LMFDB - Embedded newform 930.2.bg.e.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (of order $15$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 27x^{14} + 345x^{12} - 2652x^{10} + 13244x^{8} - 43398x^{6} + 89940x^{4} - 107433x^{2} + 58081 $ x^16 - 27x^14 + 345x^12 - 2652x^10 + 13244x^8 - 43398x^6 + 89940x^4 - 107433*x^2 + 58081
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			361.1
Root			$2.29670 - 0.743145i$ of defining polynomial
Character	$\chi$	$=$	930.361
Dual form			930.2.bg.e.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.296127 - 2.81746i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.296127 - 2.81746i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(0.669131 - 0.743145i) q^{10} +(4.49953 + 2.00332i) q^{11} +(0.978148 + 0.207912i) q^{12} +(-1.96206 + 0.417049i) q^{13} +(-2.58806 + 1.15228i) q^{14} +(0.309017 - 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(1.96255 - 0.873781i) q^{17} +(0.978148 - 0.207912i) q^{18} +(4.09257 + 0.869903i) q^{19} +(-0.913545 - 0.406737i) q^{20} +(-1.89564 + 2.10532i) q^{21} +(0.514839 - 4.89837i) q^{22} +(0.0289781 + 0.0210538i) q^{23} +(-0.104528 - 0.994522i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.00295 + 1.73715i) q^{26} +(0.809017 - 0.587785i) q^{27} +(1.89564 + 2.10532i) q^{28} +(-1.51869 - 4.67405i) q^{29} -1.00000 q^{30} +(4.43224 + 3.36976i) q^{31} -1.00000 q^{32} +(-1.52202 - 4.68429i) q^{33} +(-1.43748 - 1.59648i) q^{34} +(2.29193 - 1.66519i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(1.60764 - 2.78451i) q^{37} +(-0.437348 - 4.16108i) q^{38} +(1.62280 + 1.17903i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(3.11772 - 3.46258i) q^{41} +(2.58806 + 1.15228i) q^{42} +(-6.96026 - 1.47945i) q^{43} +(-4.81772 + 1.02404i) q^{44} +(-0.913545 + 0.406737i) q^{45} +(0.0110687 - 0.0340658i) q^{46} +(2.23178 - 6.86872i) q^{47} +(-0.913545 + 0.406737i) q^{48} +(-1.00338 + 0.213275i) q^{49} +(0.978148 + 0.207912i) q^{50} +(-1.96255 - 0.873781i) q^{51} +(1.34220 - 1.49067i) q^{52} +(1.39712 - 13.2927i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(0.514839 + 4.89837i) q^{55} +(1.41649 - 2.45344i) q^{56} +(-2.09200 - 3.62345i) q^{57} +(-3.97598 + 2.88872i) q^{58} +(2.21930 + 2.46478i) q^{59} +(0.309017 + 0.951057i) q^{60} +0.406724 q^{61} +(1.83519 - 5.25662i) q^{62} +2.83298 q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.34220 - 1.49067i) q^{65} +(-3.98469 + 2.89505i) q^{66} +(2.22585 + 3.85528i) q^{67} +(-1.07414 + 1.86046i) q^{68} +(-0.00374410 - 0.0356227i) q^{69} +(-2.29193 - 1.66519i) q^{70} +(1.08387 - 10.3123i) q^{71} +(-0.669131 + 0.743145i) q^{72} +(3.58145 + 1.59456i) q^{73} +(-3.14502 - 0.668494i) q^{74} +(0.978148 - 0.207912i) q^{75} +(-3.82228 + 1.70179i) q^{76} +(4.31185 - 13.2705i) q^{77} +(0.619855 - 1.90772i) q^{78} +(-0.705998 + 0.314330i) q^{79} +(0.978148 - 0.207912i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-4.25653 - 1.89513i) q^{82} +(-6.12048 + 6.79749i) q^{83} +(0.296127 - 2.81746i) q^{84} +(1.73799 + 1.26272i) q^{85} +(0.743799 + 7.07677i) q^{86} +(-2.45729 + 4.25615i) q^{87} +(2.46268 + 4.26548i) q^{88} +(4.61758 - 3.35487i) q^{89} +(0.669131 + 0.743145i) q^{90} +(1.75604 + 5.40453i) q^{91} -0.0358189 q^{92} +(-0.461530 - 5.54860i) q^{93} -7.22220 q^{94} +(1.29293 + 3.97922i) q^{95} +(0.669131 + 0.743145i) q^{96} +(2.01746 - 1.46577i) q^{97} +(0.512898 + 0.888365i) q^{98} +(-2.46268 + 4.26548i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} - 5 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 - 5 * q^7 + 4 * q^8 + 2 * q^9	\( 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} - 5 q^{7} + 4 q^{8} + 2 q^{9} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 4 q^{13} - 10 q^{14} - 4 q^{15} - 4 q^{16} - 22 q^{17} - 2 q^{18} - 3 q^{19} - 2 q^{20} - 11 q^{22} + 9 q^{23} + 2 q^{24} - 8 q^{25} + 11 q^{26} + 4 q^{27} - 3 q^{29} - 16 q^{30} - 15 q^{31} - 16 q^{32} - 8 q^{33} - 8 q^{34} + 5 q^{35} - 8 q^{36} - 17 q^{37} - 2 q^{38} + 3 q^{39} + 2 q^{40} + 28 q^{41} + 10 q^{42} - 28 q^{43} - 19 q^{44} - 2 q^{45} - 9 q^{46} + 9 q^{47} - 2 q^{48} + 19 q^{49} - 2 q^{50} + 22 q^{51} + 4 q^{52} + 2 q^{53} - 4 q^{54} - 11 q^{55} + 5 q^{56} - 2 q^{57} - 12 q^{58} + 24 q^{59} - 4 q^{60} - 40 q^{61} - 25 q^{62} + 10 q^{63} - 4 q^{64} - 4 q^{65} - 7 q^{66} - q^{67} - 2 q^{68} - 3 q^{69} - 5 q^{70} + 39 q^{71} - 2 q^{72} + 81 q^{73} - 8 q^{74} - 2 q^{75} + 2 q^{76} + 28 q^{77} - 8 q^{78} + 64 q^{79} - 2 q^{80} + 2 q^{81} + 32 q^{82} - 40 q^{83} + 5 q^{84} - 14 q^{85} + 13 q^{86} - 9 q^{87} - q^{88} - 7 q^{89} + 2 q^{90} - 46 q^{91} - 36 q^{92} - 20 q^{93} - 4 q^{94} - 6 q^{95} + 2 q^{96} - 17 q^{97} - 9 q^{98} + q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 - 5 * q^7 + 4 * q^8 + 2 * q^9 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 4 * q^13 - 10 * q^14 - 4 * q^15 - 4 * q^16 - 22 * q^17 - 2 * q^18 - 3 * q^19 - 2 * q^20 - 11 * q^22 + 9 * q^23 + 2 * q^24 - 8 * q^25 + 11 * q^26 + 4 * q^27 - 3 * q^29 - 16 * q^30 - 15 * q^31 - 16 * q^32 - 8 * q^33 - 8 * q^34 + 5 * q^35 - 8 * q^36 - 17 * q^37 - 2 * q^38 + 3 * q^39 + 2 * q^40 + 28 * q^41 + 10 * q^42 - 28 * q^43 - 19 * q^44 - 2 * q^45 - 9 * q^46 + 9 * q^47 - 2 * q^48 + 19 * q^49 - 2 * q^50 + 22 * q^51 + 4 * q^52 + 2 * q^53 - 4 * q^54 - 11 * q^55 + 5 * q^56 - 2 * q^57 - 12 * q^58 + 24 * q^59 - 4 * q^60 - 40 * q^61 - 25 * q^62 + 10 * q^63 - 4 * q^64 - 4 * q^65 - 7 * q^66 - q^67 - 2 * q^68 - 3 * q^69 - 5 * q^70 + 39 * q^71 - 2 * q^72 + 81 * q^73 - 8 * q^74 - 2 * q^75 + 2 * q^76 + 28 * q^77 - 8 * q^78 + 64 * q^79 - 2 * q^80 + 2 * q^81 + 32 * q^82 - 40 * q^83 + 5 * q^84 - 14 * q^85 + 13 * q^86 - 9 * q^87 - q^88 - 7 * q^89 + 2 * q^90 - 46 * q^91 - 36 * q^92 - 20 * q^93 - 4 * q^94 - 6 * q^95 + 2 * q^96 - 17 * q^97 - 9 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{15}\right)$

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 $

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	−0.669131	−	0.743145i	−0.386323	−	0.429055i
$3$	−0.669131	−	0.743145i	−0.386323	−	0.429055i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−0.296127	−	2.81746i	−0.111926	−	1.06490i	−0.895945	−	0.444165i	$-0.853500\pi$
$7$	−0.296127	−	2.81746i	−0.111926	−	1.06490i	0.784019	−	0.620736i	$-0.213166\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	−0.104528	+	0.994522i	−0.0348428	+	0.331507i
$10$	0.669131	−	0.743145i	0.211598	−	0.235003i
$11$	4.49953	+	2.00332i	1.35666	+	0.604024i	0.950770	−	0.309898i	$-0.100295\pi$
$11$	4.49953	+	2.00332i	1.35666	+	0.604024i	0.405890	+	0.913922i	$0.366962\pi$
$12$	0.978148	+	0.207912i	0.282367	+	0.0600189i
$13$	−1.96206	+	0.417049i	−0.544177	+	0.115668i	−0.471795	−	0.881708i	$-0.656394\pi$
$13$	−1.96206	+	0.417049i	−0.544177	+	0.115668i	−0.0723827	+	0.997377i	$0.523060\pi$
$14$	−2.58806	+	1.15228i	−0.691688	+	0.307959i
$15$	0.309017	−	0.951057i	0.0797878	−	0.245562i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	1.96255	−	0.873781i	0.475987	−	0.211923i	−0.154698	−	0.987962i	$-0.549441\pi$
$17$	1.96255	−	0.873781i	0.475987	−	0.211923i	0.630685	+	0.776039i	$0.282774\pi$
$18$	0.978148	−	0.207912i	0.230552	−	0.0490053i
$19$	4.09257	+	0.869903i	0.938901	+	0.199570i	0.651852	−	0.758346i	$-0.273992\pi$
$19$	4.09257	+	0.869903i	0.938901	+	0.199570i	0.287049	+	0.957916i	$0.407326\pi$
$20$	−0.913545	−	0.406737i	−0.204275	−	0.0909491i
$21$	−1.89564	+	2.10532i	−0.413662	+	0.459418i
$22$	0.514839	−	4.89837i	0.109764	−	1.04434i
$23$	0.0289781	+	0.0210538i	0.00604235	+	0.00439003i	0.590802	−	0.806816i	$-0.298811\pi$
$23$	0.0289781	+	0.0210538i	0.00604235	+	0.00439003i	−0.584760	+	0.811206i	$0.698811\pi$
$24$	−0.104528	−	0.994522i	−0.0213368	−	0.203006i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.00295	+	1.73715i	0.196694	+	0.340684i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	1.89564	+	2.10532i	0.358242	+	0.397868i
$29$	−1.51869	−	4.67405i	−0.282014	−	0.867949i	−0.987278	−	0.159004i	$-0.949172\pi$
$29$	−1.51869	−	4.67405i	−0.282014	−	0.867949i	0.705264	−	0.708944i	$-0.250828\pi$
$30$	−1.00000			−0.182574
$31$	4.43224	+	3.36976i	0.796054	+	0.605226i
$31$	4.43224	+	3.36976i	0.796054	+	0.605226i
$32$	−1.00000			−0.176777
$33$	−1.52202	−	4.68429i	−0.264949	−	0.815430i
$34$	−1.43748	−	1.59648i	−0.246525	−	0.273794i
$35$	2.29193	−	1.66519i	0.387407	−	0.281468i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	1.60764	−	2.78451i	0.264294	−	0.457771i	−0.703084	−	0.711107i	$-0.748194\pi$
$37$	1.60764	−	2.78451i	0.264294	−	0.457771i	0.967378	+	0.253335i	$0.0815277\pi$
$38$	−0.437348	−	4.16108i	−0.0709471	−	0.675017i
$39$	1.62280	+	1.17903i	0.259856	+	0.188797i
$40$	−0.104528	+	0.994522i	−0.0165274	+	0.157248i
$41$	3.11772	−	3.46258i	0.486906	−	0.540764i	−0.448760	−	0.893653i	$-0.648134\pi$
$41$	3.11772	−	3.46258i	0.486906	−	0.540764i	0.935665	+	0.352889i	$0.114801\pi$
$42$	2.58806	+	1.15228i	0.399346	+	0.177800i
$43$	−6.96026	−	1.47945i	−1.06143	−	0.225614i	−0.356067	−	0.934460i	$-0.615882\pi$
$43$	−6.96026	−	1.47945i	−1.06143	−	0.225614i	−0.705363	+	0.708847i	$0.749216\pi$
$44$	−4.81772	+	1.02404i	−0.726299	+	0.154380i
$45$	−0.913545	+	0.406737i	−0.136183	+	0.0606327i
$46$	0.0110687	−	0.0340658i	0.00163198	−	0.00502273i
$47$	2.23178	−	6.86872i	0.325539	−	1.00191i	−0.645658	−	0.763627i	$-0.723417\pi$
$47$	2.23178	−	6.86872i	0.325539	−	1.00191i	0.971197	−	0.238279i	$-0.0765832\pi$
$48$	−0.913545	+	0.406737i	−0.131859	+	0.0587074i
$49$	−1.00338	+	0.213275i	−0.143340	+	0.0304678i
$50$	0.978148	+	0.207912i	0.138331	+	0.0294032i
$51$	−1.96255	−	0.873781i	−0.274811	−	0.122354i
$52$	1.34220	−	1.49067i	0.186130	−	0.206719i
$53$	1.39712	−	13.2927i	0.191909	−	1.82589i	−0.298509	−	0.954407i	$-0.596489\pi$
$53$	1.39712	−	13.2927i	0.191909	−	1.82589i	0.490419	−	0.871487i	$-0.336844\pi$
