LMFDB - Embedded newform 637.2.bl.a.53.27

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			53.27
Character	$\chi$	$=$	637.53
Dual form			637.2.bl.a.625.27

$q$-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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{5}{21}\right)$

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	0.981185	+	0.193069i	$0.0618442\pi$
$2$	2.14872	+	1.46497i	1.51938	+	1.03589i	0.538190	+	0.842823i	$0.319108\pi$
$3$	0.378204	+	0.350922i	0.218356	+	0.202605i	0.781765	−	0.623573i	$-0.214320\pi$
$3$	0.378204	+	0.350922i	0.218356	+	0.202605i	−0.563408	+	0.826179i	$0.690510\pi$
$4$	1.74017	+	4.43389i	0.870087	+	2.21695i
$5$	0.273927	−	0.0844952i	0.122504	−	0.0377874i	−0.232897	−	0.972501i	$-0.574821\pi$
$5$	0.273927	−	0.0844952i	0.122504	−	0.0377874i	0.355401	+	0.934714i	$0.384344\pi$
$6$	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	0.959641	+	0.281230i	$0.0907423\pi$
$11$	−0.103468	+	1.38068i	−0.0311967	+	0.416291i	−0.990837	+	0.135062i	$0.956877\pi$
$12$	−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	−0.383074	−	0.923718i	$-0.625134\pi$
$17$	−1.96613	+	0.296347i	−0.476858	+	0.0718747i	−0.0937841	+	0.995593i	$0.529896\pi$
$18$	3.55479	−	6.15707i	0.837871	−	1.45124i
$19$	−2.10278	−	3.64213i	−0.482412	−	0.835562i	0.517384	−	0.855753i	$-0.326906\pi$
$19$	−2.10278	−	3.64213i	−0.482412	−	0.835562i	−0.999796	+	0.0201913i	$0.993572\pi$
$20$	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	−0.607710	−	0.794159i	$-0.707912\pi$
$23$	−6.82209	−	1.02826i	−1.42250	−	0.214408i	−0.814794	+	0.579751i	$0.803150\pi$
$24$	−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	0.731220	−	0.682142i	$-0.238951\pi$
$29$	−0.519835	−	0.651852i	−0.0965309	−	0.121046i	−0.827751	+	0.561096i	$0.810380\pi$
$30$	0.192312	+	0.333095i	0.0351112	+	0.0608145i
$31$	1.15437	−	1.99943i	0.207331	−	0.359108i	−0.743542	−	0.668690i	$-0.766856\pi$
$31$	1.15437	−	1.99943i	0.207331	−	0.359108i	0.950873	+	0.309581i	$0.100189\pi$
$32$	−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	0.412034	+	0.911168i	$0.364818\pi$
$37$	−3.10075	+	7.90058i	−0.509760	+	1.29885i	−0.921794	+	0.387679i	$0.873277\pi$
$38$	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	−0.0279056	−	0.999611i	$-0.508884\pi$
$41$	2.75943	−	12.0899i	0.430951	−	1.88812i	0.458857	−	0.888510i	$-0.348259\pi$
$42$	1.28971	+	3.30733i	0.199006	+	0.510331i
$43$	1.89945	+	8.32202i	0.289663	+	1.26910i	0.884989	+	0.465612i	$0.154166\pi$
$43$	1.89945	+	8.32202i	0.289663	+	1.26910i	−0.595326	+	0.803484i	$0.702977\pi$
$44$	−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	−0.0578202	−	0.998327i	$-0.518415\pi$
$47$	−6.91229	−	4.71272i	−1.00826	−	0.687420i	−0.950440	+	0.310907i	$0.899367\pi$
$48$	−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	0.865484	−	0.500936i	$-0.167011\pi$
$53$	−0.798507	−	2.03456i	−0.109683	−	0.279469i	−0.975168	+	0.221467i	$0.928915\pi$
$54$	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	0.979232	−	0.202744i	$-0.0649861\pi$
$59$	12.8590	+	3.96648i	1.67410	+	0.516392i	0.694869	+	0.719136i	$0.255462\pi$
$60$	−0.0526444	+	0.702491i	−0.00679636	+	0.0906912i
$61$	0.510446	−	1.30059i	0.0653559	−	0.166524i	−0.894465	−	0.447139i	$-0.852443\pi$
$61$	0.510446	−	1.30059i	0.0653559	−	0.166524i	0.959821	+	0.280615i	$0.0905383\pi$
$62$	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	−0.842503	−	0.538692i	$-0.818919\pi$
$67$	0.370545	−	0.641803i	0.0452693	−	0.0784088i	0.887772	+	0.460283i	$0.152252\pi$
$68$	−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	−0.329216	−	0.944254i	$-0.606785\pi$
$71$	5.60020	−	7.02243i	0.664621	−	0.833409i	0.993838	+	0.110846i	$0.0353560\pi$
$72$	19.4254	+	2.92791i	2.28931	+	0.345057i
$73$	−6.26868	+	4.27391i	−0.733693	+	0.500224i	−0.871598	−	0.490222i	$-0.836916\pi$
