LMFDB - Embedded newform 637.2.bl.a.625.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			625.27
Character	$\chi$	$=$	637.625
Dual form			637.2.bl.a.53.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.14872 - 1.46497i) q^{2} +(0.378204 - 0.350922i) q^{3} +(1.74017 - 4.43389i) q^{4} +(0.273927 + 0.0844952i) q^{5} +(0.298564 - 1.30809i) q^{6} +(2.61705 + 0.388620i) q^{7} +(-1.59901 - 7.00570i) q^{8} +(-0.204298 + 2.72617i) q^{9} +O(q^{10})$	\(q+(2.14872 - 1.46497i) q^{2} +(0.378204 - 0.350922i) q^{3} +(1.74017 - 4.43389i) q^{4} +(0.273927 + 0.0844952i) q^{5} +(0.298564 - 1.30809i) q^{6} +(2.61705 + 0.388620i) q^{7} +(-1.59901 - 7.00570i) q^{8} +(-0.204298 + 2.72617i) q^{9} +(0.712375 - 0.219739i) q^{10} +(-0.103468 - 1.38068i) q^{11} +(-0.897810 - 2.28758i) q^{12} +(0.900969 + 0.433884i) q^{13} +(6.19264 - 2.99888i) q^{14} +(0.133252 - 0.0641705i) q^{15} +(-6.71571 - 6.23127i) q^{16} +(-1.96613 - 0.296347i) q^{17} +(3.55479 + 6.15707i) q^{18} +(-2.10278 + 3.64213i) q^{19} +(0.851323 - 1.06752i) q^{20} +(1.12616 - 0.771405i) q^{21} +(-2.24499 - 2.81512i) q^{22} +(-6.82209 + 1.02826i) q^{23} +(-3.06321 - 2.08846i) q^{24} +(-4.06330 - 2.77031i) q^{25} +(2.57156 - 0.387600i) q^{26} +(1.84444 + 2.31286i) q^{27} +(6.27723 - 10.9275i) q^{28} +(-0.519835 + 0.651852i) q^{29} +(0.192312 - 0.333095i) q^{30} +(1.15437 + 1.99943i) q^{31} +(-9.34762 - 1.40893i) q^{32} +(-0.523644 - 0.485871i) q^{33} +(-4.65882 + 2.24357i) q^{34} +(0.684044 + 0.327582i) q^{35} +(11.7320 + 5.64985i) q^{36} +(-3.10075 - 7.90058i) q^{37} +(0.817325 + 10.9064i) q^{38} +(0.493010 - 0.152073i) q^{39} +(0.153938 - 2.05416i) q^{40} +(2.75943 + 12.0899i) q^{41} +(1.28971 - 3.30733i) q^{42} +(1.89945 - 8.32202i) q^{43} +(-6.30184 - 1.94386i) q^{44} +(-0.286311 + 0.729509i) q^{45} +(-13.1524 + 12.2036i) q^{46} +(-6.91229 + 4.71272i) q^{47} -4.72660 q^{48} +(6.69795 + 2.03408i) q^{49} -12.7893 q^{50} +(-0.847596 + 0.577881i) q^{51} +(3.49164 - 3.23977i) q^{52} +(-0.798507 + 2.03456i) q^{53} +(7.35146 + 2.26763i) q^{54} +(0.0883184 - 0.386948i) q^{55} +(-1.46213 - 18.9557i) q^{56} +(0.482823 + 2.11538i) q^{57} +(-0.162034 + 2.16219i) q^{58} +(12.8590 - 3.96648i) q^{59} +(-0.0526444 - 0.702491i) q^{60} +(0.510446 + 1.30059i) q^{61} +(5.40954 + 2.60509i) q^{62} +(-1.59410 + 7.05514i) q^{63} +(-5.64138 + 2.71674i) q^{64} +(0.210138 + 0.194980i) q^{65} +(-1.83695 - 0.276876i) q^{66} +(0.370545 + 0.641803i) q^{67} +(-4.73539 + 8.20193i) q^{68} +(-2.21930 + 2.78292i) q^{69} +(1.94972 - 0.298225i) q^{70} +(5.60020 + 7.02243i) q^{71} +(19.4254 - 2.92791i) q^{72} +(-6.26868 - 4.27391i) q^{73} +(-18.2368 - 12.4336i) q^{74} +(-2.50892 + 0.378159i) q^{75} +(12.4896 + 15.6615i) q^{76} +(0.265780 - 3.65353i) q^{77} +(0.836557 - 1.04901i) q^{78} +(7.52796 - 13.0388i) q^{79} +(-1.31310 - 2.27436i) q^{80} +(-6.60063 - 0.994885i) q^{81} +(23.6406 + 21.9353i) q^{82} +(-0.552565 + 0.266101i) q^{83} +(-1.46062 - 6.33564i) q^{84} +(-0.513537 - 0.247306i) q^{85} +(-8.11015 - 20.6643i) q^{86} +(0.0321457 + 0.428955i) q^{87} +(-9.50720 + 2.93258i) q^{88} +(0.621907 - 8.29877i) q^{89} +(0.453508 + 1.98695i) q^{90} +(2.18927 + 1.48563i) q^{91} +(-7.31241 + 32.0378i) q^{92} +(1.13823 + 0.351098i) q^{93} +(-7.94857 + 20.2526i) q^{94} +(-0.883751 + 0.820001i) q^{95} +(-4.02974 + 2.74743i) q^{96} -7.36573 q^{97} +(17.3719 - 5.44165i) q^{98} +3.78511 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) $ 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{16}{21}\right)$

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 $

$2$	2.14872	−	1.46497i	1.51938	−	1.03589i	0.538190	−	0.842823i	$-0.319108\pi$
$2$	2.14872	−	1.46497i	1.51938	−	1.03589i	0.981185	−	0.193069i	$-0.0618442\pi$
$3$	0.378204	−	0.350922i	0.218356	−	0.202605i	−0.563408	−	0.826179i	$-0.690510\pi$
$3$	0.378204	−	0.350922i	0.218356	−	0.202605i	0.781765	+	0.623573i	$0.214320\pi$
$4$	1.74017	−	4.43389i	0.870087	−	2.21695i
$5$	0.273927	+	0.0844952i	0.122504	+	0.0377874i	0.355401	−	0.934714i	$-0.384344\pi$
$5$	0.273927	+	0.0844952i	0.122504	+	0.0377874i	−0.232897	+	0.972501i	$0.574821\pi$
$6$	0.298564	−	1.30809i	0.121888	−	0.534027i
$7$	2.61705	+	0.388620i	0.989154	+	0.146885i
$7$	2.61705	+	0.388620i	0.989154	+	0.146885i
$8$	−1.59901	−	7.00570i	−0.565334	−	2.47689i
$9$	−0.204298	+	2.72617i	−0.0680994	+	0.908724i
$10$	0.712375	−	0.219739i	0.225273	−	0.0694875i
$11$	−0.103468	−	1.38068i	−0.0311967	−	0.416291i	−0.990837	−	0.135062i	$-0.956877\pi$
$11$	−0.103468	−	1.38068i	−0.0311967	−	0.416291i	0.959641	−	0.281230i	$-0.0907423\pi$
$12$	−0.897810	−	2.28758i	−0.259176	−	0.660369i
$13$	0.900969	+	0.433884i	0.249884	+	0.120338i
$13$	0.900969	+	0.433884i	0.249884	+	0.120338i
$14$	6.19264	−	2.99888i	1.65505	−	0.801484i
$15$	0.133252	−	0.0641705i	0.0344054	−	0.0165688i
$16$	−6.71571	−	6.23127i	−1.67893	−	1.55782i
$17$	−1.96613	−	0.296347i	−0.476858	−	0.0718747i	−0.0937841	−	0.995593i	$-0.529896\pi$
$17$	−1.96613	−	0.296347i	−0.476858	−	0.0718747i	−0.383074	+	0.923718i	$0.625134\pi$
$18$	3.55479	+	6.15707i	0.837871	+	1.45124i
$19$	−2.10278	+	3.64213i	−0.482412	+	0.835562i	−0.999796	−	0.0201913i	$-0.993572\pi$
$19$	−2.10278	+	3.64213i	−0.482412	+	0.835562i	0.517384	+	0.855753i	$0.326906\pi$
$20$	0.851323	−	1.06752i	0.190362	−	0.238706i
$21$	1.12616	−	0.771405i	0.245748	−	0.168334i
$22$	−2.24499	−	2.81512i	−0.478632	−	0.600186i
$23$	−6.82209	+	1.02826i	−1.42250	+	0.214408i	−0.814794	−	0.579751i	$-0.803150\pi$
$23$	−6.82209	+	1.02826i	−1.42250	+	0.214408i	−0.607710	+	0.794159i	$0.707912\pi$
$24$	−3.06321	−	2.08846i	−0.625275	−	0.426305i
$25$	−4.06330	−	2.77031i	−0.812660	−	0.554062i
$26$	2.57156	−	0.387600i	0.504324	−	0.0760147i
$27$	1.84444	+	2.31286i	0.354963	+	0.445109i
$28$	6.27723	−	10.9275i	1.18628	−	2.06510i
$29$	−0.519835	+	0.651852i	−0.0965309	+	0.121046i	−0.827751	−	0.561096i	$-0.810380\pi$
$29$	−0.519835	+	0.651852i	−0.0965309	+	0.121046i	0.731220	+	0.682142i	$0.238951\pi$
$30$	0.192312	−	0.333095i	0.0351112	−	0.0608145i
$31$	1.15437	+	1.99943i	0.207331	+	0.359108i	0.950873	−	0.309581i	$-0.100189\pi$
$31$	1.15437	+	1.99943i	0.207331	+	0.359108i	−0.743542	+	0.668690i	$0.766856\pi$
$32$	−9.34762	−	1.40893i	−1.65244	−	0.249065i
$33$	−0.523644	−	0.485871i	−0.0911547	−	0.0845792i
$34$	−4.65882	+	2.24357i	−0.798980	+	0.384769i
$35$	0.684044	+	0.327582i	0.115625	+	0.0553714i
$36$	11.7320	+	5.64985i	1.95534	+	0.941641i
$37$	−3.10075	−	7.90058i	−0.509760	−	1.29885i	−0.921794	−	0.387679i	$-0.873277\pi$
$37$	−3.10075	−	7.90058i	−0.509760	−	1.29885i	0.412034	−	0.911168i	$-0.364818\pi$
$38$	0.817325	+	10.9064i	0.132588	+	1.76926i
$39$	0.493010	−	0.152073i	0.0789448	−	0.0243512i
$40$	0.153938	−	2.05416i	0.0243397	−	0.324791i
$41$	2.75943	+	12.0899i	0.430951	+	1.88812i	0.458857	+	0.888510i	$0.348259\pi$
$41$	2.75943	+	12.0899i	0.430951	+	1.88812i	−0.0279056	+	0.999611i	$0.508884\pi$
$42$	1.28971	−	3.30733i	0.199006	−	0.510331i
$43$	1.89945	−	8.32202i	0.289663	−	1.26910i	−0.595326	−	0.803484i	$-0.702977\pi$
$43$	1.89945	−	8.32202i	0.289663	−	1.26910i	0.884989	−	0.465612i	$-0.154166\pi$
$44$	−6.30184	−	1.94386i	−0.950039	−	0.293048i
$45$	−0.286311	+	0.729509i	−0.0426807	+	0.108749i
$46$	−13.1524	+	12.2036i	−1.93921	+	1.79933i
$47$	−6.91229	+	4.71272i	−1.00826	+	0.687420i	−0.950440	−	0.310907i	$-0.899367\pi$
$47$	−6.91229	+	4.71272i	−1.00826	+	0.687420i	−0.0578202	+	0.998327i	$0.518415\pi$
$48$	−4.72660			−0.682226
$49$	6.69795	+	2.03408i	0.956850	+	0.290583i
$50$	−12.7893			−1.80868
$51$	−0.847596	+	0.577881i	−0.118687	+	0.0809195i
$52$	3.49164	−	3.23977i	0.484203	−	0.449275i
$53$	−0.798507	+	2.03456i	−0.109683	+	0.279469i	−0.975168	−	0.221467i	$-0.928915\pi$
$53$	−0.798507	+	2.03456i	−0.109683	+	0.279469i	0.865484	+	0.500936i	$0.167011\pi$
$54$	7.35146	+	2.26763i	1.00041	+	0.308585i
$55$	0.0883184	−	0.386948i	0.0119088	−	0.0521761i
$56$	−1.46213	−	18.9557i	−0.195385	−	2.53306i
$57$	0.482823	+	2.11538i	0.0639514	+	0.280189i
$58$	−0.162034	+	2.16219i	−0.0212761	+	0.283910i
$59$	12.8590	−	3.96648i	1.67410	−	0.516392i	0.694869	−	0.719136i	$-0.255462\pi$
$59$	12.8590	−	3.96648i	1.67410	−	0.516392i	0.979232	+	0.202744i	$0.0649861\pi$
$60$	−0.0526444	−	0.702491i	−0.00679636	−	0.0906912i
$61$	0.510446	+	1.30059i	0.0653559	+	0.166524i	0.959821	−	0.280615i	$-0.0905383\pi$
$61$	0.510446	+	1.30059i	0.0653559	+	0.166524i	−0.894465	+	0.447139i	$0.852443\pi$
$62$	5.40954	+	2.60509i	0.687012	+	0.330847i
$63$	−1.59410	+	7.05514i	−0.200838	+	0.888864i
$64$	−5.64138	+	2.71674i	−0.705172	+	0.339593i
$65$	0.210138	+	0.194980i	0.0260644	+	0.0241843i
$66$	−1.83695	−	0.276876i	−0.226113	−	0.0340811i
$67$	0.370545	+	0.641803i	0.0452693	+	0.0784088i	0.887772	−	0.460283i	$-0.152252\pi$
$67$	0.370545	+	0.641803i	0.0452693	+	0.0784088i	−0.842503	+	0.538692i	$0.818919\pi$
$68$	−4.73539	+	8.20193i	−0.574250	+	0.994630i
$69$	−2.21930	+	2.78292i	−0.267173	+	0.335024i
$70$	1.94972	−	0.298225i	0.233036	−	0.0356447i
$71$	5.60020	+	7.02243i	0.664621	+	0.833409i	0.993838	−	0.110846i	$-0.0353560\pi$
$71$	5.60020	+	7.02243i	0.664621	+	0.833409i	−0.329216	+	0.944254i	$0.606785\pi$
$72$	19.4254	−	2.92791i	2.28931	−	0.345057i
$73$	−6.26868	−	4.27391i	−0.733693	−	0.500224i	0.137904	−	0.990446i	$-0.455963\pi$
$73$	−6.26868	−	4.27391i	−0.733693	−	0.500224i	−0.871598	+	0.490222i	$0.836916\pi$
