LMFDB - Embedded newform 430.2.q.a.281.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			281.1
Character	$\chi$	$=$	430.281
Dual form			430.2.q.a.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.623490 + 0.781831i) q^{2} +(-0.305653 - 0.778792i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(0.0747301 - 0.997204i) q^{5} +(0.418312 - 0.724538i) q^{6} +(-1.41697 - 2.45427i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(1.68606 - 1.56444i) q^{9} +O(q^{10})$	\(q+(0.623490 + 0.781831i) q^{2} +(-0.305653 - 0.778792i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(0.0747301 - 0.997204i) q^{5} +(0.418312 - 0.724538i) q^{6} +(-1.41697 - 2.45427i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(1.68606 - 1.56444i) q^{9} +(0.826239 - 0.563320i) q^{10} +(-0.376271 - 1.64855i) q^{11} +(0.827280 - 0.124692i) q^{12} +(-3.50109 - 2.38701i) q^{13} +(1.03536 - 2.63804i) q^{14} +(-0.799456 + 0.246599i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(-0.236145 - 3.15113i) q^{17} +(2.27437 + 0.342806i) q^{18} +(4.63552 + 4.30114i) q^{19} +(0.955573 + 0.294755i) q^{20} +(-1.47826 + 1.85368i) q^{21} +(1.05429 - 1.32204i) q^{22} +(3.80843 + 1.17475i) q^{23} +(0.613289 + 0.569049i) q^{24} +(-0.988831 - 0.149042i) q^{25} +(-0.316660 - 4.22554i) q^{26} +(-3.99504 - 1.92391i) q^{27} +(2.70804 - 0.835320i) q^{28} +(1.01541 - 2.58723i) q^{29} +(-0.691252 - 0.471288i) q^{30} +(0.136147 - 0.0205209i) q^{31} +(-0.222521 - 0.974928i) q^{32} +(-1.16887 + 0.796923i) q^{33} +(2.31642 - 2.14932i) q^{34} +(-2.55330 + 1.22960i) q^{35} +(1.15003 + 1.99191i) q^{36} +(3.54642 - 6.14257i) q^{37} +(-0.472563 + 6.30592i) q^{38} +(-0.788860 + 3.45622i) q^{39} +(0.365341 + 0.930874i) q^{40} +(-0.452740 - 0.567718i) q^{41} -2.37095 q^{42} +(5.23615 + 3.94750i) q^{43} +1.69095 q^{44} +(-1.43406 - 1.79826i) q^{45} +(1.45607 + 3.70999i) q^{46} +(-2.30152 + 10.0836i) q^{47} +(-0.0625210 + 0.834285i) q^{48} +(-0.515620 + 0.893080i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-2.38190 + 1.14706i) q^{51} +(3.10623 - 2.88216i) q^{52} +(-5.31200 + 3.62166i) q^{53} +(-0.986694 - 4.32299i) q^{54} +(-1.67206 + 0.252023i) q^{55} +(2.34151 + 1.59642i) q^{56} +(1.93283 - 4.92477i) q^{57} +(2.65588 - 0.819229i) q^{58} +(6.07321 + 2.92470i) q^{59} +(-0.0625210 - 0.834285i) q^{60} +(-9.74975 - 1.46954i) q^{61} +(0.100930 + 0.0936495i) q^{62} +(-6.22865 - 1.92128i) q^{63} +(0.623490 - 0.781831i) q^{64} +(-2.64197 + 3.31292i) q^{65} +(-1.35184 - 0.416987i) q^{66} +(-3.65739 - 3.39356i) q^{67} +(3.12467 + 0.470968i) q^{68} +(-0.249177 - 3.32504i) q^{69} +(-2.55330 - 1.22960i) q^{70} +(-1.75367 + 0.540935i) q^{71} +(-0.840306 + 2.14106i) q^{72} +(6.91408 + 4.71394i) q^{73} +(7.01361 - 1.05713i) q^{74} +(0.186167 + 0.815649i) q^{75} +(-5.22480 + 3.56221i) q^{76} +(-3.51282 + 3.25942i) q^{77} +(-3.19403 + 1.53816i) q^{78} +(6.95409 + 12.0448i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(0.238422 - 3.18153i) q^{81} +(0.161581 - 0.707933i) q^{82} +(-2.00880 - 5.11834i) q^{83} +(-1.47826 - 1.85368i) q^{84} -3.15997 q^{85} +(0.178409 + 6.55501i) q^{86} -2.32528 q^{87} +(1.05429 + 1.32204i) q^{88} +(5.10849 + 13.0162i) q^{89} +(0.511811 - 2.24239i) q^{90} +(-0.897398 + 11.9749i) q^{91} +(-1.99275 + 3.45154i) q^{92} +(-0.0575953 - 0.0997580i) q^{93} +(-9.31867 + 4.48764i) q^{94} +(4.63552 - 4.30114i) q^{95} +(-0.691252 + 0.471288i) q^{96} +(-0.555383 - 2.43329i) q^{97} +(-1.01972 + 0.153698i) q^{98} +(-3.21347 - 2.19091i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9} + 3 q^{10} + 9 q^{11} - 16 q^{12} + 21 q^{13} - 6 q^{14} + 5 q^{15} - 6 q^{16} - 37 q^{17} + 19 q^{18} + 7 q^{19} + 3 q^{20} - 8 q^{21} + 16 q^{22} + 13 q^{23} + 5 q^{24} + 3 q^{25} - 21 q^{26} - 28 q^{27} - 6 q^{28} + 4 q^{29} - 2 q^{30} + 13 q^{31} - 6 q^{32} - 54 q^{33} - 23 q^{34} - 2 q^{35} - 9 q^{36} + 17 q^{37} + 28 q^{38} + 8 q^{39} + 3 q^{40} + 10 q^{41} - 50 q^{42} + 14 q^{43} - 26 q^{44} + 4 q^{45} - 8 q^{46} + 13 q^{47} - 2 q^{48} + 5 q^{49} - 18 q^{50} + 17 q^{51} - 7 q^{52} - 71 q^{53} + 7 q^{54} - 29 q^{55} + q^{56} - 70 q^{57} + 25 q^{58} + 8 q^{59} - 2 q^{60} + 25 q^{61} - 15 q^{62} + 88 q^{63} - 6 q^{64} + 7 q^{65} + 44 q^{66} + 26 q^{67} - 9 q^{68} + 78 q^{69} - 2 q^{70} - 60 q^{71} - 23 q^{72} + 7 q^{73} + 17 q^{74} - 10 q^{75} - 35 q^{76} - 5 q^{77} + 57 q^{78} + 52 q^{79} - 18 q^{80} + q^{81} - 4 q^{82} - 101 q^{83} - 8 q^{84} - 24 q^{85} + 49 q^{86} - 18 q^{87} + 16 q^{88} + 14 q^{89} - 3 q^{90} + 35 q^{91} + 6 q^{92} + 28 q^{93} - 15 q^{94} + 7 q^{95} - 2 q^{96} + 11 q^{97} + 12 q^{98} + 78 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9 + 3 * q^10 + 9 * q^11 - 16 * q^12 + 21 * q^13 - 6 * q^14 + 5 * q^15 - 6 * q^16 - 37 * q^17 + 19 * q^18 + 7 * q^19 + 3 * q^20 - 8 * q^21 + 16 * q^22 + 13 * q^23 + 5 * q^24 + 3 * q^25 - 21 * q^26 - 28 * q^27 - 6 * q^28 + 4 * q^29 - 2 * q^30 + 13 * q^31 - 6 * q^32 - 54 * q^33 - 23 * q^34 - 2 * q^35 - 9 * q^36 + 17 * q^37 + 28 * q^38 + 8 * q^39 + 3 * q^40 + 10 * q^41 - 50 * q^42 + 14 * q^43 - 26 * q^44 + 4 * q^45 - 8 * q^46 + 13 * q^47 - 2 * q^48 + 5 * q^49 - 18 * q^50 + 17 * q^51 - 7 * q^52 - 71 * q^53 + 7 * q^54 - 29 * q^55 + q^56 - 70 * q^57 + 25 * q^58 + 8 * q^59 - 2 * q^60 + 25 * q^61 - 15 * q^62 + 88 * q^63 - 6 * q^64 + 7 * q^65 + 44 * q^66 + 26 * q^67 - 9 * q^68 + 78 * q^69 - 2 * q^70 - 60 * q^71 - 23 * q^72 + 7 * q^73 + 17 * q^74 - 10 * q^75 - 35 * q^76 - 5 * q^77 + 57 * q^78 + 52 * q^79 - 18 * q^80 + q^81 - 4 * q^82 - 101 * q^83 - 8 * q^84 - 24 * q^85 + 49 * q^86 - 18 * q^87 + 16 * q^88 + 14 * q^89 - 3 * q^90 + 35 * q^91 + 6 * q^92 + 28 * q^93 - 15 * q^94 + 7 * q^95 - 2 * q^96 + 11 * q^97 + 12 * q^98 + 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{8}{21}\right)$

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 $

$2$	0.623490	+	0.781831i	0.440874	+	0.552838i
$2$	0.623490	+	0.781831i	0.440874	+	0.552838i
$3$	−0.305653	−	0.778792i	−0.176469	−	0.449636i	0.815083	−	0.579344i	$-0.196691\pi$
$3$	−0.305653	−	0.778792i	−0.176469	−	0.449636i	−0.991552	+	0.129708i	$0.958596\pi$
$4$	−0.222521	+	0.974928i	−0.111260	+	0.487464i
$5$	0.0747301	−	0.997204i	0.0334203	−	0.445963i
$5$	0.0747301	−	0.997204i	0.0334203	−	0.445963i
$6$	0.418312	−	0.724538i	0.170775	−	0.295792i
$7$	−1.41697	−	2.45427i	−0.535565	−	0.927626i	−0.999136	−	0.0415660i	$-0.986765\pi$
$7$	−1.41697	−	2.45427i	−0.535565	−	0.927626i	0.463571	−	0.886060i	$-0.346568\pi$
$8$	−0.900969	+	0.433884i	−0.318541	+	0.153401i
$9$	1.68606	−	1.56444i	0.562021	−	0.521479i
$10$	0.826239	−	0.563320i	0.261280	−	0.178137i
$11$	−0.376271	−	1.64855i	−0.113450	−	0.497057i	−0.999443	−	0.0333593i	$-0.989379\pi$
$11$	−0.376271	−	1.64855i	−0.113450	−	0.497057i	0.885993	−	0.463698i	$-0.153478\pi$
$12$	0.827280	−	0.124692i	0.238815	−	0.0359956i
$13$	−3.50109	−	2.38701i	−0.971029	−	0.662036i	−0.0297114	−	0.999559i	$-0.509459\pi$
$13$	−3.50109	−	2.38701i	−0.971029	−	0.662036i	−0.941318	+	0.337522i	$0.890411\pi$
$14$	1.03536	−	2.63804i	0.276711	−	0.705047i
$15$	−0.799456	+	0.246599i	−0.206419	+	0.0636717i
$16$	−0.900969	−	0.433884i	−0.225242	−	0.108471i
$17$	−0.236145	−	3.15113i	−0.0572735	−	0.764261i	−0.949718	−	0.313105i	$-0.898631\pi$
$17$	−0.236145	−	3.15113i	−0.0572735	−	0.764261i	0.892445	−	0.451156i	$-0.148988\pi$
$18$	2.27437	+	0.342806i	0.536074	+	0.0808001i
$19$	4.63552	+	4.30114i	1.06346	+	0.986749i	0.999937	−	0.0112314i	$-0.00357513\pi$
$19$	4.63552	+	4.30114i	1.06346	+	0.986749i	0.0635254	+	0.997980i	$0.479766\pi$
$20$	0.955573	+	0.294755i	0.213673	+	0.0659093i
$21$	−1.47826	+	1.85368i	−0.322583	+	0.404507i
$22$	1.05429	−	1.32204i	0.224775	−	0.281859i
$23$	3.80843	+	1.17475i	0.794113	+	0.244951i	0.665162	−	0.746700i	$-0.268363\pi$
$23$	3.80843	+	1.17475i	0.794113	+	0.244951i	0.128951	+	0.991651i	$0.458839\pi$
$24$	0.613289	+	0.569049i	0.125187	+	0.116157i
$25$	−0.988831	−	0.149042i	−0.197766	−	0.0298085i
$26$	−0.316660	−	4.22554i	−0.0621022	−	0.828697i
$27$	−3.99504	−	1.92391i	−0.768846	−	0.370257i
$28$	2.70804	−	0.835320i	0.511771	−	0.157861i
$29$	1.01541	−	2.58723i	0.188557	−	0.480436i	−0.805066	−	0.593185i	$-0.797870\pi$
$29$	1.01541	−	2.58723i	0.188557	−	0.480436i	0.993624	+	0.112749i	$0.0359655\pi$
$30$	−0.691252	−	0.471288i	−0.126205	−	0.0860449i
$31$	0.136147	−	0.0205209i	0.0244527	−	0.00368566i	−0.136805	−	0.990598i	$-0.543683\pi$
$31$	0.136147	−	0.0205209i	0.0244527	−	0.00368566i	0.161257	+	0.986912i	$0.448445\pi$
$32$	−0.222521	−	0.974928i	−0.0393365	−	0.172345i
$33$	−1.16887	+	0.796923i	−0.203474	+	0.138726i
$34$	2.31642	−	2.14932i	0.397263	−	0.368606i
$35$	−2.55330	+	1.22960i	−0.431586	+	0.207841i
$36$	1.15003	+	1.99191i	0.191672	+	0.331985i
$37$	3.54642	−	6.14257i	0.583027	−	1.00983i	−0.412091	−	0.911143i	$-0.635201\pi$
$37$	3.54642	−	6.14257i	0.583027	−	1.00983i	0.995118	−	0.0986900i	$-0.0314652\pi$
$38$	−0.472563	+	6.30592i	−0.0766598	+	1.02295i
$39$	−0.788860	+	3.45622i	−0.126319	+	0.553438i
$40$	0.365341	+	0.930874i	0.0577655	+	0.147184i
$41$	−0.452740	−	0.567718i	−0.0707061	−	0.0886627i	0.745221	−	0.666818i	$-0.232344\pi$
$41$	−0.452740	−	0.567718i	−0.0707061	−	0.0886627i	−0.815927	+	0.578155i	$0.803773\pi$
$42$	−2.37095			−0.365845
$43$	5.23615	+	3.94750i	0.798505	+	0.601988i
$43$	5.23615	+	3.94750i	0.798505	+	0.601988i
$44$	1.69095			0.254920
$45$	−1.43406	−	1.79826i	−0.213778	−	0.268069i
$46$	1.45607	+	3.70999i	0.214685	+	0.547009i
$47$	−2.30152	+	10.0836i	−0.335712	+	1.47085i	0.472172	+	0.881506i	$0.343470\pi$
$47$	−2.30152	+	10.0836i	−0.335712	+	1.47085i	−0.807884	+	0.589342i	$0.799387\pi$
$48$	−0.0625210	+	0.834285i	−0.00902414	+	0.120419i
$49$	−0.515620	+	0.893080i	−0.0736600	+	0.127583i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−2.38190	+	1.14706i	−0.333532	+	0.160621i
$52$	3.10623	−	2.88216i	0.430756	−	0.399683i
$53$	−5.31200	+	3.62166i	−0.729659	+	0.497473i	−0.870260	−	0.492593i	$-0.836049\pi$
