17.4405	−	10.4936i	0.556265	−	0.334694i	−0.209505	−	0.977808i	$-0.567185\pi$
$983$	17.4405	−	10.4936i	0.556265	−	0.334694i	0.765771	+	0.643114i	$0.222358\pi$
$984$		0			0
$985$	4.61104	+	28.1261i	0.146920	+	0.896172i
$986$	−0.826272	−	0.382274i	−0.0263139	−	0.0121741i
$987$		0			0
$988$	32.4735	−	24.6857i	1.03312	−	0.785356i
$989$	−43.0195	+	4.67865i	−1.36794	+	0.148772i
$990$		0			0
$991$	−6.77270	−	16.9982i	−0.215142	−	0.539965i	0.781309	−	0.624145i	$-0.214552\pi$
$991$	−6.77270	−	16.9982i	−0.215142	−	0.539965i	−0.996451	+	0.0841793i	$0.973173\pi$
$992$	−3.23975	+	11.6685i	−0.102862	+	0.370477i
$993$		0			0
$994$	6.82658	+	12.8763i	0.216526	+	0.408411i
$995$	−12.2702	−	18.0971i	−0.388990	−	0.573718i
$996$		0			0
$997$	20.0011	+	23.5471i	0.633441	+	0.745744i	0.981444	−	0.191749i	$-0.0614161\pi$
$997$	20.0011	+	23.5471i	0.633441	+	0.745744i	−0.348003	+	0.937493i	$0.613140\pi$
$998$	3.72266	−	9.34317i	0.117839	−	0.295753i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.2.i.c.64.3		140
3.2	odd	2		177.2.e.a.64.3	✓	140
59.12	even	29	inner	531.2.i.c.307.3		140
177.71	odd	58		177.2.e.a.130.3	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.e.a.64.3	✓	140	3.2	odd	2
177.2.e.a.130.3	yes	140	177.71	odd	58
531.2.i.c.64.3		140	1.1	even	1	trivial
531.2.i.c.307.3		140	59.12	even	29	inner