$74$	−18.2368	−	12.4336i	−2.11998	−	1.44538i
$75$	−2.50892	+	0.378159i	−0.289705	+	0.0436660i
$76$	12.4896	+	15.6615i	1.43266	+	1.79649i
$77$	0.265780	−	3.65353i	0.0302884	−	0.416358i
$78$	0.836557	−	1.04901i	0.0947215	−	0.118777i
$79$	7.52796	−	13.0388i	0.846961	−	1.46698i	−0.0369455	−	0.999317i	$-0.511763\pi$
$79$	7.52796	−	13.0388i	0.846961	−	1.46698i	0.883907	−	0.467663i	$-0.154904\pi$
$80$	−1.31310	−	2.27436i	−0.146809	−	0.254281i
$81$	−6.60063	−	0.994885i	−0.733404	−	0.110543i
$82$	23.6406	+	21.9353i	2.61067	+	2.42235i
$83$	−0.552565	+	0.266101i	−0.0606519	+	0.0292084i	−0.463964	−	0.885854i	$-0.653573\pi$
$83$	−0.552565	+	0.266101i	−0.0606519	+	0.0292084i	0.403312	+	0.915063i	$0.367859\pi$
$84$	−1.46062	−	6.33564i	−0.159367	−	0.691275i
$85$	−0.513537	−	0.247306i	−0.0557009	−	0.0268241i
$86$	−8.11015	−	20.6643i	−0.874540	−	2.22829i
$87$	0.0321457	+	0.428955i	0.00344639	+	0.0459888i
$88$	−9.50720	+	2.93258i	−1.01347	+	0.312614i
$89$	0.621907	−	8.29877i	0.0659220	−	0.879668i	−0.862003	−	0.506902i	$-0.830790\pi$
$89$	0.621907	−	8.29877i	0.0659220	−	0.879668i	0.927925	−	0.372766i	$-0.121591\pi$
$90$	0.453508	+	1.98695i	0.0478039	+	0.209443i
$91$	2.18927	+	1.48563i	0.229498	+	0.155737i
$92$	−7.31241	+	32.0378i	−0.762372	+	3.34017i
$93$	1.13823	+	0.351098i	0.118029	+	0.0364072i
$94$	−7.94857	+	20.2526i	−0.819833	+	2.08890i
$95$	−0.883751	+	0.820001i	−0.0906710	+	0.0841304i
$96$	−4.02974	+	2.74743i	−0.411283	+	0.280408i
$97$	−7.36573			−0.747877			−0.373938	−	0.927454i	$-0.621993\pi$
$97$	−7.36573			−0.747877			−0.373938	+	0.927454i	$0.621993\pi$
$98$	17.3719	−	5.44165i	1.75483	−	0.549689i
$99$	3.78511			0.380418
$100$	−19.3541	+	13.1954i	−1.93541	+	1.31954i
$101$	1.63096	−	1.51331i	0.162287	−	0.150580i	−0.594849	−	0.803837i	$-0.702788\pi$
$101$	1.63096	−	1.51331i	0.162287	−	0.150580i	0.757136	+	0.653257i	$0.226598\pi$
$102$	−0.974667	+	2.48341i	−0.0965064	+	0.245894i
$103$	11.8862	+	3.66642i	1.17119	+	0.361263i	0.818515	−	0.574485i	$-0.194798\pi$
$103$	11.8862	+	3.66642i	1.17119	+	0.361263i	0.352670	+	0.935748i	$0.385274\pi$
$104$	1.59901	−	7.00570i	0.156795	−	0.686965i
$105$	0.373664	−	0.116154i	0.0364659	−	0.0113354i
$106$	1.26481	+	5.54150i	0.122849	+	0.538238i
$107$	−1.23172	+	16.4361i	−0.119075	+	1.58894i	0.543150	+	0.839636i	$0.317232\pi$
$107$	−1.23172	+	16.4361i	−0.119075	+	1.58894i	−0.662224	+	0.749306i	$0.730387\pi$
$108$	13.4646	−	4.15328i	1.29563	−	0.399650i
$109$	−0.518188	−	6.91473i	−0.0496334	−	0.662311i	−0.965429	−	0.260667i	$-0.916058\pi$
$109$	−0.518188	−	6.91473i	−0.0496334	−	0.662311i	0.915796	−	0.401645i	$-0.131561\pi$
$110$	−0.377097	−	0.960827i	−0.0359548	−	0.0916113i
$111$	−3.94521	−	1.89991i	−0.374463	−	0.180332i
$112$	−15.1538	−	18.9174i	−1.43190	−	1.78753i
$113$	4.49695	−	2.16562i	0.423038	−	0.203724i	−0.210238	−	0.977650i	$-0.567424\pi$
$113$	4.49695	−	2.16562i	0.423038	−	0.203724i	0.633276	+	0.773926i	$0.281710\pi$
$114$	4.13643	+	3.83805i	0.387412	+	0.359466i
$115$	−1.95564	−	0.294765i	−0.182364	−	0.0274869i
$116$	1.98564	+	3.43923i	0.184362	+	0.319324i
$117$	−1.36691	+	2.36755i	−0.126371	+	0.218880i
$118$	21.8196	−	27.3610i	2.00866	−	2.51878i
$119$	−5.03032	−	1.53964i	−0.461128	−	0.141138i
$120$	−0.662630	−	0.830911i	−0.0604895	−	0.0758515i
$121$	8.98156	−	1.35375i	0.816506	−	0.123068i
$122$	3.00214	+	2.04683i	0.271801	+	0.185311i
$123$	5.28624	+	3.60410i	0.476644	+	0.324970i
$124$	10.8741	−	1.63900i	0.976520	−	0.147187i
$125$	−1.77262	−	2.22280i	−0.158548	−	0.198813i
$126$	6.91031	+	17.4949i	0.615619	+	1.55857i
$127$	−6.23530	+	7.81881i	−0.553293	+	0.693808i	−0.977302	−	0.211850i	$-0.932051\pi$
$127$	−6.23530	+	7.81881i	−0.553293	+	0.693808i	0.424009	+	0.905658i	$0.360622\pi$
$128$	1.31142	−	2.27144i	0.115914	−	0.200769i
$129$	−2.20200	−	3.81398i	−0.193876	−	0.335802i
$130$	0.737169	+	0.111110i	0.0646540	+	0.00974502i
$131$	−9.46166	−	8.77914i	−0.826669	−	0.767037i	0.148403	−	0.988927i	$-0.452587\pi$
$131$	−9.46166	−	8.77914i	−0.826669	−	0.767037i	−0.975072	+	0.221890i	$0.928777\pi$
$132$	−3.06553	+	1.47628i	−0.266820	+	0.128494i
$133$	−6.91851	+	8.71447i	−0.599911	+	0.755640i
$134$	1.73642	+	0.836218i	0.150004	+	0.0722382i
$135$	0.309816	+	0.789399i	0.0266648	+	0.0679407i
$136$	1.06774	+	14.2480i	0.0915580	+	1.22176i
$137$	−5.58050	+	1.72136i	−0.476774	+	0.147065i	−0.523823	−	0.851827i	$-0.675495\pi$
$137$	−5.58050	+	1.72136i	−0.476774	+	0.147065i	0.0470485	+	0.998893i	$0.485018\pi$
$138$	−0.691763	+	9.23094i	−0.0588868	+	0.785790i
$139$	−1.81108	−	7.93485i	−0.153614	−	0.673025i	−0.991817	−	0.127668i	$-0.959251\pi$
$139$	−1.81108	−	7.93485i	−0.153614	−	0.673025i	0.838203	−	0.545358i	$-0.183606\pi$
$140$	2.64282	−	2.46293i	0.223359	−	0.208156i
$141$	−0.960459	+	4.20805i	−0.0808853	+	0.354381i
$142$	22.3209	+	6.88510i	1.87313	+	0.577784i
$143$	0.505834	−	1.28884i	0.0423000	−	0.107779i
$144$	18.3595	−	17.0351i	1.52996	−	1.41959i
$145$	−0.197475	+	0.134636i	−0.0163994	+	0.0111809i
$146$	−19.7308			−1.63293
$147$	3.24700	−	1.58116i	0.267808	−	0.130412i
$148$	−40.4262			−3.32301
$149$	8.94195	−	6.09652i	0.732553	−	0.499446i	−0.138667	−	0.990339i	$-0.544282\pi$
$149$	8.94195	−	6.09652i	0.732553	−	0.499446i	0.871220	+	0.490893i	$0.163329\pi$
$150$	−4.83698	+	4.48806i	−0.394938	+	0.366449i
$151$	−5.39459	+	13.7452i	−0.439006	+	1.11857i	0.524626	+	0.851333i	$0.324205\pi$
$151$	−5.39459	+	13.7452i	−0.439006	+	1.11857i	−0.963631	+	0.267235i	$0.913890\pi$
$152$	28.8780	+	8.90769i	2.34232	+	0.722509i
$153$	1.20957	−	5.29947i	0.0977880	−	0.428437i
$154$	−4.78124	−	8.23977i	−0.385283	−	0.663980i
$155$	0.147271	+	0.645236i	0.0118291	+	0.0518266i
$156$	0.183646	−	2.45059i	0.0147035	−	0.196204i
$157$	−6.21032	+	1.91563i	−0.495638	+	0.152884i	−0.532489	−	0.846437i	$-0.678743\pi$
$157$	−6.21032	+	1.91563i	−0.495638	+	0.152884i	0.0368516	+	0.999321i	$0.488267\pi$
$158$	−2.92602	−	39.0450i	−0.232782	−	3.10625i
$159$	0.411975	+	1.04969i	0.0326717	+	0.0832462i
$160$	−2.44151	−	1.17577i	−0.193019	−	0.0929529i
$161$	−18.2534	+	0.0398246i	−1.43857	+	0.00313862i
$162$	−15.6404	+	7.53202i	−1.22883	+	0.591771i
$163$	−6.63731	−	6.15852i	−0.519874	−	0.482373i	0.376038	−	0.926604i	$-0.377286\pi$
$163$	−6.63731	−	6.15852i	−0.519874	−	0.482373i	−0.895912	+	0.444232i	$0.853477\pi$
$164$	58.4071	+	8.80345i	4.56083	+	0.687434i
$165$	−0.102386	−	0.177338i	−0.00797076	−	0.0138058i
$166$	−0.797477	+	1.38127i	−0.0618962	+	0.107207i
$167$	−3.32039	+	4.16364i	−0.256940	+	0.322192i	−0.893524	−	0.449015i	$-0.851775\pi$
$167$	−3.32039	+	4.16364i	−0.256940	+	0.322192i	0.636585	+	0.771207i	$0.280347\pi$
$168$	−7.20497	−	6.65604i	−0.555875	−	0.513524i
$169$	0.623490	+	0.781831i	0.0479608	+	0.0601409i
$170$	−1.46574	+	0.220925i	−0.112417	+	0.0169442i
$171$	−9.49947	−	6.47663i	−0.726443	−	0.495280i
$172$	−33.5935	−	22.9037i	−2.56148	−	1.74639i
$173$	11.1896	−	1.68657i	0.850732	−	0.128227i	0.290819	−	0.956778i	$-0.406072\pi$
$173$	11.1896	−	1.68657i	0.850732	−	0.128227i	0.559914	+	0.828551i	$0.310834\pi$
$174$	0.697480	+	0.874612i	0.0528758	+	0.0663042i
$175$	−9.55727	−	8.82913i	−0.722462	−	0.667419i
$176$	−7.90854	+	9.91699i	−0.596128	+	0.747521i
$177$	3.47141	−	6.01266i	0.260927	−	0.451939i
$178$	−10.8212	−	18.7428i	−0.811082	−	1.40483i
$179$	−19.6449	−	2.96099i	−1.46833	−	0.221314i	−0.634320	−	0.773071i	$-0.718720\pi$
$179$	−19.6449	−	2.96099i	−1.46833	−	0.221314i	−0.834006	+	0.551756i	$0.813958\pi$
$180$	2.73633	+	2.53894i	0.203954	+	0.189242i
$181$	−14.6838	+	7.07134i	−1.09144	+	0.525608i	−0.890956	−	0.454089i	$-0.849965\pi$
$181$	−14.6838	+	7.07134i	−1.09144	+	0.525608i	−0.200481	+	0.979698i	$0.564250\pi$
$182$	6.88054	−	0.0150117i	0.510020	−	0.00111274i
$183$	0.649461	+	0.312764i	0.0480095	+	0.0231202i
$184$	18.1123	+	46.1493i	1.33525	+	3.40217i
$185$	−0.181817	−	2.42618i	−0.0133674	−	0.178376i
$186$	2.96010	−	0.913069i	0.217045	−	0.0669495i
$187$	−0.205729	+	2.74527i	−0.0150444	+	0.200754i
$188$	8.86710	+	38.8493i	0.646699	+	2.83338i
$189$	3.92818	+	6.76966i	0.285733	+	0.492420i
$190$	−0.697655	+	3.05663i	−0.0506132	+	0.221751i
$191$	−3.07177	−	0.947517i	−0.222266	−	0.0685599i	0.181622	−	0.983368i	$-0.441865\pi$
$191$	−3.07177	−	0.947517i	−0.222266	−	0.0685599i	−0.403888	+	0.914808i	$0.632341\pi$
$192$	−1.18023	+	3.00717i	−0.0851756	+	0.217024i
$193$	2.44637	−	2.26990i	0.176093	−	0.163391i	−0.587202	−	0.809440i	$-0.699771\pi$
$193$	2.44637	−	2.26990i	0.176093	−	0.163391i	0.763295	+	0.646050i	$0.223580\pi$
$194$	−15.8269	+	10.7906i	−1.13631	+	0.774720i
$195$	0.147898			0.0105912
$196$	20.6745	−	26.1583i	1.47675	−	1.86845i
$197$	14.8625			1.05891			0.529455	−	0.848338i	$-0.322397\pi$
$197$	14.8625			1.05891			0.529455	+	0.848338i	$0.322397\pi$
$198$	8.13315	−	5.54509i	0.577998	−	0.394072i
$199$	8.75453	−	8.12302i	0.620592	−	0.575826i	−0.305935	−	0.952052i	$-0.598969\pi$
$199$	8.75453	−	8.12302i	0.620592	−	0.575826i	0.926528	+	0.376227i	$0.122779\pi$
$200$	−12.9107	+	32.8960i	−0.912926	+	2.32610i
$201$	0.365365	+	0.112700i	0.0257709	+	0.00794926i
$202$	1.28752	−	5.64100i	0.0905897	−	0.396899i
$203$	−1.61376	+	1.50391i	−0.113264	+	0.105554i
$204$	1.08730	+	4.76376i	0.0761260	+	0.333530i
$205$	−0.265653	+	3.54490i	−0.0185540	+	0.247586i
$206$	30.9114	−	9.53491i	2.15370	−	0.664329i
$207$	−1.40948	−	18.8083i	−0.0979659	−	1.30726i