$53$	−5.31200	+	3.62166i	−0.729659	+	0.497473i	0.140601	+	0.990066i	$0.455097\pi$
$54$	−0.986694	−	4.32299i	−0.134272	−	0.588284i
$55$	−1.67206	+	0.252023i	−0.225461	+	0.0339827i
$56$	2.34151	+	1.59642i	0.312898	+	0.213330i
$57$	1.93283	−	4.92477i	0.256009	−	0.652301i
$58$	2.65588	−	0.819229i	0.348734	−	0.107570i
$59$	6.07321	+	2.92470i	0.790665	+	0.380764i	0.785217	−	0.619221i	$-0.212552\pi$
$59$	6.07321	+	2.92470i	0.790665	+	0.380764i	0.00544807	+	0.999985i	$0.498266\pi$
$60$	−0.0625210	−	0.834285i	−0.00807143	−	0.107706i
$61$	−9.74975	−	1.46954i	−1.24833	−	0.188155i	−0.508565	−	0.861024i	$-0.669824\pi$
$61$	−9.74975	−	1.46954i	−1.24833	−	0.188155i	−0.739762	+	0.672869i	$0.765062\pi$
$62$	0.100930	+	0.0936495i	0.0128181	+	0.0118935i
$63$	−6.22865	−	1.92128i	−0.784736	−	0.242059i
$64$	0.623490	−	0.781831i	0.0779362	−	0.0977289i
$65$	−2.64197	+	3.31292i	−0.327696	+	0.410918i
$66$	−1.35184	−	0.416987i	−0.166400	−	0.0513275i
$67$	−3.65739	−	3.39356i	−0.446821	−	0.414590i	0.424404	−	0.905473i	$-0.360484\pi$
$67$	−3.65739	−	3.39356i	−0.446821	−	0.414590i	−0.871225	+	0.490883i	$0.836674\pi$
$68$	3.12467	+	0.470968i	0.378922	+	0.0571133i
$69$	−0.249177	−	3.32504i	−0.0299974	−	0.400288i
$70$	−2.55330	−	1.22960i	−0.305177	−	0.146966i
$71$	−1.75367	+	0.540935i	−0.208122	+	0.0641972i	−0.397063	−	0.917791i	$-0.629971\pi$
$71$	−1.75367	+	0.540935i	−0.208122	+	0.0641972i	0.188941	+	0.981988i	$0.439494\pi$
$72$	−0.840306	+	2.14106i	−0.0990310	+	0.252327i
$73$	6.91408	+	4.71394i	0.809232	+	0.551725i	0.895767	−	0.444524i	$-0.146627\pi$
$73$	6.91408	+	4.71394i	0.809232	+	0.551725i	−0.0865348	+	0.996249i	$0.527579\pi$
$74$	7.01361	−	1.05713i	0.815316	−	0.122889i
$75$	0.186167	+	0.815649i	0.0214967	+	0.0941830i
$76$	−5.22480	+	3.56221i	−0.599326	+	0.408613i
$77$	−3.51282	+	3.25942i	−0.400323	+	0.371446i
$78$	−3.19403	+	1.53816i	−0.361653	+	0.174163i
$79$	6.95409	+	12.0448i	0.782396	+	1.35515i	0.930542	+	0.366185i	$0.119336\pi$
$79$	6.95409	+	12.0448i	0.782396	+	1.35515i	−0.148146	+	0.988966i	$0.547331\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	0.238422	−	3.18153i	0.0264914	−	0.353503i
$82$	0.161581	−	0.707933i	0.0178436	−	0.0781781i
$83$	−2.00880	−	5.11834i	−0.220495	−	0.561811i	0.777231	−	0.629215i	$-0.216624\pi$
$83$	−2.00880	−	5.11834i	−0.220495	−	0.561811i	−0.997726	+	0.0674040i	$0.978528\pi$
$84$	−1.47826	−	1.85368i	−0.161292	−	0.202253i
$85$	−3.15997			−0.342746
$86$	0.178409	+	6.55501i	0.0192383	+	0.706845i
$87$	−2.32528			−0.249296
$88$	1.05429	+	1.32204i	0.112388	+	0.140930i
$89$	5.10849	+	13.0162i	0.541499	+	1.37972i	0.895747	+	0.444565i	$0.146642\pi$
$89$	5.10849	+	13.0162i	0.541499	+	1.37972i	−0.354248	+	0.935152i	$0.615263\pi$
$90$	0.511811	−	2.24239i	0.0539496	−	0.236369i
$91$	−0.897398	+	11.9749i	−0.0940729	+	1.25532i
$92$	−1.99275	+	3.45154i	−0.207758	+	0.359848i
$93$	−0.0575953	−	0.0997580i	−0.00597235	−	0.0103444i
$94$	−9.31867	+	4.48764i	−0.961148	+	0.462864i
$95$	4.63552	−	4.30114i	0.475595	−	0.441288i
$96$	−0.691252	+	0.471288i	−0.0705506	+	0.0481006i
$97$	−0.555383	−	2.43329i	−0.0563906	−	0.247063i	0.938875	−	0.344259i	$-0.111870\pi$
$97$	−0.555383	−	2.43329i	−0.0563906	−	0.247063i	−0.995265	+	0.0971957i	$0.969013\pi$
$98$	−1.01972	+	0.153698i	−0.103007	+	0.0155259i
$99$	−3.21347	−	2.19091i	−0.322966	−	0.220195i
$100$	0.365341	−	0.930874i	0.0365341	−	0.0930874i
$101$	−3.60198	+	1.11106i	−0.358410	+	0.110555i	−0.468730	−	0.883341i	$-0.655288\pi$
$101$	−3.60198	+	1.11106i	−0.358410	+	0.110555i	0.110321	+	0.993896i	$0.464812\pi$
$102$	−2.38190	−	1.14706i	−0.235843	−	0.113576i
$103$	−0.781054	−	10.4224i	−0.0769595	−	1.02695i	−0.893323	−	0.449415i	$-0.851632\pi$
$103$	−0.781054	−	10.4224i	−0.0769595	−	1.02695i	0.816363	−	0.577538i	$-0.195987\pi$
$104$	4.19006	+	0.631550i	0.410869	+	0.0619286i
$105$	1.73803	+	1.61265i	0.169614	+	0.157379i
$106$	−6.14350	−	1.89502i	−0.596710	−	0.184061i
$107$	0.418923	−	0.525313i	0.0404988	−	0.0507839i	−0.761170	−	0.648553i	$-0.775375\pi$
$107$	0.418923	−	0.525313i	0.0404988	−	0.0507839i	0.801668	+	0.597769i	$0.203946\pi$
$108$	2.76465	−	3.46677i	0.266029	−	0.333590i
$109$	10.6372	+	3.28113i	1.01885	+	0.314275i	0.758803	−	0.651320i	$-0.225784\pi$
$109$	10.6372	+	3.28113i	1.01885	+	0.314275i	0.260051	+	0.965595i	$0.416261\pi$
$110$	−1.23955	−	1.15014i	−0.118187	−	0.109661i
$111$	−5.86776	−	0.884423i	−0.556943	−	0.0839457i
$112$	0.211781	+	2.82602i	0.0200114	+	0.267034i
$113$	3.92704	+	1.89116i	0.369425	+	0.177906i	0.609380	−	0.792878i	$-0.291418\pi$
$113$	3.92704	+	1.89116i	0.369425	+	0.177906i	−0.239955	+	0.970784i	$0.577133\pi$
$114$	5.05544	−	1.55940i	0.473485	−	0.146051i
$115$	1.45607	−	3.70999i	0.135779	−	0.345959i
$116$	2.29641	+	1.56567i	0.213216	+	0.145368i
$117$	−9.63739	+	1.45260i	−0.890977	+	0.134293i
$118$	1.49996	+	6.57175i	0.138082	+	0.604979i
$119$	−7.39911	+	5.04462i	−0.678275	+	0.462440i
$120$	0.613289	−	0.569049i	0.0559854	−	0.0519469i
$121$	7.33451	−	3.53212i	0.666774	−	0.321101i
$122$	−4.92994	−	8.53890i	−0.446335	−	0.773076i
$123$	−0.303753	+	0.526115i	−0.0273885	+	0.0474382i
$124$	−0.0102892	+	0.137300i	−0.000923998	+	0.0123299i
$125$	−0.222521	+	0.974928i	−0.0199029	+	0.0872002i
$126$	−2.38138	−	6.06766i	−0.212150	−	0.540550i
$127$	−8.11946	−	10.1815i	−0.720486	−	0.903461i	0.277879	−	0.960616i	$-0.410368\pi$
$127$	−8.11946	−	10.1815i	−0.720486	−	0.903461i	−0.998365	+	0.0571551i	$0.981797\pi$
$128$	1.00000			0.0883883
$129$	1.47383	−	5.28444i	0.129764	−	0.465269i
$130$	−4.23739			−0.371644
$131$	9.11862	+	11.4344i	0.796698	+	0.999027i	0.999803	+	0.0198702i	$0.00632531\pi$
$131$	9.11862	+	11.4344i	0.796698	+	0.999027i	−0.203105	+	0.979157i	$0.565103\pi$
$132$	−0.516844	−	1.31690i	−0.0449855	−	0.114621i
$133$	3.98774	−	17.4714i	0.345781	−	1.51496i
$134$	0.372848	−	4.97532i	0.0322092	−	0.429802i
$135$	−2.21708	+	3.84010i	−0.190816	+	0.330503i
$136$	1.57998	+	2.73661i	0.135482	+	0.234662i
$137$	9.31551	−	4.48611i	0.795878	−	0.383275i	0.00867005	−	0.999962i	$-0.497240\pi$
$137$	9.31551	−	4.48611i	0.795878	−	0.383275i	0.787208	+	0.616688i	$0.211526\pi$
$138$	2.44426	−	2.26794i	0.208069	−	0.193060i
$139$	−15.3936	+	10.4952i	−1.30567	+	0.890189i	−0.998117	−	0.0613430i	$-0.980462\pi$
$139$	−15.3936	+	10.4952i	−1.30567	+	0.890189i	−0.307550	+	0.951532i	$0.599509\pi$
$140$	−0.630612	−	2.76289i	−0.0532964	−	0.233507i
$141$	8.55652	−	1.28969i	0.720589	−	0.108611i
$142$	−1.51632	−	1.03381i	−0.127246	−	0.0867551i
$143$	−2.61774	+	6.66990i	−0.218907	+	0.557765i
$144$	−2.19787	+	0.677954i	−0.183156	+	0.0564962i
$145$	−2.50411	−	1.20592i	−0.207955	−	0.100146i
$146$	0.625352	+	8.34474i	0.0517545	+	0.690616i
$147$	0.853124	+	0.128588i	0.0703645	+	0.0106057i
$148$	5.19941	+	4.82435i	0.427389	+	0.396559i
$149$	−12.0665	−	3.72201i	−0.988523	−	0.304919i	−0.241998	−	0.970277i	$-0.577803\pi$
$149$	−12.0665	−	3.72201i	−0.988523	−	0.304919i	−0.746525	+	0.665358i	$0.768279\pi$
$150$	−0.521627	+	0.654100i	−0.0425907	+	0.0534070i
$151$	11.7267	−	14.7049i	0.954308	−	1.19666i	−0.0260945	−	0.999659i	$-0.508307\pi$
$151$	11.7267	−	14.7049i	0.954308	−	1.19666i	0.980402	−	0.197005i	$-0.0631215\pi$
$152$	−6.04266	−	1.86391i	−0.490124	−	0.151183i
$153$	−5.32790	−	4.94357i	−0.430735	−	0.399664i
$154$	−4.73853	−	0.714218i	−0.381842	−	0.0575534i
$155$	−0.0102892	−	0.137300i	−0.000826449	−	0.0110282i
$156$	−3.19403	−	1.53816i	−0.255727	−	0.123152i
$157$	−14.6110	+	4.50690i	−1.16609	+	0.359690i	−0.816574	−	0.577241i	$-0.804129\pi$
$157$	−14.6110	+	4.50690i	−1.16609	+	0.359690i	−0.349513	+	0.936931i	$0.613653\pi$
$158$	−5.08123	+	12.9468i	−0.404241	+	1.02999i
$159$	4.44415	+	3.02997i	0.352444	+	0.240292i
$160$	−0.988831	+	0.149042i	−0.0781739	+	0.0117828i
$161$	−2.51330	−	11.0115i	−0.198076	−	0.867827i
$162$	2.63607	−	1.79724i	0.207109	−	0.141205i
$163$	10.9646	−	10.1737i	0.858813	−	0.796862i	−0.121854	−	0.992548i	$-0.538884\pi$
$163$	10.9646	−	10.1737i	0.858813	−	0.796862i	0.980667	+	0.195686i	$0.0626934\pi$
$164$	0.654228	−	0.315060i	0.0510866	−	0.0246020i
$165$	0.707344	+	1.22516i	0.0550667	+	0.0953783i
$166$	2.74921	−	4.76178i	0.213380	−	0.369586i
$167$	−1.06387	+	14.1963i	−0.0823245	+	1.09854i	0.791133	+	0.611644i	$0.209492\pi$
$167$	−1.06387	+	14.1963i	−0.0823245	+	1.09854i	−0.873458	+	0.486900i	$0.838127\pi$
$168$	0.527586	−	2.31150i	0.0407041	−	0.178336i
$169$	1.81043	+	4.61291i	0.139264	+	0.354839i
$170$	−1.97021	−	2.47056i	−0.151108	−	0.189483i
$171$	14.5446			1.11226
$172$	−5.01368	+	4.22647i	−0.382289	+	0.322265i
$173$	2.91160			0.221365			0.110682	−	0.993856i	$-0.464696\pi$
$173$	2.91160			0.221365			0.110682	+	0.993856i	$0.464696\pi$
$174$	−1.44979	−	1.81798i	−0.109908	−	0.137820i
$175$	1.03536	+	2.63804i	0.0782656	+	0.199417i
$176$	−0.376271	+	1.64855i	−0.0283625	+	0.124264i
$177$	0.421439	−	5.62371i	0.0316773	−	0.422704i
$178$	−6.99140	+	12.1095i	−0.524028	+	0.907642i
$179$	2.88988	+	5.00541i	0.216000	+	0.374122i	0.953581	−	0.301136i	$-0.0973657\pi$
$179$	2.88988	+	5.00541i	0.216000	+	0.374122i	−0.737582	+	0.675258i	$0.764032\pi$
$180$	2.07228	−	0.997958i	0.154459	−	0.0743834i
$181$	17.9389	−	16.6449i	1.33339	−	1.23721i	0.383914	−	0.923369i	$-0.374576\pi$
$181$	17.9389	−	16.6449i	1.33339	−	1.23721i	0.949477	−	0.313837i	$-0.101615\pi$
$182$	−9.92191	+	6.76464i	−0.735461	+	0.501429i
$183$	1.83558	+	8.04219i	0.135690	+	0.594496i
$184$	−3.94098	+	0.594007i	−0.290533	+	0.0437908i
$185$	−5.86037	−	3.99553i	−0.430863	−	0.293758i
$186$	0.0420838	−	0.107228i	0.00308574	−	0.00786233i
$187$	−5.10595	+	1.57498i	−0.373384	+	0.115174i
$188$	−9.31867	−	4.48764i	−0.679634	−	0.327295i
$189$	0.939071	+	12.5310i	0.0683073	+	0.911498i
$190$	6.25297	+	0.942483i	0.453638	+	0.0683749i
$191$	1.66113	+	1.54130i	0.120195	+	0.111525i	0.737981	−	0.674822i	$-0.235780\pi$
$191$	1.66113	+	1.54130i	0.120195	+	0.111525i	−0.617786	+	0.786347i	$0.711970\pi$
