LMFDB - Embedded newform 930.2.bg.h.541.1

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:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			541.1
Character	$\chi$	$=$	930.541
Dual form			930.2.bg.h.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.220951 + 2.10221i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(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} +(-0.220951 + 2.10221i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-0.669131 - 0.743145i) q^{10} +(1.49161 - 0.664107i) q^{11} +(0.978148 - 0.207912i) q^{12} +(-3.23736 - 0.688121i) q^{13} +(-1.93104 - 0.859754i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.273392 + 0.121722i) q^{17} +(0.978148 + 0.207912i) q^{18} +(-5.71703 + 1.21519i) q^{19} +(0.913545 - 0.406737i) q^{20} +(-1.41440 - 1.57085i) q^{21} +(0.170671 + 1.62382i) q^{22} +(-7.09945 + 5.15805i) q^{23} +(-0.104528 + 0.994522i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.65484 - 2.86627i) q^{26} +(0.809017 + 0.587785i) q^{27} +(1.41440 - 1.57085i) q^{28} +(1.04900 - 3.22848i) q^{29} +1.00000 q^{30} +(5.07568 - 2.28855i) q^{31} -1.00000 q^{32} +(-0.504553 + 1.55286i) q^{33} +(-0.200247 + 0.222397i) q^{34} +(-1.71009 - 1.24245i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.67877 + 2.90771i) q^{37} +(0.610943 - 5.81274i) q^{38} +(2.67759 - 1.94538i) q^{39} +(0.104528 + 0.994522i) q^{40} +(-6.41896 - 7.12898i) q^{41} +(1.93104 - 0.859754i) q^{42} +(2.22633 - 0.473220i) q^{43} +(-1.59709 - 0.339472i) q^{44} +(0.913545 + 0.406737i) q^{45} +(-2.71175 - 8.34590i) q^{46} +(-3.64105 - 11.2060i) q^{47} +(-0.913545 - 0.406737i) q^{48} +(2.47658 + 0.526413i) q^{49} +(0.978148 - 0.207912i) q^{50} +(-0.273392 + 0.121722i) q^{51} +(2.21461 + 2.45957i) q^{52} +(-0.744581 - 7.08421i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(-0.170671 + 1.62382i) q^{55} +(1.05689 + 1.83059i) q^{56} +(2.92238 - 5.06171i) q^{57} +(2.74631 + 1.99531i) q^{58} +(1.07573 - 1.19472i) q^{59} +(-0.309017 + 0.951057i) q^{60} -4.00470 q^{61} +(0.608066 + 5.53446i) q^{62} +2.11379 q^{63} +(0.309017 - 0.951057i) q^{64} +(2.21461 - 2.45957i) q^{65} +(-1.32094 - 0.959718i) q^{66} +(-6.30798 + 10.9257i) q^{67} +(-0.149632 - 0.259171i) q^{68} +(0.917279 - 8.72733i) q^{69} +(1.71009 - 1.24245i) q^{70} +(-0.776214 - 7.38518i) q^{71} +(-0.669131 - 0.743145i) q^{72} +(-5.59443 + 2.49080i) q^{73} +(-3.28416 + 0.698070i) q^{74} +(0.978148 + 0.207912i) q^{75} +(5.33945 + 2.37728i) q^{76} +(1.06652 + 3.28241i) q^{77} +(1.02275 + 3.14769i) q^{78} +(-7.74339 - 3.44758i) q^{79} +(-0.978148 - 0.207912i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(8.76363 - 3.90182i) q^{82} +(-1.43988 - 1.59915i) q^{83} +(0.220951 + 2.10221i) q^{84} +(-0.242110 + 0.175903i) q^{85} +(-0.237913 + 2.26359i) q^{86} +(1.69731 + 2.93983i) q^{87} +(0.816385 - 1.41402i) q^{88} +(-13.5560 - 9.84899i) q^{89} +(-0.669131 + 0.743145i) q^{90} +(2.16187 - 6.65355i) q^{91} +8.77540 q^{92} +(-1.69557 + 5.30330i) q^{93} +11.7827 q^{94} +(1.80613 - 5.55869i) q^{95} +(0.669131 - 0.743145i) q^{96} +(3.88922 + 2.82569i) q^{97} +(-1.26595 + 2.19270i) q^{98} +(-0.816385 - 1.41402i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 - 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 11 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9} - 3 q^{10} - 5 q^{11} - 3 q^{12} - 13 q^{13} - 4 q^{14} + 6 q^{15} - 6 q^{16} + 31 q^{17} - 3 q^{18} - 3 q^{19} + 3 q^{20} - 4 q^{21} + 5 q^{22} - 9 q^{23} + 3 q^{24} - 12 q^{25} + 3 q^{26} + 6 q^{27} + 4 q^{28} + 11 q^{29} + 24 q^{30} + 17 q^{31} - 24 q^{32} + 10 q^{33} + 9 q^{34} + 7 q^{35} - 12 q^{36} + 8 q^{37} - 