$208$	−3.34700	−	8.52802i	−0.232073	−	0.591312i
$209$	5.24619	+	2.52643i	0.362887	+	0.174757i
$210$	0.632739	−	0.796990i	0.0436631	−	0.0549976i
$211$	4.57446	−	2.20295i	0.314919	−	0.151657i	−0.269747	−	0.962931i	$-0.586940\pi$
$211$	4.57446	−	2.20295i	0.314919	−	0.151657i	0.584666	+	0.811274i	$0.301226\pi$
$212$	7.63149	+	7.08099i	0.524133	+	0.486324i
$213$	4.58235	+	0.690678i	0.313977	+	0.0473244i
$214$	21.4319	+	37.1211i	1.46505	+	2.53755i
$215$	1.22348	−	2.11913i	0.0834406	−	0.144523i
$216$	13.2539	−	16.6199i	0.901814	−	1.13084i
$217$	2.24404	+	5.68123i	0.152335	+	0.385667i
$218$	−11.2433	−	14.0987i	−0.761495	−	0.954885i
$219$	−3.87065	+	0.583407i	−0.261555	+	0.0394230i
$220$	−1.56200	−	1.06495i	−0.105310	−	0.0717990i
$221$	−1.64285	−	1.12007i	−0.110510	−	0.0753443i
$222$	−11.2605	+	1.69724i	−0.755753	+	0.113911i
$223$	−0.651398	−	0.816827i	−0.0436208	−	0.0546988i	0.759543	−	0.650458i	$-0.225423\pi$
$223$	−0.651398	−	0.816827i	−0.0436208	−	0.0546988i	−0.803163	+	0.595759i	$0.796851\pi$
$224$	−23.9157	−	7.31991i	−1.59793	−	0.489082i
$225$	8.38246	−	10.5113i	0.558831	−	0.700752i
$226$	6.49013	−	11.2412i	0.431717	−	0.747755i
$227$	−1.25439	−	2.17267i	−0.0832568	−	0.144205i	0.821390	−	0.570367i	$-0.193199\pi$
$227$	−1.25439	−	2.17267i	−0.0832568	−	0.144205i	−0.904647	+	0.426162i	$0.859866\pi$
$228$	10.2196	+	1.54035i	0.676808	+	0.102012i
$229$	−1.71499	−	1.59127i	−0.113329	−	0.105154i	0.621473	−	0.783436i	$-0.286535\pi$
$229$	−1.71499	−	1.59127i	−0.113329	−	0.105154i	−0.734802	+	0.678281i	$0.762725\pi$
$230$	−4.63394	+	2.23159i	−0.305553	+	0.147146i
$231$	−1.18159	−	1.47505i	−0.0777427	−	0.0970511i
$232$	5.39790	+	2.59949i	0.354390	+	0.170665i
$233$	−1.10823	−	2.82373i	−0.0726028	−	0.184989i	0.889966	−	0.456027i	$-0.150728\pi$
$233$	−1.10823	−	2.82373i	−0.0726028	−	0.184989i	−0.962568	+	0.271039i	$0.912633\pi$
$234$	0.531299	+	7.08970i	0.0347321	+	0.463468i
$235$	−2.29166	+	0.706884i	−0.149492	+	0.0461120i
$236$	4.78998	−	63.9178i	0.311801	−	4.16070i
$237$	−1.72850	−	7.57306i	−0.112278	−	0.491923i
$238$	−13.0643	+	4.06103i	−0.846831	+	0.263237i
$239$	−0.647563	+	2.83716i	−0.0418874	+	0.183521i	−0.991544	−	0.129773i	$-0.958575\pi$
$239$	−0.647563	+	2.83716i	−0.0418874	+	0.183521i	0.949656	+	0.313293i	$0.101432\pi$
$240$	−1.29474	−	0.399375i	−0.0835753	−	0.0257796i
$241$	10.2552	−	26.1298i	0.660594	−	1.68317i	−0.0675279	−	0.997717i	$-0.521511\pi$
$241$	10.2552	−	26.1298i	0.660594	−	1.68317i	0.728122	−	0.685448i	$-0.240394\pi$
$242$	17.3157	−	16.0666i	1.11309	−	1.03280i
$243$	−10.1782	+	6.93937i	−0.652931	+	0.445161i
$244$	6.65496			0.426040
$245$	1.66288	+	1.12313i	0.106237	+	0.0717543i
$246$	16.6386			1.06084
$247$	−3.47480	+	2.36908i	−0.221097	+	0.150741i
$248$	12.1616	−	11.2843i	0.772260	−	0.716553i
$249$	−0.115602	+	0.294548i	−0.00732596	+	0.0186662i
$250$	−7.06521	−	2.17933i	−0.446843	−	0.137833i
$251$	−6.40989	+	28.0836i	−0.404588	+	1.77262i	0.203835	+	0.979005i	$0.434659\pi$
$251$	−6.40989	+	28.0836i	−0.404588	+	1.77262i	−0.608423	+	0.793613i	$0.708198\pi$
$252$	28.5077	+	19.3453i	1.79582	+	1.21864i
$253$	2.12557	+	9.31274i	0.133634	+	0.585487i
$254$	−1.94356	+	25.9350i	−0.121950	+	1.62731i
$255$	−0.281007	+	0.0866792i	−0.0175974	+	0.00542806i
$256$	−1.44557	−	19.2898i	−0.0903480	−	1.20561i
$257$	−7.55289	−	19.2444i	−0.471136	−	1.20044i	−0.947091	−	0.320965i	$-0.895993\pi$
$257$	−7.55289	−	19.2444i	−0.471136	−	1.20044i	0.475955	−	0.879470i	$-0.342103\pi$
$258$	−10.3189	−	4.96931i	−0.642425	−	0.309376i
$259$	−5.04451	−	21.8813i	−0.313450	−	1.35964i
$260$	1.23020	−	0.592432i	0.0762936	−	0.0367410i
$261$	−1.67086	−	1.55033i	−0.103424	−	0.0959631i
$262$	−33.1917	−	5.00284i	−2.05059	−	0.309076i
$263$	−2.74119	−	4.74789i	−0.169029	−	0.292767i	0.769050	−	0.639189i	$-0.220730\pi$
$263$	−2.74119	−	4.74789i	−0.169029	−	0.292767i	−0.938079	+	0.346422i	$0.887397\pi$
$264$	−2.56655	+	4.44540i	−0.157961	+	0.273596i
$265$	−0.390643	+	0.489851i	−0.0239970	+	0.0300913i
$266$	−2.09948	+	28.8604i	−0.128727	+	1.76954i
$267$	−2.67702	−	3.35687i	−0.163831	−	0.205437i
$268$	3.49050	−	0.526108i	0.213216	−	0.0321372i
$269$	20.7762	+	14.1650i	1.26675	+	0.863653i	0.995113	−	0.0987475i	$-0.0314836\pi$
$269$	20.7762	+	14.1650i	1.26675	+	0.863653i	0.271634	+	0.962401i	$0.412436\pi$
$270$	1.82216	+	1.24233i	0.110893	+	0.0756056i
$271$	−13.2062	+	1.99052i	−0.802220	+	0.120915i	−0.537340	−	0.843366i	$-0.680571\pi$
$271$	−13.2062	+	1.99052i	−0.802220	+	0.120915i	−0.264881	+	0.964281i	$0.585333\pi$
$272$	11.3574	+	14.2417i	0.688642	+	0.863529i
$273$	1.34933	−	0.206391i	0.0816653	−	0.0124914i
$274$	−9.46920	+	11.8740i	−0.572055	+	0.717335i
$275$	−3.40449	+	5.89676i	−0.205299	+	0.355588i
$276$	8.47718	+	14.6829i	0.510267	+	0.883808i
$277$	7.63307	+	1.15050i	0.458627	+	0.0691268i	0.374292	−	0.927311i	$-0.377886\pi$
$277$	7.63307	+	1.15050i	0.458627	+	0.0691268i	0.0843341	+	0.996438i	$0.473124\pi$
$278$	−15.5159	−	14.3966i	−0.930579	−	0.863451i
$279$	−5.68662	+	2.73853i	−0.340449	+	0.163952i
$280$	1.20115	−	5.31602i	0.0717824	−	0.317693i
$281$	14.4897	+	6.97785i	0.864381	+	0.416264i	0.812895	−	0.582410i	$-0.197890\pi$
$281$	14.4897	+	6.97785i	0.864381	+	0.416264i	0.0514855	+	0.998674i	$0.483604\pi$
$282$	4.10092	+	10.4490i	0.244206	+	0.622227i
$283$	1.46162	+	19.5039i	0.0868840	+	1.15939i	0.854843	+	0.518887i	$0.173654\pi$
$283$	1.46162	+	19.5039i	0.0868840	+	1.15939i	−0.767959	+	0.640499i	$0.778727\pi$
$284$	40.8820	−	12.6104i	2.42590	−	0.748291i
$285$	−0.0464818	+	0.620256i	−0.00275334	+	0.0367408i
$286$	−0.801226	−	3.51040i	−0.0473775	−	0.207574i
$287$	2.52323	+	32.7122i	0.148941	+	1.93094i
$288$	5.75068	−	25.1954i	0.338862	−	1.48465i
$289$	−12.4669	−	3.84552i	−0.733346	−	0.226207i
$290$	−0.227080	+	0.578591i	−0.0133346	+	0.0339760i
$291$	−2.78575	+	2.58480i	−0.163304	+	0.151524i
$292$	−29.8587	+	20.3573i	−1.74735	+	1.19132i
$293$	−23.4346			−1.36907			−0.684533	−	0.728982i	$-0.739994\pi$
$293$	−23.4346			−1.36907			−0.684533	+	0.728982i	$0.739994\pi$
$294$	4.66053	−	8.15424i	0.271808	−	0.475565i
$295$	3.85757			0.224597
$296$	−50.3910	+	34.3560i	−2.92892	+	1.99690i
$297$	3.00248	−	2.78589i	0.174221	−	0.161654i
$298$	10.2825	−	26.1994i	0.595651	−	1.51769i
$299$	−6.59264	−	2.03356i	−0.381262	−	0.117604i
$300$	−2.68924	+	11.7823i	−0.155264	+	0.680254i
$301$	8.20505	−	21.0410i	0.472931	−	1.21278i
$302$	8.54487	+	37.4375i	0.491702	+	2.15429i
$303$	0.0857821	−	1.14468i	0.00492805	−	0.0657603i
$304$	36.8168	−	11.3565i	2.11159	−	0.651338i
$305$	0.0299307	+	0.399398i	0.00171383	+	0.0228694i
$306$	−5.16456	−	13.1591i	−0.295238	−	0.752255i
$307$	8.67580	+	4.17805i	0.495154	+	0.238454i	0.664758	−	0.747059i	$-0.268535\pi$
$307$	8.67580	+	4.17805i	0.495154	+	0.238454i	−0.169604	+	0.985512i	$0.554249\pi$
$308$	−15.7368	−	7.53621i	−0.896690	−	0.429416i
$309$	5.78206	−	2.78449i	0.328930	−	0.158404i
$310$	1.26170	+	1.17068i	0.0716596	+	0.0664904i
$311$	−27.9675	−	4.21542i	−1.58589	−	0.239035i	−0.703900	−	0.710299i	$-0.748560\pi$
$311$	−27.9675	−	4.21542i	−1.58589	−	0.239035i	−0.881992	+	0.471265i	$0.843798\pi$
$312$	−1.85371	−	3.21071i	−0.104945	−	0.181771i
$313$	8.20381	−	14.2094i	0.463707	−	0.803164i	−0.535435	−	0.844576i	$-0.679852\pi$
$313$	8.20381	−	14.2094i	0.463707	−	0.803164i	0.999142	+	0.0414123i	$0.0131857\pi$
$314$	−10.5379	+	13.2141i	−0.594688	+	0.745715i
$315$	−1.03279	+	1.79790i	−0.0581913	+	0.101300i
$316$	−44.7127	−	56.0679i	−2.51529	−	3.15407i
$317$	0.474525	−	0.0715231i	0.0266520	−	0.00401714i	−0.135703	−	0.990750i	$-0.543329\pi$
$317$	0.474525	−	0.0715231i	0.0266520	−	0.00401714i	0.162355	+	0.986732i	$0.448091\pi$
$318$	2.42299	+	1.65197i	0.135875	+	0.0926378i
$319$	0.953787	+	0.650281i	0.0534018	+	0.0364087i
$320$	−1.77488	+	0.267519i	−0.0992185	+	0.0149548i
$321$	5.30197	+	6.64846i	0.295927	+	0.371081i
$322$	−39.1631	+	26.8263i	−2.18247	+	1.49497i
$323$	5.21369	−	6.53776i	0.290098	−	0.363771i
$324$	−15.8975	+	27.5352i	−0.883192	+	1.52973i
$325$	−2.45891	−	4.25896i	−0.136396	−	0.236245i
$326$	−23.2838	−	3.50947i	−1.28957	−	0.194371i
$327$	−2.62252	−	2.43334i	−0.145025	−	0.134564i
$328$	80.2857	−	38.6635i	4.43303	−	2.13484i
$329$	−19.9213	+	9.64719i	−1.09830	+	0.531867i
$330$	−0.479796	−	0.231057i	−0.0264119	−	0.0127193i
$331$	−1.17353	−	2.99010i	−0.0645029	−	0.164351i	0.894988	−	0.446090i	$-0.147184\pi$
$331$	−1.17353	−	2.99010i	−0.0645029	−	0.164351i	−0.959491	+	0.281739i	$0.909089\pi$
$332$	0.218305	+	2.91308i	0.0119810	+	0.159876i
$333$	22.1718	−	6.83910i	1.21501	−	0.374780i
$334$	−1.03498	+	13.8108i	−0.0566313	+	0.755693i
$335$	0.0472730	+	0.207116i	0.00258280	+	0.0113160i
$336$	−12.3698	−	1.83685i	−0.674827	−	0.100208i
$337$	6.12670	−	26.8428i	0.333743	−	1.46222i	−0.478079	−	0.878317i	$-0.658667\pi$
$337$	6.12670	−	26.8428i	0.333743	−	1.46222i	0.811821	−	0.583906i	$-0.198476\pi$
$338$	2.48507	+	0.766542i	0.135170	+	0.0416944i
$339$	0.940804	−	2.39713i	0.0510974	−	0.130194i
$340$	−1.99017	+	1.84661i	−0.107932	+	0.100147i
$341$	2.64114	−	1.80070i	0.143026	−	0.0975132i
$342$	−29.8998			−1.61680
$343$	16.7384	+	7.92625i	0.903789	+	0.427977i
$344$	−61.3388			−3.30717
$345$	−0.843070	+	0.574795i	−0.0453893	+	0.0309459i
$346$	21.5726	−	20.0165i	1.15975	−	1.07609i
$347$	−7.91080	+	20.1564i	−0.424674	+	1.08205i	0.545170	+	0.838325i	$0.316465\pi$