$192$	−0.799456	−	0.246599i	−0.0576958	−	0.0177968i
$193$	10.4972	−	13.1631i	0.755605	−	0.947499i	−0.244147	−	0.969738i	$-0.578508\pi$
$193$	10.4972	−	13.1631i	0.755605	−	0.947499i	0.999753	+	0.0222389i	$0.00707944\pi$
$194$	1.55615	−	1.95135i	0.111725	−	0.140099i
$195$	3.38761	+	1.04494i	0.242591	+	0.0748296i
$196$	−0.755952	−	0.701421i	−0.0539966	−	0.0501015i
$197$	13.6527	+	2.05781i	0.972714	+	0.146613i	0.616125	−	0.787648i	$-0.288702\pi$
$197$	13.6527	+	2.05781i	0.972714	+	0.146613i	0.356589	+	0.934261i	$0.383940\pi$
$198$	−0.290646	−	3.87840i	−0.0206553	−	0.275626i
$199$	13.2242	+	6.36843i	0.937438	+	0.451446i	0.839265	−	0.543723i	$-0.182986\pi$
$199$	13.2242	+	6.36843i	0.937438	+	0.451446i	0.0981733	+	0.995169i	$0.468700\pi$
$200$	0.955573	−	0.294755i	0.0675692	−	0.0208423i
$201$	−1.52499	+	3.88560i	−0.107564	+	0.274069i
$202$	−3.11446	−	2.12340i	−0.219133	−	0.149402i
$203$	−7.78856	+	1.17394i	−0.546650	+	0.0823942i
$204$	−0.588280	−	2.57742i	−0.0411878	−	0.180456i
$205$	−0.599964	+	0.409048i	−0.0419033	+	0.0285692i
$206$	7.66161	−	7.10894i	0.533810	−	0.495303i
$207$	8.25907	−	3.97736i	0.574045	−	0.276446i
$208$	2.11869	+	3.66969i	0.146905	+	0.254447i
$209$	5.34644	−	9.26030i	0.369821	−	0.640548i
$210$	−0.177181	+	2.36432i	−0.0122267	+	0.163153i
$211$	−1.62339	+	7.11254i	−0.111759	+	0.489648i	0.887808	+	0.460214i	$0.152227\pi$
$211$	−1.62339	+	7.11254i	−0.111759	+	0.489648i	−0.999567	+	0.0294334i	$0.990630\pi$
$212$	−2.34883	−	5.98471i	−0.161318	−	0.411032i
$213$	0.957291	+	1.20040i	0.0655925	+	0.0822504i
$214$	0.671900			0.0459301
$215$	4.32776	−	4.92651i	0.295151	−	0.335985i
$216$	4.43416			0.301706
$217$	−0.243280	−	0.305064i	−0.0165149	−	0.0207091i
$218$	4.06687	+	10.3622i	0.275443	+	0.701818i
$219$	1.55787	−	6.82547i	0.105271	−	0.461222i
$220$	0.126365	−	1.68622i	0.00851951	−	0.113685i
$221$	−6.69500	+	11.5961i	−0.450355	+	0.780037i
$222$	−2.96702	−	5.13903i	−0.199133	−	0.344909i
$223$	21.2381	−	10.2277i	1.42221	−	0.684900i	0.444679	−	0.895690i	$-0.353318\pi$
$223$	21.2381	−	10.2277i	1.42221	−	0.684900i	0.977531	+	0.210790i	$0.0676035\pi$
$224$	−2.07743	+	1.92757i	−0.138804	+	0.128791i
$225$	−1.90040	+	1.29567i	−0.126693	+	0.0863780i
$226$	0.969898	+	4.24940i	0.0645167	+	0.282666i
$227$	−4.56159	+	0.687549i	−0.302763	+	0.0456342i	−0.298667	−	0.954357i	$-0.596542\pi$
$227$	−4.56159	+	0.687549i	−0.302763	+	0.0456342i	−0.00409620	+	0.999992i	$0.501304\pi$
$228$	4.37120	+	2.98023i	0.289490	+	0.197371i
$229$	3.09842	−	7.89466i	0.204750	−	0.521694i	−0.791205	−	0.611551i	$-0.790546\pi$
$229$	3.09842	−	7.89466i	0.204750	−	0.521694i	0.995955	+	0.0898575i	$0.0286411\pi$
$230$	3.80843	−	1.17475i	0.251121	−	0.0774604i
$231$	3.61212	+	1.73950i	0.237660	+	0.114451i
$232$	0.207701	+	2.77158i	0.0136363	+	0.181963i
$233$	11.2284	+	1.69241i	0.735597	+	0.110873i	0.506147	−	0.862447i	$-0.331069\pi$
$233$	11.2284	+	1.69241i	0.735597	+	0.110873i	0.229450	+	0.973320i	$0.426307\pi$
$234$	−7.14450	−	6.62913i	−0.467051	−	0.433360i
$235$	9.88344	+	3.04864i	0.644725	+	0.198871i
$236$	−4.20279	+	5.27014i	−0.273578	+	0.343057i
$237$	7.25488	−	9.09734i	0.471255	−	0.590935i
$238$	−8.55731	−	2.63958i	−0.554688	−	0.171099i
$239$	9.06574	+	8.41177i	0.586414	+	0.544112i	0.916601	−	0.399803i	$-0.130921\pi$
$239$	9.06574	+	8.41177i	0.586414	+	0.544112i	−0.330187	+	0.943915i	$0.607112\pi$
$240$	0.827280	+	0.124692i	0.0534007	+	0.00804886i
$241$	−1.28931	−	17.2047i	−0.0830519	−	1.10825i	−0.870598	−	0.491995i	$-0.836268\pi$
$241$	−1.28931	−	17.2047i	−0.0830519	−	1.10825i	0.787546	−	0.616256i	$-0.211351\pi$
$242$	7.33451	+	3.53212i	0.471480	+	0.227053i
$243$	−15.2621	+	4.70774i	−0.979065	+	0.302002i
$244$	3.60222	−	9.17830i	0.230608	−	0.587580i
$245$	0.852050	+	0.580918i	0.0544355	+	0.0371135i
$246$	−0.600720	+	0.0905440i	−0.0383005	+	0.00577287i
$247$	−5.96257	−	26.1237i	−0.379389	−	1.66221i
$248$	−0.113761	+	0.0775607i	−0.00722380	+	0.00492511i
$249$	−3.37213	+	3.12888i	−0.213700	+	0.198285i
$250$	−0.900969	+	0.433884i	−0.0569823	+	0.0274412i
$251$	1.74753	+	3.02681i	0.110303	+	0.191051i	0.915892	−	0.401424i	$-0.131485\pi$
$251$	1.74753	+	3.02681i	0.110303	+	0.191051i	−0.805589	+	0.592474i	$0.798151\pi$
$252$	3.25912	−	5.64496i	0.205305	−	0.355599i
$253$	0.503626	−	6.72042i	0.0316627	−	0.422509i
$254$	2.89780	−	12.6961i	0.181824	−	0.796625i
$255$	0.965854	+	2.46096i	0.0604841	+	0.154111i
$256$	0.623490	+	0.781831i	0.0389681	+	0.0488645i
$257$	3.31921			0.207046			0.103523	−	0.994627i	$-0.466988\pi$
$257$	3.31921			0.207046			0.103523	+	0.994627i	$0.466988\pi$
$258$	5.05046	−	2.14250i	0.314428	−	0.133387i
$259$	−20.1007			−1.24900
$260$	−2.64197	−	3.31292i	−0.163848	−	0.205459i
$261$	−2.33551	−	5.95078i	−0.144564	−	0.368344i
$262$	−3.25440	+	14.2584i	−0.201057	+	0.880890i
$263$	−2.09726	+	27.9860i	−0.129322	+	1.72569i	0.435255	+	0.900307i	$0.356658\pi$
$263$	−2.09726	+	27.9860i	−0.129322	+	1.72569i	−0.564577	+	0.825380i	$0.690961\pi$
$264$	0.707344	−	1.22516i	0.0435340	−	0.0754032i
$265$	3.21457	+	5.56779i	0.197469	+	0.342027i
$266$	16.1460	−	7.77551i	0.989976	−	0.476747i
$267$	8.57550	−	7.95690i	0.524812	−	0.486955i
$268$	4.12233	−	2.81055i	0.251811	−	0.171682i
$269$	1.75672	+	7.69670i	0.107109	+	0.469276i	0.999826	+	0.0186579i	$0.00593935\pi$
$269$	1.75672	+	7.69670i	0.107109	+	0.469276i	−0.892717	+	0.450618i	$0.851204\pi$
$270$	−4.38463	+	0.660877i	−0.266840	+	0.0402197i
$271$	−10.9738	−	7.48181i	−0.666611	−	0.454488i	0.182146	−	0.983272i	$-0.441696\pi$
$271$	−10.9738	−	7.48181i	−0.666611	−	0.454488i	−0.848756	+	0.528784i	$0.822648\pi$
$272$	−1.15447	+	2.94153i	−0.0699997	+	0.178356i
$273$	9.60028	−	2.96130i	0.581036	−	0.179226i
$274$	9.31551	+	4.48611i	0.562771	+	0.271016i
$275$	0.126365	+	1.68622i	0.00762008	+	0.101683i
$276$	3.29712	+	0.496961i	0.198463	+	0.0299136i
$277$	13.3767	+	12.4117i	0.803726	+	0.745748i	0.970721	−	0.240209i	$-0.0772161\pi$
$277$	13.3767	+	12.4117i	0.803726	+	0.745748i	−0.166996	+	0.985958i	$0.553407\pi$
$278$	−17.8032	−	5.49156i	−1.06777	−	0.329362i
$279$	0.197449	−	0.247593i	0.0118210	−	0.0148230i
$280$	1.76694	−	2.21567i	0.105595	−	0.132411i
$281$	−20.4526	−	6.30881i	−1.22010	−	0.376352i	−0.383180	−	0.923674i	$-0.625171\pi$
$281$	−20.4526	−	6.30881i	−1.22010	−	0.376352i	−0.836922	+	0.547322i	$0.815647\pi$
$282$	6.34322	+	5.88565i	0.377733	+	0.350485i
$283$	−14.6236	−	2.20415i	−0.869283	−	0.131023i	−0.300769	−	0.953697i	$-0.597243\pi$
$283$	−14.6236	−	2.20415i	−0.869283	−	0.131023i	−0.568514	+	0.822674i	$0.692482\pi$
$284$	−0.137145	−	1.83007i	−0.00813805	−	0.108595i
$285$	−4.76656	−	2.29545i	−0.282346	−	0.135971i
$286$	−6.84687	+	2.11198i	−0.404864	+	0.124884i
$287$	−0.751812	+	1.91559i	−0.0443781	+	0.113073i
$288$	−1.90040	−	1.29567i	−0.111982	−	0.0763480i
$289$	6.93627	−	1.04547i	0.408016	−	0.0614985i
$290$	−0.618465	−	2.70967i	−0.0363175	−	0.159117i
$291$	−1.72527	+	1.17627i	−0.101137	+	0.0689543i
$292$	−6.13428	+	5.69178i	−0.358982	+	0.333086i
$293$	−24.0828	+	11.5977i	−1.40693	+	0.677544i	−0.974555	−	0.224148i	$-0.928040\pi$
$293$	−24.0828	+	11.5977i	−1.40693	+	0.677544i	−0.432379	+	0.901692i	$0.642326\pi$
$294$	0.431380	+	0.747173i	0.0251586	+	0.0435760i
$295$	3.37038	−	5.83767i	0.196231	−	0.339882i
$296$	−0.530048	+	7.07300i	−0.0308084	+	0.411110i
$297$	−1.66845	+	7.30995i	−0.0968131	+	0.424166i
$298$	−4.61333	−	11.7546i	−0.267243	−	0.680924i
$299$	−10.5296	−	13.2036i	−0.608940	−	0.763587i
$300$	−0.836625			−0.0483026
$301$	2.26873	−	18.4444i	0.130768	−	1.06312i
$302$	18.8082			1.08229
$303$	1.96624	+	2.46559i	0.112958	+	0.141644i
$304$	−2.31027	−	5.88647i	−0.132503	−	0.337612i
$305$	−2.19403	+	9.61267i	−0.125630	+	0.550420i
$306$	0.543146	−	7.24778i	0.0310496	−	0.414328i
$307$	−5.11733	+	8.86347i	−0.292061	+	0.505865i	−0.974297	−	0.225267i	$-0.927675\pi$
$307$	−5.11733	+	8.86347i	−0.292061	+	0.505865i	0.682236	+	0.731132i	$0.261008\pi$
$308$	−2.39603	−	4.15004i	−0.136526	−	0.236470i
$309$	−7.87818	+	3.79393i	−0.448174	+	0.215829i
$310$	0.100930	−	0.0936495i	0.00573245	−	0.00531893i
$311$	−0.571556	+	0.389680i	−0.0324100	+	0.0220967i	−0.579417	−	0.815031i	$-0.696720\pi$
$311$	−0.571556	+	0.389680i	−0.0324100	+	0.0220967i	0.547007	+	0.837128i	$0.315767\pi$
$312$	−0.788860	−	3.45622i	−0.0446604	−	0.195670i
$313$	17.4552	−	2.63095i	0.986626	−	0.148710i	0.364143	−	0.931343i	$-0.381362\pi$
$313$	17.4552	−	2.63095i	0.986626	−	0.148710i	0.622483	+	0.782633i	$0.286124\pi$
$314$	−12.6335	−	8.61335i	−0.712948	−	0.486080i
$315$	−2.38138	+	6.06766i	−0.134176	+	0.341874i
$316$	−13.2903	+	4.09951i	−0.747637	+	0.230615i
$317$	−20.5901	−	9.91565i	−1.15645	−	0.556919i	−0.245487	−	0.969400i	$-0.578948\pi$
$317$	−20.5901	−	9.91565i	−1.15645	−	0.556919i	−0.910966	+	0.412481i	$0.864662\pi$
$318$	0.401956	+	5.36373i	0.0225406	+	0.300783i
$319$	−4.64725	−	0.700461i	−0.260196	−	0.0392183i
$320$	−0.733052	−	0.680173i	−0.0409788	−	0.0380228i
$321$	−0.537154	−	0.165690i	−0.0299810	−	0.00924793i
$322$	7.04211	−	8.83053i	0.392442	−	0.492106i
$323$	12.4588	−	15.6228i	0.693226	−	0.869278i
$324$	3.04871	+	0.940401i	0.169373	+	0.0522445i
$325$	3.10623	+	2.88216i	0.172302	+	0.159873i
$326$	14.7904	+	2.22929i	0.819164	+	0.123469i
$327$	−0.695966	−	9.28702i	−0.0384870	−	0.513573i
$328$	0.654228	+	0.315060i	0.0361237	+	0.0173963i
$329$	28.0091	−	8.63967i	1.54419	−	0.476320i
$330$	−0.516844	+	1.31690i	−0.0284513	+	0.0724928i
$331$	−5.54627	−	3.78138i	−0.304851	−	0.207844i	0.401226	−	0.915979i	$-0.368584\pi$
$331$	−5.54627	−	3.78138i	−0.304851	−	0.207844i	−0.706077	+	0.708135i	$0.749537\pi$
$332$	5.43702	−	0.819498i	0.298395	−	0.0449758i
$333$	−3.63019	−	15.9049i	−0.198933	−	0.871584i
$334$	−11.7624	+	8.01950i	−0.643612	+	0.438807i
$335$	−3.65739	+	3.39356i	−0.199825	+	0.185410i
$336$	2.13615	−	1.02872i	0.116537	−	0.0561210i
$337$	2.65177	+	4.59301i	0.144451	+	0.250197i	0.929168	−	0.369657i	$-0.120525\pi$