$73$	−6.26868	+	4.27391i	−0.733693	+	0.500224i	0.137904	+	0.990446i	$0.455963\pi$
$74$	−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	0.883907	+	0.467663i	$0.154904\pi$
$79$	7.52796	+	13.0388i	0.846961	+	1.46698i	−0.0369455	+	0.999317i	$0.511763\pi$
$80$	−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	0.403312	−	0.915063i	$-0.367859\pi$
$83$	−0.552565	−	0.266101i	−0.0606519	−	0.0292084i	−0.463964	+	0.885854i	$0.653573\pi$
$84$	−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	0.927925	+	0.372766i	$0.121591\pi$
$89$	0.621907	+	8.29877i	0.0659220	+	0.879668i	−0.862003	+	0.506902i	$0.830790\pi$
$90$	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	0.757136	−	0.653257i	$-0.226598\pi$
$101$	1.63096	+	1.51331i	0.162287	+	0.150580i	−0.594849	+	0.803837i	$0.702788\pi$
$102$	−0.974667	−	2.48341i	−0.0965064	−	0.245894i
$103$	11.8862	−	3.66642i	1.17119	−	0.361263i	0.352670	−	0.935748i	$-0.385274\pi$
$103$	11.8862	−	3.66642i	1.17119	−	0.361263i	0.818515	+	0.574485i	$0.194798\pi$
$104$	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	−0.662224	−	0.749306i	$-0.730387\pi$
$107$	−1.23172	−	16.4361i	−0.119075	−	1.58894i	0.543150	−	0.839636i	$-0.317232\pi$
$108$	13.4646	+	4.15328i	1.29563	+	0.399650i
$109$	−0.518188	+	6.91473i	−0.0496334	+	0.662311i	0.915796	+	0.401645i	$0.131561\pi$
$109$	−0.518188	+	6.91473i	−0.0496334	+	0.662311i	−0.965429	+	0.260667i	$0.916058\pi$
$110$	−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	0.633276	−	0.773926i	$-0.281710\pi$
$113$	4.49695	+	2.16562i	0.423038	+	0.203724i	−0.210238	+	0.977650i	$0.567424\pi$
$114$	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	0.424009	−	0.905658i	$-0.360622\pi$
$127$	−6.23530	−	7.81881i	−0.553293	−	0.693808i	−0.977302	+	0.211850i	$0.932051\pi$
$128$	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	−0.975072	−	0.221890i	$-0.928777\pi$
$131$	−9.46166	+	8.77914i	−0.826669	+	0.767037i	0.148403	+	0.988927i	$0.452587\pi$
$132$	−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	0.0470485	−	0.998893i	$-0.485018\pi$
$137$	−5.58050	−	1.72136i	−0.476774	−	0.147065i	−0.523823	+	0.851827i	$0.675495\pi$
$138$	−0.691763	−	9.23094i	−0.0588868	−	0.785790i
$139$	−1.81108	+	7.93485i	−0.153614	+	0.673025i	0.838203	+	0.545358i	$0.183606\pi$
$139$	−1.81108	+	7.93485i	−0.153614	+	0.673025i	−0.991817	+	0.127668i	$0.959251\pi$
$140$	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	0.871220	−	0.490893i	$-0.163329\pi$
$149$	8.94195	+	6.09652i	0.732553	+	0.499446i	−0.138667	+	0.990339i	$0.544282\pi$
$150$	−4.83698	−	4.48806i	−0.394938	−	0.366449i
$151$	−5.39459	−	13.7452i	−0.439006	−	1.11857i	−0.963631	−	0.267235i	$-0.913890\pi$
$151$	−5.39459	−	13.7452i	−0.439006	−	1.11857i	0.524626	−	0.851333i	$-0.324205\pi$
$152$	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	0.0368516	−	0.999321i	$-0.488267\pi$
$157$	−6.21032	−	1.91563i	−0.495638	−	0.152884i	−0.532489	+	0.846437i	$0.678743\pi$
$158$	−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	−0.895912	−	0.444232i	$-0.853477\pi$
$163$	−6.63731	+	6.15852i	−0.519874	+	0.482373i	0.376038	+	0.926604i	$0.377286\pi$
$164$	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	0.636585	−	0.771207i	$-0.280347\pi$
$167$	−3.32039	−	4.16364i	−0.256940	−	0.322192i	−0.893524	+	0.449015i	$0.851775\pi$
$168$	−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	0.559914	−	0.828551i	$-0.310834\pi$
$173$	11.1896	+	1.68657i	0.850732	+	0.128227i	0.290819	+	0.956778i	$0.406072\pi$
$174$	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	−0.834006	−	0.551756i	$-0.813958\pi$
$179$	−19.6449	+	2.96099i	−1.46833	+	0.221314i	−0.634320	+	0.773071i	$0.718720\pi$
$180$	2.73633	−	2.53894i	0.203954	−	0.189242i
$181$	−14.6838	−	7.07134i	−1.09144	−	0.525608i	−0.200481	−	0.979698i	$-0.564250\pi$
$181$	−14.6838	−	7.07134i	−1.09144	−	0.525608i	−0.890956	+	0.454089i	$0.849965\pi$