$347$	−7.91080	+	20.1564i	−0.424674	+	1.08205i	−0.969844	+	0.243726i	$0.921630\pi$
$348$	1.95788	+	0.603926i	0.104953	+	0.0323738i
$349$	3.67481	−	16.1004i	0.196708	−	0.861835i	−0.776171	−	0.630522i	$-0.782841\pi$
$349$	3.67481	−	16.1004i	0.196708	−	0.861835i	0.972879	−	0.231313i	$-0.0743022\pi$
$350$	−33.4704	−	4.97019i	−1.78907	−	0.265668i
$351$	0.658274	+	2.88409i	0.0351360	+	0.153941i
$352$	−0.978102	+	13.0519i	−0.0521330	+	0.695667i
$353$	−26.6201	+	8.21121i	−1.41684	+	0.437038i	−0.906235	−	0.422775i	$-0.861056\pi$
$353$	−26.6201	+	8.21121i	−1.41684	+	0.437038i	−0.510609	+	0.859813i	$0.670580\pi$
$354$	−1.34929	−	18.0050i	−0.0717140	−	0.956957i
$355$	0.940682	+	2.39682i	0.0499262	+	0.127210i
$356$	−35.7136	−	17.1988i	−1.89282	−	0.911534i
$357$	−2.44278	+	1.18295i	−0.129286	+	0.0626085i
$358$	−46.5491	+	22.4169i	−2.46020	+	1.18477i
$359$	−0.798197	−	0.740619i	−0.0421272	−	0.0390884i	0.658828	−	0.752293i	$-0.271052\pi$
$359$	−0.798197	−	0.740619i	−0.0421272	−	0.0390884i	−0.700956	+	0.713205i	$0.747243\pi$
$360$	5.56853	+	0.839321i	0.293487	+	0.0442361i
$361$	0.656593	+	1.13725i	0.0345575	+	0.0598554i
$362$	−21.1920	+	36.7057i	−1.11383	+	1.92921i
$363$	2.92180	−	3.66383i	0.153355	−	0.192301i
$364$	10.3968	−	7.12172i	0.544943	−	0.373280i
$365$	−1.35603	−	1.70041i	−0.0709780	−	0.0890036i
$366$	1.85370	−	0.279400i	0.0968945	−	0.0146045i
$367$	−16.4530	−	11.2175i	−0.858841	−	0.585548i	0.0518415	−	0.998655i	$-0.483491\pi$
$367$	−16.4530	−	11.2175i	−0.858841	−	0.585548i	−0.910682	+	0.413108i	$0.864443\pi$
$368$	52.2226	+	35.6047i	2.72229	+	1.85603i
$369$	−33.5228	+	5.05275i	−1.74513	+	0.263036i
$370$	−3.94496	−	4.94682i	−0.205089	−	0.257173i
$371$	−2.88041	+	5.01425i	−0.149543	+	0.260327i
$372$	3.53746	−	4.43583i	0.183409	−	0.229987i
$373$	4.02054	−	6.96377i	0.208175	−	0.360570i	−0.742964	−	0.669331i	$-0.766581\pi$
$373$	4.02054	−	6.96377i	0.208175	−	0.360570i	0.951140	+	0.308761i	$0.0999142\pi$
$374$	3.57969	+	6.20020i	0.185101	+	0.320605i
$375$	−1.45044	−	0.218619i	−0.0749006	−	0.0112894i
$376$	44.0687	+	40.8898i	2.27267	+	2.10873i
$377$	−0.751183	+	0.361751i	−0.0386879	+	0.0186311i
$378$	18.3579	+	8.79143i	0.944230	+	0.452182i
$379$	20.9913	+	10.1089i	1.07825	+	0.519259i	0.886758	−	0.462234i	$-0.152952\pi$
$379$	20.9913	+	10.1089i	1.07825	+	0.519259i	0.191495	+	0.981494i	$0.438666\pi$
$380$	2.09792	+	5.34540i	0.107621	+	0.274213i
$381$	0.385581	+	5.14522i	0.0197539	+	0.263597i
$382$	−7.98848	+	2.46412i	−0.408726	+	0.126075i
$383$	−0.451245	+	6.02145i	−0.0230576	+	0.307682i	0.973737	+	0.227676i	$0.0731128\pi$
$383$	−0.451245	+	6.02145i	−0.0230576	+	0.307682i	−0.996794	+	0.0800054i	$0.974506\pi$
$384$	−0.301116	−	1.31927i	−0.0153662	−	0.0673239i
$385$	0.381510	−	0.978342i	0.0194435	−	0.0498609i
$386$	1.93122	−	8.46123i	0.0982966	−	0.430665i
$387$	22.2992	+	6.87839i	1.13353	+	0.349648i
$388$	−12.8177	+	32.6589i	−0.650718	+	1.65800i
$389$	13.7875	−	12.7930i	0.699056	−	0.648629i	−0.248347	−	0.968671i	$-0.579887\pi$
$389$	13.7875	−	12.7930i	0.699056	−	0.648629i	0.947403	+	0.320042i	$0.103697\pi$
$390$	0.317792	−	0.216667i	0.0160920	−	0.0109713i
$391$	13.7179			0.693743
$392$	3.54009	−	50.1763i	0.178802	−	2.53429i
$393$	−6.65924			−0.335914
$394$	31.9354	−	21.7732i	1.60888	−	1.09692i
$395$	3.16382	−	2.93560i	0.159189	−	0.147706i
$396$	6.58675	−	16.7828i	0.330997	−	0.843366i
$397$	−23.5157	−	7.25363i	−1.18022	−	0.364049i	−0.358274	−	0.933616i	$-0.616635\pi$
$397$	−23.5157	−	7.25363i	−1.18022	−	0.364049i	−0.821945	+	0.569567i	$0.807111\pi$
$398$	6.91105	−	30.2793i	0.346419	−	1.51776i
$399$	0.441493	+	5.72371i	0.0221023	+	0.286544i
$400$	10.0254	+	43.9241i	0.501269	+	2.19620i
$401$	0.821356	−	10.9602i	0.0410165	−	0.547328i	−0.938410	−	0.345525i	$-0.887701\pi$
$401$	0.821356	−	10.9602i	0.0410165	−	0.547328i	0.979426	−	0.201803i	$-0.0646800\pi$
$402$	0.950171	−	0.293089i	0.0473902	−	0.0146179i
$403$	0.172533	+	2.30229i	0.00859446	+	0.114685i
$404$	−3.87170	−	9.86494i	−0.192624	−	0.490799i
$405$	−1.72403	−	0.830247i	−0.0856675	−	0.0412553i
$406$	−1.26432	+	5.59561i	−0.0627473	+	0.277705i
$407$	−10.5874	+	5.09860i	−0.524796	+	0.252728i
$408$	5.40377	+	5.01397i	0.267527	+	0.248228i
$409$	5.97165	+	0.900081i	0.295279	+	0.0445062i	0.295011	−	0.955494i	$-0.404677\pi$
$409$	5.97165	+	0.900081i	0.295279	+	0.0445062i	0.000267886		1.00000i	$0.499915\pi$
$410$	4.62236	+	8.00617i	0.228282	+	0.395397i
$411$	−1.50651	+	2.60935i	−0.0743105	+	0.128710i
$412$	36.9406	−	46.3221i	1.81993	−	2.28212i
$413$	35.1942	−	5.38323i	1.73179	−	0.264891i
$414$	−30.5822	−	38.3488i	−1.50303	−	1.88474i
$415$	−0.173847	+	0.0262032i	−0.00853379	+	0.00128626i
$416$	−7.81060	−	5.32518i	−0.382946	−	0.261088i
$417$	−3.46948	−	2.36545i	−0.169901	−	0.115836i
$418$	14.9738	−	2.25693i	0.732391	−	0.110390i
$419$	16.9663	+	21.2751i	0.828859	+	1.03936i	0.998549	+	0.0538583i	$0.0171519\pi$
$419$	16.9663	+	21.2751i	0.828859	+	1.03936i	−0.169690	+	0.985497i	$0.554277\pi$
$420$	0.135229	−	1.85892i	0.00659848	−	0.0907058i
$421$	15.8348	−	19.8563i	0.771743	−	0.967735i	−0.228240	−	0.973605i	$-0.573297\pi$
$421$	15.8348	−	19.8563i	0.771743	−	0.967735i	0.999983	+	0.00587008i	$0.00186852\pi$
$422$	6.60199	−	11.4350i	0.321380	−	0.556646i
$423$	−11.4355	−	19.8069i	−0.556013	−	0.963043i
$424$	15.5304	+	2.34082i	0.754221	+	0.113680i
$425$	7.16802	+	6.65095i	0.347700	+	0.322618i
$426$	10.8580	−	5.22894i	0.526072	−	0.253343i
$427$	0.830427	+	3.60210i	0.0401872	+	0.174318i
$428$	70.7327	+	34.0631i	3.41899	+	1.64650i
$429$	−0.260976	−	0.664955i	−0.0126000	−	0.0321043i
$430$	−0.475550	−	6.34578i	−0.0229331	−	0.306021i
$431$	−9.46829	+	2.92058i	−0.456071	+	0.140679i	−0.514275	−	0.857625i	$-0.671939\pi$
$431$	−9.46829	+	2.92058i	−0.456071	+	0.140679i	0.0582036	+	0.998305i	$0.481463\pi$
$432$	2.02530	−	27.0257i	0.0974421	−	1.30027i
$433$	7.83506	+	34.3276i	0.376529	+	1.64968i	0.707998	+	0.706215i	$0.249599\pi$
$433$	7.83506	+	34.3276i	0.376529	+	1.64968i	−0.331469	+	0.943466i	$0.607544\pi$
$434$	13.1447	+	8.91993i	0.630964	+	0.428170i
$435$	−0.0274391	+	0.120218i	−0.00131560	+	0.00576403i
$436$	−31.5609	−	9.73525i	−1.51149	−	0.466234i
$437$	10.6003	−	27.0092i	0.507082	−	1.29202i
$438$	−7.46228	+	6.92398i	−0.356562	+	0.330841i
$439$	2.92715	−	1.99570i	0.139705	−	0.0952496i	−0.491451	−	0.870905i	$-0.663533\pi$
$439$	2.92715	−	1.99570i	0.139705	−	0.0952496i	0.631156	+	0.775656i	$0.282581\pi$
$440$	−2.85206			−0.135967
$441$	−6.91363	+	17.8442i	−0.329220	+	0.849723i
$442$	−5.17090			−0.245954
$443$	−0.524829	+	0.357822i	−0.0249354	+	0.0170007i	−0.575724	−	0.817644i	$-0.695280\pi$
$443$	−0.524829	+	0.357822i	−0.0249354	+	0.0170007i	0.550788	+	0.834645i	$0.314327\pi$
$444$	−15.2894	+	14.1864i	−0.725601	+	0.673259i
$445$	0.871563	−	2.22071i	0.0413161	−	0.105272i
$446$	−2.59630	−	0.800853i	−0.122939	−	0.0379215i
$447$	1.24248	−	5.44366i	0.0587673	−	0.257476i
$448$	−15.8196	+	4.91752i	−0.747404	+	0.232331i
$449$	−3.00975	−	13.1866i	−0.142039	−	0.622313i	−0.994960	−	0.100273i	$-0.968028\pi$
$449$	−3.00975	−	13.1866i	−0.142039	−	0.622313i	0.852921	−	0.522040i	$-0.174829\pi$
$450$	2.61284	−	34.8659i	0.123170	−	1.64359i
$451$	16.4067	−	5.06081i	0.772564	−	0.238304i
$452$	−1.77664	−	23.7076i	−0.0835659	−	1.11511i
$453$	2.78324	+	7.09158i	0.130768	+	0.333191i
$454$	−5.87823	−	2.83081i	−0.275879	−	0.132856i
$455$	0.474170	+	0.591937i	0.0222294	+	0.0277504i
$456$	14.0477	−	6.76502i	0.657844	−	0.316801i
$457$	24.8214	+	23.0309i	1.16110	+	1.07734i	0.995843	+	0.0910887i	$0.0290347\pi$
$457$	24.8214	+	23.0309i	1.16110	+	1.07734i	0.165253	+	0.986251i	$0.447156\pi$
$458$	−6.01620	−	0.906797i	−0.281119	−	0.0423718i
$459$	−2.94101	−	5.09398i	−0.137275	−	0.237767i
$460$	−4.71010	+	8.15813i	−0.219610	+	0.380375i
$461$	−2.30078	+	2.88509i	−0.107158	+	0.134372i	−0.832518	−	0.553997i	$-0.813102\pi$
$461$	−2.30078	+	2.88509i	−0.107158	+	0.134372i	0.725360	+	0.688369i	$0.241673\pi$
$462$	−4.69981	−	1.43848i	−0.218655	−	0.0669240i
$463$	−18.0400	−	22.6214i	−0.838388	−	1.05131i	−0.997942	−	0.0641165i	$-0.979577\pi$
$463$	−18.0400	−	22.6214i	−0.838388	−	1.05131i	0.159554	−	0.987189i	$-0.448994\pi$
$464$	7.55293	−	1.13842i	0.350636	−	0.0528498i
$465$	0.282126	+	0.192350i	0.0130833	+	0.00892004i
$466$	−6.51798	−	4.44388i	−0.301939	−	0.205859i
$467$	0.540911	−	0.0815292i	0.0250304	−	0.00377272i	−0.136515	−	0.990638i	$-0.543590\pi$
$467$	0.540911	−	0.0815292i	0.0250304	−	0.00377272i	0.161546	+	0.986865i	$0.448352\pi$
$468$	8.11882	+	10.1807i	0.375292	+	0.470602i
$469$	0.720320	+	1.82364i	0.0332613	+	0.0842077i
$470$	−3.88858	+	4.87612i	−0.179367	+	0.224919i
$471$	−1.67653	+	2.90384i	−0.0772506	+	0.133802i
$472$	−48.3496	−	83.7440i	−2.22547	−	3.85463i
$473$	−11.6866	−	1.76147i	−0.537350	−	0.0809924i
$474$	−14.8084	−	13.7402i	−0.680173	−	0.631108i
$475$	18.6341	−	8.97369i	0.854990	−	0.411741i
$476$	−15.5802	+	19.6246i	−0.714117	+	0.899494i
$477$	−5.38343	−	2.59252i	−0.246490	−	0.118704i
$478$	2.76493	+	7.04492i	0.126465	+	0.322227i
$479$	−2.76106	−	36.8437i	−0.126156	−	1.68343i	−0.597801	−	0.801645i	$-0.703959\pi$
$479$	−2.76106	−	36.8437i	−0.126156	−	1.68343i	0.471645	−	0.881789i	$-0.343660\pi$
$480$	−1.33600	+	0.412100i	−0.0609796	+	0.0188097i
$481$	0.634255	−	8.46354i	0.0289195	−	0.385904i