$337$	2.65177	+	4.59301i	0.144451	+	0.250197i	−0.784717	+	0.619854i	$0.787192\pi$
$338$	−2.47773	+	4.29156i	−0.134771	+	0.233430i
$339$	0.272509	−	3.63639i	0.0148007	−	0.197501i
$340$	0.703158	−	3.08074i	0.0381341	−	0.167077i
$341$	−0.0850580	−	0.216724i	−0.00460615	−	0.0117363i
$342$	9.06844	+	11.3715i	0.490365	+	0.614898i
$343$	−16.9151			−0.913331
$344$	−6.43036	−	1.28469i	−0.346702	−	0.0692659i
$345$	−3.33437			−0.179516
$346$	1.81535	+	2.27638i	0.0975940	+	0.122379i
$347$	8.03357	+	20.4692i	0.431265	+	1.09884i	0.967072	+	0.254504i	$0.0819122\pi$
$347$	8.03357	+	20.4692i	0.431265	+	1.09884i	−0.535807	+	0.844341i	$0.679993\pi$
$348$	0.517423	−	2.26698i	0.0277368	−	0.121523i
$349$	2.61661	−	34.9163i	0.140064	−	1.86903i	−0.277963	−	0.960592i	$-0.589659\pi$
$349$	2.61661	−	34.9163i	0.140064	−	1.86903i	0.418027	−	0.908435i	$-0.362722\pi$
$350$	−1.41697	+	2.45427i	−0.0757403	+	0.131186i
$351$	9.39463	+	16.2720i	0.501448	+	0.868534i
$352$	−1.52349	+	0.733675i	−0.0812024	+	0.0391050i
$353$	−27.4880	+	25.5051i	−1.46304	+	1.35750i	−0.687560	+	0.726127i	$0.741318\pi$
$353$	−27.4880	+	25.5051i	−1.46304	+	1.35750i	−0.775478	+	0.631374i	$0.782491\pi$
$354$	4.65956	−	3.17683i	0.247653	−	0.168847i
$355$	0.408371	+	1.78919i	0.0216741	+	0.0949603i
$356$	−13.8266	+	2.08403i	−0.732810	+	0.110453i
$357$	6.19028	+	4.22046i	0.327624	+	0.223370i
$358$	−2.11158	+	5.38022i	−0.111601	+	0.284354i
$359$	−10.5854	+	3.26515i	−0.558674	+	0.172328i	−0.561217	−	0.827669i	$-0.689667\pi$
$359$	−10.5854	+	3.26515i	−0.558674	+	0.172328i	0.00254299	+	0.999997i	$0.499191\pi$
$360$	2.07228	+	0.997958i	0.109219	+	0.0525970i
$361$	1.56843	+	20.9292i	0.0825488	+	1.10154i
$362$	24.1983	+	3.64730i	1.27183	+	0.191698i
$363$	−4.99260	−	4.63246i	−0.262044	−	0.243141i
$364$	−11.4750	−	3.53957i	−0.601454	−	0.185524i
$365$	5.21745	−	6.54248i	0.273094	−	0.342449i
$366$	−5.14318	+	6.44934i	−0.268838	+	0.337112i
$367$	−20.5773	−	6.34725i	−1.07413	−	0.331324i	−0.293266	−	0.956031i	$-0.594742\pi$
$367$	−20.5773	−	6.34725i	−1.07413	−	0.331324i	−0.780859	+	0.624707i	$0.785218\pi$
$368$	−2.92158	−	2.71083i	−0.152298	−	0.141312i
$369$	−1.65151	−	0.248925i	−0.0859740	−	0.0129585i
$370$	−0.530048	−	7.07300i	−0.0275559	−	0.367708i
$371$	16.4155	+	7.90528i	0.852249	+	0.410421i
$372$	0.110073	−	0.0339530i	0.00570702	−	0.00176038i
$373$	−4.03050	+	10.2695i	−0.208691	+	0.531737i	−0.996444	−	0.0842546i	$-0.973149\pi$
$373$	−4.03050	+	10.2695i	−0.208691	+	0.531737i	0.787753	+	0.615991i	$0.211244\pi$
$374$	−4.41487	−	3.01001i	−0.228288	−	0.155644i
$375$	0.827280	−	0.124692i	0.0427206	−	0.00643909i
$376$	−2.30152	−	10.0836i	−0.118692	−	0.520023i
$377$	−9.73079	+	6.63434i	−0.501161	+	0.341686i
$378$	−9.21165	+	8.54716i	−0.473796	+	0.439619i
$379$	−27.5454	+	13.2651i	−1.41491	+	0.681385i	−0.976125	−	0.217207i	$-0.930305\pi$
$379$	−27.5454	+	13.2651i	−1.41491	+	0.681385i	−0.438785	+	0.898592i	$0.644591\pi$
$380$	3.16180	+	5.47640i	0.162197	+	0.280933i
$381$	−5.44752	+	9.43538i	−0.279085	+	0.483389i
$382$	−0.169341	+	2.25970i	−0.00866426	+	0.115617i
$383$	5.67371	−	24.8582i	0.289913	−	1.27019i	−0.594731	−	0.803925i	$-0.702741\pi$
$383$	5.67371	−	24.8582i	0.289913	−	1.27019i	0.884644	−	0.466267i	$-0.154402\pi$
$384$	−0.305653	−	0.778792i	−0.0155978	−	0.0397426i
$385$	2.98780	+	3.74658i	0.152272	+	0.190943i
$386$	16.8362			0.856941
$387$	15.0041	−	1.53590i	0.762701	−	0.0780743i
$388$	2.49587			0.126709
$389$	1.30034	+	1.63058i	0.0659299	+	0.0826735i	0.813703	−	0.581281i	$-0.197448\pi$
$389$	1.30034	+	1.63058i	0.0659299	+	0.0826735i	−0.747773	+	0.663954i	$0.768877\pi$
$390$	1.29517	+	3.30004i	0.0655836	+	0.167104i
$391$	2.80244	−	12.2783i	0.141725	−	0.620939i
$392$	0.0770646	−	1.02836i	0.00389235	−	0.0519398i
$393$	6.11787	−	10.5965i	0.308606	−	0.534521i
$394$	6.90345	+	11.9571i	0.347791	+	0.602391i
$395$	12.5308	−	6.03453i	0.630495	−	0.303630i
$396$	2.85104	−	2.64538i	0.143270	−	0.132935i
$397$	−17.6388	+	12.0259i	−0.885264	+	0.603563i	−0.918297	−	0.395891i	$-0.870436\pi$
$397$	−17.6388	+	12.0259i	−0.885264	+	0.603563i	0.0330330	+	0.999454i	$0.489483\pi$
$398$	3.26611	+	14.3097i	0.163715	+	0.717283i
$399$	−14.8255	+	2.23458i	−0.742201	+	0.111869i
$400$	0.826239	+	0.563320i	0.0413119	+	0.0281660i
$401$	6.12803	−	15.6140i	0.306019	−	0.779724i	−0.692291	−	0.721618i	$-0.743399\pi$
$401$	6.12803	−	15.6140i	0.306019	−	0.779724i	0.998310	−	0.0581060i	$-0.0185061\pi$
$402$	−3.98870	+	1.23035i	−0.198938	+	0.0613643i
$403$	−0.525647	−	0.253138i	−0.0261844	−	0.0126097i
$404$	−0.281691	−	3.75890i	−0.0140146	−	0.187012i
$405$	−3.15481	−	0.475512i	−0.156764	−	0.0236284i
$406$	−5.77391	−	5.35741i	−0.286554	−	0.265884i
$407$	−11.4608	−	3.53518i	−0.568089	−	0.175232i
$408$	1.64832	−	2.06693i	0.0816042	−	0.102328i
$409$	−21.8248	+	27.3674i	−1.07917	+	1.35323i	−0.147853	+	0.989009i	$0.547236\pi$
$409$	−21.8248	+	27.3674i	−1.07917	+	1.35323i	−0.931312	+	0.364222i	$0.881335\pi$
$410$	−0.693878	−	0.214033i	−0.0342682	−	0.0105703i
$411$	−6.34107	−	5.88365i	−0.312782	−	0.290219i
$412$	10.3349	+	1.55774i	0.509165	+	0.0767443i
$413$	−1.42756	−	19.0495i	−0.0702458	−	0.937365i
$414$	8.25907	+	3.97736i	0.405911	+	0.195477i
$415$	−5.25415	+	1.62069i	−0.257916	+	0.0795566i
$416$	−1.54809	+	3.94447i	−0.0759015	+	0.193394i
$417$	12.8787	+	8.78052i	0.630671	+	0.429984i
$418$	10.5734	−	1.59369i	0.517164	−	0.0779499i
$419$	−1.81759	−	7.96340i	−0.0887953	−	0.389038i	0.910928	−	0.412566i	$-0.135367\pi$
$419$	−1.81759	−	7.96340i	−0.0887953	−	0.389038i	−0.999723	+	0.0235280i	$0.992510\pi$
$420$	−1.95897	+	1.33560i	−0.0955879	+	0.0651707i
$421$	−22.7915	+	21.1474i	−1.11079	+	1.03066i	−0.111471	+	0.993768i	$0.535556\pi$
$421$	−22.7915	+	21.1474i	−1.11079	+	1.03066i	−0.999319	+	0.0368953i	$0.988253\pi$
$422$	−6.57298	+	3.16538i	−0.319968	+	0.154088i
$423$	11.8947	+	20.6022i	0.578340	+	1.00171i
$424$	3.21457	−	5.56779i	0.156113	−	0.270396i
$425$	−0.236145	+	3.15113i	−0.0114547	+	0.152852i
$426$	−0.341653	+	1.49688i	−0.0165532	+	0.0725241i
$427$	10.2085	+	26.0108i	0.494023	+	1.25875i
$428$	0.418923	+	0.525313i	0.0202494	+	0.0253919i
$429$	5.99459			0.289421
$430$	6.55001	+	0.311946i	0.315870	+	0.0150434i
$431$	1.03713			0.0499566			0.0249783	−	0.999688i	$-0.492048\pi$
$431$	1.03713			0.0499566			0.0249783	+	0.999688i	$0.492048\pi$
$432$	2.76465	+	3.46677i	0.133014	+	0.166795i
$433$	8.87769	+	22.6200i	0.426634	+	1.08705i	0.969034	+	0.246926i	$0.0794206\pi$
$433$	8.87769	+	22.6200i	0.426634	+	1.08705i	−0.542400	+	0.840120i	$0.682484\pi$
$434$	0.0868257	−	0.380408i	0.00416777	−	0.0182602i
$435$	−0.173768	+	2.31878i	−0.00833155	+	0.111177i
$436$	−5.56585	+	9.64034i	−0.266556	+	0.461689i
$437$	12.6013	+	21.8262i	0.602804	+	1.04409i
$438$	6.30768	−	3.03762i	0.301393	−	0.145143i
$439$	6.76577	−	6.27772i	0.322913	−	0.299619i	−0.502013	−	0.864860i	$-0.667407\pi$
$439$	6.76577	−	6.27772i	0.322913	−	0.299619i	0.824926	+	0.565241i	$0.191217\pi$
$440$	1.39713	−	0.952545i	0.0666054	−	0.0454108i
$441$	0.527800	+	2.31244i	0.0251333	+	0.110116i
$442$	−13.2404	+	1.99568i	−0.629784	+	0.0949246i
$443$	−11.0308	−	7.52067i	−0.524089	−	0.357318i	0.272194	−	0.962242i	$-0.412251\pi$
$443$	−11.0308	−	7.52067i	−0.524089	−	0.357318i	−0.796283	+	0.604925i	$0.793203\pi$
$444$	2.16795	−	5.52384i	0.102886	−	0.262150i
$445$	13.3616	−	4.12150i	0.633400	−	0.195378i
$446$	21.2381	+	10.2277i	1.00565	+	0.484298i
$447$	0.789482	+	10.5349i	0.0373412	+	0.498284i
$448$	−2.80229	−	0.422377i	−0.132396	−	0.0199555i
$449$	29.6254	+	27.4884i	1.39811	+	1.29726i	0.903789	+	0.427979i	$0.140774\pi$
$449$	29.6254	+	27.4884i	1.39811	+	1.29726i	0.494323	+	0.869279i	$0.335416\pi$
$450$	−2.19787	−	0.677954i	−0.103609	−	0.0319591i
$451$	−0.765560	+	0.959982i	−0.0360488	+	0.0452038i
$452$	−2.71759	+	3.40776i	−0.127825	+	0.160287i
$453$	−15.0363	−	4.63810i	−0.706469	−	0.217917i
$454$	−3.38165	−	3.13771i	−0.158709	−	0.147260i
$455$	11.8744	+	1.78978i	0.556680	+	0.0839061i
$456$	0.395358	+	5.27569i	0.0185143	+	0.247057i
$457$	23.9389	+	11.5284i	1.11982	+	0.539275i	0.899836	−	0.436229i	$-0.143686\pi$
$457$	23.9389	+	11.5284i	1.11982	+	0.539275i	0.219981	+	0.975504i	$0.429400\pi$
$458$	8.10413	−	2.49979i	0.378681	−	0.116808i
$459$	−5.11908	+	13.0432i	−0.238938	+	0.608805i
$460$	3.29297	+	2.24511i	0.153536	+	0.104679i
$461$	−40.6070	+	6.12053i	−1.89126	+	0.285061i	−0.989202	−	0.146557i	$-0.953181\pi$
$461$	−40.6070	+	6.12053i	−1.89126	+	0.285061i	−0.902056	+	0.431619i	$0.857943\pi$
$462$	0.892120	+	3.90863i	0.0415052	+	0.181846i
$463$	−17.6584	+	12.0393i	−0.820654	+	0.559513i	−0.899271	−	0.437392i	$-0.855902\pi$
$463$	−17.6584	+	12.0393i	−0.820654	+	0.559513i	0.0786164	+	0.996905i	$0.474950\pi$
$464$	−2.03741	+	1.89044i	−0.0945845	+	0.0877615i
$465$	−0.103783	+	0.0499793i	−0.00481283	+	0.00231774i
$466$	5.67762	+	9.83392i	0.263010	+	0.455547i
$467$	−2.80132	+	4.85203i	−0.129630	+	0.224525i	−0.923533	−	0.383519i	$-0.874712\pi$
$467$	−2.80132	+	4.85203i	−0.129630	+	0.224525i	0.793903	+	0.608044i	$0.208046\pi$
$468$	0.728338	−	9.71899i	0.0336674	−	0.449261i
$469$	−3.14629	+	13.7848i	−0.145282	+	0.636523i
$470$	3.77870	+	9.62798i	0.174299	+	0.444106i
$471$	7.97585	+	10.0014i	0.367508	+	0.460840i
$472$	−6.74076			−0.310268
$473$	4.53744	−	10.1174i	0.208632	−	0.465198i
$474$	11.6359			0.534456
$475$	−3.94270	−	4.94399i	−0.180903	−	0.226846i
$476$	−3.27169	−	8.33613i	−0.149958	−	0.382086i
$477$	−3.29050	+	14.4166i	−0.150662	+	0.660092i
$478$	−0.924196	+	12.3325i	−0.0422717	+	0.564077i
$479$	−0.449160	+	0.777968i	−0.0205227	+	0.0355463i	−0.876104	−	0.482122i	$-0.839866\pi$
$479$	−0.449160	+	0.777968i	−0.0205227	+	0.0355463i	0.855582	+	0.517668i	$0.173200\pi$
$480$	0.418312	+	0.724538i	0.0190933	+	0.0330705i
$481$	−27.0787	+	13.0404i	−1.23468	+	0.594592i
$482$	12.6473	−	11.7350i	0.576068	−	0.534513i
$483$	−7.80746	+	5.32304i	−0.355252	+	0.242207i