$54$	−0.809017	−	0.587785i	−0.110093	−	0.0799874i
$55$	0.514839	+	4.89837i	0.0694209	+	0.660496i
$56$	1.41649	−	2.45344i	0.189287	−	0.327854i
$57$	−2.09200	−	3.62345i	−0.277092	−	0.479938i
$58$	−3.97598	+	2.88872i	−0.522072	+	0.379307i
$59$	2.21930	+	2.46478i	0.288928	+	0.320888i	0.870083	−	0.492906i	$-0.164065\pi$
$59$	2.21930	+	2.46478i	0.288928	+	0.320888i	−0.581154	+	0.813793i	$0.697399\pi$
$60$	0.309017	+	0.951057i	0.0398939	+	0.122781i
$61$	0.406724			0.0520757			0.0260379	−	0.999661i	$-0.491711\pi$
$61$	0.406724			0.0520757			0.0260379	+	0.999661i	$0.491711\pi$
$62$	1.83519	−	5.25662i	0.233069	−	0.667592i
$63$	2.83298			0.356922
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−1.34220	−	1.49067i	−0.166480	−	0.184895i
$66$	−3.98469	+	2.89505i	−0.490482	+	0.356356i
$67$	2.22585	+	3.85528i	0.271930	+	0.470997i	0.969356	−	0.245660i	$-0.0790046\pi$
$67$	2.22585	+	3.85528i	0.271930	+	0.470997i	−0.697426	+	0.716657i	$0.745671\pi$
$68$	−1.07414	+	1.86046i	−0.130258	+	0.225614i
$69$	−0.00374410	−	0.0356227i	−0.000450736	−	0.00428847i
$70$	−2.29193	−	1.66519i	−0.273938	−	0.199028i
$71$	1.08387	−	10.3123i	0.128631	−	1.22384i	−0.719664	−	0.694322i	$-0.755704\pi$
$71$	1.08387	−	10.3123i	0.128631	−	1.22384i	0.848296	−	0.529523i	$-0.177629\pi$
$72$	−0.669131	+	0.743145i	−0.0788578	+	0.0875805i
$73$	3.58145	+	1.59456i	0.419177	+	0.186629i	0.605476	−	0.795864i	$-0.292983\pi$
$73$	3.58145	+	1.59456i	0.419177	+	0.186629i	−0.186299	+	0.982493i	$0.559649\pi$
$74$	−3.14502	−	0.668494i	−0.365601	−	0.0777108i
$75$	0.978148	−	0.207912i	0.112947	−	0.0240076i
$76$	−3.82228	+	1.70179i	−0.438445	+	0.195208i
$77$	4.31185	−	13.2705i	0.491381	−	1.51231i
$78$	0.619855	−	1.90772i	0.0701847	−	0.216006i
$79$	−0.705998	+	0.314330i	−0.0794309	+	0.0353649i	−0.446068	−	0.894999i	$-0.647176\pi$
$79$	−0.705998	+	0.314330i	−0.0794309	+	0.0353649i	0.366637	+	0.930364i	$0.380509\pi$
$80$	0.978148	−	0.207912i	0.109360	−	0.0232452i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	−4.25653	−	1.89513i	−0.470055	−	0.209282i
$83$	−6.12048	+	6.79749i	−0.671810	+	0.746121i	−0.978626	−	0.205648i	$-0.934070\pi$
$83$	−6.12048	+	6.79749i	−0.671810	+	0.746121i	0.306816	+	0.951769i	$0.400737\pi$
$84$	0.296127	−	2.81746i	0.0323102	−	0.307411i
$85$	1.73799	+	1.26272i	0.188511	+	0.136962i
$86$	0.743799	+	7.07677i	0.0802059	+	0.763108i
$87$	−2.45729	+	4.25615i	−0.263449	+	0.456308i
$88$	2.46268	+	4.26548i	0.262522	+	0.454702i
$89$	4.61758	−	3.35487i	0.489462	−	0.355615i	−0.315515	−	0.948921i	$-0.602177\pi$
$89$	4.61758	−	3.35487i	0.489462	−	0.355615i	0.804978	+	0.593305i	$0.202177\pi$
$90$	0.669131	+	0.743145i	0.0705326	+	0.0783343i
$91$	1.75604	+	5.40453i	0.184083	+	0.566549i
$92$	−0.0358189			−0.00373438
$93$	−0.461530	−	5.54860i	−0.0478585	−	0.575363i
$94$	−7.22220			−0.744913
$95$	1.29293	+	3.97922i	0.132652	+	0.408260i
$96$	0.669131	+	0.743145i	0.0682929	+	0.0758469i
$97$	2.01746	−	1.46577i	0.204842	−	0.148827i	−0.480635	−	0.876921i	$-0.659594\pi$
$97$	2.01746	−	1.46577i	0.204842	−	0.148827i	0.685477	+	0.728094i	$0.259594\pi$
$98$	0.512898	+	0.888365i	0.0518105	+	0.0897384i
$99$	−2.46268	+	4.26548i	−0.247508	+	0.428697i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	−8.76759	−	6.37003i	−0.872408	−	0.633841i	0.0588241	−	0.998268i	$-0.481265\pi$
$101$	−8.76759	−	6.37003i	−0.872408	−	0.633841i	−0.931232	+	0.364427i	$0.881265\pi$
$102$	−0.224556	+	2.13650i	−0.0222343	+	0.211545i
$103$	−3.24509	+	3.60404i	−0.319748	+	0.355117i	−0.881495	−	0.472192i	$-0.843463\pi$
$103$	−3.24509	+	3.60404i	−0.319748	+	0.355117i	0.561747	+	0.827309i	$0.310129\pi$
$104$	−1.83247	−	0.815870i	−0.179689	−	0.0800026i
$105$	−2.77108	−	0.589010i	−0.270429	−	0.0574815i
$106$	−13.0738	+	2.77893i	−1.26984	+	0.269914i
$107$	−8.56504	+	3.81340i	−0.828014	+	0.368656i	−0.776578	−	0.630021i	$-0.783046\pi$
$107$	−8.56504	+	3.81340i	−0.828014	+	0.368656i	−0.0514358	+	0.998676i	$0.516380\pi$
$108$	−0.309017	+	0.951057i	−0.0297352	+	0.0915155i
$109$	−1.19553	+	3.67948i	−0.114511	+	0.352430i	−0.991845	−	0.127451i	$-0.959320\pi$
$109$	−1.19553	+	3.67948i	−0.114511	+	0.352430i	0.877333	+	0.479881i	$0.159320\pi$
$110$	4.49953	−	2.00332i	0.429013	−	0.191009i
$111$	−3.14502	+	0.668494i	−0.298512	+	0.0634506i
$112$	−2.77108	−	0.589010i	−0.261842	−	0.0556563i
$113$	−0.472568	−	0.210401i	−0.0444554	−	0.0197928i	0.384389	−	0.923171i	$-0.374412\pi$
$113$	−0.472568	−	0.210401i	−0.0444554	−	0.0197928i	−0.428844	+	0.903379i	$0.641079\pi$
$114$	−2.79965	+	3.10932i	−0.262211	+	0.291215i
$115$	−0.00374410	+	0.0356227i	−0.000349139	+	0.00332183i
$116$	3.97598	+	2.88872i	0.369161	+	0.268211i
$117$	−0.209673	−	1.99490i	−0.0193843	−	0.184429i
$118$	1.65835	−	2.87234i	0.152663	−	0.264420i
$119$	−3.04301	−	5.27065i	−0.278952	−	0.483160i
$120$	0.809017	−	0.587785i	0.0738528	−	0.0536572i
$121$	8.87205	+	9.85341i	0.806550	+	0.895765i
$122$	−0.125685	−	0.386818i	−0.0113790	−	0.0350208i
$123$	−4.65936			−0.420120
$124$	−5.56645	−	0.120985i	−0.499882	−	0.0108648i
$125$	−1.00000			−0.0894427
$126$	−0.875440	−	2.69433i	−0.0779904	−	0.240030i
$127$	1.07969	+	1.19912i	0.0958071	+	0.106405i	0.789142	−	0.614211i	$-0.210526\pi$
$127$	1.07969	+	1.19912i	0.0958071	+	0.106405i	−0.693334	+	0.720616i	$0.743859\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	3.55788	+	6.16242i	0.313254	+	0.542571i
$130$	−1.00295	+	1.73715i	−0.0879642	+	0.152358i
$131$	−0.0739454	−	0.703543i	−0.00646064	−	0.0614689i	0.990817	−	0.135213i	$-0.0431719\pi$
$131$	−0.0739454	−	0.703543i	−0.00646064	−	0.0614689i	−0.997277	+	0.0737441i	$0.976505\pi$
$132$	3.98469	+	2.89505i	0.346823	+	0.251982i
$133$	1.23900	−	11.7883i	0.107435	−	1.02217i
$134$	2.97876	−	3.30825i	0.257326	−	0.285789i
$135$	0.913545	+	0.406737i	0.0786255	+	0.0350063i
$136$	2.10133	+	0.446651i	0.180187	+	0.0383000i
$137$	16.5524	−	3.51832i	1.41417	−	0.300591i	0.563423	−	0.826169i	$-0.309484\pi$
$137$	16.5524	−	3.51832i	1.41417	−	0.300591i	0.850745	+	0.525578i	$0.176151\pi$
$138$	−0.0327222	+	0.0145689i	−0.00278550	+	0.00124018i
$139$	−1.26342	+	3.88840i	−0.107162	+	0.329810i	−0.990232	−	0.139431i	$-0.955473\pi$
$139$	−1.26342	+	3.88840i	−0.107162	+	0.329810i	0.883070	+	0.469241i	$0.155473\pi$
$140$	−0.875440	+	2.69433i	−0.0739882	+	0.227712i
$141$	−6.59781	+	2.93753i	−0.555636	+	0.247385i
$142$	−10.1425	+	2.15586i	−0.851141	+	0.180916i
$143$	−9.66383	−	2.05411i	−0.808130	−	0.171773i
$144$	0.913545	+	0.406737i	0.0761288	+	0.0338947i
$145$	3.28850	−	3.65225i	0.273095	−	0.303303i
$146$	0.409791	−	3.89890i	0.0339146	−	0.322676i
$147$	0.829886	+	0.602948i	0.0684479	+	0.0497303i
$148$	0.336088	+	3.19766i	0.0276263	+	0.262846i
$149$	−0.714475	+	1.23751i	−0.0585320	+	0.101380i	−0.893807	−	0.448453i	$-0.851975\pi$
$149$	−0.714475	+	1.23751i	−0.0585320	+	0.101380i	0.835275	+	0.549833i	$0.185309\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	8.87161	−	6.44560i	0.721961	−	0.524536i	−0.165049	−	0.986285i	$-0.552778\pi$
$151$	8.87161	−	6.44560i	0.721961	−	0.524536i	0.887010	+	0.461750i	$0.152778\pi$
$152$	2.79965	+	3.10932i	0.227081	+	0.252199i
$153$	0.663853	+	2.04313i	0.0536693	+	0.165177i
$154$	−13.9534			−1.12440
$155$	−0.702175	+	5.52331i	−0.0564000	+	0.443643i
$156$	−2.00589			−0.160600
$157$	0.935642	+	2.87961i	0.0746724	+	0.229818i	0.981425	−	0.191844i	$-0.0614468\pi$
$157$	0.935642	+	2.87961i	0.0746724	+	0.229818i	−0.906753	+	0.421662i	$0.861447\pi$
$158$	0.517111	+	0.574310i	0.0411392	+	0.0456897i
$159$	−10.8133	+	7.85629i	−0.857547	+	0.623045i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	0.0507372	−	0.0878794i	0.00399865	−	0.00692587i
$162$	0.104528	+	0.994522i	0.00821253	+	0.0781370i
$163$	7.11186	+	5.16707i	0.557044	+	0.404716i	0.830376	−	0.557204i	$-0.188126\pi$
$163$	7.11186	+	5.16707i	0.557044	+	0.404716i	−0.273332	+	0.961920i	$0.588126\pi$
$164$	−0.487035	+	4.63383i	−0.0380311	+	0.361841i
$165$	3.29570	−	3.66025i	0.256570	−	0.284950i
$166$	8.35613	+	3.72039i	0.648561	+	0.288758i
$167$	22.2591	+	4.73133i	1.72246	+	0.366121i	0.959802	−	0.280677i	$-0.0905590\pi$
$167$	22.2591	+	4.73133i	1.72246	+	0.366121i	0.762661	+	0.646798i	$0.223892\pi$
$168$	−2.77108	+	0.589010i	−0.213793	+	0.0454431i
$169$	−8.20034	+	3.65103i	−0.630796	+	0.280848i
$170$	0.663853	−	2.04313i	0.0509152	−	0.156701i
$171$	−1.29293	+	3.97922i	−0.0988727	+	0.304299i
$172$	6.50057	−	2.89424i	0.495663	−	0.220684i
$173$	8.46683	−	1.79968i	0.643721	−	0.136827i	0.125527	−	0.992090i	$-0.459938\pi$
$173$	8.46683	−	1.79968i	0.643721	−	0.136827i	0.518194	+	0.855263i	$0.326605\pi$
$174$	4.80719	+	1.02180i	0.364432	+	0.0774624i
$175$	2.58806	+	1.15228i	0.195639	+	0.0871040i
$176$	3.29570	−	3.66025i	0.248423	−	0.275902i
$177$	0.346689	−	3.29852i	0.0260587	−	0.247932i
$178$	−4.61758	−	3.35487i	−0.346102	−	0.251458i
$179$	2.37055	+	22.5543i	0.177184	+	1.68579i	0.616420	+	0.787417i	$0.288582\pi$
$179$	2.37055	+	22.5543i	0.177184	+	1.68579i	−0.439237	+	0.898371i	$0.644751\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	0.430204	+	0.745135i	0.0319768	+	0.0553855i	0.881571	−	0.472052i	$-0.156486\pi$
$181$	0.430204	+	0.745135i	0.0319768	+	0.0553855i	−0.849594	+	0.527437i	$0.823153\pi$
$182$	4.59737	−	3.34018i	0.340780	−	0.247591i
$183$	−0.272152	−	0.302255i	−0.0201180	−	0.0223433i
$184$	0.0110687	+	0.0340658i	0.000815992	+	0.00251136i
$185$	3.21528			0.236392
$186$	−5.13441	+	2.15355i	−0.376473	+	0.157906i
$187$	10.5810			0.773759
$188$	2.23178	+	6.86872i	0.162769	+	0.500953i
$189$	−1.89564	−	2.10532i	−0.137887	−	0.153139i
$190$	3.38493	−	2.45930i	0.245569	−	0.178416i
$191$	6.79727	+	11.7732i	0.491833	+	0.851880i	0.999956	−	0.00940506i	$-0.00299377\pi$
$191$	6.79727	+	11.7732i	0.491833	+	0.851880i	−0.508123	+	0.861285i	$0.669660\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	2.61508	+	24.8808i	0.188237	+	1.79096i	0.526774	+	0.850006i	$0.323401\pi$