$182$	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	−0.403888	−	0.914808i	$-0.632341\pi$
$191$	−3.07177	+	0.947517i	−0.222266	+	0.0685599i	0.181622	+	0.983368i	$0.441865\pi$
$192$	−1.18023	−	3.00717i	−0.0851756	−	0.217024i
$193$	2.44637	+	2.26990i	0.176093	+	0.163391i	0.763295	−	0.646050i	$-0.223580\pi$
$193$	2.44637	+	2.26990i	0.176093	+	0.163391i	−0.587202	+	0.809440i	$0.699771\pi$
$194$	−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	0.926528	−	0.376227i	$-0.122779\pi$
$199$	8.75453	+	8.12302i	0.620592	+	0.575826i	−0.305935	+	0.952052i	$0.598969\pi$
$200$	−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	0.584666	−	0.811274i	$-0.301226\pi$
$211$	4.57446	+	2.20295i	0.314919	+	0.151657i	−0.269747	+	0.962931i	$0.586940\pi$
$212$	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	−0.803163	−	0.595759i	$-0.796851\pi$
$223$	−0.651398	+	0.816827i	−0.0436208	+	0.0546988i	0.759543	+	0.650458i	$0.225423\pi$
$224$	−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	−0.904647	−	0.426162i	$-0.859866\pi$
$227$	−1.25439	+	2.17267i	−0.0832568	+	0.144205i	0.821390	+	0.570367i	$0.193199\pi$
$228$	10.2196	−	1.54035i	0.676808	−	0.102012i
$229$	−1.71499	+	1.59127i	−0.113329	+	0.105154i	−0.734802	−	0.678281i	$-0.762725\pi$
$229$	−1.71499	+	1.59127i	−0.113329	+	0.105154i	0.621473	+	0.783436i	$0.286535\pi$
$230$	−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	−0.962568	−	0.271039i	$-0.912633\pi$
$233$	−1.10823	+	2.82373i	−0.0726028	+	0.184989i	0.889966	+	0.456027i	$0.150728\pi$
$234$	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	0.949656	−	0.313293i	$-0.101432\pi$
$239$	−0.647563	−	2.83716i	−0.0418874	−	0.183521i	−0.991544	+	0.129773i	$0.958575\pi$
$240$	−1.29474	+	0.399375i	−0.0835753	+	0.0257796i
$241$	10.2552	+	26.1298i	0.660594	+	1.68317i	0.728122	+	0.685448i	$0.240394\pi$
$241$	10.2552	+	26.1298i	0.660594	+	1.68317i	−0.0675279	+	0.997717i	$0.521511\pi$
$242$	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	−0.608423	−	0.793613i	$-0.708198\pi$
$251$	−6.40989	−	28.0836i	−0.404588	−	1.77262i	0.203835	−	0.979005i	$-0.434659\pi$
$252$	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	0.475955	+	0.879470i	$0.342103\pi$
$257$	−7.55289	+	19.2444i	−0.471136	+	1.20044i	−0.947091	+	0.320965i	$0.895993\pi$
$258$	−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	−0.938079	−	0.346422i	$-0.887397\pi$
$263$	−2.74119	+	4.74789i	−0.169029	+	0.292767i	0.769050	+	0.639189i	$0.220730\pi$
$264$	−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	0.271634	−	0.962401i	$-0.412436\pi$
$269$	20.7762	−	14.1650i	1.26675	−	0.863653i	0.995113	+	0.0987475i	$0.0314836\pi$
$270$	1.82216	−	1.24233i	0.110893	−	0.0756056i
$271$	−13.2062	−	1.99052i	−0.802220	−	0.120915i	−0.264881	−	0.964281i	$-0.585333\pi$
$271$	−13.2062	−	1.99052i	−0.802220	−	0.120915i	−0.537340	+	0.843366i	$0.680571\pi$
$272$	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	0.0843341	−	0.996438i	$-0.473124\pi$
$277$	7.63307	−	1.15050i	0.458627	−	0.0691268i	0.374292	+	0.927311i	$0.377886\pi$
$278$	−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	0.0514855	−	0.998674i	$-0.483604\pi$
$281$	14.4897	−	6.97785i	0.864381	−	0.416264i	0.812895	+	0.582410i	$0.197890\pi$
$282$	4.10092	−	10.4490i	0.244206	−	0.622227i
$283$	1.46162	−	19.5039i	0.0868840	−	1.15939i	−0.767959	−	0.640499i	$-0.778727\pi$
$283$	1.46162	−	19.5039i	0.0868840	−	1.15939i	0.854843	−	0.518887i	$-0.173654\pi$
$284$	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	−0.169604	−	0.985512i	$-0.554249\pi$
$307$	8.67580	−	4.17805i	0.495154	−	0.238454i	0.664758	+	0.747059i	$0.268535\pi$
$308$	−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	−0.881992	−	0.471265i	$-0.843798\pi$
$311$	−27.9675	+	4.21542i	−1.58589	+	0.239035i	−0.703900	+	0.710299i	$0.748560\pi$