$484$	1.81148	+	7.93659i	0.0823398	+	0.360754i
$485$	−2.46799	+	0.371990i	−0.112066	+	0.0168912i
$486$	−13.1964	−	8.99717i	−0.598602	−	0.408120i
$487$	11.9872	−	30.5429i	0.543192	−	1.38403i	−0.351012	−	0.936371i	$-0.614162\pi$
$487$	11.9872	−	30.5429i	0.543192	−	1.38403i	0.894204	−	0.447660i	$-0.147743\pi$
$488$	9.42183	−	2.90625i	0.426506	−	0.131560i
$489$	−11.2745	−	5.42952i	−0.509852	−	0.245532i
$490$	0.0770646	+	1.02836i	0.00348143	+	0.0464564i
$491$	−9.32376	−	1.40533i	−0.420776	−	0.0634217i	−0.0647580	−	0.997901i	$-0.520628\pi$
$491$	−9.32376	−	1.40533i	−0.420776	−	0.0634217i	−0.356018	+	0.934479i	$0.615866\pi$
$492$	−0.445333	−	0.413209i	−0.0200772	−	0.0186289i
$493$	−8.39248	−	2.58874i	−0.377978	−	0.116591i
$494$	16.7067	−	20.9496i	0.751672	−	0.942567i
$495$	−2.42493	+	3.04076i	−0.108992	+	0.136672i
$496$	−0.131568	−	0.0405833i	−0.00590757	−	0.00182225i
$497$	3.81250	+	3.53748i	0.171014	+	0.158678i
$498$	−4.54874	−	0.685613i	−0.203834	−	0.0307230i
$499$	−3.02353	−	40.3462i	−0.135352	−	1.80614i	−0.490616	−	0.871376i	$-0.663228\pi$
$499$	−3.02353	−	40.3462i	−0.135352	−	1.80614i	0.355264	−	0.934766i	$-0.384391\pi$
$500$	−0.900969	−	0.433884i	−0.0402926	−	0.0194039i
$501$	11.3812	−	3.51062i	0.508473	−	0.156843i
$502$	−1.27689	+	3.25346i	−0.0569903	+	0.145209i
$503$	−2.06580	−	1.40844i	−0.0921095	−	0.0627992i	0.516390	−	0.856354i	$-0.327276\pi$
$503$	−2.06580	−	1.40844i	−0.0921095	−	0.0627992i	−0.608499	+	0.793555i	$0.708228\pi$
$504$	6.44544	−	0.971493i	0.287103	−	0.0432737i
$505$	0.838779	+	3.67493i	0.0373252	+	0.163532i
$506$	5.56824	−	3.79636i	0.247539	−	0.168769i
$507$	3.03913	−	2.81990i	0.134973	−	0.125236i
$508$	11.7330	−	5.65030i	0.520566	−	0.250691i
$509$	−19.5687	−	33.8939i	−0.867366	−	1.50232i	−0.864679	−	0.502325i	$-0.832478\pi$
$509$	−19.5687	−	33.8939i	−0.867366	−	1.50232i	−0.00268646	−	0.999996i	$-0.500855\pi$
$510$	−1.32185	+	2.28952i	−0.0585326	+	0.101381i
$511$	1.77221	−	23.6485i	0.0783981	−	1.04615i
$512$	−0.222521	+	0.974928i	−0.00983413	+	0.0430861i
$513$	−10.2441	−	26.1016i	−0.452288	−	1.15241i
$514$	2.06949	+	2.59506i	0.0912814	+	0.114463i
$515$	−10.4517			−0.460555
$516$	4.82399	+	2.61278i	0.212364	+	0.115021i
$517$	17.4894			0.769182
$518$	−12.5326	−	15.7154i	−0.550650	−	0.690493i
$519$	−0.889940	−	2.26753i	−0.0390640	−	0.0995336i
$520$	0.942908	−	4.13115i	0.0413492	−	0.181163i
$521$	−0.266976	+	3.56255i	−0.0116964	+	0.156078i	0.988297	+	0.152540i	$0.0487453\pi$
$521$	−0.266976	+	3.56255i	−0.0116964	+	0.156078i	−0.999994	+	0.00353815i	$0.998874\pi$
$522$	3.19634	−	5.53622i	0.139900	−	0.242314i
$523$	11.5857	+	20.0670i	0.506607	+	0.877470i	0.999971	+	0.00764631i	$0.00243392\pi$
$523$	11.5857	+	20.0670i	0.506607	+	0.877470i	−0.493363	+	0.869823i	$0.664233\pi$
$524$	−13.1768	+	6.34561i	−0.575631	+	0.277209i
$525$	1.73803	−	1.61265i	0.0758538	−	0.0703820i
$526$	−23.1879	+	15.8093i	−1.01104	+	0.689316i
$527$	−0.0968143	−	0.424171i	−0.00421730	−	0.0184772i
$528$	1.39889	−	0.210848i	0.0608788	−	0.00917600i
$529$	−5.87937	−	4.00848i	−0.255625	−	0.174282i
$530$	−2.34883	+	5.98471i	−0.102026	+	0.259959i
$531$	14.8153	−	4.56992i	0.642931	−	0.198318i
$532$	16.1460	+	7.77551i	0.700018	+	0.337111i
$533$	0.229939	+	3.06833i	0.00995978	+	0.132904i
$534$	11.5677	+	1.74355i	0.500583	+	0.0754508i
$535$	−0.492538	−	0.457008i	−0.0212943	−	0.0197582i
$536$	4.76761	+	1.47061i	0.205929	+	0.0635208i
$537$	3.01488	−	3.78054i	0.130102	−	0.163142i
$538$	−4.92223	+	6.17228i	−0.212212	+	0.266106i
$539$	1.66630	+	0.513986i	0.0717727	+	0.0221389i
$540$	−3.25047	−	3.01600i	−0.139878	−	0.129788i
$541$	−22.4286	−	3.38056i	−0.964279	−	0.145342i	−0.352014	−	0.935995i	$-0.614503\pi$
$541$	−22.4286	−	3.38056i	−0.964279	−	0.145342i	−0.612265	+	0.790653i	$0.709741\pi$
$542$	−0.992538	−	13.2445i	−0.0426331	−	0.568900i
$543$	−18.4460	−	8.88313i	−0.791594	−	0.381212i
$544$	−3.01958	+	0.931416i	−0.129463	+	0.0399341i
$545$	4.06687	−	10.3622i	0.174206	−	0.443868i
$546$	8.30091	+	5.65947i	0.355246	+	0.242203i
$547$	−12.1522	+	1.83165i	−0.519591	+	0.0783158i	−0.403602	−	0.914935i	$-0.632242\pi$
$547$	−12.1522	+	1.83165i	−0.519591	+	0.0783158i	−0.115989	+	0.993250i	$0.537004\pi$
$548$	2.30074	+	10.0802i	0.0982828	+	0.430605i
$549$	−18.7377	+	12.7751i	−0.799705	+	0.545229i
$550$	−1.23955	+	1.15014i	−0.0528547	+	0.0490420i
$551$	15.8350	−	7.62573i	0.674594	−	0.324867i
$552$	1.66718	+	2.88764i	0.0709600	+	0.122906i
$553$	19.7075	−	34.1344i	0.838048	−	1.45154i
$554$	−1.36367	+	18.1969i	−0.0579367	+	0.773111i
$555$	−1.32045	+	5.78526i	−0.0560499	+	0.245571i
$556$	−6.80664	−	17.3430i	−0.288666	−	0.735509i
$557$	9.23176	+	11.5763i	0.391162	+	0.490502i	0.937951	−	0.346769i	$-0.112721\pi$
$557$	9.23176	+	11.5763i	0.391162	+	0.490502i	−0.546788	+	0.837271i	$0.684150\pi$
$558$	0.316683			0.0134063
$559$	−8.90956	−	26.3193i	−0.376834	−	1.11319i
$560$	2.83394			0.119756
$561$	2.78723	+	3.49507i	0.117677	+	0.147562i
$562$	−7.81959	−	19.9240i	−0.329850	−	0.840443i
$563$	−6.30376	+	27.6186i	−0.265672	+	1.16399i	0.649321	+	0.760515i	$0.275053\pi$
$563$	−6.30376	+	27.6186i	−0.265672	+	1.16399i	−0.914993	+	0.403470i	$0.867804\pi$
$564$	−0.646652	+	8.62897i	−0.0272290	+	0.363345i
$565$	2.17934	−	3.77473i	0.0916856	−	0.158804i
$566$	−7.39439	−	12.8075i	−0.310810	−	0.538338i
$567$	−8.14616	+	3.92298i	−0.342106	+	0.164750i
$568$	1.34530	−	1.24825i	0.0564475	−	0.0523756i
$569$	9.41335	−	6.41792i	0.394628	−	0.269053i	−0.349707	−	0.936859i	$-0.613719\pi$
$569$	9.41335	−	6.41792i	0.394628	−	0.269053i	0.744335	+	0.667806i	$0.232766\pi$
$570$	−1.17724	−	5.15784i	−0.0493092	−	0.216038i
$571$	13.5587	−	2.04365i	0.567415	−	0.0855240i	0.140931	−	0.990019i	$-0.454990\pi$
$571$	13.5587	−	2.04365i	0.567415	−	0.0855240i	0.426484	+	0.904495i	$0.359752\pi$
$572$	−5.92017	−	4.03630i	−0.247535	−	0.168766i
$573$	0.692623	−	1.76477i	0.0289347	−	0.0737245i
$574$	−1.96641	+	0.606558i	−0.0820765	+	0.0253172i
$575$	−3.59081	−	1.72924i	−0.149747	−	0.0721144i
$576$	−0.171884	−	2.29363i	−0.00716182	−	0.0955678i
$577$	27.4322	+	4.13474i	1.14202	+	0.172131i	0.692690	−	0.721236i	$-0.256426\pi$
$577$	27.4322	+	4.13474i	1.14202	+	0.172131i	0.449327	+	0.893367i	$0.351664\pi$
$578$	5.14208	+	4.77115i	0.213882	+	0.198454i
$579$	−13.4598	−	4.15180i	−0.559371	−	0.172543i
$580$	1.73290	−	2.17299i	0.0719547	−	0.0902284i
$581$	−9.71537	+	12.1827i	−0.403061	+	0.505423i
$582$	−1.99534	−	0.615480i	−0.0827094	−	0.0255125i
$583$	7.96925	+	7.39438i	0.330053	+	0.306244i
$584$	−8.27468	−	1.24721i	−0.342409	−	0.0516098i
$585$	0.728338	+	9.71899i	0.0301131	+	0.401831i
$586$	−24.0828	−	11.5977i	−0.994853	−	0.479096i
$587$	19.0015	−	5.86118i	0.784274	−	0.241917i	0.123344	−	0.992364i	$-0.460638\pi$
$587$	19.0015	−	5.86118i	0.784274	−	0.241917i	0.660930	+	0.750447i	$0.270162\pi$
$588$	−0.315202	+	0.803121i	−0.0129987	+	0.0331202i
$589$	0.719376	+	0.490462i	0.0296414	+	0.0202092i
$590$	6.66547	−	1.00466i	0.274413	−	0.0413611i
$591$	−2.57038	−	11.2616i	−0.105731	−	0.463240i
$592$	−5.86037	+	3.99553i	−0.240860	+	0.164215i
$593$	−20.2509	+	18.7901i	−0.831604	+	0.771616i	−0.975969	−	0.217909i	$-0.930077\pi$
$593$	−20.2509	+	18.7901i	−0.831604	+	0.771616i	0.144365	+	0.989524i	$0.453886\pi$
$594$	−6.75541	+	3.25323i	−0.277178	+	0.133482i
$595$	4.47758	+	7.75540i	0.183563	+	0.317940i
$596$	6.31373	−	10.9357i	0.258621	−	0.447944i
$597$	0.917668	−	12.2454i	0.0375577	−	0.501172i
$598$	3.75796	−	16.4647i	0.153674	−	0.673291i
$599$	−3.90077	−	9.93900i	−0.159381	−	0.406096i	0.828768	−	0.559592i	$-0.189042\pi$
$599$	−3.90077	−	9.93900i	−0.159381	−	0.406096i	−0.988149	+	0.153496i	$0.950947\pi$
$600$	−0.521627	−	0.654100i	−0.0212953	−	0.0267035i
$601$	−15.2946			−0.623878			−0.311939	−	0.950102i	$-0.600978\pi$
$601$	−15.2946			−0.623878			−0.311939	+	0.950102i	$0.600978\pi$
$602$	15.8350	−	9.72613i	0.645384	−	0.396408i
$603$	−11.4756			−0.467323
$604$	11.7267	+	14.7049i	0.477154	+	0.598332i
$605$	−2.97413	−	7.57796i	−0.120916	−	0.308088i
$606$	−0.701744	+	3.07454i	−0.0285064	+	0.124895i
$607$	2.32607	−	31.0393i	0.0944124	−	1.25985i	−0.725848	−	0.687855i	$-0.758552\pi$
$607$	2.32607	−	31.0393i	0.0944124	−	1.25985i	0.820260	−	0.571991i	$-0.193829\pi$
$608$	3.16180	−	5.47640i	0.128228	−	0.222097i
$609$	3.29485	+	5.70685i	0.133514	+	0.231253i
$610$	−8.88344	+	4.27804i	−0.359680	+	0.173213i
$611$	32.1275	−	29.8100i	1.29974	−	1.20598i
$612$	6.00519	−	4.09427i	0.242745	−	0.165501i
$613$	3.56959	+	15.6394i	0.144174	+	0.631669i	0.994439	+	0.105314i	$0.0335846\pi$
$613$	3.56959	+	15.6394i	0.144174	+	0.631669i	−0.850265	+	0.526355i	$0.823558\pi$
$614$	−10.1203	+	1.52540i	−0.408424	+	0.0615600i
$615$	0.501945	+	0.342220i	0.0202404	+	0.0137996i
$616$	1.75073	−	4.46080i	0.0705391	−	0.179731i
$617$	42.1391	−	12.9982i	1.69645	−	0.523287i	0.712495	−	0.701677i	$-0.247565\pi$
$617$	42.1391	−	12.9982i	1.69645	−	0.523287i	0.983960	+	0.178390i	$0.0570889\pi$
$618$	−7.87818	−	3.79393i	−0.316907	−	0.152614i
$619$	−0.362300	−	4.83455i	−0.0145620	−	0.194317i	−0.999740	−	0.0227840i	$-0.992747\pi$
$619$	−0.362300	−	4.83455i	−0.0145620	−	0.194317i	0.985178	−	0.171533i	$-0.0548720\pi$
$620$	0.136147	+	0.0205209i	0.00546780	+	0.000824138i
$621$	−12.9547	−	12.0202i	−0.519856	−	0.482356i
$622$	−0.661024	−	0.203899i	−0.0265046	−	0.00817560i
$623$	24.7067	−	30.9812i	0.989853	−	1.24124i
$624$	2.21034	−	2.77167i	0.0884843	−	0.110956i
$625$	0.955573	+	0.294755i	0.0382229	+	0.0117902i
$626$	12.9401	+	12.0067i	0.517190	+	0.479883i
$627$	−8.84601	−	1.33332i	−0.353275	−	0.0532477i
$628$	−1.14265	−	15.2476i	−0.0455966	−	0.608445i
$629$	−20.1935	−	9.72468i	−0.805168	−	0.387748i
$630$	−6.22865	+	1.92128i	−0.248155	+	0.0765458i
$631$	−12.6956	+	32.3479i	−0.505404	+	1.28775i	0.419572	+	0.907722i	$0.362180\pi$
$631$	−12.6956	+	32.3479i	−0.505404	+	1.28775i	−0.924976	+	0.380026i	$0.875915\pi$
$632$	−11.4915	−	7.83476i	−0.457106	−	0.311650i