$482$	−16.2439	−	71.1691i	−0.739889	−	3.24166i
$483$	−6.88954	+	6.42058i	−0.313485	+	0.292147i
$484$	9.62709	−	42.1790i	0.437595	−	1.91723i
$485$	−2.01767	−	0.622369i	−0.0916177	−	0.0282603i
$486$	−11.7041	+	29.8216i	−0.530909	+	1.35273i
$487$	−20.4846	+	19.0069i	−0.928244	+	0.861285i	−0.990603	−	0.136769i	$-0.956328\pi$
$487$	−20.4846	+	19.0069i	−0.928244	+	0.861285i	0.0623585	+	0.998054i	$0.480138\pi$
$488$	8.29537	−	5.65569i	0.375514	−	0.256021i
$489$	−4.67142			−0.211249
$490$	5.21842	−	0.0227708i	0.235744	−	0.00102868i
$491$	39.5850			1.78645			0.893223	−	0.449615i	$-0.148439\pi$
$491$	39.5850			1.78645			0.893223	+	0.449615i	$0.148439\pi$
$492$	25.1791	−	17.1668i	1.13516	−	0.773941i
$493$	1.21524	−	1.12758i	0.0547317	−	0.0507836i
$494$	−3.99575	+	10.1810i	−0.179777	+	0.458065i
$495$	1.03684	+	0.319824i	0.0466026	+	0.0143750i
$496$	4.70656	−	20.6208i	0.211331	−	0.925901i
$497$	11.9270	+	20.5544i	0.534998	+	0.921992i
$498$	0.183110	+	0.802255i	0.00820533	+	0.0359499i
$499$	1.49046	−	19.8888i	0.0667222	−	0.890346i	−0.858960	−	0.512043i	$-0.828889\pi$
$499$	1.49046	−	19.8888i	0.0667222	−	0.890346i	0.925682	−	0.378303i	$-0.123492\pi$
$500$	−12.9403	+	3.99156i	−0.578709	+	0.178508i
$501$	0.205328	+	2.73991i	0.00917336	+	0.122410i
$502$	27.3686	+	69.7340i	1.22152	+	3.11238i
$503$	16.2718	+	7.83610i	0.725525	+	0.349395i	0.759923	−	0.650014i	$-0.225237\pi$
$503$	16.2718	+	7.83610i	0.725525	+	0.349395i	−0.0343972	+	0.999408i	$0.510951\pi$
$504$	51.9752	−	0.113398i	2.31516	−	0.00505114i
$505$	0.574632	−	0.276728i	0.0255708	−	0.0123142i
$506$	18.2102	+	16.8966i	0.809541	+	0.751145i
$507$	0.510169	+	0.0768956i	0.0226574	+	0.00341505i
$508$	23.8173	+	41.2527i	1.05672	+	1.83029i
$509$	10.6926	−	18.5202i	0.473942	−	0.820892i	−0.525613	−	0.850724i	$-0.676164\pi$
$509$	10.6926	−	18.5202i	0.473942	−	0.820892i	0.999555	+	0.0298319i	$0.00949720\pi$
$510$	−0.476823	+	0.597918i	−0.0211141	+	0.0264762i
$511$	−14.7445	−	13.6212i	−0.652260	−	0.602566i
$512$	−28.0945	−	35.2294i	−1.24161	−	1.55693i
$513$	−12.3022	+	1.85426i	−0.543155	+	0.0818674i
$514$	−44.4216	−	30.2862i	−1.95935	−	1.33587i
$515$	2.94616	+	2.00866i	0.129823	+	0.0885121i
$516$	−20.7426	+	3.12645i	−0.913144	+	0.137634i
$517$	7.22196	+	9.05605i	0.317621	+	0.398285i
$518$	−42.8947	−	39.6267i	−1.88469	−	1.74110i
$519$	3.64012	−	4.56456i	0.159783	−	0.200362i
$520$	1.02996	−	1.78394i	0.0451667	−	0.0782309i
$521$	−1.81855	−	3.14983i	−0.0796722	−	0.137996i	0.823436	−	0.567409i	$-0.192054\pi$
$521$	−1.81855	−	3.14983i	−0.0796722	−	0.137996i	−0.903109	+	0.429412i	$0.858721\pi$
$522$	−5.86140	−	0.883465i	−0.256547	−	0.0386682i
$523$	28.4024	+	26.3535i	1.24195	+	1.15236i	0.982432	+	0.186621i	$0.0597538\pi$
$523$	28.4024	+	26.3535i	1.24195	+	1.15236i	0.259517	+	0.965739i	$0.416437\pi$
$524$	−55.3907	+	26.6747i	−2.41975	+	1.16529i
$525$	−6.71294	+	0.0146461i	−0.292977	+	0.000639207i
$526$	−12.8456	−	6.18611i	−0.560094	−	0.269727i
$527$	−1.67712	−	4.27324i	−0.0730567	−	0.186145i
$528$	0.489051	+	6.52593i	0.0212832	+	0.284005i
$529$	23.5054	−	7.25046i	1.02197	−	0.315237i
$530$	−0.121765	+	1.62483i	−0.00528911	+	0.0705783i
$531$	8.18623	+	35.8662i	0.355252	+	1.55646i
$532$	26.5996	+	45.8406i	1.15324	+	1.98744i
$533$	−2.75943	+	12.0899i	−0.119524	+	0.523670i
$534$	−10.6699	−	3.29123i	−0.461732	−	0.142425i
$535$	−1.72618	+	4.39822i	−0.0746291	+	0.190152i
$536$	3.90378	−	3.62218i	0.168618	−	0.156454i
$537$	−8.46885	+	5.77396i	−0.365458	+	0.249165i
$538$	65.3935			2.81932
$539$	2.11539	−	9.45820i	0.0911164	−	0.407393i
$540$	4.03925			0.173821
$541$	−7.79917	+	5.31739i	−0.335313	+	0.228612i	−0.719257	−	0.694744i	$-0.755518\pi$
$541$	−7.79917	+	5.31739i	−0.335313	+	0.228612i	0.383945	+	0.923356i	$0.374565\pi$
$542$	−25.4604	+	23.6238i	−1.09362	+	1.01473i
$543$	−3.07198	+	7.82728i	−0.131831	+	0.335901i
$544$	17.9611	+	5.54028i	0.770078	+	0.237538i
$545$	0.442316	−	1.93791i	0.0189467	−	0.0830111i
$546$	2.59698	−	2.42021i	0.111141	−	0.103576i
$547$	7.84137	+	34.3553i	0.335273	+	1.46893i	0.808767	+	0.588130i	$0.200135\pi$
$547$	7.84137	+	34.3553i	0.335273	+	1.46893i	−0.473494	+	0.880797i	$0.657007\pi$
$548$	−2.07874	+	27.7388i	−0.0887992	+	1.18494i
$549$	−3.64993	+	1.12585i	−0.155775	+	0.0480502i
$550$	1.32328	+	17.6580i	0.0564250	+	0.752939i
$551$	−1.28103	−	3.26401i	−0.0545737	−	0.139052i
$552$	23.0450	+	11.0979i	0.980859	+	0.472357i
$553$	24.7682	−	31.1978i	1.05325	−	1.32666i
$554$	18.0868	−	8.71014i	0.768434	−	0.370058i
$555$	−0.920164	−	0.853787i	−0.0390588	−	0.0362413i
$556$	−38.3339	−	5.77790i	−1.62572	−	0.245038i
$557$	17.6453	+	30.5625i	0.747654	+	1.29498i	0.948944	+	0.315444i	$0.102153\pi$
$557$	17.6453	+	30.5625i	0.747654	+	1.29498i	−0.201290	+	0.979532i	$0.564513\pi$
$558$	−8.20709	+	14.2151i	−0.347434	+	0.601773i
$559$	5.32213	−	6.67374i	0.225102	−	0.282269i
$560$	−2.55259	−	6.46241i	−0.107867	−	0.273087i
$561$	0.885568	+	1.11047i	0.0373887	+	0.0468840i
$562$	41.3566	−	6.23351i	1.74452	−	0.262945i
$563$	3.96701	+	2.70466i	0.167189	+	0.113988i	0.644024	−	0.765005i	$-0.277264\pi$
$563$	3.96701	+	2.70466i	0.167189	+	0.113988i	−0.476835	+	0.878993i	$0.658216\pi$
$564$	16.9867	+	11.5813i	0.715267	+	0.487661i
$565$	1.41482	−	0.213250i	0.0595219	−	0.00897148i
$566$	31.7133	+	39.7672i	1.33301	+	1.67154i
$567$	−16.8876	−	5.16881i	−0.709212	−	0.217069i
$568$	40.2423	−	50.4622i	1.68853	−	2.11735i
$569$	−6.47087	+	11.2079i	−0.271273	+	0.469858i	−0.969188	−	0.246322i	$-0.920778\pi$
$569$	−6.47087	+	11.2079i	−0.271273	+	0.469858i	0.697915	+	0.716180i	$0.254111\pi$
$570$	0.808782	+	1.40085i	0.0338762	+	0.0586752i
$571$	−29.0521	−	4.37889i	−1.21579	−	0.183251i	−0.490344	−	0.871529i	$-0.663129\pi$
$571$	−29.0521	−	4.37889i	−1.21579	−	0.183251i	−0.725447	+	0.688278i	$0.758367\pi$
$572$	−4.83436	−	4.48563i	−0.202135	−	0.187553i
$573$	−1.49426	+	0.719600i	−0.0624238	+	0.0300617i
$574$	53.3442	+	66.5930i	2.22655	+	2.77954i
$575$	30.5688	+	14.7212i	1.27481	+	0.613915i
$576$	−6.25378	−	15.9344i	−0.260574	−	0.663933i
$577$	−3.20673	−	42.7908i	−0.133498	−	1.78140i	−0.515152	−	0.857099i	$-0.672264\pi$
$577$	−3.20673	−	42.7908i	−0.133498	−	1.78140i	0.381654	−	0.924305i	$-0.375355\pi$
$578$	−32.4214	+	10.0007i	−1.34855	+	0.415974i
$579$	0.128669	−	1.71697i	0.00534730	−	0.0713548i
$580$	0.253321	+	1.10987i	0.0105186	+	0.0460850i
$581$	−1.54951	+	0.481664i	−0.0642843	+	0.0199828i
$582$	−2.19914	+	9.63507i	−0.0911574	+	0.399386i
$583$	2.89170	+	0.891972i	0.119762	+	0.0369417i
$584$	−19.9181	+	50.7505i	−0.824217	+	2.10007i
$585$	−0.574479	+	0.533039i	−0.0237518	+	0.0220384i
$586$	−50.3545	+	34.3311i	−2.08012	+	1.41820i
$587$	2.14757			0.0886396			0.0443198	−	0.999017i	$-0.485888\pi$
$587$	2.14757			0.0886396			0.0443198	+	0.999017i	$0.485888\pi$
$588$	−1.36036	−	17.1483i	−0.0561004	−	0.707185i
$589$	−9.70958			−0.400076
$590$	8.28885	−	5.65124i	0.341247	−	0.232658i
$591$	5.62106	−	5.21559i	0.231220	−	0.214541i
$592$	−28.4069	+	72.3796i	−1.16752	+	2.97478i
$593$	−7.12310	−	2.19719i	−0.292511	−	0.0902277i	0.145027	−	0.989428i	$-0.453673\pi$
$593$	−7.12310	−	2.19719i	−0.292511	−	0.0902277i	−0.437538	+	0.899200i	$0.644149\pi$
$594$	2.37023	−	10.3847i	0.0972517	−	0.426088i
$595$	−1.24785	−	0.846785i	−0.0511567	−	0.0347148i
$596$	−11.4708	−	50.2566i	−0.469860	−	2.05859i
$597$	0.460453	−	6.14432i	0.0188451	−	0.251470i
$598$	−17.1449	+	5.28849i	−0.701105	+	0.216262i
$599$	1.36526	+	18.2181i	0.0557830	+	0.744372i	0.953036	+	0.302856i	$0.0979402\pi$
$599$	1.36526	+	18.2181i	0.0557830	+	0.744372i	−0.897253	+	0.441516i	$0.854441\pi$
$600$	6.66105	+	16.9721i	0.271936	+	0.692882i
$601$	38.3761	+	18.4810i	1.56540	+	0.753855i	0.997595	−	0.0693118i	$-0.0220803\pi$
$601$	38.3761	+	18.4810i	1.56540	+	0.753855i	0.567800	+	0.823166i	$0.307795\pi$
$602$	−13.1941	−	57.2314i	−0.537753	−	2.33258i
$603$	−1.82537	+	0.879051i	−0.0743347	+	0.0357977i
$604$	51.5572	+	47.8381i	2.09783	+	1.94650i
$605$	2.57468	+	0.388070i	0.104675	+	0.0157773i
$606$	−1.49261	−	2.58527i	−0.0606330	−	0.105019i
$607$	−23.6731	+	41.0029i	−0.960860	+	1.66426i	−0.240510	+	0.970647i	$0.577315\pi$
$607$	−23.6731	+	41.0029i	−0.960860	+	1.66426i	−0.720349	+	0.693611i	$0.756019\pi$
$608$	24.7875	−	31.0826i	1.00527	−	1.26057i
$609$	−0.0825733	+	1.13509i	−0.00334604	+	0.0459962i
$610$	0.649420	+	0.814347i	0.0262942	+	0.0329719i
$611$	−8.27253	+	1.24688i	−0.334671	+	0.0504435i
$612$	−21.3924	−	14.5851i	−0.864738	−	0.589568i
$613$	−28.7059	−	19.5714i	−1.15942	−	0.790480i	−0.178320	−	0.983973i	$-0.557066\pi$
$613$	−28.7059	−	19.5714i	−1.15942	−	0.790480i	−0.981102	+	0.193492i	$0.938019\pi$
$614$	24.7626	−	3.73236i	0.999338	−	0.150626i
$615$	1.14351	+	1.43392i	0.0461109	+	0.0578212i
$616$	−26.0205	+	3.98004i	−1.04840	+	0.160360i
$617$	12.2047	−	15.3043i	0.491344	−	0.616126i	−0.472908	−	0.881112i	$-0.656796\pi$
$617$	12.2047	−	15.3043i	0.491344	−	0.616126i	0.964252	+	0.264985i	$0.0853671\pi$
$618$	8.34482	−	14.4537i	0.335678	−	0.581411i
$619$	10.9182	+	18.9108i	0.438838	+	0.760090i	0.997600	−	0.0692382i	$-0.0220568\pi$
$619$	10.9182	+	18.9108i	0.438838	+	0.760090i	−0.558762	+	0.829328i	$0.688724\pi$
$620$	3.11718	+	0.469840i	0.125189	+	0.0188692i
$621$	−14.9612	−	13.8819i	−0.600371	−	0.557063i
$622$	−66.2699	+	31.9139i	−2.65718	+	1.27963i
$623$	4.85263	−	21.4767i	0.194417	−	0.860444i