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:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	531.i (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.288668 - 0.0972636i) q^{2} +(-1.51832 - 1.15419i) q^{4} +(1.30154 - 3.26662i) q^{5} +(-3.34578 + 1.54792i) q^{7} +(0.667919 + 0.985107i) q^{8} +O(q^{10})\)	\(q+(-0.288668 - 0.0972636i) q^{2} +(-1.51832 - 1.15419i) q^{4} +(1.30154 - 3.26662i) q^{5} +(-3.34578 + 1.54792i) q^{7} +(0.667919 + 0.985107i) q^{8} +(-0.693437 + 0.816377i) q^{10} +(0.412947 - 1.48730i) q^{11} +(1.27783 - 2.41025i) q^{13} +(1.11638 - 0.121413i) q^{14} +(0.923474 + 3.32605i) q^{16} +(-1.02833 - 0.475754i) q^{17} +(-7.65671 + 1.68537i) q^{19} +(-5.74647 + 3.45753i) q^{20} +(-0.263865 + 0.389171i) q^{22} +(-0.600176 + 3.66091i) q^{23} +(-5.34682 - 5.06478i) q^{25} +(-0.603299 + 0.571476i) q^{26} +(6.86657 + 1.51145i) q^{28} +(-2.49973 + 0.842256i) q^{29} +(-3.44618 - 0.758561i) q^{31} +(0.185798 - 3.42683i) q^{32} +(0.250571 + 0.237354i) q^{34} +(0.701808 + 12.9441i) q^{35} +(0.779638 - 1.14988i) q^{37} +(2.37417 + 0.258207i) q^{38} +(4.08729 - 0.899681i) q^{40} +(-0.0782668 - 0.477406i) q^{41} +(3.12061 + 11.2394i) q^{43} +(-2.34362 + 1.78157i) q^{44} +(0.529325 - 0.998413i) q^{46} +(-4.90708 - 12.3158i) q^{47} +(4.26650 - 5.02291i) q^{49} +(1.05084 + 1.98209i) q^{50} +(-4.72205 + 2.18465i) q^{52} +(-5.82908 - 6.86252i) q^{53} +(-4.32097 - 3.28472i) q^{55} +(-3.75959 - 2.26207i) q^{56} +0.803513 q^{58} +(6.04918 - 4.73365i) q^{59} +(-7.45245 - 2.51102i) q^{61} +(0.921021 + 0.554160i) q^{62} +(2.16840 - 5.44227i) q^{64} +(-6.21022 - 7.31123i) q^{65} +(-5.86524 - 8.65058i) q^{67} +(1.01221 + 1.90923i) q^{68} +(1.05640 - 3.80481i) q^{70} +(4.80372 + 12.0564i) q^{71} +(4.65164 - 0.505896i) q^{73} +(-0.336898 + 0.256103i) q^{74} +(13.5706 + 6.27841i) q^{76} +(0.920597 + 5.61539i) q^{77} +(0.589897 - 0.354930i) q^{79} +(12.0669 + 1.31235i) q^{80} +(-0.0238411 + 0.145425i) q^{82} +(-0.522637 - 9.63947i) q^{83} +(-2.89251 + 2.73993i) q^{85} +(0.192366 - 3.54799i) q^{86} +(1.74096 - 0.586599i) q^{88} +(16.4014 - 5.52628i) q^{89} +(-0.544470 + 10.0422i) q^{91} +(5.13666 - 4.86570i) q^{92} +(0.218634 + 4.03247i) q^{94} +(-4.46006 + 27.2051i) q^{95} +(-2.49438 - 0.271280i) q^{97} +(-1.72015 + 1.03498i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8}+O(q^{10}) \) 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8	\( 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8} + 88 q^{10} + 14 q^{11} - 12 q^{13} + q^{14} - 41 q^{16} + 16 q^{17} - 10 q^{19} + 32 q^{20} - 26 q^{22} + 22 q^{23} + 27 q^{25} + 56 q^{26} - 50 q^{28} + 24 q^{29} - 24 q^{31} - 106 q^{32} - 54 q^{34} + 70 q^{35} - 28 q^{37} + 80 q^{38} - 50 q^{40} + 40 q^{41} + 4 q^{43} + 104 q^{44} - 28 q^{46} - 31 q^{47} - q^{49} - 39 q^{50} + 62 q^{52} - 4 q^{53} + 5 q^{55} - 96 q^{56} + 128 q^{58} + q^{59} - 16 q^{61} - 223 q^{62} + 97 q^{64} - 121 q^{65} - 12 q^{67} - 10 q^{68} - 2 q^{70} + 22 q^{71} + 179 q^{73} + 38 q^{74} + 112 q^{76} + 62 q^{77} - 84 q^{79} - 204 q^{80} - 152 q^{82} + 88 q^{83} - 118 q^{85} + 118 q^{86} + 18 q^{88} + 86 q^{89} + 78 q^{91} + 174 q^{92} - 164 q^{94} - 218 q^{95} - 84 q^{97} - 129 q^{98}+O(q^{100}) \) 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8 + 88 * q^10 + 14 * q^11 - 12 * q^13 + q^14 - 41 * q^16 + 16 * q^17 - 10 * q^19 + 32 * q^20 - 26 * q^22 + 22 * q^23 + 27 * q^25 + 56 * q^26 - 50 * q^28 + 24 * q^29 - 24 * q^31 - 106 * q^32 - 54 * q^34 + 70 * q^35 - 28 * q^37 + 80 * q^38 - 50 * q^40 + 40 * q^41 + 4 * q^43 + 104 * q^44 - 28 * q^46 - 31 * q^47 - q^49 - 39 * q^50 + 62 * q^52 - 4 * q^53 + 5 * q^55 - 96 * q^56 + 128 * q^58 + q^59 - 16 * q^61 - 223 * q^62 + 97 * q^64 - 121 * q^65 - 12 * q^67 - 10 * q^68 - 2 * q^70 + 22 * q^71 + 179 * q^73 + 38 * q^74 + 112 * q^76 + 62 * q^77 - 84 * q^79 - 204 * q^80 - 152 * q^82 + 88 * q^83 - 118 * q^85 + 118 * q^86 + 18 * q^88 + 86 * q^89 + 78 * q^91 + 174 * q^92 - 164 * q^94 - 218 * q^95 - 84 * q^97 - 129 * q^98

Introduction

L-functions

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