$312$	−1.85371	+	3.21071i	−0.104945	+	0.181771i
$313$	8.20381	+	14.2094i	0.463707	+	0.803164i	0.999142	−	0.0414123i	$-0.0131857\pi$
$313$	8.20381	+	14.2094i	0.463707	+	0.803164i	−0.535435	+	0.844576i	$0.679852\pi$
$314$	−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	0.162355	−	0.986732i	$-0.448091\pi$
$317$	0.474525	+	0.0715231i	0.0266520	+	0.00401714i	−0.135703	+	0.990750i	$0.543329\pi$
$318$	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	−0.959491	−	0.281739i	$-0.909089\pi$
$331$	−1.17353	+	2.99010i	−0.0645029	+	0.164351i	0.894988	+	0.446090i	$0.147184\pi$
$332$	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	0.811821	+	0.583906i	$0.198476\pi$
$337$	6.12670	+	26.8428i	0.333743	+	1.46222i	−0.478079	+	0.878317i	$0.658667\pi$
$338$	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	−0.969844	−	0.243726i	$-0.921630\pi$
$347$	−7.91080	−	20.1564i	−0.424674	−	1.08205i	0.545170	−	0.838325i	$-0.316465\pi$
$348$	1.95788	−	0.603926i	0.104953	−	0.0323738i
$349$	3.67481	+	16.1004i	0.196708	+	0.861835i	0.972879	+	0.231313i	$0.0743022\pi$
$349$	3.67481	+	16.1004i	0.196708	+	0.861835i	−0.776171	+	0.630522i	$0.782841\pi$
$350$	−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	−0.510609	−	0.859813i	$-0.670580\pi$
$353$	−26.6201	−	8.21121i	−1.41684	−	0.437038i	−0.906235	+	0.422775i	$0.861056\pi$
$354$	−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	−0.700956	−	0.713205i	$-0.747243\pi$
$359$	−0.798197	+	0.740619i	−0.0421272	+	0.0390884i	0.658828	+	0.752293i	$0.271052\pi$
$360$	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	−0.910682	−	0.413108i	$-0.864443\pi$
$367$	−16.4530	+	11.2175i	−0.858841	+	0.585548i	0.0518415	+	0.998655i	$0.483491\pi$
$368$	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	0.951140	−	0.308761i	$-0.0999142\pi$
$373$	4.02054	+	6.96377i	0.208175	+	0.360570i	−0.742964	+	0.669331i	$0.766581\pi$
$374$	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	0.191495	−	0.981494i	$-0.438666\pi$
$379$	20.9913	−	10.1089i	1.07825	−	0.519259i	0.886758	+	0.462234i	$0.152952\pi$
$380$	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	−0.996794	−	0.0800054i	$-0.974506\pi$
$383$	−0.451245	−	6.02145i	−0.0230576	−	0.307682i	0.973737	−	0.227676i	$-0.0731128\pi$
$384$	−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	0.947403	−	0.320042i	$-0.103697\pi$
$389$	13.7875	+	12.7930i	0.699056	+	0.648629i	−0.248347	+	0.968671i	$0.579887\pi$
$390$	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	−0.821945	−	0.569567i	$-0.807111\pi$
$397$	−23.5157	+	7.25363i	−1.18022	+	0.364049i	−0.358274	+	0.933616i	$0.616635\pi$
$398$	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	0.979426	+	0.201803i	$0.0646800\pi$
$401$	0.821356	+	10.9602i	0.0410165	+	0.547328i	−0.938410	+	0.345525i	$0.887701\pi$
$402$	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	0.000267886	−	1.00000i	$-0.499915\pi$
$409$	5.97165	−	0.900081i	0.295279	−	0.0445062i	0.295011	+	0.955494i	$0.404677\pi$
$410$	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	−0.169690	−	0.985497i	$-0.554277\pi$
$419$	16.9663	−	21.2751i	0.828859	−	1.03936i	0.998549	−	0.0538583i	$-0.0171519\pi$
$420$	0.135229	+	1.85892i	0.00659848	+	0.0907058i
$421$	15.8348	+	19.8563i	0.771743	+	0.967735i	0.999983	−	0.00587008i	$-0.00186852\pi$
$421$	15.8348	+	19.8563i	0.771743	+	0.967735i	−0.228240	+	0.973605i	$0.573297\pi$
$422$	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	0.0582036	−	0.998305i	$-0.481463\pi$
$431$	−9.46829	−	2.92058i	−0.456071	−	0.140679i	−0.514275	+	0.857625i	$0.671939\pi$
$432$	2.02530	+	27.0257i	0.0974421	+	1.30027i
$433$	7.83506	−	34.3276i	0.376529	−	1.64968i	−0.331469	−	0.943466i	$-0.607544\pi$
$433$	7.83506	−	34.3276i	0.376529	−	1.64968i	0.707998	−	0.706215i	$-0.249599\pi$
$434$	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	0.631156	−	0.775656i	$-0.282581\pi$