$193$	2.61508	+	24.8808i	0.188237	+	1.79096i	−0.338536	+	0.940953i	$0.609932\pi$
$194$	−2.01746	−	1.46577i	−0.144845	−	0.105236i
$195$	−0.209673	+	1.99490i	−0.0150150	+	0.142858i
$196$	0.686391	−	0.762315i	0.0490280	−	0.0544511i
$197$	19.7613	+	8.79831i	1.40794	+	0.626853i	0.963194	−	0.268806i	$-0.0866290\pi$
$197$	19.7613	+	8.79831i	1.40794	+	0.626853i	0.444741	+	0.895659i	$0.353296\pi$
$198$	4.81772	+	1.02404i	0.342380	+	0.0727752i
$199$	−14.9353	+	3.17460i	−1.05874	+	0.225042i	−0.704201	−	0.710000i	$-0.748695\pi$
$199$	−14.9353	+	3.17460i	−1.05874	+	0.225042i	−0.354537	+	0.935042i	$0.615361\pi$
$200$	−0.913545	+	0.406737i	−0.0645974	+	0.0287606i
$201$	1.37565	−	4.23381i	0.0970308	−	0.298630i
$202$	−3.34892	+	10.3069i	−0.235629	+	0.725192i
$203$	−12.7192	+	5.66297i	−0.892715	+	0.397462i
$204$	2.10133	−	0.446651i	0.147122	−	0.0312718i
$205$	4.55754	+	0.968735i	0.318312	+	0.0676594i
$206$	4.43043	+	1.97256i	0.308683	+	0.137435i
$207$	−0.0239675	+	0.0266186i	−0.00166586	+	0.00185012i
$208$	−0.209673	+	1.99490i	−0.0145382	+	0.138322i
$209$	16.6720	+	12.1129i	1.15322	+	0.837866i
$210$	0.296127	+	2.81746i	0.0204347	+	0.194423i
$211$	−1.07675	+	1.86498i	−0.0741263	+	0.128390i	−0.900706	−	0.434429i	$-0.856950\pi$
$211$	−1.07675	+	1.86498i	−0.0741263	+	0.128390i	0.826580	+	0.562820i	$0.190283\pi$
$212$	6.68296	+	11.5752i	0.458988	+	0.794990i
$213$	−8.38878	+	6.09481i	−0.574790	+	0.417609i
$214$	6.27351	+	6.96743i	0.428848	+	0.476284i
$215$	−2.19889	−	6.76748i	−0.149963	−	0.461539i
$216$	1.00000			0.0680414
$217$	8.18166	−	13.4856i	0.555407	−	0.915459i
$218$	3.86883			0.262030
$219$	−1.21146	−	3.72850i	−0.0818632	−	0.251949i
$220$	−3.29570	−	3.66025i	−0.222196	−	0.246774i
$221$	−3.48622	+	2.53289i	−0.234509	+	0.170380i
$222$	1.60764	+	2.78451i	0.107898	+	0.186884i
$223$	0.115641	−	0.200296i	0.00774390	−	0.0134128i	−0.862127	−	0.506691i	$-0.830868\pi$
$223$	0.115641	−	0.200296i	0.00774390	−	0.0134128i	0.869871	+	0.493279i	$0.164202\pi$
$224$	0.296127	+	2.81746i	0.0197858	+	0.188250i
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$	−0.0540715	+	0.514456i	−0.00359678	+	0.0342211i
$227$	10.1223	−	11.2419i	0.671839	−	0.746153i	−0.306792	−	0.951777i	$-0.599256\pi$
$227$	10.1223	−	11.2419i	0.671839	−	0.746153i	0.978631	+	0.205624i	$0.0659222\pi$
$228$	3.82228	+	1.70179i	0.253137	+	0.112704i
$229$	−23.9966	−	5.10064i	−1.58574	−	0.337060i	−0.671113	−	0.741355i	$-0.734184\pi$
$229$	−23.9966	−	5.10064i	−1.58574	−	0.337060i	−0.914629	+	0.404295i	$0.867517\pi$
$230$	0.0350362	−	0.00744717i	0.00231022	−	0.000491052i
$231$	−12.7471	+	5.67537i	−0.838697	+	0.373412i
$232$	1.51869	−	4.67405i	0.0997069	−	0.306866i
$233$	−1.19461	+	3.67664i	−0.0782617	+	0.240865i	−0.982531	−	0.186097i	$-0.940416\pi$
$233$	−1.19461	+	3.67664i	−0.0782617	+	0.240865i	0.904270	+	0.426962i	$0.140416\pi$
$234$	−1.83247	+	0.815870i	−0.119793	+	0.0533351i
$235$	7.06438	−	1.50158i	0.460829	−	0.0979522i
$236$	−3.24422	−	0.689579i	−0.211180	−	0.0448878i
$237$	0.705998	+	0.314330i	0.0458595	+	0.0204180i
$238$	−4.07234	+	4.52280i	−0.263971	+	0.293169i
$239$	−0.385773	+	3.67038i	−0.0249536	+	0.237417i	0.974935	+	0.222490i	$0.0714184\pi$
$239$	−0.385773	+	3.67038i	−0.0249536	+	0.237417i	−0.999889	+	0.0149275i	$0.995248\pi$
$240$	−0.809017	−	0.587785i	−0.0522218	−	0.0379414i
$241$	−0.535680	−	5.09665i	−0.0345062	−	0.328304i	−0.998134	−	0.0610573i	$-0.980553\pi$
$241$	−0.535680	−	5.09665i	−0.0345062	−	0.328304i	0.963628	−	0.267247i	$-0.0861139\pi$
$242$	6.62954	−	11.4827i	0.426163	−	0.738136i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−0.329047	+	0.239067i	−0.0210651	+	0.0153047i
$245$	−0.686391	−	0.762315i	−0.0438519	−	0.0487025i
$246$	1.43982	+	4.43131i	0.0917996	+	0.282530i
$247$	−8.39266			−0.534012
$248$	1.60506	+	5.33139i	0.101922	+	0.338544i
$249$	9.14692			0.579663
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	−20.2239	−	22.4610i	−1.27652	−	1.41772i	−0.861376	−	0.507969i	$-0.830397\pi$
$251$	−20.2239	−	22.4610i	−1.27652	−	1.41772i	−0.415148	−	0.909754i	$-0.636270\pi$
$252$	−2.29193	+	1.66519i	−0.144378	+	0.104897i
$253$	0.0882103	+	0.152785i	0.00554574	+	0.00960550i
$254$	0.806786	−	1.39739i	0.0506223	−	0.0876804i
$255$	−0.224556	−	2.13650i	−0.0140622	−	0.133793i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	3.03468	−	28.8731i	0.189298	−	1.80105i	−0.327402	−	0.944885i	$-0.606173\pi$
$257$	3.03468	−	28.8731i	0.189298	−	1.80105i	0.516700	−	0.856166i	$-0.327160\pi$
$258$	4.76137	−	5.28804i	0.296430	−	0.329219i
$259$	−8.32133	−	3.70490i	−0.517062	−	0.230211i
$260$	1.96206	+	0.417049i	0.121682	+	0.0258643i
$261$	4.80719	−	1.02180i	0.297557	−	0.0632478i
$262$	−0.646259	+	0.287733i	−0.0399260	+	0.0177762i
$263$	−2.98219	+	9.17824i	−0.183890	+	0.565955i	−0.999927	−	0.0120441i	$-0.996166\pi$
$263$	−2.98219	+	9.17824i	−0.183890	+	0.565955i	0.816038	+	0.577999i	$0.196166\pi$
$264$	1.52202	−	4.68429i	0.0936737	−	0.288298i
$265$	12.2104	−	5.43641i	0.750078	−	0.333956i
$266$	−11.5942	+	2.46442i	−0.710886	+	0.151103i
$267$	−5.58292	−	1.18669i	−0.341669	−	0.0726240i
$268$	−4.06682	−	1.81067i	−0.248421	−	0.110604i
$269$	3.00962	−	3.34252i	0.183500	−	0.203797i	−0.644376	−	0.764709i	$-0.722883\pi$
$269$	3.00962	−	3.34252i	0.183500	−	0.203797i	0.827876	+	0.560912i	$0.189549\pi$
$270$	0.104528	−	0.994522i	0.00636140	−	0.0605247i
$271$	21.1450	+	15.3627i	1.28447	+	0.933220i	0.999678	−	0.0253699i	$-0.00807637\pi$
$271$	21.1450	+	15.3627i	1.28447	+	0.933220i	0.284789	+	0.958590i	$0.408076\pi$
$272$	−0.224556	−	2.13650i	−0.0136157	−	0.129545i
$273$	2.84133	−	4.92133i	0.171965	−	0.297852i
$274$	−8.46110	−	14.6551i	−0.511154	−	0.885344i
$275$	−3.98469	+	2.89505i	−0.240286	+	0.174578i
$276$	0.0239675	+	0.0266186i	0.00144268	+	0.00160225i
$277$	−6.14598	−	18.9154i	−0.369276	−	1.13652i	−0.947260	−	0.320467i	$-0.896160\pi$
$277$	−6.14598	−	18.9154i	−0.369276	−	1.13652i	0.577983	−	0.816048i	$-0.303840\pi$
$278$	4.08851			0.245212
$279$	−3.81459	+	4.05572i	−0.228374	+	0.242810i
$280$	2.83298			0.169303
$281$	2.67421	+	8.23037i	0.159530	+	0.490982i	0.998592	−	0.0530537i	$-0.0168954\pi$
$281$	2.67421	+	8.23037i	0.159530	+	0.490982i	−0.839062	+	0.544036i	$0.816895\pi$
$282$	4.83259	+	5.36714i	0.287777	+	0.319609i
$283$	−6.21988	+	4.51901i	−0.369734	+	0.268627i	−0.757100	−	0.653298i	$-0.773385\pi$
$283$	−6.21988	+	4.51901i	−0.369734	+	0.268627i	0.387367	+	0.921926i	$0.373385\pi$
$284$	5.18455	+	8.97991i	0.307647	+	0.532859i
$285$	2.09200	−	3.62345i	0.123920	−	0.214635i
$286$	1.03271	+	9.82560i	0.0610656	+	0.581000i
$287$	−10.6789	−	7.75869i	−0.630357	−	0.457981i
$288$	0.104528	−	0.994522i	0.00615940	−	0.0586028i
$289$	−8.28713	+	9.20379i	−0.487478	+	0.541399i
$290$	−4.48970	−	1.99894i	−0.263644	−	0.117382i
$291$	−2.43923	−	0.518474i	−0.142990	−	0.0303935i
$292$	−3.83471	+	0.815093i	−0.224409	+	0.0476997i
$293$	−12.0009	+	5.34314i	−0.701100	+	0.312150i	−0.726150	−	0.687536i	$-0.758692\pi$
$293$	−12.0009	+	5.34314i	−0.701100	+	0.312150i	0.0250500	+	0.999686i	$0.492026\pi$
$294$	0.316988	−	0.975590i	0.0184871	−	0.0568976i
$295$	−1.02491	+	3.15436i	−0.0596728	+	0.183654i
$296$	2.93730	−	1.30777i	0.170727	−	0.0760127i
$297$	4.81772	−	1.02404i	0.279552	−	0.0594207i
$298$	1.39772	+	0.297095i	0.0809679	+	0.0172103i
$299$	−0.0656372	−	0.0292236i	−0.00379590	−	0.00169004i
$300$	−0.669131	+	0.743145i	−0.0386323	+	0.0429055i
$301$	−2.10717	+	20.0484i	−0.121455	+	1.15557i
$302$	−8.87161	−	6.44560i	−0.510504	−	0.370903i
$303$	1.13281	+	10.7780i	0.0650783	+	0.619178i
$304$	2.09200	−	3.62345i	0.119985	−	0.207819i
$305$	0.203362	+	0.352234i	0.0116445	+	0.0201688i
$306$	1.73799	−	1.26272i	0.0993543	−	0.0721851i
$307$	7.42057	+	8.24138i	0.423514	+	0.470360i	0.916707	−	0.399560i	$-0.130837\pi$
$307$	7.42057	+	8.24138i	0.423514	+	0.470360i	−0.493193	+	0.869920i	$0.664170\pi$
$308$	4.31185	+	13.2705i	0.245690	+	0.756157i
$309$	4.84971			0.275891
$310$	5.46996	−	1.03899i	0.310673	−	0.0590106i
$311$	−24.7191			−1.40169			−0.700846	−	0.713313i	$-0.747194\pi$
$311$	−24.7191			−1.40169			−0.700846	+	0.713313i	$0.747194\pi$
$312$	0.619855	+	1.90772i	0.0350924	+	0.108003i
$313$	−14.0840	−	15.6419i	−0.796076	−	0.884132i	0.199325	−	0.979934i	$-0.436125\pi$
$313$	−14.0840	−	15.6419i	−0.796076	−	0.884132i	−0.995400	+	0.0958017i	$0.969459\pi$
$314$	2.44954	−	1.77970i	0.138236	−	0.100434i
$315$	1.41649	+	2.45344i	0.0798103	+	0.138235i
$316$	0.386405	−	0.669274i	0.0217370	−	0.0376496i
$317$	3.14114	+	29.8859i	0.176424	+	1.67856i	0.621768	+	0.783201i	$0.286415\pi$
$317$	3.14114	+	29.8859i	0.176424	+	1.67856i	−0.445344	+	0.895359i	$0.646919\pi$
$318$	10.8133	+	7.85629i	0.606378	+	0.440559i
$319$	2.53022	−	24.0734i	0.141665	−	1.34785i
$320$	−0.669131	+	0.743145i	−0.0374055	+	0.0415431i
$321$	8.56504	+	3.81340i	0.478054	+	0.212843i
$322$	−0.0992569	−	0.0210977i	−0.00553137	−	0.00117573i
$323$	8.79197	−	1.86879i	0.489198	−	0.103982i
$324$	0.913545	−	0.406737i	0.0507525	−	0.0225965i
$325$	0.619855	−	1.90772i	0.0343834	−	0.105821i
$326$	2.71649	−	8.36050i	0.150452	−	0.463045i
$327$	3.53435	−	1.57360i	0.195450	−	0.0870200i
$328$	4.55754	−	0.968735i	0.251648	−	0.0534894i
$329$	−20.0133	−	4.25395i	−1.10337	−	0.234528i
$330$	−4.49953	−	2.00332i	−0.247691	−	0.110279i
$331$	−0.0383546	+	0.0425971i	−0.00210816	+	0.00234135i	−0.744198	−	0.667959i	$-0.767168\pi$
$331$	−0.0383546	+	0.0425971i	−0.00210816	+	0.00234135i	0.742090	+	0.670300i	$0.233835\pi$
$332$	0.956114	−	9.09681i	0.0524735	−	0.499252i
$333$	2.60121	+	1.88989i	0.142546	+	0.103566i
$334$	−2.37869	−	22.6318i	−0.130156	−	1.23835i
$335$	−2.22585	+	3.85528i	−0.121611	+	0.210636i
$336$	1.41649	+	2.45344i	0.0772760	+	0.133846i
$337$	−27.1360	+	19.7155i	−1.47819	+	1.07397i	−0.500062	+	0.865990i	$0.666689\pi$