$633$	6.03539	−	0.909688i	0.239885	−	0.0361569i
$634$	−5.08533	−	22.2803i	−0.201964	−	0.884863i
$635$	−10.7598	+	7.33590i	−0.426989	+	0.291116i
$636$	−3.94292	+	3.65849i	−0.156347	+	0.145069i
$637$	3.93702	−	1.89597i	0.155990	−	0.0751210i
$638$	−2.34987	−	4.07010i	−0.0930323	−	0.161137i
$639$	−2.11054	+	3.65556i	−0.0834915	+	0.144612i
$640$	0.0747301	−	0.997204i	0.00295397	−	0.0394179i
$641$	−2.54192	+	11.1369i	−0.100400	+	0.439880i	0.899595	+	0.436725i	$0.143862\pi$
$641$	−2.54192	+	11.1369i	−0.100400	+	0.439880i	−0.999995	+	0.00315543i	$0.998996\pi$
$642$	−0.205369	−	0.523270i	−0.00810525	−	0.0206518i
$643$	−4.37594	−	5.48726i	−0.172570	−	0.216396i	0.688023	−	0.725689i	$-0.258479\pi$
$643$	−4.37594	−	5.48726i	−0.172570	−	0.216396i	−0.860594	+	0.509292i	$0.829907\pi$
$644$	11.2947			0.445073
$645$	−5.15952	−	1.86462i	−0.203156	−	0.0734192i
$646$	19.9824			0.786195
$647$	30.3514	+	38.0595i	1.19324	+	1.49627i	0.823670	+	0.567069i	$0.191923\pi$
$647$	30.3514	+	38.0595i	1.19324	+	1.49627i	0.369568	+	0.929204i	$0.379506\pi$
$648$	1.16560	+	2.96990i	0.0457892	+	0.116669i
$649$	2.53635	−	11.1125i	0.0995606	−	0.436203i
$650$	−0.316660	+	4.22554i	−0.0124204	+	0.165739i
$651$	−0.163222	+	0.282709i	−0.00639717	+	0.0110802i
$652$	7.47873	+	12.9535i	0.292890	+	0.507300i
$653$	22.6734	−	10.9189i	0.887278	−	0.427291i	0.0660006	−	0.997820i	$-0.478976\pi$
$653$	22.6734	−	10.9189i	0.887278	−	0.427291i	0.821277	+	0.570529i	$0.193262\pi$
$654$	6.82696	−	6.33449i	0.266955	−	0.247698i
$655$	12.0839	−	8.23863i	0.472155	−	0.321910i
$656$	0.161581	+	0.707933i	0.00630868	+	0.0276401i
$657$	19.0322	−	2.86865i	0.742519	−	0.111917i
$658$	24.2182	+	16.5117i	0.944122	+	0.643692i
$659$	8.30253	−	21.1545i	0.323421	−	0.824062i	−0.673009	−	0.739634i	$-0.734999\pi$
$659$	8.30253	−	21.1545i	0.323421	−	0.824062i	0.996430	−	0.0844279i	$-0.0269063\pi$
$660$	−1.35184	+	0.416987i	−0.0526202	+	0.0162312i
$661$	9.69254	+	4.66768i	0.376996	+	0.181552i	0.612780	−	0.790254i	$-0.290051\pi$
$661$	9.69254	+	4.66768i	0.376996	+	0.181552i	−0.235783	+	0.971806i	$0.575766\pi$
$662$	−0.501639	−	6.69390i	−0.0194967	−	0.260166i
$663$	11.0773	+	1.66963i	0.430206	+	0.0648431i
$664$	4.03063	+	3.73988i	0.156419	+	0.145136i
$665$	−17.1246	−	5.28223i	−0.664062	−	0.204836i
$666$	10.1716	−	12.7547i	0.394140	−	0.494236i
$667$	6.90646	−	8.66043i	0.267419	−	0.335333i
$668$	−13.6037	−	4.19617i	−0.526341	−	0.162355i
$669$	−14.4568	−	13.4139i	−0.558932	−	0.518613i
$670$	−4.93354	−	0.743612i	−0.190599	−	0.0287282i
$671$	1.24594	+	16.6259i	0.0480990	+	0.641836i
$672$	2.13615	+	1.02872i	0.0824038	+	0.0396836i
$673$	15.9012	−	4.90487i	0.612947	−	0.189069i	0.0272890	−	0.999628i	$-0.491313\pi$
$673$	15.9012	−	4.90487i	0.612947	−	0.189069i	0.585658	+	0.810559i	$0.300836\pi$
$674$	−1.93760	+	4.93693i	−0.0746337	+	0.190164i
$675$	3.66368	+	2.49785i	0.141015	+	0.0961424i
$676$	−4.90012	+	0.738574i	−0.188466	+	0.0284067i
$677$	−5.38738	−	23.6037i	−0.207054	−	0.907163i	−0.966515	−	0.256610i	$-0.917394\pi$
$677$	−5.38738	−	23.6037i	−0.207054	−	0.907163i	0.759461	−	0.650553i	$-0.225463\pi$
$678$	3.01295	−	2.05419i	0.115712	−	0.0788908i
$679$	−5.18499	+	4.81097i	−0.198982	+	0.184628i
$680$	2.84703	−	1.37106i	0.109179	−	0.0525777i
$681$	1.92972	+	3.34238i	0.0739471	+	0.128080i
$682$	0.116409	−	0.201626i	0.00445753	−	0.00772067i
$683$	0.601077	−	8.02081i	0.0229996	−	0.306908i	−0.973826	−	0.227294i	$-0.927012\pi$
$683$	0.601077	−	8.02081i	0.0229996	−	0.306908i	0.996826	−	0.0796140i	$-0.0253688\pi$
$684$	−3.23649	+	14.1800i	−0.123750	+	0.542185i
$685$	−3.77742	−	9.62471i	−0.144328	−	0.367741i
$686$	−10.5464	−	13.2248i	−0.402664	−	0.504925i
$687$	−7.09534			−0.270704
$688$	−3.00485	−	5.82845i	−0.114559	−	0.222208i
$689$	27.2427			1.03787
$690$	−2.07894	−	2.60691i	−0.0791440	−	0.0992434i
$691$	3.60468	+	9.18458i	0.137129	+	0.349398i	0.982898	−	0.184151i	$-0.0589534\pi$
$691$	3.60468	+	9.18458i	0.137129	+	0.349398i	−0.845769	+	0.533548i	$0.820858\pi$
$692$	−0.647892	+	2.83860i	−0.0246292	+	0.107907i
$693$	−0.823675	+	10.9912i	−0.0312888	+	0.417521i
$694$	−10.9946	+	19.0432i	−0.417350	+	0.722872i
$695$	9.31546	+	16.1349i	0.353356	+	0.612030i
$696$	2.09500	−	1.00890i	0.0794109	−	0.0382423i
$697$	−1.68204	+	1.56071i	−0.0637118	+	0.0591160i
$698$	28.9301	−	19.7242i	1.09502	−	0.746572i
$699$	−2.11396	−	9.26188i	−0.0799575	−	0.350317i
$700$	−2.80229	+	0.422377i	−0.105917	+	0.0159644i
$701$	−9.57833	−	6.53039i	−0.361768	−	0.246650i	0.368771	−	0.929520i	$-0.379779\pi$
$701$	−9.57833	−	6.53039i	−0.361768	−	0.246650i	−0.730539	+	0.682871i	$0.760731\pi$
$702$	−6.86449	+	17.4904i	−0.259083	+	0.660134i
$703$	42.8596	−	13.2204i	1.61648	−	0.498618i
$704$	−1.52349	−	0.733675i	−0.0574187	−	0.0276514i
$705$	−0.646652	−	8.62897i	−0.0243543	−	0.324986i
$706$	−37.0792	−	5.58879i	−1.39549	−	0.210337i
$707$	7.83074	+	7.26587i	0.294505	+	0.273261i
$708$	5.38894	+	1.66227i	0.202529	+	0.0624718i
$709$	−3.49314	+	4.38026i	−0.131188	+	0.164504i	−0.843087	−	0.537778i	$-0.819264\pi$
$709$	−3.49314	+	4.38026i	−0.131188	+	0.164504i	0.711899	+	0.702282i	$0.247835\pi$
$710$	−1.14423	+	1.43482i	−0.0429422	+	0.0538478i
$711$	30.5684	+	9.42911i	1.14641	+	0.353619i
$712$	−10.2501	−	9.51072i	−0.384139	−	0.356429i
$713$	0.542614	+	0.0817858i	0.0203210	+	0.00306290i
$714$	0.559886	+	7.47116i	0.0209532	+	0.279601i
$715$	6.45563	+	3.10887i	0.241427	+	0.116265i
$716$	−5.52298	+	1.70361i	−0.206403	+	0.0636670i
$717$	3.78005	−	9.63141i	0.141169	−	0.359692i
$718$	−9.15267	−	6.24018i	−0.341574	−	0.232882i
$719$	6.11110	−	0.921099i	0.227905	−	0.0343512i	−0.0340966	−	0.999419i	$-0.510855\pi$
$719$	6.11110	−	0.921099i	0.227905	−	0.0343512i	0.262002	+	0.965067i	$0.415617\pi$
$720$	0.511811	+	2.24239i	0.0190741	+	0.0835690i
$721$	−24.4727	+	16.6852i	−0.911412	+	0.621390i
$722$	−15.3852	+	14.2754i	−0.572578	+	0.531275i
$723$	−13.0048	+	6.26278i	−0.483653	+	0.232915i
$724$	12.2358	+	21.1930i	0.454740	+	0.787632i
$725$	−1.38968	+	2.40699i	−0.0516113	+	0.0893934i
$726$	0.508965	−	6.79166i	0.0188895	−	0.252062i
$727$	2.73816	−	11.9967i	0.101553	−	0.444932i	−0.898430	−	0.439116i	$-0.855292\pi$
$727$	2.73816	−	11.9967i	0.101553	−	0.444932i	0.999983	−	0.00581586i	$-0.00185125\pi$
$728$	−4.38721	−	11.1784i	−0.162601	−	0.414300i
$729$	2.36363	+	2.96390i	0.0875418	+	0.109774i
$730$	8.36814			0.309719
$731$	11.2026	−	17.4320i	0.414343	−	0.644745i
$732$	−8.24901			−0.304892
$733$	9.77742	+	12.2605i	0.361137	+	0.452852i	0.928895	−	0.370344i	$-0.120760\pi$
$733$	9.77742	+	12.2605i	0.361137	+	0.452852i	−0.567757	+	0.823196i	$0.692189\pi$
$734$	−7.86724	−	20.0454i	−0.290385	−	0.739890i
$735$	0.191982	−	0.841129i	0.00708137	−	0.0310255i
$736$	0.297837	−	3.97435i	0.0109784	−	0.146497i
$737$	−4.21830	+	7.30630i	−0.155383	+	0.269131i
$738$	−0.835081	−	1.44640i	−0.0307397	−	0.0532428i
$739$	28.2502	−	13.6046i	1.03920	−	0.500453i	0.165141	−	0.986270i	$-0.447192\pi$
$739$	28.2502	−	13.6046i	1.03920	−	0.500453i	0.874061	+	0.485817i	$0.161478\pi$
$740$	5.19941	−	4.82435i	0.191134	−	0.177347i
$741$	−18.5225	+	12.6284i	−0.680440	+	0.463916i
$742$	4.05429	+	17.7630i	0.148838	+	0.652100i
$743$	−22.4341	+	3.38139i	−0.823026	+	0.124051i	−0.547036	−	0.837109i	$-0.684244\pi$
$743$	−22.4341	+	3.38139i	−0.823026	+	0.124051i	−0.275990	+	0.961160i	$0.589006\pi$
$744$	0.0951749	+	0.0648892i	0.00348928	+	0.00237895i
$745$	−4.61333	+	11.7546i	−0.169019	+	0.430654i
$746$	−10.5420	+	3.25178i	−0.385971	+	0.119056i
$747$	−11.3943	−	5.48720i	−0.416895	−	0.200766i
$748$	−0.399308	−	5.32840i	−0.0146002	−	0.194825i
$749$	−1.88286	−	0.283795i	−0.0687982	−	0.0103697i
$750$	0.613289	+	0.569049i	0.0223942	+	0.0207787i
$751$	3.20524	+	0.988687i	0.116961	+	0.0360777i	0.352683	−	0.935743i	$-0.385269\pi$
$751$	3.20524	+	0.988687i	0.116961	+	0.0360777i	−0.235722	+	0.971820i	$0.575746\pi$
$752$	6.44872	−	8.08644i	0.235161	−	0.294882i
$753$	1.82312	−	2.28612i	0.0664381	−	0.0833107i
$754$	−11.2540	−	3.47139i	−0.409846	−	0.126421i
$755$	−13.7874	−	12.7928i	−0.501775	−	0.465579i
$756$	−12.4258	−	1.87289i	−0.451922	−	0.0681163i
$757$	1.96835	+	26.2658i	0.0715409	+	0.954647i	0.911315	+	0.411711i	$0.135069\pi$
$757$	1.96835	+	26.2658i	0.0715409	+	0.954647i	−0.839774	+	0.542936i	$0.817312\pi$
$758$	−27.5454	−	13.2651i	−1.00049	−	0.481812i
$759$	−5.38775	+	1.66190i	−0.195563	+	0.0603231i
$760$	−2.31027	+	5.88647i	−0.0838023	+	0.213525i
$761$	−14.4771	−	9.87031i	−0.524794	−	0.357799i	0.271761	−	0.962365i	$-0.412394\pi$
$761$	−14.4771	−	9.87031i	−0.524794	−	0.357799i	−0.796555	+	0.604566i	$0.793346\pi$
$762$	−10.7734	+	1.62382i	−0.390277	+	0.0588248i
$763$	−7.01979	−	30.7557i	−0.254133	−	1.11343i
$764$	−1.87229	+	1.27651i	−0.0677371	+	0.0461824i
$765$	−5.32790	+	4.94357i	−0.192631	+	0.178735i
$766$	22.9724	−	11.0629i	0.830026	−	0.399720i
$767$	−14.2816	−	24.7365i	−0.515679	−	0.893182i
$768$	0.418312	−	0.724538i	0.0150945	−	0.0261445i
$769$	0.00294602	−	0.0393119i	0.000106236	−	0.00141763i	−0.997150	−	0.0754389i	$-0.975964\pi$
$769$	0.00294602	−	0.0393119i	0.000106236	−	0.00141763i	0.997257	+	0.0740213i	$0.0235833\pi$
$770$	−1.06633	+	4.67191i	−0.0384279	+	0.168364i
$771$	−1.01453	−	2.58497i	−0.0365373	−	0.0930955i
$772$	10.4972	+	13.1631i	0.377803	+	0.473750i
$773$	−39.5599			−1.42287			−0.711435	−	0.702752i	$-0.751954\pi$
$773$	−39.5599			−1.42287			−0.711435	+	0.702752i	$0.751954\pi$
$774$	10.5557	+	10.7730i	0.379417	+	0.387229i
$775$	−0.137685			−0.00494579
$776$	1.55615	+	1.95135i	0.0558625	+	0.0700494i
$777$	6.14384	+	15.6543i	0.220409	+	0.561593i
$778$	−0.464086	+	2.03330i	−0.0166383	+	0.0728972i
$779$	0.343146	−	4.57897i	0.0122945	−	0.164059i
$780$	−1.77255	+	3.07015i	−0.0634676	+	0.109929i
$781$	1.55162	+	2.68748i	0.0555212	+	0.0961655i
$782$	11.3468	−	5.46435i	0.405762	−	0.195405i
$783$	−9.03421	+	8.38252i	−0.322856	+	0.299567i
$784$	0.852050	−	0.580918i	0.0304304	−	0.0207471i