$624$	−4.25852	−	2.05080i	−0.170477	−	0.0820975i
$625$	8.68566	+	22.1307i	0.347427	+	0.885228i
$626$	−3.18872	−	42.5505i	−0.127447	−	1.70066i
$627$	2.87071	−	0.885498i	0.114645	−	0.0353634i
$628$	−2.31334	+	30.8694i	−0.0923124	+	1.23182i
$629$	3.75518	+	16.4525i	0.149729	+	0.656004i
$630$	0.414688	+	5.37620i	0.0165215	+	0.214193i
$631$	−3.67424	+	16.0979i	−0.146269	+	0.640846i	0.847633	+	0.530582i	$0.178027\pi$
$631$	−3.67424	+	16.0979i	−0.146269	+	0.640846i	−0.993902	+	0.110264i	$0.964830\pi$
$632$	−103.383	−	31.8895i	−4.11236	−	1.26850i
$633$	0.957019	−	2.43845i	0.0380381	−	0.0969195i
$634$	0.914842	−	0.848849i	0.0363330	−	0.0337121i
$635$	−2.36867	+	1.61493i	−0.0939976	+	0.0640865i
$636$	5.37114			0.212980
$637$	5.15209	+	4.73877i	0.204133	+	0.187757i
$638$	3.00207			0.118853
$639$	−20.2884	+	13.8324i	−0.802598	+	0.547202i
$640$	0.551158	−	0.511399i	0.0217864	−	0.0202148i
$641$	−12.2009	+	31.0873i	−0.481906	+	1.22788i	0.458766	+	0.888557i	$0.348292\pi$
$641$	−12.2009	+	31.0873i	−0.481906	+	1.22788i	−0.940672	+	0.339318i	$0.889804\pi$
$642$	21.1323	+	6.51844i	0.834024	+	0.257262i
$643$	−1.25770	+	5.51036i	−0.0495990	+	0.217307i	−0.993654	−	0.112481i	$-0.964120\pi$
$643$	−1.25770	+	5.51036i	−0.0495990	+	0.217307i	0.944055	+	0.329788i	$0.106977\pi$
$644$	−31.5875	+	81.0028i	−1.24472	+	3.19196i
$645$	−0.280924	−	1.23081i	−0.0110614	−	0.0484631i
$646$	1.62512	−	21.6858i	0.0639396	−	0.853215i
$647$	−26.7860	+	8.26239i	−1.05307	+	0.324828i	−0.772505	−	0.635008i	$-0.780997\pi$
$647$	−26.7860	+	8.26239i	−1.05307	+	0.324828i	−0.280561	+	0.959836i	$0.590521\pi$
$648$	3.58458	+	47.8329i	0.140816	+	1.87905i
$649$	−6.80694	−	17.3438i	−0.267196	−	0.680804i
$650$	−11.5228	−	5.54908i	−0.451961	−	0.217653i
$651$	2.84237	+	1.36118i	0.111401	+	0.0533490i
$652$	−38.8563	+	18.7122i	−1.52173	+	0.732826i
$653$	−10.9376	−	10.1486i	−0.428020	−	0.397145i	0.436531	−	0.899689i	$-0.356207\pi$
$653$	−10.9376	−	10.1486i	−0.428020	−	0.397145i	−0.864551	+	0.502544i	$0.832397\pi$
$654$	−9.19983	−	1.38665i	−0.359742	−	0.0542224i
$655$	−1.85001	−	3.20430i	−0.0722857	−	0.125203i
$656$	56.8037	−	98.3868i	2.21781	−	3.84136i
$657$	12.9321	−	16.2163i	0.504529	−	0.632659i
$658$	−28.6724	+	49.9133i	−1.11777	+	1.94582i
$659$	22.3619	+	28.0409i	0.871096	+	1.09232i	0.994985	+	0.100023i	$0.0318917\pi$
$659$	22.3619	+	28.0409i	0.871096	+	1.09232i	−0.123890	+	0.992296i	$0.539537\pi$
$660$	−0.964469	+	0.145370i	−0.0375419	+	0.00565853i
$661$	22.8950	+	15.6096i	0.890513	+	0.607142i	0.919782	−	0.392430i	$-0.128365\pi$
$661$	22.8950	+	15.6096i	0.890513	+	0.607142i	−0.0292685	+	0.999572i	$0.509318\pi$
$662$	−6.90200	−	4.70570i	−0.268254	−	0.182892i
$663$	−1.01439	+	0.152895i	−0.0393957	+	0.00593794i
$664$	2.74778	+	3.44561i	0.106635	+	0.133716i
$665$	−2.63149	+	1.80254i	−0.102045	+	0.0698997i
$666$	37.6219	−	47.1764i	1.45782	−	1.82805i
$667$	2.87608	−	4.98152i	0.111362	−	0.192885i
$668$	12.6831	+	21.9677i	0.490723	+	0.849956i
$669$	−0.533005	−	0.0803375i	−0.0206071	−	0.00310603i
$670$	0.404996	+	0.375782i	0.0156464	+	0.0145177i
$671$	1.74289	−	0.839333i	0.0672836	−	0.0324021i
$672$	−11.6137	+	5.62413i	−0.448010	+	0.216956i
$673$	13.6589	+	6.57776i	0.526511	+	0.253554i	0.678204	−	0.734873i	$-0.262758\pi$
$673$	13.6589	+	6.57776i	0.526511	+	0.253554i	−0.151694	+	0.988428i	$0.548473\pi$
$674$	−26.1595	−	66.6532i	−1.00763	−	2.56739i
$675$	−1.08719	−	14.5075i	−0.0418458	−	0.558394i
$676$	4.55154	−	1.40396i	0.175059	−	0.0539986i
$677$	−0.407566	+	5.43860i	−0.0156641	+	0.209022i	0.983880	+	0.178830i	$0.0572311\pi$
$677$	−0.407566	+	5.43860i	−0.0156641	+	0.209022i	−0.999544	+	0.0301926i	$0.990388\pi$
$678$	−1.49020	−	6.52901i	−0.0572310	−	0.250745i
$679$	−19.2765	−	2.86247i	−0.739765	−	0.109852i
$680$	−0.911406	+	3.99313i	−0.0349508	+	0.153129i
$681$	−1.23685	−	0.381519i	−0.0473963	−	0.0146198i
$682$	3.03709	−	7.73839i	0.116296	−	0.296318i
$683$	−22.3425	+	20.7309i	−0.854914	+	0.793244i	−0.980020	−	0.198899i	$-0.936263\pi$
$683$	−22.3425	+	20.7309i	−0.854914	+	0.793244i	0.125106	+	0.992143i	$0.460073\pi$
$684$	−45.2474	+	30.8492i	−1.73008	+	1.17955i
$685$	−1.67409			−0.0639639
$686$	47.5779	−	7.49003i	1.81653	−	0.285970i
$687$	−1.20703			−0.0460510
$688$	−64.6128	+	44.0523i	−2.46334	+	1.67948i
$689$	−1.60219	+	1.48662i	−0.0610387	+	0.0566356i
$690$	−0.969462	+	2.47015i	−0.0369068	+	0.0940370i
$691$	21.8029	+	6.72529i	0.829420	+	0.255842i	0.680260	−	0.732971i	$-0.261867\pi$
$691$	21.8029	+	6.72529i	0.829420	+	0.255842i	0.149160	+	0.988813i	$0.452343\pi$
$692$	11.9939	−	52.5486i	0.455938	−	1.99760i
$693$	9.90584	+	1.47097i	0.376292	+	0.0558775i
$694$	12.5305	+	54.8995i	0.475650	+	2.08396i
$695$	0.174354	−	2.32659i	0.00661363	−	0.0882528i
$696$	2.95373	−	0.911105i	0.111961	−	0.0345354i
$697$	−1.84262	−	24.5881i	−0.0697942	−	0.931339i
$698$	−15.6905	−	39.9788i	−0.593895	−	1.51322i
$699$	−1.41005	−	0.679044i	−0.0533330	−	0.0256838i
$700$	−55.7787	+	27.0117i	−2.10824	+	1.02095i
$701$	−9.92005	+	4.77724i	−0.374675	+	0.180434i	−0.611738	−	0.791060i	$-0.709529\pi$
$701$	−9.92005	+	4.77724i	−0.374675	+	0.180434i	0.237063	+	0.971494i	$0.423815\pi$
$702$	5.63955	+	5.23274i	0.212851	+	0.197497i
$703$	35.2951	+	5.31989i	1.33118	+	0.200643i
$704$	4.33466	+	7.50785i	0.163369	+	0.282963i
$705$	−0.618655	+	1.07154i	−0.0232999	+	0.0403566i
$706$	−45.1699	+	56.6413i	−1.69999	+	2.13172i
$707$	4.85642	−	3.32660i	0.182644	−	0.125109i
$708$	−20.6186	−	25.8549i	−0.774895	−	0.971687i
$709$	43.1823	−	6.50868i	1.62175	−	0.244439i	0.725573	−	0.688145i	$-0.241575\pi$
$709$	43.1823	−	6.50868i	1.62175	−	0.244439i	0.896172	+	0.443706i	$0.146337\pi$
$710$	5.53254	+	3.77202i	0.207633	+	0.141561i
$711$	34.0081	+	23.1863i	1.27540	+	0.869554i
$712$	−59.1332	+	8.91289i	−2.21611	+	0.334025i
$713$	−9.93117	−	12.4533i	−0.371925	−	0.466380i
$714$	−3.51586	+	6.12044i	−0.131578	+	0.229052i
$715$	0.247463	−	0.310308i	0.00925457	−	0.0116049i
$716$	−47.3142	+	81.9505i	−1.76821	+	3.06264i
$717$	0.750711	+	1.30027i	0.0280358	+	0.0485595i
$718$	−2.80009	−	0.422046i	−0.104498	−	0.0157506i
$719$	11.7619	+	10.9134i	0.438644	+	0.407002i	0.868339	−	0.495972i	$-0.165188\pi$
$719$	11.7619	+	10.9134i	0.438644	+	0.407002i	−0.429694	+	0.902974i	$0.641379\pi$
$720$	6.46854	−	3.11509i	0.241068	−	0.116092i
$721$	29.6821	+	14.2144i	1.10542	+	0.529374i
$722$	3.07688	+	1.48175i	0.114510	+	0.0551449i
$723$	−5.29096	−	13.4812i	−0.196773	−	0.501370i
$724$	5.80120	+	77.4117i	0.215600	+	2.87698i
$725$	3.91808	−	1.20857i	0.145514	−	0.0448850i
$726$	0.910735	−	12.1529i	0.0338005	−	0.451037i
$727$	−8.05489	−	35.2908i	−0.298739	−	1.30886i	−0.872007	−	0.489494i	$-0.837181\pi$
$727$	−8.05489	−	35.2908i	−0.298739	−	1.30886i	0.573267	−	0.819368i	$-0.305676\pi$
$728$	6.90724	−	17.7129i	0.255999	−	0.656484i
$729$	3.04185	−	13.3272i	0.112661	−	0.493601i
$730$	−5.40480	−	1.66716i	−0.200040	−	0.0617043i
$731$	−6.20077	+	15.7993i	−0.229344	+	0.584358i
$732$	2.51693	−	2.33537i	0.0930286	−	0.0863179i
$733$	6.39764	−	4.36183i	0.236302	−	0.161108i	−0.439380	−	0.898301i	$-0.644802\pi$
$733$	6.39764	−	4.36183i	0.236302	−	0.161108i	0.675682	+	0.737193i	$0.263849\pi$
$734$	−51.7863			−1.91147
$735$	1.02304	−	0.158767i	0.0377354	−	0.00585621i
$736$	65.2191			2.40401
$737$	0.847787	−	0.578011i	0.0312286	−	0.0212913i
$738$	−64.6290	+	59.9670i	−2.37903	+	2.20741i
$739$	8.33358	−	21.2336i	0.306556	−	0.781091i	−0.691707	−	0.722178i	$-0.743141\pi$
$739$	8.33358	−	21.2336i	0.306556	−	0.781091i	0.998263	−	0.0589133i	$-0.0187635\pi$
$740$	−11.0738	−	3.41582i	−0.407081	−	0.125568i
$741$	−0.482823	+	2.11538i	−0.0177369	+	0.0777106i
$742$	1.15654	+	14.9939i	0.0424580	+	0.550445i
$743$	−11.6649	−	51.1072i	−0.427943	−	1.87494i	−0.481618	−	0.876381i	$-0.659951\pi$
$743$	−11.6649	−	51.1072i	−0.427943	−	1.87494i	0.0536751	−	0.998558i	$-0.482906\pi$
$744$	0.639650	−	8.53553i	0.0234507	−	0.312928i
$745$	2.96457	−	0.914447i	0.108613	−	0.0335028i
$746$	−1.56273	−	20.8532i	−0.0572156	−	0.763489i
$747$	−0.612550	−	1.56075i	−0.0224120	−	0.0571049i
$748$	11.8142	+	5.68943i	0.431971	+	0.208026i
$749$	−9.61089	+	42.5356i	−0.351174	+	1.55422i
$750$	−3.43687	+	1.65511i	−0.125497	+	0.0604361i
$751$	29.4159	+	27.2940i	1.07340	+	0.995972i	0.999999	−	0.00133063i	$-0.000423553\pi$
$751$	29.4159	+	27.2940i	1.07340	+	0.995972i	0.0734031	+	0.997302i	$0.476614\pi$
$752$	75.7871	+	11.4231i	2.76367	+	0.416557i
$753$	7.43090	+	12.8707i	0.270797	+	0.469034i
$754$	−1.08413	+	1.87777i	−0.0394816	+	0.0683842i
$755$	−2.63912	+	3.30936i	−0.0960476	+	0.120440i
$756$	36.8517	−	5.63675i	1.34028	−	0.205007i
$757$	14.1188	+	17.7045i	0.513158	+	0.643480i	0.969141	−	0.246509i	$-0.0792835\pi$
$757$	14.1188	+	17.7045i	0.513158	+	0.643480i	−0.455983	+	0.889989i	$0.650712\pi$
$758$	59.9138	−	9.03056i	2.17617	−	0.328005i
$759$	4.07195	+	2.77621i	0.147802	+	0.100770i
$760$	7.15781	+	4.88011i	0.259641	+	0.177020i
$761$	−9.06507	+	1.36634i	−0.328608	+	0.0495297i	−0.311275	−	0.950320i	$-0.600756\pi$
$761$	−9.06507	+	1.36634i	−0.328608	+	0.0495297i	−0.0173338	+	0.999850i	$0.505518\pi$
$762$	8.36611	+	10.4908i	0.303072	+	0.380040i
$763$	1.33108	−	18.2976i	0.0481883	−	0.662418i
$764$	−9.54661	+	11.9711i	−0.345384	+	0.433098i
$765$	0.779114	−	1.34946i	0.0281689	−	0.0487900i
$766$	7.85166	+	13.5995i	0.283692	+	0.491369i