$337$	−27.1360	+	19.7155i	−1.47819	+	1.07397i	−0.978133	+	0.207981i	$0.933311\pi$
$338$	6.00638	+	6.67076i	0.326704	+	0.362842i
$339$	0.159851	+	0.491972i	0.00868193	+	0.0267202i
$340$	−2.14827			−0.116506
$341$	13.1923	+	24.0415i	0.714403	+	1.30192i
$342$	4.18400			0.226245
$343$	−5.23006	−	16.0965i	−0.282397	−	0.869127i
$344$	−4.76137	−	5.28804i	−0.256716	−	0.285112i
$345$	0.0289781	−	0.0210538i	0.00156013	−	0.00113350i
$346$	−4.32799	−	7.49630i	−0.232674	−	0.403004i
$347$	−14.6496	+	25.3739i	−0.786434	+	1.36214i	0.141705	+	0.989909i	$0.454742\pi$
$347$	−14.6496	+	25.3739i	−0.786434	+	1.36214i	−0.928139	+	0.372235i	$0.878592\pi$
$348$	−0.513714	−	4.88766i	−0.0275380	−	0.262006i
$349$	21.0613	+	15.3019i	1.12738	+	0.819093i	0.985312	−	0.170763i	$-0.0546233\pi$
$349$	21.0613	+	15.3019i	1.12738	+	0.819093i	0.142073	+	0.989856i	$0.454623\pi$
$350$	0.296127	−	2.81746i	0.0158287	−	0.150600i
$351$	−1.34220	+	1.49067i	−0.0716416	+	0.0795660i
$352$	−4.49953	−	2.00332i	−0.239826	−	0.106777i
$353$	−27.2782	−	5.79817i	−1.45187	−	0.308605i	−0.586589	−	0.809885i	$-0.699530\pi$
$353$	−27.2782	−	5.79817i	−1.45187	−	0.308605i	−0.865285	+	0.501279i	$0.832863\pi$
$354$	−3.24422	+	0.689579i	−0.172428	+	0.0366507i
$355$	9.47265	−	4.21749i	0.502756	−	0.223841i
$356$	−1.76376	+	5.42829i	−0.0934790	+	0.287699i
$357$	−1.88068	+	5.78815i	−0.0995364	+	0.306341i
$358$	20.7179	−	9.22420i	1.09497	−	0.487514i
$359$	18.0303	−	3.83247i	0.951604	−	0.202270i	0.294146	−	0.955761i	$-0.404965\pi$
$359$	18.0303	−	3.83247i	0.951604	−	0.202270i	0.657459	+	0.753491i	$0.271631\pi$
$360$	−0.978148	−	0.207912i	−0.0515529	−	0.0109579i
$361$	−1.36493	−	0.607708i	−0.0718387	−	0.0319846i
$362$	0.575726	−	0.639408i	0.0302595	−	0.0336065i
$363$	1.38595	−	13.1864i	0.0727435	−	0.692109i
$364$	−4.59737	−	3.34018i	−0.240968	−	0.175073i
$365$	0.409791	+	3.89890i	0.0214495	+	0.204078i
$366$	−0.203362	+	0.352234i	−0.0106299	+	0.0184115i
$367$	−17.2499	−	29.8777i	−0.900437	−	1.55960i	−0.826928	−	0.562307i	$-0.809914\pi$
$367$	−17.2499	−	29.8777i	−0.900437	−	1.55960i	−0.0735084	−	0.997295i	$-0.523420\pi$
$368$	0.0289781	−	0.0210538i	0.00151059	−	0.00109751i
$369$	3.11772	+	3.46258i	0.162302	+	0.180255i
$370$	−0.993576	−	3.05791i	−0.0516535	−	0.158973i
$371$	−37.8655			−1.96588
$372$	3.63477	+	4.21763i	0.188454	+	0.218674i
$373$	9.92163			0.513722			0.256861	−	0.966448i	$-0.417312\pi$
$373$	9.92163			0.513722			0.256861	+	0.966448i	$0.417312\pi$
$374$	−3.26971	−	10.0631i	−0.169073	−	0.520352i
$375$	0.669131	+	0.743145i	0.0345538	+	0.0383758i
$376$	5.84288	−	4.24510i	0.301324	−	0.218924i
$377$	4.92906	+	8.53739i	0.253860	+	0.439698i
$378$	−1.41649	+	2.45344i	−0.0728565	+	0.126191i
$379$	3.70828	+	35.2820i	0.190482	+	1.81231i	0.505064	+	0.863082i	$0.331469\pi$
$379$	3.70828	+	35.2820i	0.190482	+	1.81231i	−0.314582	+	0.949230i	$0.601864\pi$
$380$	−3.38493	−	2.45930i	−0.173643	−	0.126159i
$381$	0.168664	−	1.60473i	0.00864093	−	0.0822130i
$382$	9.09652	−	10.1027i	0.465418	−	0.516899i
$383$	−8.32853	−	3.70810i	−0.425568	−	0.189475i	0.182766	−	0.983156i	$-0.441495\pi$
$383$	−8.32853	−	3.70810i	−0.425568	−	0.189475i	−0.608334	+	0.793682i	$0.708162\pi$
$384$	−0.978148	−	0.207912i	−0.0499159	−	0.0106099i
$385$	13.6485	−	2.90108i	0.695593	−	0.147853i
$386$	22.8549	−	10.1757i	1.16329	−	0.517928i
$387$	2.19889	−	6.76748i	0.111776	−	0.344011i
$388$	−0.770602	+	2.37167i	−0.0391214	+	0.120403i
$389$	−9.68791	+	4.31333i	−0.491196	+	0.218695i	−0.637361	−	0.770566i	$-0.719974\pi$
$389$	−9.68791	+	4.31333i	−0.491196	+	0.218695i	0.146164	+	0.989260i	$0.453307\pi$
$390$	1.96206	−	0.417049i	0.0993527	−	0.0211181i
$391$	0.0752673	+	0.0159986i	0.00380643	+	0.000809082i
$392$	−0.937111	−	0.417229i	−0.0473313	−	0.0210732i
$393$	−0.473356	+	0.525715i	−0.0238776	+	0.0265188i
$394$	2.26110	−	21.5130i	0.113913	−	1.08381i
$395$	−0.625217	−	0.454247i	−0.0314581	−	0.0228556i
$396$	−0.514839	−	4.89837i	−0.0258716	−	0.246152i
$397$	0.183163	−	0.317248i	0.00919268	−	0.0159222i	−0.861392	−	0.507940i	$-0.830407\pi$
$397$	0.183163	−	0.317248i	0.00919268	−	0.0159222i	0.870585	+	0.492018i	$0.163741\pi$
$398$	7.63450	+	13.2233i	0.382683	+	0.662826i
$399$	−9.58945	+	6.96715i	−0.480073	+	0.348794i
$400$	0.669131	+	0.743145i	0.0334565	+	0.0371572i
$401$	−7.01270	−	21.5829i	−0.350197	−	1.07780i	−0.958742	−	0.284277i	$-0.908246\pi$
$401$	−7.01270	−	21.5829i	−0.350197	−	1.07780i	0.608545	−	0.793520i	$-0.291754\pi$
$402$	−4.45169			−0.222030
$403$	−10.1017	−	4.76320i	−0.503200	−	0.237272i
$404$	10.8373			0.539178
$405$	−0.309017	−	0.951057i	−0.0153552	−	0.0472584i
$406$	9.31626	+	10.3468i	0.462358	+	0.513501i
$407$	12.8119	−	9.30839i	0.635062	−	0.461400i
$408$	−1.07414	−	1.86046i	−0.0531777	−	0.0921065i
$409$	10.5444	−	18.2634i	0.521385	−	0.903065i	−0.478306	−	0.878193i	$-0.658749\pi$
$409$	10.5444	−	18.2634i	0.521385	−	0.903065i	0.999691	−	0.0248716i	$-0.00791769\pi$
$410$	−0.487035	−	4.63383i	−0.0240530	−	0.228849i
$411$	−13.6903	−	9.94662i	−0.675295	−	0.490631i
$412$	0.506933	−	4.82315i	0.0249748	−	0.237619i
$413$	6.28724	−	6.98269i	0.309375	−	0.343596i
$414$	0.0327222	+	0.0145689i	0.00160821	+	0.000716021i
$415$	−8.94704	−	1.90175i	−0.439193	−	0.0933533i
$416$	1.96206	−	0.417049i	0.0961979	−	0.0204475i
$417$	3.73504	−	1.66295i	0.182906	−	0.0814348i
$418$	6.36813	−	19.5991i	0.311475	−	0.958622i
$419$	10.1861	−	31.3497i	0.497625	−	1.53153i	−0.315201	−	0.949025i	$-0.602072\pi$
$419$	10.1861	−	31.3497i	0.497625	−	1.53153i	0.812826	−	0.582507i	$-0.197928\pi$
$420$	2.58806	−	1.15228i	0.126284	−	0.0562254i
$421$	−8.83638	+	1.87823i	−0.430659	+	0.0915394i	−0.418141	−	0.908382i	$-0.637318\pi$
$421$	−8.83638	+	1.87823i	−0.430659	+	0.0915394i	−0.0125182	+	0.999922i	$0.503985\pi$
$422$	2.10643	+	0.447736i	0.102540	+	0.0217955i
$423$	6.59781	+	2.93753i	0.320796	+	0.142828i
$424$	8.94355	−	9.93282i	0.434337	−	0.482380i
$425$	−0.224556	+	2.13650i	−0.0108926	+	0.103636i
$426$	8.38878	+	6.09481i	0.406438	+	0.295294i
$427$	−0.120442	−	1.14593i	−0.00582861	−	0.0554555i
$428$	4.68780	−	8.11952i	0.226594	−	0.392472i
$429$	4.93986	+	8.55609i	0.238499	+	0.413092i
$430$	−5.75677	+	4.18254i	−0.277616	+	0.201700i
$431$	−15.3172	−	17.0115i	−0.737805	−	0.819415i	0.251101	−	0.967961i	$-0.419208\pi$
$431$	−15.3172	−	17.0115i	−0.737805	−	0.819415i	−0.988906	+	0.148546i	$0.952541\pi$
$432$	−0.309017	−	0.951057i	−0.0148676	−	0.0457577i
$433$	−3.84469			−0.184764			−0.0923820	−	0.995724i	$-0.529448\pi$
$433$	−3.84469			−0.184764			−0.0923820	+	0.995724i	$0.529448\pi$
$434$	−15.3538	−	3.61396i	−0.737006	−	0.173475i
$435$	−4.91458			−0.235636
$436$	−1.19553	−	3.67948i	−0.0572557	−	0.176215i
$437$	0.100280	+	0.111372i	0.00479705	+	0.00532767i
$438$	−3.17165	+	2.30434i	−0.151548	+	0.110106i
$439$	17.6507	+	30.5720i	0.842423	+	1.45912i	0.887840	+	0.460152i	$0.152205\pi$
$439$	17.6507	+	30.5720i	0.842423	+	1.45912i	−0.0454173	+	0.998968i	$0.514462\pi$
$440$	−2.46268	+	4.26548i	−0.117403	+	0.203349i
$441$	−0.107225	−	1.02018i	−0.00510595	−	0.0485798i
$442$	3.48622	+	2.53289i	0.165823	+	0.120477i
$443$	−2.32532	+	22.1239i	−0.110479	+	1.05114i	0.789065	+	0.614309i	$0.210565\pi$
$443$	−2.32532	+	22.1239i	−0.110479	+	1.05114i	−0.899544	+	0.436829i	$0.856101\pi$
$444$	2.15144	−	2.38942i	0.102103	−	0.113397i
$445$	5.21419	+	2.32151i	0.247176	+	0.110050i
$446$	−0.226228	−	0.0480863i	−0.0107122	−	0.00227695i
$447$	1.39772	−	0.297095i	0.0661100	−	0.0140521i
$448$	2.58806	−	1.15228i	0.122274	−	0.0544400i
$449$	0.445916	−	1.37239i	0.0210441	−	0.0647670i	−0.939983	−	0.341221i	$-0.889159\pi$
$449$	0.445916	−	1.37239i	0.0210441	−	0.0647670i	0.961027	+	0.276454i	$0.0891594\pi$
$450$	−0.309017	+	0.951057i	−0.0145672	+	0.0448332i
$451$	20.9649	−	9.33418i	0.987199	−	0.439529i
$452$	0.505986	−	0.107551i	0.0237996	−	0.00505875i
$453$	−10.7263	−	2.27994i	−0.503965	−	0.107121i
$454$	−13.8197	−	6.15291i	−0.648589	−	0.288770i
$455$	−3.80244	+	4.22304i	−0.178261	+	0.197979i
$456$	0.437348	−	4.16108i	0.0204807	−	0.194861i
$457$	−22.3398	−	16.2308i	−1.04501	−	0.759245i	−0.0737531	−	0.997277i	$-0.523498\pi$
$457$	−22.3398	−	16.2308i	−1.04501	−	0.759245i	−0.971257	+	0.238032i	$0.923498\pi$
$458$	2.56437	+	24.3983i	0.119825	+	1.14006i
$459$	1.07414	−	1.86046i	0.0501364	−	0.0868388i
$460$	−0.0179095	−	0.0310201i	−0.000835033	−	0.00144632i
$461$	14.6814	−	10.6667i	0.683781	−	0.496796i	−0.190829	−	0.981623i	$-0.561118\pi$
$461$	14.6814	−	10.6667i	0.683781	−	0.496796i	0.874610	+	0.484827i	$0.161118\pi$
$462$	9.33667	+	10.3694i	0.434381	+	0.482429i
$463$	−2.15601	−	6.63552i	−0.100198	−	0.308379i	0.888375	−	0.459118i	$-0.151835\pi$
$463$	−2.15601	−	6.63552i	−0.100198	−	0.308379i	−0.988574	+	0.150739i	$0.951835\pi$
$464$	−4.91458			−0.228154
$465$	4.57447	−	3.17400i	0.212136	−	0.147191i
$466$	3.86585			0.179082
$467$	4.02503	+	12.3878i	0.186256	+	0.573238i	0.999968	−	0.00803105i	$-0.00255639\pi$
$467$	4.02503	+	12.3878i	0.186256	+	0.573238i	−0.813711	+	0.581269i	$0.802556\pi$
$468$	1.34220	+	1.49067i	0.0620434	+	0.0689062i
$469$	10.2030	−	7.41289i	0.471130	−	0.342296i
$470$	−3.61110	−	6.25461i	−0.166568	−	0.288504i
$471$	1.51390	−	2.62215i	0.0697569	−	0.120822i
$472$	0.346689	+	3.29852i	0.0159576	+	0.151827i
$473$	−28.3541	−	20.6005i	−1.30372	−	0.947210i
$474$	0.0807807	−	0.768577i	0.00371038	−	0.0353019i
$475$	−2.79965	+	3.10932i	−0.128457	+	0.142665i
$476$	5.55986	+	2.47541i	0.254836	+	0.113460i
$477$	13.0738	+	2.77893i	0.598610	+	0.127239i
$478$	3.60995	−	0.767319i	0.165115	−	0.0350963i
$479$	9.05446	−	4.03131i	0.413709	−	0.184195i	−0.189318	−	0.981916i	$-0.560628\pi$
$479$	9.05446	−	4.03131i	0.413709	−	0.184195i	0.603027	+	0.797721i	$0.293961\pi$
$480$	−0.309017	+	0.951057i	−0.0141046	+	0.0434096i
$481$	−1.99301	+	6.13384i	−0.0908733	+	0.279679i