$785$	3.40242	+	14.9070i	0.121438	+	0.532053i
$786$	12.0991	−	1.82364i	0.431560	−	0.0650472i
$787$	−6.25068	−	4.26164i	−0.222813	−	0.151911i	0.446770	−	0.894649i	$-0.352574\pi$
$787$	−6.25068	−	4.26164i	−0.222813	−	0.151911i	−0.669582	+	0.742738i	$0.733527\pi$
$788$	−5.04423	+	12.8525i	−0.179693	+	0.457851i
$789$	22.4363	−	6.92067i	0.798752	−	0.246383i
$790$	12.5308	+	6.03453i	0.445827	+	0.214699i
$791$	−0.923086	−	12.3177i	−0.0328212	−	0.437968i
$792$	3.84584	+	0.579667i	0.136656	+	0.0205976i
$793$	30.6270	+	28.4177i	1.08760	+	1.00914i
$794$	−20.3998	−	6.29251i	−0.723963	−	0.223313i
$795$	3.35361	−	4.20529i	0.118940	−	0.149146i
$796$	−9.15142	+	11.4755i	−0.324364	+	0.406739i
$797$	−50.7537	−	15.6554i	−1.79779	−	0.554544i	−0.798889	−	0.601479i	$-0.794578\pi$
$797$	−50.7537	−	15.6554i	−1.79779	−	0.554544i	−0.998898	+	0.0469353i	$0.985055\pi$
$798$	−10.9906	−	10.1978i	−0.389063	−	0.360997i
$799$	32.3183	+	4.87120i	1.14334	+	0.172331i
$800$	0.0747301	+	0.997204i	0.00264211	+	0.0352565i
$801$	28.9763	+	13.9542i	1.02383	+	0.493049i
$802$	16.0283	−	4.94406i	0.565977	−	0.174581i
$803$	5.16961	−	13.1720i	0.182432	−	0.464828i
$804$	−3.44884	−	2.35138i	−0.121631	−	0.0829267i
$805$	−11.1685	+	1.68338i	−0.393639	+	0.0593315i
$806$	−0.129824	−	0.568797i	−0.00457286	−	0.0200350i
$807$	5.45718	−	3.72065i	0.192102	−	0.130973i
$808$	2.76320	−	2.56387i	0.0972089	−	0.0901967i
$809$	−36.3783	+	17.5189i	−1.27899	+	0.615930i	−0.945131	−	0.326692i	$-0.894066\pi$
$809$	−36.3783	+	17.5189i	−1.27899	+	0.615930i	−0.333862	+	0.942622i	$0.608352\pi$
$810$	−1.59522	−	2.76301i	−0.0560505	−	0.0970822i
$811$	0.174122	−	0.301589i	0.00611426	−	0.0105902i	−0.862952	−	0.505286i	$-0.831387\pi$
$811$	0.174122	−	0.301589i	0.00611426	−	0.0105902i	0.869066	+	0.494696i	$0.164720\pi$
$812$	0.588614	−	7.85451i	0.0206563	−	0.275639i
$813$	−2.47260	+	10.8331i	−0.0867177	+	0.379935i
$814$	−4.38176	−	11.1645i	−0.153581	−	0.391317i
$815$	−9.32582	−	11.6942i	−0.326669	−	0.409630i
$816$	2.64371			0.0925482
$817$	7.29357	+	40.8201i	0.255170	+	1.42812i
$818$	−35.0042			−1.22389
$819$	17.2210	+	21.5944i	0.601750	+	0.754570i
$820$	−0.265288	−	0.675943i	−0.00926427	−	0.0236050i
$821$	−2.41187	+	10.5671i	−0.0841747	+	0.368793i	−0.999418	−	0.0341078i	$-0.989141\pi$
$821$	−2.41187	+	10.5671i	−0.0841747	+	0.368793i	0.915243	+	0.402901i	$0.131998\pi$
$822$	0.646432	−	8.62604i	0.0225469	−	0.300868i
$823$	−10.2920	+	17.8262i	−0.358756	+	0.621383i	−0.987753	−	0.156024i	$-0.950132\pi$
$823$	−10.2920	+	17.8262i	−0.358756	+	0.621383i	0.628997	+	0.777407i	$0.283466\pi$
$824$	5.22583	+	9.05141i	0.182051	+	0.315321i
$825$	1.27459	−	0.613811i	0.0443756	−	0.0213701i
$826$	14.0034	−	12.9933i	0.487242	−	0.452094i
$827$	−30.9134	+	21.0764i	−1.07497	+	0.732899i	−0.965319	−	0.261072i	$-0.915924\pi$
$827$	−30.9134	+	21.0764i	−1.07497	+	0.732899i	−0.109646	+	0.993971i	$0.534972\pi$
$828$	2.03982	+	8.93704i	0.0708887	+	0.310584i
$829$	38.8262	−	5.85210i	1.34849	−	0.203252i	0.565222	−	0.824939i	$-0.308790\pi$
$829$	38.8262	−	5.85210i	1.34849	−	0.203252i	0.783266	+	0.621687i	$0.213552\pi$
$830$	−4.54302	−	3.09738i	−0.157690	−	0.107511i
$831$	5.57753	−	14.2113i	0.193482	−	0.492985i
$832$	−4.04913	+	1.24899i	−0.140378	+	0.0433010i
$833$	2.93597	+	1.41389i	0.101725	+	0.0489883i
$834$	1.16482	+	15.5435i	0.0403346	+	0.538228i
$835$	14.0771	+	2.12179i	0.487159	+	0.0734274i
$836$	7.83843	+	7.27300i	0.271098	+	0.251542i
$837$	−0.583393	−	0.179953i	−0.0201650	−	0.00622009i
$838$	5.09279	−	6.38615i	0.175927	−	0.220606i
$839$	17.2069	−	21.5767i	0.594047	−	0.744911i	−0.390390	−	0.920650i	$-0.627660\pi$
$839$	17.2069	−	21.5767i	0.594047	−	0.744911i	0.984437	+	0.175738i	$0.0562313\pi$
$840$	−2.26561	−	0.698849i	−0.0781711	−	0.0241126i
$841$	15.5958	+	14.4708i	0.537787	+	0.498993i
$842$	−30.7440	−	4.63391i	−1.05951	−	0.159695i
$843$	1.33817	+	17.8567i	0.0460891	+	0.615016i
$844$	−6.57298	−	3.16538i	−0.226251	−	0.108957i
$845$	4.73531	−	1.46065i	0.162899	−	0.0502478i
$846$	−8.69124	+	22.1449i	−0.298811	+	0.761358i
$847$	−19.0616	−	12.9959i	−0.654963	−	0.446546i
$848$	6.35732	−	0.958212i	0.218311	−	0.0329051i
$849$	2.75318	+	12.0625i	0.0944888	+	0.413982i
$850$	−2.61089	+	1.78007i	−0.0895527	+	0.0610560i
$851$	20.7222	−	19.2274i	0.710349	−	0.659108i
$852$	−1.38333	+	0.666174i	−0.0473920	+	0.0228228i
$853$	18.7500	+	32.4759i	0.641988	+	1.11196i	0.984988	+	0.172620i	$0.0552233\pi$
$853$	18.7500	+	32.4759i	0.641988	+	1.11196i	−0.343001	+	0.939335i	$0.611443\pi$
$854$	−13.9712	+	24.1988i	−0.478083	+	0.828065i
$855$	1.08692	−	14.5040i	0.0371720	−	0.496026i
$856$	−0.149512	+	0.655054i	−0.00511021	+	0.0223893i
$857$	−3.30436	−	8.41938i	−0.112875	−	0.287601i	0.863262	−	0.504756i	$-0.168417\pi$
$857$	−3.30436	−	8.41938i	−0.112875	−	0.287601i	−0.976137	+	0.217155i	$0.930322\pi$
$858$	3.73756	+	4.68676i	0.127598	+	0.160003i
$859$	11.9005			0.406038			0.203019	−	0.979175i	$-0.434925\pi$
$859$	11.9005			0.406038			0.203019	+	0.979175i	$0.434925\pi$
$860$	3.83998	+	5.31550i	0.130942	+	0.181257i
$861$	1.72164			0.0586732
$862$	0.646638	+	0.810858i	0.0220246	+	0.0276179i
$863$	−0.740812	−	1.88756i	−0.0252175	−	0.0642532i	0.917710	−	0.397250i	$-0.130035\pi$
$863$	−0.740812	−	1.88756i	−0.0252175	−	0.0642532i	−0.942928	+	0.332997i	$0.891940\pi$
$864$	−0.986694	+	4.32299i	−0.0335680	+	0.147071i
$865$	0.217584	−	2.90346i	0.00739808	−	0.0987206i
$866$	−12.1499	+	21.0442i	−0.412869	+	0.715110i
$867$	−2.93430	−	5.08236i	−0.0996541	−	0.172606i
$868$	0.351550	−	0.169298i	0.0119324	−	0.00574634i
$869$	17.2399	−	15.9963i	0.584824	−	0.542638i
$870$	−1.92123	+	1.30988i	−0.0651359	+	0.0444089i
$871$	4.70442	+	20.6114i	0.159403	+	0.698391i
$872$	−11.0074	+	1.65909i	−0.372757	+	0.0561840i
$873$	−4.74315	−	3.23382i	−0.160531	−	0.109448i
$874$	−9.20757	+	23.4605i	−0.311451	+	0.793564i
$875$	2.70804	−	0.835320i	0.0915485	−	0.0282390i
$876$	6.30768	+	3.03762i	0.213117	+	0.102632i
$877$	−1.87332	−	24.9977i	−0.0632575	−	0.844112i	−0.935113	−	0.354349i	$-0.884702\pi$
$877$	−1.87332	−	24.9977i	−0.0632575	−	0.844112i	0.871856	−	0.489763i	$-0.162917\pi$
$878$	9.12650	+	1.37560i	0.308005	+	0.0464242i
$879$	16.3932	+	15.2106i	0.552928	+	0.513042i
$880$	1.61582	+	0.498416i	0.0544694	+	0.0168016i
$881$	30.4953	−	38.2399i	1.02741	−	1.28833i	0.0706374	−	0.997502i	$-0.477497\pi$
$881$	30.4953	−	38.2399i	1.02741	−	1.28833i	0.956774	−	0.290831i	$-0.0939319\pi$
$882$	−1.47886	+	1.85444i	−0.0497959	+	0.0624421i
$883$	15.6501	+	4.82740i	0.526666	+	0.162455i	0.546675	−	0.837345i	$-0.315893\pi$
$883$	15.6501	+	4.82740i	0.526666	+	0.162455i	−0.0200089	+	0.999800i	$0.506369\pi$
$884$	−9.81557	−	9.10751i	−0.330133	−	0.306319i
$885$	−5.57650	−	0.840521i	−0.187452	−	0.0282538i
$886$	−0.997692	−	13.3133i	−0.0335181	−	0.447268i
$887$	−7.68910	−	3.70287i	−0.258175	−	0.124330i	0.300320	−	0.953839i	$-0.402907\pi$
$887$	−7.68910	−	3.70287i	−0.258175	−	0.124330i	−0.558495	+	0.829508i	$0.688621\pi$
$888$	5.67041	−	1.74909i	0.190286	−	0.0586956i
$889$	−13.4830	+	34.3542i	−0.452207	+	1.15220i
$890$	11.5531	+	7.87679i	0.387262	+	0.264031i
$891$	−5.33463	+	0.804065i	−0.178717	+	0.0269372i
$892$	5.24538	+	22.9815i	0.175628	+	0.769479i
$893$	−54.0399	+	36.8437i	−1.80837	+	1.23293i
$894$	−7.74429	+	7.18565i	−0.259008	+	0.240324i
$895$	5.20738	−	2.50774i	0.174063	−	0.0838246i
$896$	−1.41697	−	2.45427i	−0.0473377	−	0.0819913i
$897$	−7.06450	+	12.2361i	−0.235877	+	0.408551i
$898$	−3.02013	+	40.3008i	−0.100783	+	1.34486i
$899$	0.0851532	−	0.373081i	0.00284002	−	0.0124429i
$900$	−0.840306	−	2.14106i	−0.0280102	−	0.0713688i
$901$	12.6667	+	15.8836i	0.421990	+	0.529158i
$902$	−1.22786			−0.0408834
$903$	−15.0578	+	3.87072i	−0.501092	+	0.128810i
$904$	−4.35868			−0.144968
$905$	−15.2578	−	19.1327i	−0.507186	−	0.635991i
$906$	−5.74880	−	14.6477i	−0.190991	−	0.486637i
$907$	−8.65511	+	37.9205i	−0.287388	+	1.25913i	0.600706	+	0.799470i	$0.294886\pi$
$907$	−8.65511	+	37.9205i	−0.287388	+	1.25913i	−0.888095	+	0.459661i	$0.847971\pi$
$908$	0.344738	−	4.60021i	0.0114405	−	0.152663i
$909$	−4.33497	+	7.50838i	−0.143782	+	0.249037i
$910$	6.00426	+	10.3997i	0.199039	+	0.344746i
$911$	39.9340	−	19.2312i	1.32307	−	0.637158i	0.366981	−	0.930228i	$-0.380391\pi$
$911$	39.9340	−	19.2312i	1.32307	−	0.637158i	0.956091	+	0.293070i	$0.0946771\pi$
$912$	−3.87820	+	3.59844i	−0.128420	+	0.119156i
$913$	−7.68200	+	5.23750i	−0.254237	+	0.173336i
$914$	5.91243	+	25.9041i	0.195566	+	0.856830i
$915$	8.15688	−	1.22945i	0.269658	−	0.0406444i
$916$	7.00726	+	4.77747i	0.231526	+	0.157852i
$917$	15.1422	−	38.5817i	0.500040	−	1.27408i
$918$	−13.3893	+	4.13005i	−0.441912	+	0.136312i
$919$	−20.7449	−	9.99021i	−0.684311	−	0.329547i	0.0592234	−	0.998245i	$-0.481138\pi$
$919$	−20.7449	−	9.99021i	−0.684311	−	0.329547i	−0.743534	+	0.668698i	$0.766852\pi$
$920$	0.297837	+	3.97435i	0.00981938	+	0.131031i
$921$	8.46693	+	1.27618i	0.278995	+	0.0420517i
$922$	−30.1033	−	27.9318i	−0.991399	−	0.919884i
$923$	7.43098	+	2.29215i	0.244594	+	0.0754471i
$924$	−2.49966	+	3.13448i	−0.0822329	+	0.103117i
$925$	−4.42231	+	5.54540i	−0.145405	+	0.182332i
$926$	−20.4225	−	6.29951i	−0.671125	−	0.207015i
$927$	−17.6222	−	16.3510i	−0.578788	−	0.537037i
$928$	−2.74831	−	0.414241i	−0.0902178	−	0.0135981i
$929$	3.85751	+	51.4748i	0.126561	+	1.68883i	0.593728	+	0.804666i	$0.297656\pi$
$929$	3.85751	+	51.4748i	0.126561	+	1.68883i	−0.467167	+	0.884169i	$0.654725\pi$
$930$	−0.103783	−	0.0499793i	−0.00340318	−	0.00163889i
$931$	−6.23143	+	1.92214i	−0.204227	+	0.0629956i
$932$	−4.14853	+	10.5703i	−0.135890	+	0.346241i
$933$	0.478178	+	0.326016i	0.0156548	+	0.0106733i
$934$	−5.54006	+	0.835030i	−0.181276	+	0.0273230i
$935$	1.18900	+	5.20937i	0.0388846	+	0.170365i
$936$	8.05272	−	5.49025i	0.263212	−	0.179455i
$937$	−1.80563	+	1.67538i	−0.0589873	+	0.0547322i	−0.709116	−	0.705092i	$-0.750906\pi$