$439$	2.92715	+	1.99570i	0.139705	+	0.0952496i	−0.491451	+	0.870905i	$0.663533\pi$
$440$	−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	0.550788	−	0.834645i	$-0.314327\pi$
$443$	−0.524829	−	0.357822i	−0.0249354	−	0.0170007i	−0.575724	+	0.817644i	$0.695280\pi$
$444$	−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	0.852921	+	0.522040i	$0.174829\pi$
$449$	−3.00975	+	13.1866i	−0.142039	+	0.622313i	−0.994960	+	0.100273i	$0.968028\pi$
$450$	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	0.165253	−	0.986251i	$-0.447156\pi$
$457$	24.8214	−	23.0309i	1.16110	−	1.07734i	0.995843	−	0.0910887i	$-0.0290347\pi$
$458$	−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	0.725360	−	0.688369i	$-0.241673\pi$
$461$	−2.30078	−	2.88509i	−0.107158	−	0.134372i	−0.832518	+	0.553997i	$0.813102\pi$
$462$	−4.69981	+	1.43848i	−0.218655	+	0.0669240i
$463$	−18.0400	+	22.6214i	−0.838388	+	1.05131i	0.159554	+	0.987189i	$0.448994\pi$
$463$	−18.0400	+	22.6214i	−0.838388	+	1.05131i	−0.997942	+	0.0641165i	$0.979577\pi$
$464$	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	0.161546	−	0.986865i	$-0.448352\pi$
$467$	0.540911	+	0.0815292i	0.0250304	+	0.00377272i	−0.136515	+	0.990638i	$0.543590\pi$
$468$	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	0.471645	+	0.881789i	$0.343660\pi$
$479$	−2.76106	+	36.8437i	−0.126156	+	1.68343i	−0.597801	+	0.801645i	$0.703959\pi$
$480$	−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	0.0623585	−	0.998054i	$-0.480138\pi$
$487$	−20.4846	−	19.0069i	−0.928244	−	0.861285i	−0.990603	+	0.136769i	$0.956328\pi$
$488$	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	0.925682	+	0.378303i	$0.123492\pi$
$499$	1.49046	+	19.8888i	0.0667222	+	0.890346i	−0.858960	+	0.512043i	$0.828889\pi$
$500$	−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	−0.0343972	−	0.999408i	$-0.510951\pi$
$503$	16.2718	−	7.83610i	0.725525	−	0.349395i	0.759923	+	0.650014i	$0.225237\pi$
$504$	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	0.999555	−	0.0298319i	$-0.00949720\pi$
$509$	10.6926	+	18.5202i	0.473942	+	0.820892i	−0.525613	+	0.850724i	$0.676164\pi$
$510$	−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	−0.903109	−	0.429412i	$-0.858721\pi$
$521$	−1.81855	+	3.14983i	−0.0796722	+	0.137996i	0.823436	+	0.567409i	$0.192054\pi$
$522$	−5.86140	+	0.883465i	−0.256547	+	0.0386682i
$523$	28.4024	−	26.3535i	1.24195	−	1.15236i	0.259517	−	0.965739i	$-0.416437\pi$
$523$	28.4024	−	26.3535i	1.24195	−	1.15236i	0.982432	−	0.186621i	$-0.0597538\pi$
$524$	−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	0.383945	−	0.923356i	$-0.374565\pi$
$541$	−7.79917	−	5.31739i	−0.335313	−	0.228612i	−0.719257	+	0.694744i	$0.755518\pi$
$542$	−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	−0.473494	−	0.880797i	$-0.657007\pi$
$547$	7.84137	−	34.3553i	0.335273	−	1.46893i	0.808767	−	0.588130i	$-0.200135\pi$
$548$	−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	−0.201290	−	0.979532i	$-0.564513\pi$
$557$	17.6453	−	30.5625i	0.747654	−	1.29498i	0.948944	−	0.315444i	$-0.102153\pi$
$558$	−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	−0.476835	−	0.878993i	$-0.658216\pi$
$563$	3.96701	−	2.70466i	0.167189	−	0.113988i	0.644024	+	0.765005i	$0.277264\pi$
$564$	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	0.697915	−	0.716180i	$-0.254111\pi$
$569$	−6.47087	−	11.2079i	−0.271273	−	0.469858i	−0.969188	+	0.246322i	$0.920778\pi$
$570$	0.808782	−	1.40085i	0.0338762	−	0.0586752i
$571$	−29.0521	+	4.37889i	−1.21579	+	0.183251i	−0.725447	−	0.688278i	$-0.758367\pi$
$571$	−29.0521	+	4.37889i	−1.21579	+	0.183251i	−0.490344	+	0.871529i	$0.663129\pi$
$572$	−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	0.381654	+	0.924305i	$0.375355\pi$
$577$	−3.20673	+	42.7908i	−0.133498	+	1.78140i	−0.515152	+	0.857099i	$0.672264\pi$