$482$	−4.68167	+	2.08441i	−0.213244	+	0.0949424i
$483$	−0.0992569	+	0.0210977i	−0.00451635	+	0.000959979i
$484$	−12.9693	−	2.75672i	−0.589515	−	0.125305i
$485$	2.27813	+	1.01429i	0.103444	+	0.0460564i
$486$	0.669131	−	0.743145i	0.0303524	−	0.0337097i
$487$	−2.97052	+	28.2626i	−0.134607	+	1.28070i	0.693633	+	0.720329i	$0.256009\pi$
$487$	−2.97052	+	28.2626i	−0.134607	+	1.28070i	−0.828240	+	0.560373i	$0.810658\pi$
$488$	0.329047	+	0.239067i	0.0148953	+	0.0108220i
$489$	−0.918883	−	8.74259i	−0.0415533	−	0.395354i
$490$	−0.512898	+	0.888365i	−0.0231704	+	0.0401323i
$491$	−17.0227	−	29.4842i	−0.768223	−	1.33060i	−0.938525	−	0.345210i	$-0.887808\pi$
$491$	−17.0227	−	29.4842i	−0.768223	−	1.33060i	0.170302	−	0.985392i	$-0.445526\pi$
$492$	3.76950	−	2.73870i	0.169942	−	0.123470i
$493$	−7.06459	−	7.84603i	−0.318173	−	0.353367i
$494$	2.59348	+	7.98190i	0.116686	+	0.359123i
$495$	−4.92535			−0.221378
$496$	4.57447	−	3.17400i	0.205400	−	0.142517i
$497$	−29.3755			−1.31767
$498$	−2.82655	−	8.69924i	−0.126661	−	0.389822i
$499$	19.9375	+	22.1429i	0.892526	+	0.991251i	0.999996	−	0.00295743i	$-0.000941379\pi$
$499$	19.9375	+	22.1429i	0.892526	+	0.991251i	−0.107469	+	0.994208i	$0.534275\pi$
$500$	0.809017	−	0.587785i	0.0361803	−	0.0262866i
$501$	−11.3782	−	19.7076i	−0.508341	−	0.880472i
$502$	−15.1121	+	26.1749i	−0.674486	+	1.16824i
$503$	2.92578	+	27.8369i	0.130454	+	1.24119i	0.842361	+	0.538914i	$0.181165\pi$
$503$	2.92578	+	27.8369i	0.130454	+	1.24119i	−0.711907	+	0.702274i	$0.752168\pi$
$504$	2.29193	+	1.66519i	0.102091	+	0.0741733i
$505$	1.13281	−	10.7780i	0.0504094	−	0.479613i
$506$	0.118048	−	0.131106i	0.00524789	−	0.00582838i
$507$	8.20034	+	3.65103i	0.364190	+	0.162148i
$508$	−1.57831	−	0.335481i	−0.0700263	−	0.0148845i
$509$	−35.3819	+	7.52065i	−1.56827	+	0.333347i	−0.908424	−	0.418050i	$-0.862714\pi$
$509$	−35.3819	+	7.52065i	−1.56827	+	0.333347i	−0.659850	+	0.751397i	$0.729380\pi$
$510$	−1.96255	+	0.873781i	−0.0869030	+	0.0386917i
$511$	3.43206	−	10.5628i	0.151825	−	0.467270i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	3.82228	−	1.70179i	0.168758	−	0.0751358i
$514$	−28.3977	+	6.03611i	−1.25257	+	0.266241i
$515$	−4.74374	−	1.00831i	−0.209034	−	0.0444315i
$516$	−6.50057	−	2.89424i	−0.286171	−	0.127412i
$517$	23.8022	−	26.4350i	1.04682	−	1.16261i
$518$	−0.952132	+	9.05893i	−0.0418343	+	0.398027i
$519$	−7.00284	−	5.08786i	−0.307390	−	0.223332i
$520$	−0.209673	−	1.99490i	−0.00919476	−	0.0874823i
$521$	13.0186	−	22.5488i	0.570354	−	0.987882i	−0.426175	−	0.904641i	$-0.640139\pi$
$521$	13.0186	−	22.5488i	0.570354	−	0.987882i	0.996529	−	0.0832418i	$-0.0265274\pi$
$522$	−2.45729	−	4.25615i	−0.107553	−	0.186287i
$523$	−18.4356	+	13.3942i	−0.806130	+	0.585688i	−0.912706	−	0.408617i	$-0.866011\pi$
$523$	−18.4356	+	13.3942i	−0.806130	+	0.585688i	0.106576	+	0.994305i	$0.466011\pi$
$524$	0.473356	+	0.525715i	0.0206786	+	0.0229659i
$525$	−0.875440	−	2.69433i	−0.0382073	−	0.117590i
$526$	9.65057			0.420785
$527$	11.6429	+	2.74049i	0.507173	+	0.119378i
$528$	−4.92535			−0.214348
$529$	−7.10699	−	21.8731i	−0.309000	−	0.951003i
$530$	−8.94355	−	9.93282i	−0.388483	−	0.431454i
$531$	−2.68326	+	1.94950i	−0.116444	+	0.0846013i
$532$	5.92661	+	10.2652i	0.256951	+	0.445052i
$533$	−4.67308	+	8.09402i	−0.202414	+	0.350591i
$534$	0.596611	+	5.67638i	0.0258179	+	0.245641i
$535$	−7.58503	−	5.51084i	−0.327929	−	0.238255i
$536$	−0.465329	+	4.42730i	−0.0200991	+	0.191230i
$537$	15.1749	−	16.8534i	0.654846	−	0.727280i
$538$	−4.10895	−	1.82942i	−0.177150	−	0.0788721i
$539$	−4.94200	−	1.05045i	−0.212867	−	0.0452462i
$540$	−0.978148	+	0.207912i	−0.0420928	+	0.00894709i
$541$	15.4418	−	6.87515i	0.663897	−	0.295586i	−0.0469868	−	0.998896i	$-0.514962\pi$
$541$	15.4418	−	6.87515i	0.663897	−	0.295586i	0.710884	+	0.703310i	$0.248295\pi$
$542$	8.07667	−	24.8574i	0.346923	−	1.06772i
$543$	0.265881	−	0.818297i	0.0114100	−	0.0351165i
$544$	−1.96255	+	0.873781i	−0.0841434	+	0.0374631i
$545$	−3.78429	+	0.804375i	−0.162101	+	0.0344557i
$546$	−5.55848	−	1.18149i	−0.237881	−	0.0505632i
$547$	11.0787	+	4.93254i	0.473690	+	0.210900i	0.629674	−	0.776859i	$-0.283188\pi$
$547$	11.0787	+	4.93254i	0.473690	+	0.210900i	−0.155985	+	0.987759i	$0.549855\pi$
$548$	−11.3232	+	12.5756i	−0.483702	+	0.537205i
$549$	−0.0425143	+	0.404496i	−0.00181446	+	0.0172635i
$550$	3.98469	+	2.89505i	0.169908	+	0.123445i
$551$	−2.14938	−	20.4500i	−0.0915667	−	0.871199i
$552$	0.0179095	−	0.0310201i	0.000762277	−	0.00132030i
$553$	1.09468	+	1.89604i	0.0465505	+	0.0806279i
$554$	−16.0904	+	11.6904i	−0.683615	+	0.496675i
$555$	−2.15144	−	2.38942i	−0.0913236	−	0.101425i
$556$	−1.26342	−	3.88840i	−0.0535809	−	0.164905i
$557$	−9.94742			−0.421486			−0.210743	−	0.977542i	$-0.567588\pi$
$557$	−9.94742			−0.421486			−0.210743	+	0.977542i	$0.567588\pi$
$558$	5.03600	+	2.37460i	0.213191	+	0.100525i
$559$	14.2734			0.603702
$560$	−0.875440	−	2.69433i	−0.0369941	−	0.113856i
$561$	−7.08007	−	7.86321i	−0.298921	−	0.331985i
$562$	7.00117	−	5.08665i	0.295326	−	0.214567i
$563$	6.31763	+	10.9425i	0.266257	+	0.461170i	0.967892	−	0.251366i	$-0.0808798\pi$
$563$	6.31763	+	10.9425i	0.266257	+	0.461170i	−0.701636	+	0.712536i	$0.747547\pi$
$564$	3.61110	−	6.25461i	0.152055	−	0.263366i
$565$	−0.0540715	−	0.514456i	−0.00227481	−	0.0216433i
$566$	6.21988	+	4.51901i	0.261441	+	0.189948i
$567$	−0.296127	+	2.81746i	−0.0124362	+	0.118322i
$568$	6.93828	−	7.70575i	0.291124	−	0.323326i
$569$	1.55342	+	0.691629i	0.0651229	+	0.0289946i	0.439040	−	0.898468i	$-0.355319\pi$
$569$	1.55342	+	0.691629i	0.0651229	+	0.0289946i	−0.373917	+	0.927462i	$0.621985\pi$
$570$	−4.09257	−	0.869903i	−0.171419	−	0.0364362i
$571$	−9.46052	+	2.01090i	−0.395911	+	0.0841534i	−0.401565	−	0.915831i	$-0.631534\pi$
$571$	−9.46052	+	2.01090i	−0.395911	+	0.0841534i	0.00565424	+	0.999984i	$0.498200\pi$
$572$	9.02558	−	4.01845i	0.377378	−	0.168020i
$573$	4.20094	−	12.9292i	0.175497	−	0.540124i
$574$	−4.07899	+	12.5538i	−0.170254	+	0.523987i
$575$	−0.0327222	+	0.0145689i	−0.00136461	+	0.000607564i
$576$	−0.978148	+	0.207912i	−0.0407562	+	0.00866299i
$577$	−43.4479	−	9.23514i	−1.80876	−	0.384464i	−0.825170	−	0.564884i	$-0.808921\pi$
$577$	−43.4479	−	9.23514i	−1.80876	−	0.384464i	−0.983590	+	0.180420i	$0.942254\pi$
$578$	11.3142	+	5.03740i	0.470608	+	0.209528i
$579$	16.7402	−	18.5919i	0.695699	−	0.772652i
$580$	−0.513714	+	4.88766i	−0.0213308	+	0.202949i
$581$	20.9641	+	15.2313i	0.869738	+	0.631902i
$582$	0.260665	+	2.48006i	0.0108049	+	0.102802i
$583$	32.9159	−	57.0121i	1.36324	−	2.36120i
$584$	1.96019	+	3.39515i	0.0811133	+	0.140492i
$585$	1.62280	−	1.17903i	0.0670946	−	0.0487471i
$586$	8.79011	+	9.76241i	0.363116	+	0.403281i
$587$	3.41332	+	10.5051i	0.140883	+	0.433593i	0.996459	−	0.0840849i	$-0.0267967\pi$
$587$	3.41332	+	10.5051i	0.140883	+	0.433593i	−0.855576	+	0.517678i	$0.826797\pi$
$588$	−1.02580			−0.0423031
$589$	15.2079	+	17.6466i	0.626631	+	0.727115i
$590$	3.31669			0.136546
$591$	−6.68449	−	20.5727i	−0.274963	−	0.846249i
$592$	−2.15144	−	2.38942i	−0.0884237	−	0.0982045i
$593$	22.7448	−	16.5251i	0.934018	−	0.678604i	−0.0129556	−	0.999916i	$-0.504124\pi$
$593$	22.7448	−	16.5251i	0.934018	−	0.678604i	0.946973	+	0.321313i	$0.104124\pi$
$594$	−2.46268	−	4.26548i	−0.101045	−	0.175015i
$595$	3.04301	−	5.27065i	0.124751	−	0.216076i
$596$	−0.149366	−	1.42112i	−0.00611826	−	0.0582114i
$597$	12.3529	+	8.97489i	0.505570	+	0.367318i
$598$	−0.00751025	+	0.0714553i	−0.000307117	+	0.00292202i
$599$	−9.39982	+	10.4396i	−0.384066	+	0.426549i	−0.903917	−	0.427709i	$-0.859321\pi$
$599$	−9.39982	+	10.4396i	−0.384066	+	0.426549i	0.519851	+	0.854257i	$0.325988\pi$
$600$	0.913545	+	0.406737i	0.0372953	+	0.0166050i
$601$	−27.6870	−	5.88504i	−1.12937	−	0.240056i	−0.394921	−	0.918715i	$-0.629228\pi$
$601$	−27.6870	−	5.88504i	−1.12937	−	0.240056i	−0.734453	+	0.678659i	$0.762561\pi$
$602$	19.7183	−	4.19125i	0.803658	−	0.170823i
$603$	−4.06682	+	1.81067i	−0.165614	+	0.0737360i
$604$	−3.38865	+	10.4292i	−0.137882	+	0.424358i
$605$	−4.09728	+	12.6101i	−0.166578	+	0.512675i
$606$	9.90040	−	4.40794i	0.402176	−	0.179060i
$607$	−22.7077	+	4.82667i	−0.921677	+	0.195908i	−0.644229	−	0.764832i	$-0.722822\pi$
$607$	−22.7077	+	4.82667i	−0.921677	+	0.195908i	−0.277448	+	0.960741i	$0.589488\pi$
$608$	−4.09257	−	0.869903i	−0.165976	−	0.0352792i
$609$	12.7192	+	5.66297i	0.515409	+	0.229475i
$610$	0.272152	−	0.302255i	0.0110191	−	0.0122380i
$611$	−1.51430	+	14.4076i	−0.0612620	+	0.582869i
$612$	−1.73799	−	1.26272i	−0.0702541	−	0.0510426i
$613$	−2.86266	−	27.2363i	−0.115622	−	1.10007i	−0.886386	−	0.462946i	$-0.846792\pi$
$613$	−2.86266	−	27.2363i	−0.115622	−	1.10007i	0.770765	−	0.637120i	$-0.219874\pi$
$614$	5.54494	−	9.60411i	0.223775	−	0.387590i
$615$	−2.32968	−	4.03512i	−0.0939417	−	0.162712i
$616$	11.2886	−	8.20162i	0.454829	−	0.330453i
$617$	16.8237	+	18.6846i	0.677296	+	0.752214i	0.979591	−	0.201001i	$-0.0644194\pi$
$617$	16.8237	+	18.6846i	0.677296	+	0.752214i	−0.302295	+	0.953214i	$0.597753\pi$
$618$	−1.49864	−	4.61235i	−0.0602843	−	0.185536i
$619$	−32.4538			−1.30443			−0.652215	−	0.758034i	$-0.726160\pi$
$619$	−32.4538			−1.30443			−0.652215	+	0.758034i	$0.726160\pi$
$620$	−2.67845	−	4.88118i	−0.107569	−	0.196033i
$621$	0.0358189			0.00143736
$622$	7.63862	+	23.5093i	0.306281	+	0.942635i
$623$	−10.8196	−	12.0164i	−0.433479	−	0.481427i
$624$	1.62280	−	1.17903i	0.0649640	−	0.0471991i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−10.5241	+	18.2283i	−0.420628	+	0.728550i
$627$	−2.15409	−	20.4948i	−0.0860261	−	0.818483i
$628$	−2.44954	−	1.77970i	−0.0977474	−	0.0710177i
$629$	0.722009	−	6.86946i	0.0287884	−	0.273903i
$630$	1.89564	−	2.10532i	0.0755239	−	0.0838778i
$631$	7.74445	+	3.44805i	0.308302	+	0.137265i	0.555055	−	0.831814i	$-0.312697\pi$
$631$	7.74445	+	3.44805i	0.308302	+	0.137265i	−0.246754	+	0.969078i	$0.579364\pi$