$937$	−1.80563	+	1.67538i	−0.0589873	+	0.0547322i	0.650128	+	0.759824i	$0.274715\pi$
$938$	−12.7391	+	6.13481i	−0.415945	+	0.200309i
$939$	−7.38420	−	12.7898i	−0.240974	−	0.417380i
$940$	−5.17147	+	8.95726i	−0.168675	+	0.292153i
$941$	3.81372	−	50.8906i	0.124324	−	1.65899i	−0.491333	−	0.870972i	$-0.663490\pi$
$941$	3.81372	−	50.8906i	0.124324	−	1.65899i	0.615656	−	0.788015i	$-0.288891\pi$
$942$	−2.84655	+	12.4715i	−0.0927456	+	0.406345i
$943$	−1.05731	−	2.69397i	−0.0344306	−	0.0877277i
$944$	−4.20279	−	5.27014i	−0.136789	−	0.171528i
$945$	12.5662			0.408777
$946$	10.7391	−	2.76058i	0.349160	−	0.0897542i
$947$	−8.62082			−0.280139			−0.140069	−	0.990142i	$-0.544733\pi$
$947$	−8.62082			−0.280139			−0.140069	+	0.990142i	$0.544733\pi$
$948$	7.25488	+	9.09734i	0.235628	+	0.295468i
$949$	−12.9547	−	33.0079i	−0.420526	−	1.07148i
$950$	1.40713	−	6.16505i	0.0456534	−	0.200021i
$951$	−1.42881	+	19.0661i	−0.0463323	+	0.618262i
$952$	4.47758	−	7.75540i	0.145119	−	0.251354i
$953$	9.38151	+	16.2492i	0.303897	+	0.526365i	0.977015	−	0.213170i	$-0.0683788\pi$
$953$	9.38151	+	16.2492i	0.303897	+	0.526365i	−0.673118	+	0.739535i	$0.735046\pi$
$954$	−13.3230	+	6.41601i	−0.431347	+	0.207726i
$955$	1.66113	−	1.54130i	0.0537528	−	0.0498753i
$956$	−10.2182	+	6.96664i	−0.330480	+	0.225317i
$957$	0.874935	+	3.83334i	0.0282826	+	0.123914i
$958$	−0.888287	+	0.133888i	−0.0286993	+	0.00432572i
$959$	−24.2099	−	16.5061i	−0.781780	−	0.533008i
$960$	−0.305653	+	0.778792i	−0.00986492	+	0.0251354i
$961$	−29.6046	+	9.13182i	−0.954988	+	0.294575i
$962$	−27.0787	−	13.0404i	−0.873052	−	0.420440i
$963$	−0.115489	−	1.54109i	−0.00372157	−	0.0496609i
$964$	17.0602	+	2.57142i	0.549473	+	0.0828197i
$965$	−12.3418	−	11.4515i	−0.397297	−	0.368638i
$966$	−9.02959	−	2.78526i	−0.290522	−	0.0896143i
$967$	−34.9863	+	43.8715i	−1.12508	+	1.41081i	−0.225403	+	0.974266i	$0.572370\pi$
$967$	−34.9863	+	43.8715i	−1.12508	+	1.41081i	−0.899682	+	0.436546i	$0.856202\pi$
$968$	−5.07564	+	6.36465i	−0.163137	+	0.204568i
$969$	−15.9750	−	4.92764i	−0.513191	−	0.158299i
$970$	−1.82960	−	1.69762i	−0.0587450	−	0.0545074i
$971$	−30.9627	−	4.66688i	−0.993641	−	0.149767i	−0.367956	−	0.929843i	$-0.619942\pi$
$971$	−30.9627	−	4.66688i	−0.993641	−	0.149767i	−0.625685	+	0.780076i	$0.715180\pi$
$972$	−1.19357	−	15.9270i	−0.0382836	−	0.510860i
$973$	47.5702	+	22.9086i	1.52503	+	0.734417i
$974$	31.3533	−	9.67121i	1.00462	−	0.309886i
$975$	1.29517	−	3.30004i	0.0414787	−	0.105686i
$976$	8.14661	+	5.55426i	0.260767	+	0.177788i
$977$	59.2649	−	8.93275i	1.89605	−	0.285784i	0.905653	−	0.424019i	$-0.139381\pi$
$977$	59.2649	−	8.93275i	1.89605	−	0.285784i	0.990399	+	0.138235i	$0.0441429\pi$
$978$	−2.78458	−	12.2000i	−0.0890410	−	0.390114i
$979$	19.5357	−	13.3192i	0.624365	−	0.425685i
$980$	−0.755952	+	0.701421i	−0.0241480	+	0.0224061i
$981$	23.0680	−	11.1090i	0.736505	−	0.354682i
$982$	−4.71454	−	8.16582i	−0.150447	−	0.260582i
$983$	−15.6259	+	27.0648i	−0.498388	+	0.863234i	−0.999998	−	0.00186010i	$-0.999408\pi$
$983$	−15.6259	+	27.0648i	−0.498388	+	0.863234i	0.501610	+	0.865094i	$0.332741\pi$
$984$	0.0453989	−	0.605807i	0.00144727	−	0.0193124i
$985$	3.07232	−	13.4607i	0.0978924	−	0.428895i
$986$	−3.20867	−	8.17555i	−0.102185	−	0.260363i
$987$	−15.2896	−	19.1725i	−0.486673	−	0.610269i
$988$	26.7955			0.852480
$989$	15.3042	+	21.1849i	0.486646	+	0.673641i
$990$	−3.88928			−0.123609
$991$	30.0496	+	37.6810i	0.954558	+	1.19698i	0.980341	+	0.197310i	$0.0632205\pi$
$991$	30.0496	+	37.6810i	0.954558	+	1.19698i	−0.0257834	+	0.999668i	$0.508208\pi$
$992$	−0.0503019	−	0.128167i	−0.00159709	−	0.00406931i
$993$	−1.24968	+	5.47518i	−0.0396572	+	0.173750i
$994$	−0.388661	+	5.18632i	−0.0123276	+	0.164500i
$995$	7.33887	−	12.7113i	0.232658	−	0.402975i
$996$	−2.30006	−	3.98382i	−0.0728802	−	0.126232i
$997$	−38.1549	+	18.3744i	−1.20838	+	0.581924i	−0.926052	−	0.377395i	$-0.876820\pi$
$997$	−38.1549	+	18.3744i	−1.20838	+	0.581924i	−0.282325	+	0.959319i	$0.591106\pi$
$998$	29.6588	−	27.5193i	0.938832	−	0.871108i
$999$	−25.9858	+	17.7168i	−0.822155	+	0.560536i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.a.281.1	yes	36
43.15	even	21	inner	430.2.q.a.101.1	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.a.101.1	✓	36	43.15	even	21	inner
430.2.q.a.281.1	yes	36	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.623490 + 0.781831i) q^{2} +(-0.305653 - 0.778792i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(0.0747301 - 0.997204i) q^{5} +(0.418312 - 0.724538i) q^{6} +(-1.41697 - 2.45427i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(1.68606 - 1.56444i) q^{9} +O(q^{10})\)	\(q+(0.623490 + 0.781831i) q^{2} +(-0.305653 - 0.778792i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(0.0747301 - 0.997204i) q^{5} +(0.418312 - 0.724538i) q^{6} +(-1.41697 - 2.45427i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(1.68606 - 1.56444i) q^{9} +(0.826239 - 0.563320i) q^{10} +(-0.376271 - 1.64855i) q^{11} +(0.827280 - 0.124692i) q^{12} +(-3.50109 - 2.38701i) q^{13} +(1.03536 - 2.63804i) q^{14} +(-0.799456 + 0.246599i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(-0.236145 - 3.15113i) q^{17} +(2.27437 + 0.342806i) q^{18} +(4.63552 + 4.30114i) q^{19} +(0.955573 + 0.294755i) q^{20} +(-1.47826 + 1.85368i) q^{21} +(1.05429 - 1.32204i) q^{22} +(3.80843 + 1.17475i) q^{23} +(0.613289 + 0.569049i) q^{24} +(-0.988831 - 0.149042i) q^{25} +(-0.316660 - 4.22554i) q^{26} +(-3.99504 - 1.92391i) q^{27} +(2.70804 - 0.835320i) q^{28} +(1.01541 - 2.58723i) q^{29} +(-0.691252 - 0.471288i) q^{30} +(0.136147 - 0.0205209i) q^{31} +(-0.222521 - 0.974928i) q^{32} +(-1.16887 + 0.796923i) q^{33} +(2.31642 - 2.14932i) q^{34} +(-2.55330 + 1.22960i) q^{35} +(1.15003 + 1.99191i) q^{36} +(3.54642 - 6.14257i) q^{37} +(-0.472563 + 6.30592i) q^{38} +(-0.788860 + 3.45622i) q^{39} +(0.365341 + 0.930874i) q^{40} +(-0.452740 - 0.567718i) q^{41} -2.37095 q^{42} +(5.23615 + 3.94750i) q^{43} +1.69095 q^{44} +(-1.43406 - 1.79826i) q^{45} +(1.45607 + 3.70999i) q^{46} +(-2.30152 + 10.0836i) q^{47} +(-0.0625210 + 0.834285i) q^{48} +(-0.515620 + 0.893080i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-2.38190 + 1.14706i) q^{51} +(3.10623 - 2.88216i) q^{52} +(-5.31200 + 3.62166i) q^{53} +(-0.986694 - 4.32299i) q^{54} +(-1.67206 + 0.252023i) q^{55} +(2.34151 + 1.59642i) q^{56} +(1.93283 - 4.92477i) q^{57} +(2.65588 - 0.819229i) q^{58} +(6.07321 + 2.92470i) q^{59} +(-0.0625210 - 0.834285i) q^{60} +(-9.74975 - 1.46954i) q^{61} +(0.100930 + 0.0936495i) q^{62} +(-6.22865 - 1.92128i) q^{63} +(0.623490 - 0.781831i) q^{64} +(-2.64197 + 3.31292i) q^{65} +(-1.35184 - 0.416987i) q^{66} +(-3.65739 - 3.39356i) q^{67} +(3.12467 + 0.470968i) q^{68} +(-0.249177 - 3.32504i) q^{69} +(-2.55330 - 1.22960i) q^{70} +(-1.75367 + 0.540935i) q^{71} +(-0.840306 + 2.14106i) q^{72} +(6.91408 + 4.71394i) q^{73} +(7.01361 - 1.05713i) q^{74} +(0.186167 + 0.815649i) q^{75} +(-5.22480 + 3.56221i) q^{76} +(-3.51282 + 3.25942i) q^{77} +(-3.19403 + 1.53816i) q^{78} +(6.95409 + 12.0448i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(0.238422 - 3.18153i) q^{81} +(0.161581 - 0.707933i) q^{82} +(-2.00880 - 5.11834i) q^{83} +(-1.47826 - 1.85368i) q^{84} -3.15997 q^{85} +(0.178409 + 6.55501i) q^{86} -2.32528 q^{87} +(1.05429 + 1.32204i) q^{88} +(5.10849 + 13.0162i) q^{89} +(0.511811 - 2.24239i) q^{90} +(-0.897398 + 11.9749i) q^{91} +(-1.99275 + 3.45154i) q^{92} +(-0.0575953 - 0.0997580i) q^{93} +(-9.31867 + 4.48764i) q^{94} +(4.63552 - 4.30114i) q^{95} +(-0.691252 + 0.471288i) q^{96} +(-0.555383 - 2.43329i) q^{97} +(-1.01972 + 0.153698i) q^{98} +(-3.21347 - 2.19091i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9} + 3 q^{10} + 9 q^{11} - 16 q^{12} + 21 q^{13} - 6 q^{14} + 5 q^{15} - 6 q^{16} - 37 q^{17} + 19 q^{18} + 7 q^{19} + 3 q^{20} - 8 q^{21} + 16 q^{22} + 13 q^{23} + 5 q^{24} + 3 q^{25} - 21 q^{26} - 28 q^{27} - 6 q^{28} + 4 q^{29} - 2 q^{30} + 13 q^{31} - 6 q^{32} - 54 q^{33} - 23 q^{34} - 2 q^{35} - 9 q^{36} + 17 q^{37} + 28 q^{38} + 8 q^{39} + 3 q^{40} + 10 q^{41} - 50 q^{42} + 14 q^{43} - 26 q^{44} + 4 q^{45} - 8 q^{46} + 13 q^{47} - 2 q^{48} + 5 q^{49} - 18 q^{50} + 17 q^{51} - 7 q^{52} - 71 q^{53} + 7 q^{54} - 29 q^{55} + q^{56} - 70 q^{57} + 25 q^{58} + 8 q^{59} - 2 q^{60} + 25 q^{61} - 15 q^{62} + 88 q^{63} - 6 q^{64} + 7 q^{65} + 44 q^{66} + 26 q^{67} - 9 q^{68} + 78 q^{69} - 2 q^{70} - 60 q^{71} - 23 q^{72} + 7 q^{73} + 17 q^{74} - 10 q^{75} - 35 q^{76} - 5 q^{77} + 57 q^{78} + 52 q^{79} - 18 q^{80} + q^{81} - 4 q^{82} - 101 q^{83} - 8 q^{84} - 24 q^{85} + 49 q^{86} - 18 q^{87} + 16 q^{88} + 14 q^{89} - 3 q^{90} + 35 q^{91} + 6 q^{92} + 28 q^{93} - 15 q^{94} + 7 q^{95} - 2 q^{96} + 11 q^{97} + 12 q^{98} + 78 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9 + 3 * q^10 + 9 * q^11 - 16 * q^12 + 21 * q^13 - 6 * q^14 + 5 * q^15 - 6 * q^16 - 37 * q^17 + 19 * q^18 + 7 * q^19 + 3 * q^20 - 8 * q^21 + 16 * q^22 + 13 * q^23 + 5 * q^24 + 3 * q^25 - 21 * q^26 - 28 * q^27 - 6 * q^28 + 4 * q^29 - 2 * q^30 + 13 * q^31 - 6 * q^32 - 54 * q^33 - 23 * q^34 - 2 * q^35 - 9 * q^36 + 17 * q^37 + 28 * q^38 + 8 * q^39 + 3 * q^40 + 10 * q^41 - 50 * q^42 + 14 * q^43 - 26 * q^44 + 4 * q^45 - 8 * q^46 + 13 * q^47 - 2 * q^48 + 5 * q^49 - 18 * q^50 + 17 * q^51 - 7 * q^52 - 71 * q^53 + 7 * q^54 - 29 * q^55 + q^56 - 70 * q^57 + 25 * q^58 + 8 * q^59 - 2 * q^60 + 25 * q^61 - 15 * q^62 + 88 * q^63 - 6 * q^64 + 7 * q^65 + 44 * q^66 + 26 * q^67 - 9 * q^68 + 78 * q^69 - 2 * q^70 - 60 * q^71 - 23 * q^72 + 7 * q^73 + 17 * q^74 - 10 * q^75 - 35 * q^76 - 5 * q^77 + 57 * q^78 + 52 * q^79 - 18 * q^80 + q^81 - 4 * q^82 - 101 * q^83 - 8 * q^84 - 24 * q^85 + 49 * q^86 - 18 * q^87 + 16 * q^88 + 14 * q^89 - 3 * q^90 + 35 * q^91 + 6 * q^92 + 28 * q^93 - 15 * q^94 + 7 * q^95 - 2 * q^96 + 11 * q^97 + 12 * q^98 + 78 * q^99

Introduction

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