$767$	13.3066	+	2.00564i	0.480472	+	0.0724195i
$768$	−7.31593	−	6.78820i	−0.263991	−	0.244948i
$769$	6.23927	−	3.00467i	0.224994	−	0.108351i	−0.317991	−	0.948094i	$-0.603008\pi$
$769$	6.23927	−	3.00467i	0.224994	−	0.108351i	0.542985	+	0.839742i	$0.317294\pi$
$770$	−0.613487	−	2.66109i	−0.0221085	−	0.0958989i
$771$	−9.60984	−	4.62785i	−0.346090	−	0.166668i
$772$	−5.80737	−	14.7969i	−0.209012	−	0.532553i
$773$	−2.04269	−	27.2578i	−0.0734704	−	0.980395i	−0.905137	−	0.425120i	$-0.860232\pi$
$773$	−2.04269	−	27.2578i	−0.0734704	−	0.980395i	0.831667	−	0.555275i	$-0.187387\pi$
$774$	57.9914	−	17.8880i	2.08446	−	0.642970i
$775$	0.848485	−	11.3222i	0.0304785	−	0.406707i
$776$	11.7778	+	51.6021i	0.422800	+	1.85241i
$777$	−9.58648	−	6.50536i	−0.343913	−	0.233378i
$778$	10.8842	−	47.6869i	0.390218	−	1.70966i
$779$	−49.8354	−	15.3722i	−1.78554	−	0.550765i
$780$	0.257368	−	0.655764i	0.00921527	−	0.0234801i
$781$	9.11629	−	8.45868i	0.326207	−	0.302676i
$782$	29.4759	−	20.0963i	1.05406	−	0.718643i
$783$	−2.46645			−0.0881436
$784$	−32.3066	−	55.3970i	−1.15381	−	1.97846i
$785$	−1.86303			−0.0664945
$786$	−14.3088	+	9.75560i	−0.510380	+	0.347971i
$787$	−37.3597	+	34.6647i	−1.33173	+	1.23566i	−0.381403	+	0.924409i	$0.624559\pi$
$787$	−37.3597	+	34.6647i	−1.33173	+	1.23566i	−0.950326	+	0.311255i	$0.899251\pi$
$788$	25.8633	−	65.8987i	0.921344	−	2.34755i
$789$	−2.70287	−	0.833725i	−0.0962247	−	0.0296814i
$790$	2.49760	−	10.9427i	0.0888607	−	0.389324i
$791$	12.6104	−	3.91994i	0.448373	−	0.139377i
$792$	−6.05241	−	26.5174i	−0.215063	−	0.942253i
$793$	−0.104411	+	1.39327i	−0.00370775	+	0.0494764i
$794$	−61.1551	+	18.8638i	−2.17031	+	0.669453i
$795$	0.0241567	+	0.322349i	0.000856751	+	0.0114325i
$796$	−20.7822	−	52.9521i	−0.736605	−	1.87684i
$797$	9.19325	+	4.42723i	0.325641	+	0.156821i	0.589561	−	0.807724i	$-0.299301\pi$
$797$	9.19325	+	4.42723i	0.325641	+	0.156821i	−0.263919	+	0.964545i	$0.585015\pi$
$798$	9.33373	+	11.6519i	0.330410	+	0.412472i
$799$	14.9871	−	7.21740i	0.530205	−	0.255333i
$800$	34.0790	+	31.6207i	1.20487	+	1.11796i
$801$	22.4968	+	3.39085i	0.794886	+	0.119810i
$802$	−14.2916	−	24.7537i	−0.504653	−	0.874085i
$803$	−5.25231	+	9.09726i	−0.185350	+	0.321035i
$804$	1.13550	−	1.42387i	0.0400460	−	0.0502161i
$805$	−5.00345	−	1.53141i	−0.176349	−	0.0539753i
$806$	3.74351	+	4.69422i	0.131860	+	0.165347i
$807$	12.8284	−	1.93358i	0.451583	−	0.0680652i
$808$	−13.2097	−	9.00624i	−0.464717	−	0.316838i
$809$	−4.15999	−	2.83624i	−0.146258	−	0.0997167i	0.487980	−	0.872855i	$-0.337734\pi$
$809$	−4.15999	−	2.83624i	−0.146258	−	0.0997167i	−0.634238	+	0.773138i	$0.718686\pi$
$810$	−4.92074	+	0.741682i	−0.172897	+	0.0260601i
$811$	−0.874994	−	1.09721i	−0.0307252	−	0.0385282i	0.766232	−	0.642565i	$-0.222130\pi$
$811$	−0.874994	−	1.09721i	−0.0307252	−	0.0385282i	−0.796957	+	0.604036i	$0.793558\pi$
$812$	3.85997	+	9.77231i	0.135459	+	0.342941i
$813$	−4.29613	+	5.38718i	−0.150672	+	0.188937i
$814$	−15.2800	+	26.4657i	−0.535562	+	0.927621i
$815$	−1.29777	−	2.24780i	−0.0454589	−	0.0787371i
$816$	9.29314	+	1.40072i	0.325325	+	0.0490348i
$817$	26.3157	+	24.4174i	0.920671	+	0.854258i
$818$	14.1500	−	6.81428i	0.494743	−	0.238256i
$819$	−4.49735	+	5.66481i	−0.157150	+	0.197944i
$820$	15.2554	+	7.34662i	0.532742	+	0.256555i
$821$	−7.86254	−	20.0334i	−0.274405	−	0.699171i	−0.999940	−	0.0109862i	$-0.996503\pi$
$821$	−7.86254	−	20.0334i	−0.274405	−	0.699171i	0.725535	−	0.688185i	$-0.241592\pi$
$822$	0.585560	+	7.81376i	0.0204238	+	0.272536i
$823$	51.7545	−	15.9641i	1.80405	−	0.556475i	0.804739	−	0.593629i	$-0.202305\pi$
$823$	51.7545	−	15.9641i	1.80405	−	0.556475i	0.999310	+	0.0371543i	$0.0118293\pi$
$824$	6.67967	−	89.1340i	0.232697	−	3.10513i
$825$	0.781710	+	3.42489i	0.0272156	+	0.119239i
$826$	67.7362	−	63.1256i	2.35684	−	2.19642i
$827$	2.00586	−	8.78824i	0.0697505	−	0.305597i	−0.928004	−	0.372569i	$-0.878477\pi$
$827$	2.00586	−	8.78824i	0.0697505	−	0.305597i	0.997755	+	0.0669725i	$0.0213340\pi$
$828$	−85.8465	−	26.4801i	−2.98337	−	0.920249i
$829$	4.10424	−	10.4574i	0.142546	−	0.363201i	−0.841715	−	0.539922i	$-0.818454\pi$
$829$	4.10424	−	10.4574i	0.142546	−	0.363201i	0.984261	+	0.176721i	$0.0565489\pi$
$830$	−0.335161	+	0.310984i	−0.0116336	+	0.0107944i
$831$	3.29060	−	2.24349i	0.114150	−	0.0778258i
$832$	−6.26146			−0.217077
$833$	−12.5663	−	5.98419i	−0.435396	−	0.207340i
$834$	−10.9203			−0.378137
$835$	−1.26135	+	0.859975i	−0.0436509	+	0.0297607i
$836$	20.3312	−	18.8646i	0.703170	−	0.652446i
$837$	−2.49522	+	6.35773i	−0.0862476	+	0.219755i
$838$	67.6233	+	20.8590i	2.33601	+	0.720563i
$839$	−11.7643	+	51.5426i	−0.406147	+	1.77945i	0.195520	+	0.980700i	$0.437361\pi$
$839$	−11.7643	+	51.5426i	−0.406147	+	1.77945i	−0.601667	+	0.798747i	$0.705496\pi$
$840$	−1.41123	−	2.43205i	−0.0486920	−	0.0839137i
$841$	6.29842	+	27.5952i	0.217187	+	0.951559i
$842$	4.93576	−	65.8632i	0.170098	−	2.26980i
$843$	7.92874	−	2.44569i	0.273080	−	0.0842341i
$844$	−1.80726	−	24.1162i	−0.0622084	−	0.830113i
$845$	0.104729	+	0.266846i	0.00360280	+	0.00917979i
$846$	−53.5883	−	25.8067i	−1.84240	−	0.887254i
$847$	24.0313	−	0.0524308i	0.825726	−	0.00180154i
$848$	18.0404	−	8.68782i	0.619511	−	0.298341i
$849$	7.39715	+	6.86355i	0.253869	+	0.235556i
$850$	25.1455	+	3.79008i	0.862485	+	0.129999i
$851$	29.2775	+	50.7101i	1.00362	+	1.73832i
$852$	11.0365	−	19.1157i	0.378103	−	0.654894i
$853$	−24.7549	+	31.0417i	−0.847593	+	1.06285i	0.149657	+	0.988738i	$0.452183\pi$
$853$	−24.7549	+	31.0417i	−0.847593	+	1.06285i	−0.997250	+	0.0741097i	$0.976388\pi$
$854$	7.06133	+	6.52335i	0.241634	+	0.223224i
$855$	−2.05491	−	2.57678i	−0.0702766	−	0.0881241i
$856$	117.116	−	17.6524i	4.00295	−	0.603348i
$857$	33.2901	+	22.6968i	1.13717	+	0.775308i	0.977306	−	0.211832i	$-0.0679429\pi$
$857$	33.2901	+	22.6968i	1.13717	+	0.775308i	0.159861	+	0.987139i	$0.448895\pi$
$858$	−1.53491	−	1.04648i	−0.0524008	−	0.0357263i
$859$	15.9072	−	2.39762i	0.542746	−	0.0818057i	0.128053	−	0.991767i	$-0.459127\pi$
$859$	15.9072	−	2.39762i	0.542746	−	0.0818057i	0.414693	+	0.909962i	$0.363889\pi$
$860$	−7.26692	−	9.11243i	−0.247800	−	0.310731i
$861$	12.4337	+	11.4865i	0.423741	+	0.391457i
$862$	−16.0661	+	20.1463i	−0.547215	+	0.686186i
$863$	9.07595	−	15.7200i	0.308949	−	0.535115i	−0.669184	−	0.743097i	$-0.733356\pi$
$863$	9.07595	−	15.7200i	0.308949	−	0.535115i	0.978133	+	0.207982i	$0.0666894\pi$
$864$	−13.9825	−	24.2184i	−0.475694	−	0.823926i
$865$	3.20765	+	0.483475i	0.109063	+	0.0164386i
$866$	67.1244	+	62.2824i	2.28098	+	2.11644i
$867$	−6.06451	+	2.92051i	−0.205961	+	0.0991858i
$868$	29.0950	−	0.0634784i	0.987548	−	0.00215460i
$869$	−18.7813	−	9.04462i	−0.637113	−	0.306818i
$870$	0.117158	+	0.298513i	0.00397202	+	0.0101206i
$871$	0.0553818	+	0.739018i	0.00187654	+	0.0250407i
$872$	−47.6140	+	14.6870i	−1.61241	+	0.497363i
$873$	1.50481	−	20.0802i	0.0509300	−	0.679613i
$874$	−16.7906	−	73.5643i	−0.567950	−	2.48835i
$875$	−3.77523	−	6.50606i	−0.127626	−	0.219945i
$876$	−4.14885	+	18.1773i	−0.140177	+	0.614154i
$877$	29.4735	+	9.09138i	0.995251	+	0.306994i	0.749258	−	0.662278i	$-0.230410\pi$
$877$	29.4735	+	9.09138i	0.995251	+	0.306994i	0.245992	+	0.969272i	$0.420886\pi$
$878$	3.36599	−	8.57641i	0.113597	−	0.289440i
$879$	−8.86308	+	8.22374i	−0.298944	+	0.277380i
$880$	−3.00430	+	2.04830i	−0.101275	+	0.0690480i
$881$	10.6989			0.360455			0.180228	−	0.983625i	$-0.442317\pi$
$881$	10.6989			0.360455			0.180228	+	0.983625i	$0.442317\pi$
$882$	11.2858	+	48.4705i	0.380013	+	1.63209i
$883$	1.00570			0.0338443			0.0169222	−	0.999857i	$-0.494613\pi$
$883$	1.00570			0.0338443			0.0169222	+	0.999857i	$0.494613\pi$
$884$	−7.82512	+	5.33508i	−0.263187	+	0.179438i
$885$	1.45895	−	1.35371i	0.0490421	−	0.0455044i
$886$	−0.603511	+	1.53772i	−0.0202754	+	0.0516608i
$887$	−41.0629	−	12.6662i	−1.37876	−	0.425290i	−0.485264	−	0.874368i	$-0.661277\pi$
$887$	−41.0629	−	12.6662i	−1.37876	−	0.425290i	−0.893493	+	0.449077i	$0.851753\pi$
$888$	−7.00181	+	30.6769i	−0.234965	+	1.02945i
$889$	−19.3567	+	18.0391i	−0.649201	+	0.605012i
$890$	−1.38053	−	6.04850i	−0.0462755	−	0.202746i
$891$	−0.690667	+	9.21631i	−0.0231382	+	0.308758i
$892$	−4.75527	+	1.46681i	−0.159218	+	0.0491123i
$893$	−2.62928	−	35.0853i	−0.0879854	−	1.17408i
$894$	−5.30508	−	13.5171i	−0.177428	−	0.452080i
$895$	−5.13106	−	2.47099i	−0.171512	−	0.0825960i
$896$	4.31477	−	5.43484i	0.144146	−	0.181565i
$897$	−3.20699	+	1.54440i	−0.107078	+	0.0515661i
$898$	−25.7851	−	23.9251i	−0.860460	−	0.798390i
$899$	−1.90342	−	0.286894i	−0.0634825	−	0.00956844i
$900$	−32.0189	−	55.4584i	−1.06730	−	1.84861i
$901$	2.17291	−	3.76359i	0.0723901	−	0.125383i
$902$	27.8396	−	34.9097i	0.926957	−	1.16237i
$903$	−4.28057	−	10.8371i	−0.142449	−	0.360637i
$904$	−22.3623	−	28.0415i	−0.743760	−	0.932646i
$905$	−4.61977	+	0.696319i	−0.153566	+	0.0231464i
$906$	16.3694	+	11.1605i	0.543836	+	0.370781i
$907$	−30.5992	−	20.8622i	−1.01603	−	0.692718i	−0.0637572	−	0.997965i	$-0.520308\pi$
$907$	−30.5992	−	20.8622i	−1.01603	−	0.692718i	−0.952273	+	0.305248i	$0.901261\pi$
$908$	−11.8162	+	1.78101i	−0.392135	+	0.0591049i
$909$	3.79234	+	4.75545i	0.125784	+	0.157728i
$910$	1.88603	+	0.577260i	0.0625213	+	0.0191360i
$911$	21.1980	−	26.5814i	0.702320	−	0.880681i	−0.294875	−	0.955536i	$-0.595278\pi$
$911$	21.1980	−	26.5814i	0.702320	−	0.880681i	0.997194	+	0.0748550i	$0.0238494\pi$