$632$	−0.755923	−	0.160676i	−0.0300690	−	0.00639136i
$633$	2.10643	−	0.447736i	0.0837232	−	0.0177959i
$634$	27.4525	−	12.2227i	1.09028	−	0.485424i
$635$	−0.498621	+	1.53460i	−0.0197872	+	0.0608987i
$636$	4.13030	−	12.7118i	0.163777	−	0.504054i
$637$	1.87974	−	0.836916i	0.0744782	−	0.0331598i
$638$	−23.6771	+	5.03272i	−0.937385	+	0.199247i
$639$	10.1425	+	2.15586i	0.401232	+	0.0852844i
$640$	0.913545	+	0.406737i	0.0361111	+	0.0160777i
$641$	14.8032	−	16.4406i	0.584691	−	0.649365i	−0.376120	−	0.926571i	$-0.622742\pi$
$641$	14.8032	−	16.4406i	0.584691	−	0.649365i	0.960810	+	0.277206i	$0.0894085\pi$
$642$	0.980018	−	9.32425i	0.0386782	−	0.367999i
$643$	6.16146	+	4.47656i	0.242984	+	0.176538i	0.702612	−	0.711573i	$-0.252017\pi$
$643$	6.16146	+	4.47656i	0.242984	+	0.176538i	−0.459628	+	0.888112i	$0.652017\pi$
$644$	0.0106070	+	0.100918i	0.000417973	+	0.00397675i
$645$	−3.55788	+	6.16242i	−0.140091	+	0.242645i
$646$	−4.49419	−	7.78417i	−0.176822	−	0.306264i
$647$	−26.3897	+	19.1732i	−1.03749	+	0.753778i	−0.969793	−	0.243928i	$-0.921564\pi$
$647$	−26.3897	+	19.1732i	−1.03749	+	0.753778i	−0.0676931	+	0.997706i	$0.521564\pi$
$648$	−0.669131	−	0.743145i	−0.0262859	−	0.0291935i
$649$	5.04806	+	15.5363i	0.198154	+	0.609855i
$650$	−2.00589			−0.0786776
$651$	−15.4963	+	2.94344i	−0.607349	+	0.115362i
$652$	−8.79075			−0.344272
$653$	−12.1753	−	37.4717i	−0.476457	−	1.46638i	−0.843983	−	0.536370i	$-0.819795\pi$
$653$	−12.1753	−	37.4717i	−0.476457	−	1.46638i	0.367527	−	0.930013i	$-0.380205\pi$
$654$	−2.58875	−	2.87510i	−0.101228	−	0.112425i
$655$	0.572314	−	0.415810i	0.0223622	−	0.0162471i
$656$	−2.32968	−	4.03512i	−0.0909586	−	0.157545i
$657$	−1.96019	+	3.39515i	−0.0764743	+	0.132457i
$658$	2.13869	+	20.3483i	0.0833749	+	0.793259i
$659$	18.3506	+	13.3325i	0.714839	+	0.519361i	0.884731	−	0.466102i	$-0.154342\pi$
$659$	18.3506	+	13.3325i	0.714839	+	0.519361i	−0.169892	+	0.985463i	$0.554342\pi$
$660$	−0.514839	+	4.89837i	−0.0200401	+	0.190669i
$661$	28.0978	−	31.2058i	1.09288	−	1.21377i	0.117537	−	0.993068i	$-0.462500\pi$
$661$	28.0978	−	31.2058i	1.09288	−	1.21377i	0.975342	−	0.220697i	$-0.0708333\pi$
$662$	0.0523645	+	0.0233142i	0.00203520	+	0.000906131i
$663$	4.21504	+	0.895934i	0.163699	+	0.0347952i
$664$	−8.94704	+	1.90175i	−0.347212	+	0.0738023i
$665$	10.8285	−	4.82114i	0.419909	−	0.186956i
$666$	0.993576	−	3.05791i	0.0385003	−	0.118492i
$667$	0.0543978	−	0.167419i	0.00210629	−	0.00648250i
$668$	−20.7890	+	9.25587i	−0.804351	+	0.358120i
$669$	−0.226228	+	0.0480863i	−0.00874649	+	0.00185912i
$670$	4.35441	+	0.925559i	0.168226	+	0.0357575i
$671$	1.83007	+	0.814799i	0.0706490	+	0.0314550i
$672$	1.89564	−	2.10532i	0.0731257	−	0.0812144i
$673$	−3.75569	+	35.7330i	−0.144771	+	1.37741i	0.645083	+	0.764112i	$0.276823\pi$
$673$	−3.75569	+	35.7330i	−0.144771	+	1.37741i	−0.789854	+	0.613294i	$0.789844\pi$
$674$	27.1360	+	19.7155i	1.04524	+	0.759412i
$675$	0.104528	+	0.994522i	0.00402330	+	0.0382792i
$676$	4.48820	−	7.77379i	0.172623	−	0.298992i
$677$	0.801474	+	1.38819i	0.0308031	+	0.0533526i	0.881016	−	0.473086i	$-0.156860\pi$
$677$	0.801474	+	1.38819i	0.0308031	+	0.0533526i	−0.850213	+	0.526439i	$0.823527\pi$
$678$	0.418496	−	0.304055i	0.0160722	−	0.0116772i
$679$	−4.72719	−	5.25007i	−0.181413	−	0.201479i
$680$	0.663853	+	2.04313i	0.0254576	+	0.0783504i
$681$	−15.1275			−0.579687
$682$	18.7882	−	19.9759i	0.719437	−	0.764915i
$683$	21.8209			0.834954			0.417477	−	0.908687i	$-0.362914\pi$
$683$	21.8209			0.834954			0.417477	+	0.908687i	$0.362914\pi$
$684$	−1.29293	−	3.97922i	−0.0494364	−	0.152149i
$685$	11.3232	+	12.5756i	0.432636	+	0.480491i
$686$	−13.6925	+	9.94816i	−0.522781	+	0.379823i
$687$	12.2664	+	21.2460i	0.467991	+	0.810584i
$688$	−3.55788	+	6.16242i	−0.135643	+	0.234940i
$689$	2.80247	+	26.6637i	0.106766	+	1.01581i
$690$	−0.0289781	−	0.0210538i	−0.00110318	−	0.000801505i
$691$	−3.40893	+	32.4338i	−0.129682	+	1.23384i	0.715213	+	0.698906i	$0.246330\pi$
$691$	−3.40893	+	32.4338i	−0.129682	+	1.23384i	−0.844895	+	0.534932i	$0.820337\pi$
$692$	−5.79198	+	6.43265i	−0.220178	+	0.244533i
$693$	12.7471	+	5.67537i	0.484222	+	0.215590i
$694$	28.6590	+	6.09166i	1.08788	+	0.231236i
$695$	−3.99916	+	0.850048i	−0.151697	+	0.0322442i
$696$	−4.48970	+	1.99894i	−0.170181	+	0.0757697i
$697$	3.09313	−	9.51967i	0.117161	−	0.360583i
$698$	8.04470	−	24.7590i	0.304496	−	0.937143i
$699$	3.53163	−	1.57238i	0.133578	−	0.0594729i
$700$	−2.77108	+	0.589010i	−0.104737	+	0.0222625i
$701$	6.70706	+	1.42563i	0.253322	+	0.0538453i	0.332822	−	0.942990i	$-0.391999\pi$
$701$	6.70706	+	1.42563i	0.253322	+	0.0538453i	−0.0795002	+	0.996835i	$0.525332\pi$
$702$	1.83247	+	0.815870i	0.0691623	+	0.0307930i
$703$	9.00164	−	9.99733i	0.339503	−	0.377057i
$704$	−0.514839	+	4.89837i	−0.0194037	+	0.184614i
$705$	−5.84288	−	4.24510i	−0.220056	−	0.159880i
$706$	2.91505	+	27.7349i	0.109709	+	1.04382i
$707$	−15.3510	+	26.5887i	−0.577334	+	0.999971i
$708$	1.65835	+	2.87234i	0.0623245	+	0.107949i
$709$	−33.8982	+	24.6285i	−1.27307	+	0.924942i	−0.999321	−	0.0368579i	$-0.988265\pi$
$709$	−33.8982	+	24.6285i	−1.27307	+	0.924942i	−0.273753	+	0.961800i	$0.588265\pi$
$710$	−6.93828	−	7.70575i	−0.260389	−	0.289191i
$711$	−0.238812	−	0.734987i	−0.00895614	−	0.0275641i
$712$	5.70764			0.213903
$713$	0.0574916	+	0.190965i	0.00215308	+	0.00715169i
$714$	6.08602			0.227764
$715$	−3.05300	−	9.39618i	−0.114176	−	0.351397i
$716$	−15.1749	−	16.8534i	−0.567113	−	0.629843i
$717$	2.98576	−	2.16928i	0.111505	−	0.0810132i
$718$	−9.21657	−	15.9636i	−0.343959	−	0.595755i
$719$	18.8759	−	32.6941i	0.703954	−	1.21928i	−0.263114	−	0.964765i	$-0.584750\pi$
$719$	18.8759	−	32.6941i	0.703954	−	1.21928i	0.967068	−	0.254519i	$-0.0819171\pi$
$720$	0.104528	+	0.994522i	0.00389555	+	0.0370636i
$721$	11.1152	+	8.07568i	0.413952	+	0.300754i
$722$	−0.156177	+	1.48592i	−0.00581230	+	0.0553003i
$723$	−3.42911	+	3.80841i	−0.127530	+	0.141636i
$724$	−0.786022	−	0.349960i	−0.0292123	−	0.0130061i
$725$	4.80719	+	1.02180i	0.178534	+	0.0379487i
$726$	−12.9693	+	2.75672i	−0.481337	+	0.102311i
$727$	4.10492	−	1.82763i	0.152243	−	0.0677830i	−0.329201	−	0.944260i	$-0.606779\pi$
$727$	4.10492	−	1.82763i	0.152243	−	0.0677830i	0.481444	+	0.876477i	$0.340113\pi$
$728$	−1.75604	+	5.40453i	−0.0650831	+	0.200305i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	3.58145	−	1.59456i	0.132555	−	0.0590174i
$731$	−14.9525	+	3.17826i	−0.553040	+	0.117552i
$732$	0.397836	+	0.0845627i	0.0147045	+	0.00312553i
$733$	36.1560	+	16.0977i	1.33545	+	0.594582i	0.945310	−	0.326172i	$-0.105759\pi$
$733$	36.1560	+	16.0977i	1.33545	+	0.594582i	0.390143	+	0.920754i	$0.372426\pi$
$734$	−23.0849	+	25.6383i	−0.852077	+	0.946328i
$735$	−0.107225	+	1.02018i	−0.00395505	+	0.0376298i
$736$	−0.0289781	−	0.0210538i	−0.00106815	−	0.000776054i
$737$	2.29191	+	21.8060i	0.0844234	+	0.803235i
$738$	2.32968	−	4.03512i	0.0857566	−	0.148535i
$739$	19.1696	+	33.2027i	0.705165	+	1.22138i	0.966632	+	0.256169i	$0.0824603\pi$
$739$	19.1696	+	33.2027i	0.705165	+	1.22138i	−0.261467	+	0.965212i	$0.584206\pi$
$740$	−2.60121	+	1.88989i	−0.0956226	+	0.0694739i
$741$	5.61579	+	6.23696i	0.206301	+	0.229121i
$742$	11.7011	+	36.0122i	0.429560	+	1.32205i
$743$	−11.0075			−0.403826			−0.201913	−	0.979403i	$-0.564716\pi$
$743$	−11.0075			−0.403826			−0.201913	+	0.979403i	$0.564716\pi$
$744$	2.88800	−	4.76019i	0.105879	−	0.174517i
$745$	−1.42895			−0.0523527
$746$	−3.06595	−	9.43603i	−0.112252	−	0.345478i
$747$	−6.12048	−	6.79749i	−0.223937	−	0.248707i
$748$	−8.56021	+	6.21935i	−0.312992	+	0.227402i
$749$	13.2805	+	23.0025i	0.485258	+	0.840491i
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	1.97112	+	18.7539i	0.0719272	+	0.684341i	0.969769	+	0.244024i	$0.0784675\pi$
$751$	1.97112	+	18.7539i	0.0719272	+	0.684341i	−0.897842	+	0.440318i	$0.854866\pi$
$752$	−5.84288	−	4.24510i	−0.213068	−	0.154803i
$753$	−3.15929	+	30.0586i	−0.115131	+	1.09540i
$754$	6.59637	−	7.32602i	0.240226	−	0.266798i
$755$	10.0179	+	4.46024i	0.364587	+	0.162325i
$756$	2.77108	+	0.589010i	0.100783	+	0.0214221i
$757$	−48.5841	+	10.3269i	−1.76582	+	0.375336i	−0.972396	−	0.233336i	$-0.925036\pi$
$757$	−48.5841	+	10.3269i	−1.76582	+	0.375336i	−0.793422	+	0.608672i	$0.791703\pi$
$758$	32.4092	−	14.4295i	1.17716	−	0.524103i
$759$	0.0545170	−	0.167786i	0.00197884	−	0.00609025i
$760$	−1.29293	+	3.97922i	−0.0468994	+	0.144342i
$761$	4.76293	−	2.12059i	0.172656	−	0.0768715i	−0.318588	−	0.947893i	$-0.603209\pi$
$761$	4.76293	−	2.12059i	0.172656	−	0.0768715i	0.491245	+	0.871022i	$0.336542\pi$
$762$	−1.57831	+	0.335481i	−0.0571762	+	0.0121532i
$763$	10.7208	+	2.27878i	0.388120	+	0.0824974i
$764$	−12.4192	−	5.52939i	−0.449312	−	0.200046i
$765$	−1.43748	+	1.59648i	−0.0519720	+	0.0577208i
$766$	−0.952955	+	9.06676i	−0.0344317	+	0.327596i
$767$	−5.38233	−	3.91050i	−0.194345	−	0.141200i
$768$	0.104528	+	0.994522i	0.00377185	+	0.0358867i
$769$	10.6351	−	18.4205i	0.383512	−	0.664262i	−0.608050	−	0.793899i	$-0.708048\pi$
$769$	10.6351	−	18.4205i	0.383512	−	0.664262i	0.991561	+	0.129637i	$0.0413813\pi$
$770$	−6.97672	−	12.0840i	−0.251423	−	0.435478i
$771$	−23.4875	+	17.0646i	−0.845880	+	0.614568i
$772$	−16.7402	−	18.5919i	−0.602493	−	0.669136i
$773$	8.37508	+	25.7758i	0.301231	+	0.927093i	0.981057	+	0.193720i	$0.0620552\pi$
$773$	8.37508	+	25.7758i	0.301231	+	0.927093i	−0.679826	+	0.733373i	$0.737945\pi$
$774$	−7.11575			−0.255771
$775$	−5.13441	+	2.15355i	−0.184434	+	0.0773579i
$776$	2.49372			0.0895193
$777$	2.81478	+	8.66301i	0.100980	+	0.310784i
$778$	7.09595	+	7.88085i	0.254402	+	0.282542i
$779$	15.7716	−	11.4587i	0.565076	−	0.410552i
$780$	−1.00295	−	1.73715i	−0.0359112	−	0.0622001i
$781$	25.5357	−	44.2292i	0.913740	−	1.58264i
$782$	−0.00804334	−	0.0765273i	−0.000287629	−	0.00273661i