$578$	−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	−0.437538	−	0.899200i	$-0.644149\pi$
$593$	−7.12310	+	2.19719i	−0.292511	+	0.0902277i	0.145027	+	0.989428i	$0.453673\pi$
$594$	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	−0.897253	−	0.441516i	$-0.854441\pi$
$599$	1.36526	−	18.2181i	0.0557830	−	0.744372i	0.953036	−	0.302856i	$-0.0979402\pi$
$600$	6.66105	−	16.9721i	0.271936	−	0.692882i
$601$	38.3761	−	18.4810i	1.56540	−	0.753855i	0.567800	−	0.823166i	$-0.307795\pi$
$601$	38.3761	−	18.4810i	1.56540	−	0.753855i	0.997595	+	0.0693118i	$0.0220803\pi$
$602$	−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	−0.720349	−	0.693611i	$-0.756019\pi$
$607$	−23.6731	−	41.0029i	−0.960860	−	1.66426i	−0.240510	−	0.970647i	$-0.577315\pi$
$608$	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	−0.981102	−	0.193492i	$-0.938019\pi$
$613$	−28.7059	+	19.5714i	−1.15942	+	0.790480i	−0.178320	+	0.983973i	$0.557066\pi$
$614$	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	0.964252	−	0.264985i	$-0.0853671\pi$
$617$	12.2047	+	15.3043i	0.491344	+	0.616126i	−0.472908	+	0.881112i	$0.656796\pi$
$618$	8.34482	+	14.4537i	0.335678	+	0.581411i
$619$	10.9182	−	18.9108i	0.438838	−	0.760090i	−0.558762	−	0.829328i	$-0.688724\pi$
$619$	10.9182	−	18.9108i	0.438838	−	0.760090i	0.997600	+	0.0692382i	$0.0220568\pi$
$620$	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	−0.993902	−	0.110264i	$-0.964830\pi$
$631$	−3.67424	−	16.0979i	−0.146269	−	0.640846i	0.847633	−	0.530582i	$-0.178027\pi$
$632$	−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	−0.940672	−	0.339318i	$-0.889804\pi$
$641$	−12.2009	−	31.0873i	−0.481906	−	1.22788i	0.458766	−	0.888557i	$-0.348292\pi$
$642$	21.1323	−	6.51844i	0.834024	−	0.257262i
$643$	−1.25770	−	5.51036i	−0.0495990	−	0.217307i	0.944055	−	0.329788i	$-0.106977\pi$
$643$	−1.25770	−	5.51036i	−0.0495990	−	0.217307i	−0.993654	+	0.112481i	$0.964120\pi$
$644$	−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	−0.280561	−	0.959836i	$-0.590521\pi$
$647$	−26.7860	−	8.26239i	−1.05307	−	0.324828i	−0.772505	+	0.635008i	$0.780997\pi$
$648$	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	−0.864551	−	0.502544i	$-0.832397\pi$
$653$	−10.9376	+	10.1486i	−0.428020	+	0.397145i	0.436531	+	0.899689i	$0.356207\pi$
$654$	−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	−0.123890	−	0.992296i	$-0.539537\pi$
$659$	22.3619	−	28.0409i	0.871096	−	1.09232i	0.994985	−	0.100023i	$-0.0318917\pi$
$660$	−0.964469	−	0.145370i	−0.0375419	−	0.00565853i
$661$	22.8950	−	15.6096i	0.890513	−	0.607142i	−0.0292685	−	0.999572i	$-0.509318\pi$
$661$	22.8950	−	15.6096i	0.890513	−	0.607142i	0.919782	+	0.392430i	$0.128365\pi$
$662$	−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	−0.151694	−	0.988428i	$-0.548473\pi$
$673$	13.6589	−	6.57776i	0.526511	−	0.253554i	0.678204	+	0.734873i	$0.262758\pi$
$674$	−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	−0.999544	−	0.0301926i	$-0.990388\pi$
$677$	−0.407566	−	5.43860i	−0.0156641	−	0.209022i	0.983880	−	0.178830i	$-0.0572311\pi$
$678$	−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	0.125106	−	0.992143i	$-0.460073\pi$
$683$	−22.3425	−	20.7309i	−0.854914	−	0.793244i	−0.980020	+	0.198899i	$0.936263\pi$
$684$	−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	0.149160	−	0.988813i	$-0.452343\pi$
$691$	21.8029	−	6.72529i	0.829420	−	0.255842i	0.680260	+	0.732971i	$0.261867\pi$
$692$	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	0.237063	−	0.971494i	$-0.423815\pi$
$701$	−9.92005	−	4.77724i	−0.374675	−	0.180434i	−0.611738	+	0.791060i	$0.709529\pi$
$702$	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	0.896172	−	0.443706i	$-0.146337\pi$
$709$	43.1823	+	6.50868i	1.62175	+	0.244439i	0.725573	+	0.688145i	$0.241575\pi$