$912$	9.93903	−	17.2149i	0.329114	−	0.570042i
$913$	0.424574	+	0.735384i	0.0140513	+	0.0243376i
$914$	87.0739	+	13.1243i	2.88015	+	0.434113i
$915$	0.151478	+	0.140551i	0.00500769	+	0.00464646i
$916$	−10.0399	+	4.83497i	−0.331728	+	0.159752i
$917$	−21.3499	−	26.6525i	−0.705037	−	0.880142i
$918$	−13.7820	−	6.63704i	−0.454873	−	0.219055i
$919$	−2.91863	−	7.43655i	−0.0962767	−	0.245309i	0.874619	−	0.484810i	$-0.161111\pi$
$919$	−2.91863	−	7.43655i	−0.0962767	−	0.245309i	−0.970896	+	0.239501i	$0.923016\pi$
$920$	1.06204	+	14.1719i	0.0350144	+	0.467235i
$921$	4.74740	−	1.46438i	0.156432	−	0.0482529i
$922$	−0.717161	+	9.56984i	−0.0236184	+	0.315166i
$923$	1.99869	+	8.75682i	0.0657876	+	0.288234i
$924$	−8.59637	+	2.67218i	−0.282800	+	0.0879084i
$925$	−9.28778	+	40.6924i	−0.305380	+	1.33796i
$926$	−71.9026	−	22.1790i	−2.36287	−	0.728848i
$927$	−12.4236	+	31.6549i	−0.408045	+	1.03968i
$928$	5.77763	−	5.36086i	0.189660	−	0.175979i
$929$	−42.3993	+	28.9073i	−1.39108	+	0.948419i	−0.391474	+	0.920189i	$0.628035\pi$
$929$	−42.3993	+	28.9073i	−1.39108	+	0.948419i	−0.999601	+	0.0282298i	$0.991013\pi$
$930$	0.887999			0.0291186
$931$	−21.4927	+	20.1176i	−0.704396	+	0.659327i
$932$	−14.4486			−0.473281
$933$	−12.0567	+	8.22013i	−0.394719	+	0.269115i
$934$	1.04283	−	0.967604i	0.0341224	−	0.0316610i
$935$	−0.288317	+	0.734619i	−0.00942896	+	0.0240246i
$936$	18.7721	+	5.79041i	0.613584	+	0.189266i
$937$	−2.60572	+	11.4164i	−0.0851252	+	0.372958i	−0.999490	−	0.0319336i	$-0.989833\pi$
$937$	−2.60572	+	11.4164i	−0.0851252	+	0.372958i	0.914365	+	0.404891i	$0.132691\pi$
$938$	4.21934	+	2.86324i	0.137766	+	0.0934880i
$939$	−1.88369	−	8.25297i	−0.0614718	−	0.269325i
$940$	−0.853643	+	11.3911i	−0.0278428	+	0.371536i
$941$	−9.33136	+	2.87834i	−0.304193	+	0.0938313i	−0.443094	−	0.896475i	$-0.646119\pi$
$941$	−9.33136	+	2.87834i	−0.304193	+	0.0938313i	0.138901	+	0.990306i	$0.455643\pi$
$942$	0.651647	+	8.69562i	0.0212318	+	0.283319i
$943$	−31.2567	−	79.6408i	−1.01786	−	2.59346i
$944$	−111.074	−	53.4902i	−3.61514	−	1.74096i
$945$	0.504030	+	2.18630i	0.0163961	+	0.0711204i
$946$	−27.6917	+	13.3356i	−0.900335	+	0.433579i
$947$	4.74311	+	4.40096i	0.154130	+	0.143012i	0.753469	−	0.657484i	$-0.228379\pi$
$947$	4.74311	+	4.40096i	0.154130	+	0.143012i	−0.599338	+	0.800496i	$0.704570\pi$
$948$	−36.5860	−	5.51446i	−1.18826	−	0.179101i
$949$	−3.79350	−	6.57054i	−0.123142	−	0.213289i
$950$	26.8932	−	46.5804i	0.872530	−	1.51127i
$951$	0.154368	−	0.193572i	0.00500573	−	0.00627699i
$952$	−2.74272	+	37.7028i	−0.0888922	+	1.22195i
$953$	19.0012	+	23.8267i	0.615508	+	0.771822i	0.987705	−	0.156332i	$-0.0499668\pi$
$953$	19.0012	+	23.8267i	0.615508	+	0.771822i	−0.372197	+	0.928154i	$0.621395\pi$
$954$	−15.3655	+	2.31597i	−0.497475	+	0.0749824i
$955$	−0.761380	−	0.519100i	−0.0246377	−	0.0167977i
$956$	11.4528	+	7.80837i	0.370409	+	0.252541i
$957$	0.588924	−	0.0887661i	0.0190372	−	0.00286940i
$958$	−59.9078	−	75.1221i	−1.93553	−	2.42708i
$959$	−15.2734	+	2.33619i	−0.493205	+	0.0754395i
$960$	−0.577387	+	0.724020i	−0.0186351	+	0.0233677i
$961$	12.8349	−	22.2306i	0.414027	−	0.717117i
$962$	−11.0360	−	19.1150i	−0.355816	−	0.616291i
$963$	−44.5561	−	6.71575i	−1.43580	−	0.216412i
$964$	−98.0107	−	90.9406i	−3.15671	−	2.92900i
$965$	0.861920	−	0.415079i	0.0277462	−	0.0133619i
$966$	−5.39771	+	23.8890i	−0.173668	+	0.768617i
$967$	−33.9023	−	16.3265i	−1.09022	−	0.525024i	−0.199652	−	0.979867i	$-0.563981\pi$
$967$	−33.9023	−	16.3265i	−1.09022	−	0.525024i	−0.890572	+	0.454843i	$0.849695\pi$
$968$	−23.8456	−	60.7575i	−0.766425	−	1.95282i
$969$	−0.322406	−	4.30221i	−0.0103572	−	0.138207i
$970$	−5.24717	+	1.61854i	−0.168476	+	0.0519681i
$971$	−0.154505	+	2.06172i	−0.00495829	+	0.0661638i	−0.999134	−	0.0416070i	$-0.986752\pi$
$971$	−0.154505	+	2.06172i	−0.00495829	+	0.0661638i	0.994176	+	0.107771i	$0.0343713\pi$
$972$	13.0566	+	57.2047i	0.418791	+	1.83484i
$973$	−1.65605	−	21.4698i	−0.0530905	−	0.688289i
$974$	−16.1710	+	70.8499i	−0.518153	+	2.27018i
$975$	−2.42454	−	0.747870i	−0.0776473	−	0.0239510i
$976$	4.67635	−	11.9151i	0.149686	−	0.381394i
$977$	−2.44612	+	2.26967i	−0.0782585	+	0.0726132i	−0.718332	−	0.695700i	$-0.755094\pi$
$977$	−2.44612	+	2.26967i	−0.0782585	+	0.0726132i	0.640074	+	0.768313i	$0.278904\pi$
$978$	−10.0376	+	6.84351i	−0.320967	+	0.218831i
$979$	−11.5223			−0.368255
$980$	7.87355	−	5.41857i	0.251511	−	0.173090i
$981$	18.9566			0.605238
$982$	85.0571	−	57.9909i	2.71428	−	1.85057i
$983$	−23.7160	+	22.0052i	−0.756422	+	0.701857i	−0.960864	−	0.277021i	$-0.910653\pi$
$983$	−23.7160	+	22.0052i	−0.756422	+	0.701857i	0.204441	+	0.978879i	$0.434462\pi$
$984$	16.7965	−	42.7968i	0.535453	−	1.36431i
$985$	4.07124	+	1.25581i	0.129720	+	0.0400134i
$986$	0.959340	−	4.20314i	0.0305516	−	0.133855i
$987$	−4.14891	+	10.6394i	−0.132061	+	0.338657i
$988$	4.45749	+	19.5295i	0.141812	+	0.621317i
$989$	−4.40096	+	58.7267i	−0.139942	+	1.86740i
$990$	2.69642	−	0.831735i	0.0856978	−	0.0264343i
$991$	−1.67074	−	22.2945i	−0.0530729	−	0.708208i	−0.958752	−	0.284244i	$-0.908257\pi$
$991$	−1.67074	−	22.2945i	−0.0530729	−	0.708208i	0.905679	−	0.423964i	$-0.139362\pi$
$992$	−7.97358	−	20.3163i	−0.253161	−	0.645044i
$993$	−1.49313	−	0.719051i	−0.0473829	−	0.0228184i
$994$	55.7394	+	26.6930i	1.76795	+	0.846651i
$995$	3.08446	−	1.48540i	0.0977838	−	0.0470902i
$996$	1.10483	+	1.02513i	0.0350078	+	0.0324825i
$997$	−17.0263	−	2.56630i	−0.539227	−	0.0812754i	−0.126218	−	0.992002i	$-0.540284\pi$
$997$	−17.0263	−	2.56630i	−0.539227	−	0.0812754i	−0.413009	+	0.910727i	$0.635522\pi$
$998$	−25.9340	−	44.9190i	−0.820926	−	1.42189i
$999$	12.5538	−	21.7437i	0.397183	−	0.687942i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.a.625.27	yes	324
49.4	even	21	inner	637.2.bl.a.53.27	✓	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.a.53.27	✓	324	49.4	even	21	inner
637.2.bl.a.625.27	yes	324	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.14872 - 1.46497i) q^{2} +(0.378204 - 0.350922i) q^{3} +(1.74017 - 4.43389i) q^{4} +(0.273927 + 0.0844952i) q^{5} +(0.298564 - 1.30809i) q^{6} +(2.61705 + 0.388620i) q^{7} +(-1.59901 - 7.00570i) q^{8} +(-0.204298 + 2.72617i) q^{9} +O(q^{10})\)	\(q+(2.14872 - 1.46497i) q^{2} +(0.378204 - 0.350922i) q^{3} +(1.74017 - 4.43389i) q^{4} +(0.273927 + 0.0844952i) q^{5} +(0.298564 - 1.30809i) q^{6} +(2.61705 + 0.388620i) q^{7} +(-1.59901 - 7.00570i) q^{8} +(-0.204298 + 2.72617i) q^{9} +(0.712375 - 0.219739i) q^{10} +(-0.103468 - 1.38068i) q^{11} +(-0.897810 - 2.28758i) q^{12} +(0.900969 + 0.433884i) q^{13} +(6.19264 - 2.99888i) q^{14} +(0.133252 - 0.0641705i) q^{15} +(-6.71571 - 6.23127i) q^{16} +(-1.96613 - 0.296347i) q^{17} +(3.55479 + 6.15707i) q^{18} +(-2.10278 + 3.64213i) q^{19} +(0.851323 - 1.06752i) q^{20} +(1.12616 - 0.771405i) q^{21} +(-2.24499 - 2.81512i) q^{22} +(-6.82209 + 1.02826i) q^{23} +(-3.06321 - 2.08846i) q^{24} +(-4.06330 - 2.77031i) q^{25} +(2.57156 - 0.387600i) q^{26} +(1.84444 + 2.31286i) q^{27} +(6.27723 - 10.9275i) q^{28} +(-0.519835 + 0.651852i) q^{29} +(0.192312 - 0.333095i) q^{30} +(1.15437 + 1.99943i) q^{31} +(-9.34762 - 1.40893i) q^{32} +(-0.523644 - 0.485871i) q^{33} +(-4.65882 + 2.24357i) q^{34} +(0.684044 + 0.327582i) q^{35} +(11.7320 + 5.64985i) q^{36} +(-3.10075 - 7.90058i) q^{37} +(0.817325 + 10.9064i) q^{38} +(0.493010 - 0.152073i) q^{39} +(0.153938 - 2.05416i) q^{40} +(2.75943 + 12.0899i) q^{41} +(1.28971 - 3.30733i) q^{42} +(1.89945 - 8.32202i) q^{43} +(-6.30184 - 1.94386i) q^{44} +(-0.286311 + 0.729509i) q^{45} +(-13.1524 + 12.2036i) q^{46} +(-6.91229 + 4.71272i) q^{47} -4.72660 q^{48} +(6.69795 + 2.03408i) q^{49} -12.7893 q^{50} +(-0.847596 + 0.577881i) q^{51} +(3.49164 - 3.23977i) q^{52} +(-0.798507 + 2.03456i) q^{53} +(7.35146 + 2.26763i) q^{54} +(0.0883184 - 0.386948i) q^{55} +(-1.46213 - 18.9557i) q^{56} +(0.482823 + 2.11538i) q^{57} +(-0.162034 + 2.16219i) q^{58} +(12.8590 - 3.96648i) q^{59} +(-0.0526444 - 0.702491i) q^{60} +(0.510446 + 1.30059i) q^{61} +(5.40954 + 2.60509i) q^{62} +(-1.59410 + 7.05514i) q^{63} +(-5.64138 + 2.71674i) q^{64} +(0.210138 + 0.194980i) q^{65} +(-1.83695 - 0.276876i) q^{66} +(0.370545 + 0.641803i) q^{67} +(-4.73539 + 8.20193i) q^{68} +(-2.21930 + 2.78292i) q^{69} +(1.94972 - 0.298225i) q^{70} +(5.60020 + 7.02243i) q^{71} +(19.4254 - 2.92791i) q^{72} +(-6.26868 - 4.27391i) q^{73} +(-18.2368 - 12.4336i) q^{74} +(-2.50892 + 0.378159i) q^{75} +(12.4896 + 15.6615i) q^{76} +(0.265780 - 3.65353i) q^{77} +(0.836557 - 1.04901i) q^{78} +(7.52796 - 13.0388i) q^{79} +(-1.31310 - 2.27436i) q^{80} +(-6.60063 - 0.994885i) q^{81} +(23.6406 + 21.9353i) q^{82} +(-0.552565 + 0.266101i) q^{83} +(-1.46062 - 6.33564i) q^{84} +(-0.513537 - 0.247306i) q^{85} +(-8.11015 - 20.6643i) q^{86} +(0.0321457 + 0.428955i) q^{87} +(-9.50720 + 2.93258i) q^{88} +(0.621907 - 8.29877i) q^{89} +(0.453508 + 1.98695i) q^{90} +(2.18927 + 1.48563i) q^{91} +(-7.31241 + 32.0378i) q^{92} +(1.13823 + 0.351098i) q^{93} +(-7.94857 + 20.2526i) q^{94} +(-0.883751 + 0.820001i) q^{95} +(-4.02974 + 2.74743i) q^{96} -7.36573 q^{97} +(17.3719 - 5.44165i) q^{98} +3.78511 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Introduction

L-functions

Modular forms

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