$783$	−3.97598	−	2.88872i	−0.142090	−	0.103234i
$784$	−0.107225	+	1.02018i	−0.00382946	+	0.0364349i
$785$	−2.02600	+	2.25010i	−0.0723109	+	0.0803094i
$786$	0.646259	+	0.287733i	0.0230513	+	0.0102631i
$787$	47.7008	+	10.1391i	1.70035	+	0.361421i	0.952991	−	0.302999i	$-0.0979879\pi$
$787$	47.7008	+	10.1391i	1.70035	+	0.361421i	0.747360	+	0.664420i	$0.231321\pi$
$788$	−21.1588	+	4.49743i	−0.753749	+	0.160214i
$789$	8.81624	−	3.92524i	0.313866	−	0.139742i
$790$	−0.238812	+	0.734987i	−0.00849654	+	0.0261496i
$791$	−0.452856	+	1.39375i	−0.0161017	+	0.0495560i
$792$	−4.49953	+	2.00332i	−0.159884	+	0.0711849i
$793$	−0.798017	+	0.169624i	−0.0283384	+	0.00602352i
$794$	−0.358321	−	0.0761634i	−0.0127163	−	0.00270294i
$795$	−12.2104	−	5.43641i	−0.433058	−	0.192810i
$796$	10.2170	−	11.3471i	0.362130	−	0.402187i
$797$	−3.26891	+	31.1016i	−0.115791	+	1.10167i	0.770146	+	0.637868i	$0.220183\pi$
$797$	−3.26891	+	31.1016i	−0.115791	+	1.10167i	−0.885936	+	0.463807i	$0.846483\pi$
$798$	9.58945	+	6.96715i	0.339463	+	0.246634i
$799$	−1.62179	−	15.4303i	−0.0573747	−	0.545883i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	2.85382	+	4.94296i	0.100835	+	0.174651i
$802$	−18.3595	+	13.3389i	−0.648296	+	0.471015i
$803$	12.9204	+	14.3496i	0.455951	+	0.506385i
$804$	1.37565	+	4.23381i	0.0485154	+	0.149315i
$805$	0.101474			0.00357650
$806$	−1.40849	+	11.0792i	−0.0496118	+	0.390247i
$807$	−4.49781			−0.158330
$808$	−3.34892	−	10.3069i	−0.117815	−	0.362596i
$809$	−27.9584	−	31.0509i	−0.982965	−	1.09169i	−0.995780	−	0.0917750i	$-0.970746\pi$
$809$	−27.9584	−	31.0509i	−0.982965	−	1.09169i	0.0128151	−	0.999918i	$-0.495921\pi$
$810$	−0.809017	+	0.587785i	−0.0284260	+	0.0206527i
$811$	20.1426	+	34.8880i	0.707302	+	1.22508i	0.965854	+	0.259086i	$0.0834212\pi$
$811$	20.1426	+	34.8880i	0.707302	+	1.22508i	−0.258552	+	0.965997i	$0.583245\pi$
$812$	6.96147	−	12.0576i	0.244300	−	0.423139i
$813$	−2.73202	−	25.9935i	−0.0958163	−	0.911631i
$814$	−12.8119	−	9.30839i	−0.449057	−	0.326259i
$815$	−0.918883	+	8.74259i	−0.0321871	+	0.306240i
$816$	−1.43748	+	1.59648i	−0.0503217	+	0.0558879i
$817$	−27.1984	−	12.1095i	−0.951551	−	0.423658i
$818$	−20.6279	−	4.38459i	−0.721237	−	0.153304i
$819$	−5.55848	+	1.18149i	−0.194229	+	0.0412847i
$820$	−4.25653	+	1.89513i	−0.148645	+	0.0661808i
$821$	−5.53801	+	17.0442i	−0.193278	+	0.594848i	0.806714	+	0.590941i	$0.201244\pi$
$821$	−5.53801	+	17.0442i	−0.193278	+	0.594848i	−0.999992	+	0.00390684i	$0.998756\pi$
$822$	−5.22925	+	16.0940i	−0.182391	+	0.561342i
$823$	5.11752	−	2.27847i	0.178385	−	0.0794223i	−0.315601	−	0.948892i	$-0.602206\pi$
$823$	5.11752	−	2.27847i	0.178385	−	0.0794223i	0.493986	+	0.869470i	$0.335539\pi$
$824$	−4.74374	+	1.00831i	−0.165256	+	0.0351262i
$825$	4.81772	+	1.02404i	0.167731	+	0.0356524i
$826$	−8.58380	−	3.82175i	−0.298669	−	0.132976i
$827$	−34.3486	+	38.1479i	−1.19442	+	1.32653i	−0.262035	+	0.965058i	$0.584394\pi$
$827$	−34.3486	+	38.1479i	−1.19442	+	1.32653i	−0.932381	+	0.361476i	$0.882273\pi$
$828$	0.00374410	−	0.0356227i	0.000130116	−	0.00123797i
$829$	−1.59601	−	1.15957i	−0.0554316	−	0.0402734i	0.559724	−	0.828679i	$-0.310907\pi$
$829$	−1.59601	−	1.15957i	−0.0554316	−	0.0402734i	−0.615156	+	0.788405i	$0.710907\pi$
$830$	0.956114	+	9.09681i	0.0331872	+	0.315755i
$831$	−9.94441	+	17.2242i	−0.344968	+	0.597501i
$832$	−1.00295	−	1.73715i	−0.0347709	−	0.0602250i
$833$	−1.78282	+	1.29530i	−0.0617711	+	0.0448794i
$834$	−2.73574	−	3.03835i	−0.0947311	−	0.105210i
$835$	7.03212	+	21.6426i	0.243357	+	0.748974i
$836$	−20.6077			−0.712732
$837$	5.56645	+	0.120985i	0.192405	+	0.00418185i
$838$	−32.9630			−1.13869
$839$	6.94768	+	21.3828i	0.239861	+	0.738215i	0.996439	+	0.0843123i	$0.0268693\pi$
$839$	6.94768	+	21.3828i	0.239861	+	0.738215i	−0.756579	+	0.653902i	$0.773131\pi$
$840$	−1.89564	−	2.10532i	−0.0654057	−	0.0726403i
$841$	3.92120	−	2.84892i	0.135214	−	0.0982385i
$842$	4.51690	+	7.82350i	0.155663	+	0.269615i
$843$	4.32696	−	7.49451i	0.149028	−	0.258125i
$844$	−0.225101	−	2.14170i	−0.00774831	−	0.0737202i
$845$	−7.26206	−	5.27619i	−0.249822	−	0.181507i
$846$	0.754925	−	7.18263i	0.0259549	−	0.246944i
$847$	25.1344	−	27.9146i	0.863627	−	0.959155i
$848$	−12.2104	−	5.43641i	−0.419306	−	0.186687i
$849$	7.52019	+	1.59847i	0.258092	+	0.0548592i
$850$	2.10133	−	0.446651i	0.0720750	−	0.0153200i
$851$	0.105211	−	0.0468430i	0.00360659	−	0.00160576i
$852$	3.20423	−	9.86160i	0.109775	−	0.337853i
$853$	−2.91160	+	8.96098i	−0.0996912	+	0.306818i	−0.988448	−	0.151561i	$-0.951570\pi$
$853$	−2.91160	+	8.96098i	−0.0996912	+	0.306818i	0.888757	+	0.458379i	$0.151570\pi$
$854$	−1.05263	+	0.468660i	−0.0360201	+	0.0160372i
$855$	−4.09257	+	0.869903i	−0.139963	+	0.0297501i
$856$	−9.17073	−	1.94930i	−0.313449	−	0.0666257i
$857$	−34.8081	−	15.4976i	−1.18902	−	0.529387i	−0.285687	−	0.958323i	$-0.592222\pi$
$857$	−34.8081	−	15.4976i	−1.18902	−	0.529387i	−0.903335	+	0.428936i	$0.858889\pi$
$858$	6.61083	−	7.34207i	0.225690	−	0.250654i
$859$	5.15281	−	49.0257i	0.175812	−	1.67274i	−0.450205	−	0.892925i	$-0.648649\pi$
$859$	5.15281	−	49.0257i	0.175812	−	1.67274i	0.626016	−	0.779810i	$-0.284684\pi$
$860$	5.75677	+	4.18254i	0.196304	+	0.142623i
$861$	1.37976	+	13.1276i	0.0470222	+	0.447386i
$862$	−11.4456	+	19.8244i	−0.389839	+	0.675222i
$863$	−14.8856	−	25.7826i	−0.506712	−	0.877651i	−0.999970	−	0.00776802i	$-0.997527\pi$
$863$	−14.8856	−	25.7826i	−0.506712	−	0.877651i	0.493258	−	0.869883i	$-0.335806\pi$
$864$	−0.809017	+	0.587785i	−0.0275233	+	0.0199969i
$865$	5.79198	+	6.43265i	0.196933	+	0.218717i
$866$	1.18807	+	3.65652i	0.0403724	+	0.124253i
$867$	12.3849			0.420614
$868$	1.30751	+	15.7191i	0.0443797	+	0.533541i
$869$	−3.80636			−0.129122
$870$	1.51869	+	4.67405i	0.0514884	+	0.158465i
$871$	−5.97508	−	6.63600i	−0.202458	−	0.224852i
$872$	−3.12995	+	2.27404i	−0.105993	+	0.0770088i
$873$	1.24686	+	2.15963i	0.0421998	+	0.0730922i
$874$	0.0749332	−	0.129788i	0.00253465	−	0.00439015i
$875$	0.296127	+	2.81746i	0.0100109	+	0.0952477i
$876$	3.17165	+	2.30434i	0.107160	+	0.0778565i
$877$	−4.12322	+	39.2298i	−0.139231	+	1.32470i	0.672252	+	0.740322i	$0.265327\pi$
$877$	−4.12322	+	39.2298i	−0.139231	+	1.32470i	−0.811484	+	0.584375i	$0.801340\pi$
$878$	23.6213	−	26.2341i	0.797180	−	0.885358i
$879$	12.0009	+	5.34314i	0.404780	+	0.180220i
$880$	4.81772	+	1.02404i	0.162405	+	0.0345203i
$881$	27.0708	−	5.75407i	0.912037	−	0.193859i	0.272084	−	0.962274i	$-0.412287\pi$
$881$	27.0708	−	5.75407i	0.912037	−	0.193859i	0.639953	+	0.768414i	$0.278954\pi$
$882$	−0.937111	+	0.417229i	−0.0315542	+	0.0140488i
$883$	5.93606	−	18.2693i	0.199764	−	0.614811i	−0.800124	−	0.599835i	$-0.795233\pi$
$883$	5.93606	−	18.2693i	0.199764	−	0.614811i	0.999888	−	0.0149761i	$-0.00476721\pi$
$884$	1.33162	−	4.09830i	0.0447872	−	0.137841i
$885$	3.02995	−	1.34902i	0.101851	−	0.0453468i
$886$	21.7597	−	4.62516i	0.731030	−	0.155385i
$887$	47.8315	+	10.1669i	1.60603	+	0.341371i	0.921730	−	0.387833i	$-0.126776\pi$
$887$	47.8315	+	10.1669i	1.60603	+	0.341371i	0.684296	+	0.729204i	$0.260110\pi$
$888$	−2.93730	−	1.30777i	−0.0985694	−	0.0438859i
$889$	3.05875	−	3.39708i	0.102587	−	0.113934i
$890$	0.596611	−	5.67638i	0.0199984	−	0.190273i
$891$	−3.98469	−	2.89505i	−0.133492	−	0.0969878i
$892$	0.0241756	+	0.230015i	0.000809458	+	0.00770148i
$893$	15.1089	−	26.1693i	0.505599	−	0.875722i
$894$	−0.714475	−	1.23751i	−0.0238956	−	0.0413884i
$895$	−18.3473	+	13.3301i	−0.613284	+	0.445577i
$896$	−1.89564	−	2.10532i	−0.0633288	−	0.0703337i
$897$	0.0222025	+	0.0683324i	0.000741321	+	0.00228155i
$898$	−1.44301			−0.0481540
$899$	9.01920	−	25.8341i	0.300807	−	0.861616i
$900$	1.00000			0.0333333
$901$	−8.87301	−	27.3083i	−0.295603	−	0.909772i
$902$	−15.3559	−	17.0544i	−0.511294	−	0.567849i
$903$	16.3088	−	11.8491i	0.542724	−	0.394312i
$904$	−0.258645	−	0.447986i	−0.00860240	−	0.0148998i
$905$	−0.430204	+	0.745135i	−0.0143005	+	0.0247691i
$906$	1.14625	+	10.9058i	0.0380816	+	0.362322i
$907$	−22.2993	−	16.2014i	−0.740435	−	0.537957i	0.152413	−	0.988317i	$-0.451296\pi$
$907$	−22.2993	−	16.2014i	−0.740435	−	0.537957i	−0.892847	+	0.450360i	$0.851296\pi$
$908$	−1.58126	+	15.0446i	−0.0524758	+	0.499274i
$909$	7.25159	−	8.05371i	0.240520	−	0.267125i
$910$	5.19137	+	2.31135i	0.172092	+	0.0766204i
$911$	−18.5953	−	3.95256i	−0.616091	−	0.130954i	−0.110713	−	0.993852i	$-0.535313\pi$
$911$	−18.5953	−	3.95256i	−0.616091	−	0.130954i	−0.505378	+	0.862898i	$0.668647\pi$
$912$	−4.09257	+	0.869903i	−0.135519	+	0.0288054i
$913$	−41.1569	+	18.3242i	−1.36209	+	0.606443i
$914$	−8.53303	+	26.2620i	−0.282248	+	0.868669i
$915$	0.125685	−	0.386818i	0.00415501	−	0.0127878i
$916$	22.4118	−	9.97836i	0.740506	−	0.329694i
$917$	−1.96031	+	0.416677i	−0.0647352	+	0.0137599i
$918$	−2.10133	−	0.446651i	−0.0693542	−	0.0147417i
$919$	49.1296	+	21.8739i	1.62064	+	0.721554i	0.998134	−	0.0610630i	$-0.0194490\pi$
$919$	49.1296	+	21.8739i	1.62064	+	0.721554i	0.622503	+	0.782617i	$0.286116\pi$
$920$	−0.0239675	+	0.0266186i	−0.000790186	+	0.000877590i
$921$	1.15921	−	11.0291i	0.0381972	−	0.363422i
$922$	−14.6814	−	10.6667i	−0.483506	−	0.351288i
$923$	2.17412	+	20.6854i	0.0715620	+	0.680867i
$924$	6.97672	−	12.0840i	0.229517	−	0.397535i
$925$	1.60764	+	2.78451i	0.0528589	+	0.0915542i
$926$	−5.64451	+	4.10098i	−0.185490	+	0.134766i
$927$	−3.24509	−	3.60404i	−0.106583	−	0.118372i
$928$	1.51869	+	4.67405i	0.0498534	+	0.153433i
$929$	36.0247			1.18193			0.590965	−	0.806697i	$-0.298747\pi$
$929$	36.0247			1.18193			0.590965	+	0.806697i	$0.298747\pi$
$930$	−4.43224	−	3.36976i	−0.145339	−	0.110499i
$931$	−4.29193			−0.140662
$932$	−1.19461	−	3.67664i	−0.0391308	−	0.120432i
$933$	16.5403	+	18.3699i	0.541505	+	0.601403i
$934$	10.5377	−	7.65607i	0.344803	−	0.250514i
$935$	5.29050	+	9.16341i	0.173018	+	0.299676i
$936$	1.00295	−	1.73715i	0.0327823	−	0.0567807i