$710$	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	−0.429694	−	0.902974i	$-0.641379\pi$
$719$	11.7619	−	10.9134i	0.438644	−	0.407002i	0.868339	+	0.495972i	$0.165188\pi$
$720$	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	0.573267	+	0.819368i	$0.305676\pi$
$727$	−8.05489	+	35.2908i	−0.298739	+	1.30886i	−0.872007	+	0.489494i	$0.837181\pi$
$728$	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	0.675682	−	0.737193i	$-0.263849\pi$
$733$	6.39764	+	4.36183i	0.236302	+	0.161108i	−0.439380	+	0.898301i	$0.644802\pi$
$734$	−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	0.998263	+	0.0589133i	$0.0187635\pi$
$739$	8.33358	+	21.2336i	0.306556	+	0.781091i	−0.691707	+	0.722178i	$0.743141\pi$
$740$	−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	0.0536751	+	0.998558i	$0.482906\pi$
$743$	−11.6649	+	51.1072i	−0.427943	+	1.87494i	−0.481618	+	0.876381i	$0.659951\pi$
$744$	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	0.0734031	−	0.997302i	$-0.476614\pi$
$751$	29.4159	−	27.2940i	1.07340	−	0.995972i	0.999999	+	0.00133063i	$0.000423553\pi$
$752$	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	−0.455983	−	0.889989i	$-0.650712\pi$
$757$	14.1188	−	17.7045i	0.513158	−	0.643480i	0.969141	+	0.246509i	$0.0792835\pi$
$758$	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	−0.0173338	−	0.999850i	$-0.505518\pi$
$761$	−9.06507	−	1.36634i	−0.328608	−	0.0495297i	−0.311275	+	0.950320i	$0.600756\pi$
$762$	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	0.542985	−	0.839742i	$-0.317294\pi$
$769$	6.23927	+	3.00467i	0.224994	+	0.108351i	−0.317991	+	0.948094i	$0.603008\pi$
$770$	−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	0.831667	+	0.555275i	$0.187387\pi$
$773$	−2.04269	+	27.2578i	−0.0734704	+	0.980395i	−0.905137	+	0.425120i	$0.860232\pi$
$774$	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	−0.950326	−	0.311255i	$-0.899251\pi$
$787$	−37.3597	−	34.6647i	−1.33173	−	1.23566i	−0.381403	−	0.924409i	$-0.624559\pi$
$788$	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	−0.263919	−	0.964545i	$-0.585015\pi$
$797$	9.19325	−	4.42723i	0.325641	−	0.156821i	0.589561	+	0.807724i	$0.299301\pi$
$798$	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	−0.634238	−	0.773138i	$-0.718686\pi$
$809$	−4.15999	+	2.83624i	−0.146258	+	0.0997167i	0.487980	+	0.872855i	$0.337734\pi$
$810$	−4.92074	−	0.741682i	−0.172897	−	0.0260601i
$811$	−0.874994	+	1.09721i	−0.0307252	+	0.0385282i	−0.796957	−	0.604036i	$-0.793558\pi$
$811$	−0.874994	+	1.09721i	−0.0307252	+	0.0385282i	0.766232	+	0.642565i	$0.222130\pi$
$812$	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	0.725535	+	0.688185i	$0.241592\pi$
$821$	−7.86254	+	20.0334i	−0.274405	+	0.699171i	−0.999940	+	0.0109862i	$0.996503\pi$
$822$	0.585560	−	7.81376i	0.0204238	−	0.272536i
$823$	51.7545	+	15.9641i	1.80405	+	0.556475i	0.999310	−	0.0371543i	$-0.0118293\pi$
$823$	51.7545	+	15.9641i	1.80405	+	0.556475i	0.804739	+	0.593629i	$0.202305\pi$
$824$	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	0.997755	−	0.0669725i	$-0.0213340\pi$
$827$	2.00586	+	8.78824i	0.0697505	+	0.305597i	−0.928004	+	0.372569i	$0.878477\pi$
$828$	−85.8465	+	26.4801i	−2.98337	+	0.920249i
$829$	4.10424	+	10.4574i	0.142546	+	0.363201i	0.984261	−	0.176721i	$-0.0565489\pi$
$829$	4.10424	+	10.4574i	0.142546	+	0.363201i	−0.841715	+	0.539922i	$0.818454\pi$
$830$	−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	−0.601667	−	0.798747i	$-0.705496\pi$
$839$	−11.7643	−	51.5426i	−0.406147	−	1.77945i	0.195520	−	0.980700i	$-0.437361\pi$
$840$	−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	−0.997250	−	0.0741097i	$-0.976388\pi$
$853$	−24.7549	−	31.0417i	−0.847593	−	1.06285i	0.149657	−	0.988738i	$-0.452183\pi$
$854$	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	0.159861	−	0.987139i	$-0.448895\pi$