$937$	2.38771	+	22.7175i	0.0780030	+	0.742149i	0.961703	+	0.274095i	$0.0883782\pi$
$937$	2.38771	+	22.7175i	0.0780030	+	0.742149i	−0.883700	+	0.468054i	$0.844955\pi$
$938$	−10.2030	−	7.41289i	−0.333139	−	0.242040i
$939$	−2.20014	+	20.9329i	−0.0717989	+	0.683120i
$940$	−4.83259	+	5.36714i	−0.157622	+	0.175057i
$941$	46.0371	+	20.4970i	1.50077	+	0.668184i	0.982368	−	0.186956i	$-0.0598623\pi$
$941$	46.0371	+	20.4970i	1.50077	+	0.668184i	0.518397	+	0.855140i	$0.326529\pi$
$942$	−2.96164	−	0.629516i	−0.0964954	−	0.0205107i
$943$	0.163246	−	0.0346990i	0.00531602	−	0.00112996i
$944$	3.02995	−	1.34902i	0.0986165	−	0.0439069i
$945$	0.875440	−	2.69433i	0.0284781	−	0.0876465i
$946$	−10.8303	+	33.3322i	−0.352123	+	1.08372i
$947$	−46.1450	+	20.5451i	−1.49951	+	0.667626i	−0.982143	−	0.188137i	$-0.939755\pi$
$947$	−46.1450	+	20.5451i	−1.49951	+	0.667626i	−0.517369	+	0.855763i	$0.673088\pi$
$948$	−0.755923	+	0.160676i	−0.0245512	+	0.00521853i
$949$	−7.69202	−	1.63499i	−0.249693	−	0.0530740i
$950$	3.82228	+	1.70179i	0.124011	+	0.0552133i
$951$	20.1077	−	22.3319i	0.652038	−	0.724162i
$952$	0.636163	−	6.05268i	0.0206181	−	0.196169i
$953$	26.6475	+	19.3605i	0.863196	+	0.627149i	0.928753	−	0.370700i	$-0.120882\pi$
$953$	26.6475	+	19.3605i	0.863196	+	0.627149i	−0.0655564	+	0.997849i	$0.520882\pi$
$954$	−1.39712	−	13.2927i	−0.0452334	−	0.430367i
$955$	−6.79727	+	11.7732i	−0.219954	+	0.380972i
$956$	−1.84530	−	3.19615i	−0.0596813	−	0.103371i
$957$	−19.5831	+	14.2280i	−0.633032	+	0.459925i
$958$	−6.63198	−	7.36556i	−0.214270	−	0.237971i
$959$	−14.8144	−	45.5940i	−0.478381	−	1.47231i
$960$	1.00000			0.0322749
$961$	8.28949	+	29.8711i	0.267403	+	0.963585i
$962$	6.44950			0.207940
$963$	−2.89722	−	8.91673i	−0.0933617	−	0.287338i
$964$	3.42911	+	3.80841i	0.110444	+	0.122661i
$965$	−20.2399	+	14.7051i	−0.651544	+	0.473375i
$966$	0.0507372	+	0.0878794i	0.00163244	+	0.00282747i
$967$	−14.1189	+	24.4546i	−0.454032	+	0.786407i	−0.998632	−	0.0522892i	$-0.983348\pi$
$967$	−14.1189	+	24.4546i	−0.454032	+	0.786407i	0.544600	+	0.838696i	$0.316682\pi$
$968$	1.38595	+	13.1864i	0.0445461	+	0.423828i
$969$	−7.27176	−	5.28324i	−0.233602	−	0.169722i
$970$	0.260665	−	2.48006i	0.00836944	−	0.0796299i
$971$	−37.2916	+	41.4165i	−1.19674	+	1.32912i	−0.265767	+	0.964037i	$0.585625\pi$
$971$	−37.2916	+	41.4165i	−1.19674	+	1.32912i	−0.930976	+	0.365081i	$0.881041\pi$
$972$	−0.913545	−	0.406737i	−0.0293020	−	0.0130461i
$973$	11.3296	+	2.40817i	0.363209	+	0.0772025i
$974$	27.7973	−	5.90850i	0.890683	−	0.189321i
$975$	−1.83247	+	0.815870i	−0.0586861	+	0.0261288i
$976$	0.125685	−	0.386818i	0.00402307	−	0.0123817i
$977$	1.94140	−	5.97501i	0.0621108	−	0.191157i	−0.915186	−	0.403031i	$-0.867957\pi$
$977$	1.94140	−	5.97501i	0.0621108	−	0.191157i	0.977297	+	0.211874i	$0.0679566\pi$
$978$	−8.03075	+	3.57552i	−0.256795	+	0.114332i
$979$	27.4978	−	5.84484i	0.878834	−	0.186802i
$980$	1.00338	+	0.213275i	0.0320518	+	0.00681282i
$981$	−3.53435	−	1.57360i	−0.112843	−	0.0502410i
$982$	−22.7808	+	25.3007i	−0.726965	+	0.807376i
$983$	2.86957	−	27.3022i	0.0915252	−	0.870804i	−0.848384	−	0.529381i	$-0.822424\pi$
$983$	2.86957	−	27.3022i	0.0915252	−	0.870804i	0.939910	−	0.341423i	$-0.110909\pi$
$984$	−3.76950	−	2.73870i	−0.120167	−	0.0873066i
$985$	2.26110	+	21.5130i	0.0720447	+	0.685460i
$986$	−5.27893	+	9.14338i	−0.168116	+	0.291185i
$987$	10.2302	+	17.7192i	0.325630	+	0.564008i
$988$	6.78981	−	4.93308i	0.216013	−	0.156942i
$989$	−0.170547	−	0.189412i	−0.00542308	−	0.00602294i
$990$	1.52202	+	4.68429i	0.0483729	+	0.148876i
$991$	−15.8596			−0.503797			−0.251898	−	0.967754i	$-0.581055\pi$
$991$	−15.8596			−0.503797			−0.251898	+	0.967754i	$0.581055\pi$
$992$	−4.43224	−	3.36976i	−0.140724	−	0.106990i
$993$	0.0573201			0.00181900
$994$	9.07753	+	27.9378i	0.287922	+	0.886132i
$995$	−10.2170	−	11.3471i	−0.323899	−	0.359727i
$996$	−7.40001	+	5.37643i	−0.234478	+	0.170359i
$997$	−13.9338	−	24.1341i	−0.441289	−	0.764335i	0.556496	−	0.830850i	$-0.312145\pi$
$997$	−13.9338	−	24.1341i	−0.441289	−	0.764335i	−0.997785	+	0.0665151i	$0.978812\pi$
$998$	14.8981	−	25.8042i	0.471591	−	0.816819i
$999$	−0.336088	−	3.19766i	−0.0106334	−	0.101170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.e.361.1	✓	16
31.14	even	15	inner	930.2.bg.e.541.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.e.361.1	✓	16	1.1	even	1	trivial
930.2.bg.e.541.1	yes	16	31.14	even	15	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.296127 - 2.81746i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.296127 - 2.81746i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(0.669131 - 0.743145i) q^{10} +(4.49953 + 2.00332i) q^{11} +(0.978148 + 0.207912i) q^{12} +(-1.96206 + 0.417049i) q^{13} +(-2.58806 + 1.15228i) q^{14} +(0.309017 - 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(1.96255 - 0.873781i) q^{17} +(0.978148 - 0.207912i) q^{18} +(4.09257 + 0.869903i) q^{19} +(-0.913545 - 0.406737i) q^{20} +(-1.89564 + 2.10532i) q^{21} +(0.514839 - 4.89837i) q^{22} +(0.0289781 + 0.0210538i) q^{23} +(-0.104528 - 0.994522i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.00295 + 1.73715i) q^{26} +(0.809017 - 0.587785i) q^{27} +(1.89564 + 2.10532i) q^{28} +(-1.51869 - 4.67405i) q^{29} -1.00000 q^{30} +(4.43224 + 3.36976i) q^{31} -1.00000 q^{32} +(-1.52202 - 4.68429i) q^{33} +(-1.43748 - 1.59648i) q^{34} +(2.29193 - 1.66519i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(1.60764 - 2.78451i) q^{37} +(-0.437348 - 4.16108i) q^{38} +(1.62280 + 1.17903i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(3.11772 - 3.46258i) q^{41} +(2.58806 + 1.15228i) q^{42} +(-6.96026 - 1.47945i) q^{43} +(-4.81772 + 1.02404i) q^{44} +(-0.913545 + 0.406737i) q^{45} +(0.0110687 - 0.0340658i) q^{46} +(2.23178 - 6.86872i) q^{47} +(-0.913545 + 0.406737i) q^{48} +(-1.00338 + 0.213275i) q^{49} +(0.978148 + 0.207912i) q^{50} +(-1.96255 - 0.873781i) q^{51} +(1.34220 - 1.49067i) q^{52} +(1.39712 - 13.2927i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(0.514839 + 4.89837i) q^{55} +(1.41649 - 2.45344i) q^{56} +(-2.09200 - 3.62345i) q^{57} +(-3.97598 + 2.88872i) q^{58} +(2.21930 + 2.46478i) q^{59} +(0.309017 + 0.951057i) q^{60} +0.406724 q^{61} +(1.83519 - 5.25662i) q^{62} +2.83298 q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.34220 - 1.49067i) q^{65} +(-3.98469 + 2.89505i) q^{66} +(2.22585 + 3.85528i) q^{67} +(-1.07414 + 1.86046i) q^{68} +(-0.00374410 - 0.0356227i) q^{69} +(-2.29193 - 1.66519i) q^{70} +(1.08387 - 10.3123i) q^{71} +(-0.669131 + 0.743145i) q^{72} +(3.58145 + 1.59456i) q^{73} +(-3.14502 - 0.668494i) q^{74} +(0.978148 - 0.207912i) q^{75} +(-3.82228 + 1.70179i) q^{76} +(4.31185 - 13.2705i) q^{77} +(0.619855 - 1.90772i) q^{78} +(-0.705998 + 0.314330i) q^{79} +(0.978148 - 0.207912i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-4.25653 - 1.89513i) q^{82} +(-6.12048 + 6.79749i) q^{83} +(0.296127 - 2.81746i) q^{84} +(1.73799 + 1.26272i) q^{85} +(0.743799 + 7.07677i) q^{86} +(-2.45729 + 4.25615i) q^{87} +(2.46268 + 4.26548i) q^{88} +(4.61758 - 3.35487i) q^{89} +(0.669131 + 0.743145i) q^{90} +(1.75604 + 5.40453i) q^{91} -0.0358189 q^{92} +(-0.461530 - 5.54860i) q^{93} -7.22220 q^{94} +(1.29293 + 3.97922i) q^{95} +(0.669131 + 0.743145i) q^{96} +(2.01746 - 1.46577i) q^{97} +(0.512898 + 0.888365i) q^{98} +(-2.46268 + 4.26548i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} - 5 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 - 5 * q^7 + 4 * q^8 + 2 * q^9	\( 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} - 5 q^{7} + 4 q^{8} + 2 q^{9} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 4 q^{13} - 10 q^{14} - 4 q^{15} - 4 q^{16} - 22 q^{17} - 2 q^{18} - 3 q^{19} - 2 q^{20} - 11 q^{22} + 9 q^{23} + 2 q^{24} - 8 q^{25} + 11 q^{26} + 4 q^{27} - 3 q^{29} - 16 q^{30} - 15 q^{31} - 16 q^{32} - 8 q^{33} - 8 q^{34} + 5 q^{35} - 8 q^{36} - 17 q^{37} - 2 q^{38} + 3 q^{39} + 2 q^{40} + 28 q^{41} + 10 q^{42} - 28 q^{43} - 19 q^{44} - 2 q^{45} - 9 q^{46} + 9 q^{47} - 2 q^{48} + 19 q^{49} - 2 q^{50} + 22 q^{51} + 4 q^{52} + 2 q^{53} - 4 q^{54} - 11 q^{55} + 5 q^{56} - 2 q^{57} - 12 q^{58} + 24 q^{59} - 4 q^{60} - 40 q^{61} - 25 q^{62} + 10 q^{63} - 4 q^{64} - 4 q^{65} - 7 q^{66} - q^{67} - 2 q^{68} - 3 q^{69} - 5 q^{70} + 39 q^{71} - 2 q^{72} + 81 q^{73} - 8 q^{74} - 2 q^{75} + 2 q^{76} + 28 q^{77} - 8 q^{78} + 64 q^{79} - 2 q^{80} + 2 q^{81} + 32 q^{82} - 40 q^{83} + 5 q^{84} - 14 q^{85} + 13 q^{86} - 9 q^{87} - q^{88} - 7 q^{89} + 2 q^{90} - 46 q^{91} - 36 q^{92} - 20 q^{93} - 4 q^{94} - 6 q^{95} + 2 q^{96} - 17 q^{97} - 9 q^{98} + q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 - 5 * q^7 + 4 * q^8 + 2 * q^9 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 4 * q^13 - 10 * q^14 - 4 * q^15 - 4 * q^16 - 22 * q^17 - 2 * q^18 - 3 * q^19 - 2 * q^20 - 11 * q^22 + 9 * q^23 + 2 * q^24 - 8 * q^25 + 11 * q^26 + 4 * q^27 - 3 * q^29 - 16 * q^30 - 15 * q^31 - 16 * q^32 - 8 * q^33 - 8 * q^34 + 5 * q^35 - 8 * q^36 - 17 * q^37 - 2 * q^38 + 3 * q^39 + 2 * q^40 + 28 * q^41 + 10 * q^42 - 28 * q^43 - 19 * q^44 - 2 * q^45 - 9 * q^46 + 9 * q^47 - 2 * q^48 + 19 * q^49 - 2 * q^50 + 22 * q^51 + 4 * q^52 + 2 * q^53 - 4 * q^54 - 11 * q^55 + 5 * q^56 - 2 * q^57 - 12 * q^58 + 24 * q^59 - 4 * q^60 - 40 * q^61 - 25 * q^62 + 10 * q^63 - 4 * q^64 - 4 * q^65 - 7 * q^66 - q^67 - 2 * q^68 - 3 * q^69 - 5 * q^70 + 39 * q^71 - 2 * q^72 + 81 * q^73 - 8 * q^74 - 2 * q^75 + 2 * q^76 + 28 * q^77 - 8 * q^78 + 64 * q^79 - 2 * q^80 + 2 * q^81 + 32 * q^82 - 40 * q^83 + 5 * q^84 - 14 * q^85 + 13 * q^86 - 9 * q^87 - q^88 - 7 * q^89 + 2 * q^90 - 46 * q^91 - 36 * q^92 - 20 * q^93 - 4 * q^94 - 6 * q^95 + 2 * q^96 - 17 * q^97 - 9 * q^98 + q^99

Introduction

L-functions

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