$857$	33.2901	−	22.6968i	1.13717	−	0.775308i	0.977306	+	0.211832i	$0.0679429\pi$
$858$	−1.53491	+	1.04648i	−0.0524008	+	0.0357263i
$859$	15.9072	+	2.39762i	0.542746	+	0.0818057i	0.414693	−	0.909962i	$-0.363889\pi$
$859$	15.9072	+	2.39762i	0.542746	+	0.0818057i	0.128053	+	0.991767i	$0.459127\pi$
$860$	−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	0.978133	−	0.207982i	$-0.0666894\pi$
$863$	9.07595	+	15.7200i	0.308949	+	0.535115i	−0.669184	+	0.743097i	$0.733356\pi$
$864$	−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	0.245992	−	0.969272i	$-0.420886\pi$
$877$	29.4735	−	9.09138i	0.995251	−	0.306994i	0.749258	+	0.662278i	$0.230410\pi$
$878$	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	−0.893493	−	0.449077i	$-0.851753\pi$
$887$	−41.0629	+	12.6662i	−1.37876	+	0.425290i	−0.485264	+	0.874368i	$0.661277\pi$
$888$	−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	−0.952273	−	0.305248i	$-0.901261\pi$
$907$	−30.5992	+	20.8622i	−1.01603	+	0.692718i	−0.0637572	+	0.997965i	$0.520308\pi$
$908$	−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	0.997194	−	0.0748550i	$-0.0238494\pi$
$911$	21.1980	+	26.5814i	0.702320	+	0.880681i	−0.294875	+	0.955536i	$0.595278\pi$
$912$	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	−0.970896	−	0.239501i	$-0.923016\pi$
$919$	−2.91863	+	7.43655i	−0.0962767	+	0.245309i	0.874619	+	0.484810i	$0.161111\pi$
$920$	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	−0.999601	−	0.0282298i	$-0.991013\pi$
$929$	−42.3993	−	28.9073i	−1.39108	−	0.948419i	−0.391474	−	0.920189i	$-0.628035\pi$
$930$	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	0.914365	−	0.404891i	$-0.132691\pi$
$937$	−2.60572	−	11.4164i	−0.0851252	−	0.372958i	−0.999490	+	0.0319336i	$0.989833\pi$
$938$	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	0.138901	−	0.990306i	$-0.455643\pi$
$941$	−9.33136	−	2.87834i	−0.304193	−	0.0938313i	−0.443094	+	0.896475i	$0.646119\pi$
$942$	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	−0.599338	−	0.800496i	$-0.704570\pi$
$947$	4.74311	−	4.40096i	0.154130	−	0.143012i	0.753469	+	0.657484i	$0.228379\pi$
$948$	−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	−0.372197	−	0.928154i	$-0.621395\pi$
$953$	19.0012	−	23.8267i	0.615508	−	0.771822i	0.987705	+	0.156332i	$0.0499668\pi$
$954$	−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	−0.890572	−	0.454843i	$-0.849695\pi$
$967$	−33.9023	+	16.3265i	−1.09022	+	0.525024i	−0.199652	+	0.979867i	$0.563981\pi$
$968$	−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	0.994176	−	0.107771i	$-0.0343713\pi$
$971$	−0.154505	−	2.06172i	−0.00495829	−	0.0661638i	−0.999134	+	0.0416070i	$0.986752\pi$
$972$	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	0.640074	−	0.768313i	$-0.278904\pi$
$977$	−2.44612	−	2.26967i	−0.0782585	−	0.0726132i	−0.718332	+	0.695700i	$0.755094\pi$
$978$	−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	0.204441	−	0.978879i	$-0.434462\pi$
$983$	−23.7160	−	22.0052i	−0.756422	−	0.701857i	−0.960864	+	0.277021i	$0.910653\pi$
$984$	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	0.905679	+	0.423964i	$0.139362\pi$
$991$	−1.67074	+	22.2945i	−0.0530729	+	0.708208i	−0.958752	+	0.284244i	$0.908257\pi$
$992$	−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	−0.413009	−	0.910727i	$-0.635522\pi$
$997$	−17.0263	+	2.56630i	−0.539227	+	0.0812754i	−0.126218	+	0.992002i	$0.540284\pi$
$998$	−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.53.27	✓	324
49.37	even	21	inner	637.2.bl.a.625.27	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.a.53.27	✓	324	1.1	even	1	trivial
637.2.bl.a.625.27	yes	324	49.37	even	21	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
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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Database

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