2 q^{38} - q^{39} - 3 q^{40} + 12 q^{41} + 4 q^{42} - 7 q^{43} - 10 q^{44} + 3 q^{45} - 6 q^{46} - 46 q^{47} - 3 q^{48} + 20 q^{49} - 3 q^{50} - 31 q^{51} + 17 q^{52} + 48 q^{53} - 6 q^{54} - 5 q^{55} + q^{56} - 2 q^{57} + 14 q^{58} + 12 q^{59} + 6 q^{60} - 4 q^{61} + 13 q^{62} + 2 q^{63} - 6 q^{64} + 17 q^{65} + 10 q^{66} - 33 q^{67} + q^{68} - 12 q^{69} - 7 q^{70} - 35 q^{71} - 3 q^{72} + 19 q^{73} + 7 q^{74} - 3 q^{75} + 2 q^{76} + 26 q^{77} - 4 q^{78} - 12 q^{79} + 3 q^{80} + 3 q^{81} - 12 q^{82} + 11 q^{84} - 2 q^{85} - 48 q^{86} + 3 q^{87} + 21 q^{89} - 3 q^{90} + 72 q^{91} + 6 q^{92} + 19 q^{93} - 14 q^{94} + 6 q^{95} + 3 q^{96} - 35 q^{97} - 5 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 - 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 11 * q^7 + 6 * q^8 + 3 * q^9 - 3 * q^10 - 5 * q^11 - 3 * q^12 - 13 * q^13 - 4 * q^14 + 6 * q^15 - 6 * q^16 + 31 * q^17 - 3 * q^18 - 3 * q^19 + 3 * q^20 - 4 * q^21 + 5 * q^22 - 9 * q^23 + 3 * q^24 - 12 * q^25 + 3 * q^26 + 6 * q^27 + 4 * q^28 + 11 * q^29 + 24 * q^30 + 17 * q^31 - 24 * q^32 + 10 * q^33 + 9 * q^34 + 7 * q^35 - 12 * q^36 + 8 * q^37 - 2 * q^38 - q^39 - 3 * q^40 + 12 * q^41 + 4 * q^42 - 7 * q^43 - 10 * q^44 + 3 * q^45 - 6 * q^46 - 46 * q^47 - 3 * q^48 + 20 * q^49 - 3 * q^50 - 31 * q^51 + 17 * q^52 + 48 * q^53 - 6 * q^54 - 5 * q^55 + q^56 - 2 * q^57 + 14 * q^58 + 12 * q^59 + 6 * q^60 - 4 * q^61 + 13 * q^62 + 2 * q^63 - 6 * q^64 + 17 * q^65 + 10 * q^66 - 33 * q^67 + q^68 - 12 * q^69 - 7 * q^70 - 35 * q^71 - 3 * q^72 + 19 * q^73 + 7 * q^74 - 3 * q^75 + 2 * q^76 + 26 * q^77 - 4 * q^78 - 12 * q^79 + 3 * q^80 + 3 * q^81 - 12 * q^82 + 11 * q^84 - 2 * q^85 - 48 * q^86 + 3 * q^87 + 21 * q^89 - 3 * q^90 + 72 * q^91 + 6 * q^92 + 19 * q^93 - 14 * q^94 + 6 * q^95 + 3 * q^96 - 35 * q^97 - 5 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{11}{15}\right)$

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
$7$	−0.220951	+	2.10221i	−0.0835116	+	0.794559i	0.869969	+	0.493106i	$0.164138\pi$
$7$	−0.220951	+	2.10221i	−0.0835116	+	0.794559i	−0.953481	+	0.301454i	$0.902528\pi$
$8$	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
$11$	1.49161	−	0.664107i	0.449737	−	0.200236i	−0.169354	−	0.985555i	$-0.554168\pi$
$11$	1.49161	−	0.664107i	0.449737	−	0.200236i	0.619091	+	0.785320i	$0.287501\pi$
$12$	0.978148	−	0.207912i	0.282367	−	0.0600189i
$13$	−3.23736	−	0.688121i	−0.897881	−	0.190850i	−0.264221	−	0.964462i	$-0.585115\pi$
$13$	−3.23736	−	0.688121i	−0.897881	−	0.190850i	−0.633660	+	0.773612i	$0.718448\pi$
$14$	−1.93104	−	0.859754i	−0.516092	−	0.229779i
$15$	−0.309017	−	0.951057i	−0.0797878	−	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.273392	+	0.121722i	0.0663073	+	0.0295219i	0.439622	−	0.898183i	$-0.355112\pi$
$17$	0.273392	+	0.121722i	0.0663073	+	0.0295219i	−0.373315	+	0.927705i	$0.621779\pi$
$18$	0.978148	+	0.207912i	0.230552	+	0.0490053i
$19$	−5.71703	+	1.21519i	−1.31158	+	0.278784i	−0.810052	−	0.586358i	$-0.800561\pi$
$19$	−5.71703	+	1.21519i	−1.31158	+	0.278784i	−0.501526	+	0.865143i	$0.667228\pi$
$20$	0.913545	−	0.406737i	0.204275	−	0.0909491i
$21$	−1.41440	−	1.57085i	−0.308647	−	0.342787i
$22$	0.170671	+	1.62382i	0.0363871	+	0.346201i
$23$	−7.09945	+	5.15805i	−1.48034	+	1.07553i	−0.502889	+	0.864351i	$0.667730\pi$
$23$	−7.09945	+	5.15805i	−1.48034	+	1.07553i	−0.977448	+	0.211177i	$0.932270\pi$
$24$	−0.104528	+	0.994522i	−0.0213368	+	0.203006i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.65484	−	2.86627i	0.324541	−	0.562121i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	1.41440	−	1.57085i	0.267296	−	0.296863i
$29$	1.04900	−	3.22848i	0.194794	−	0.599513i	−0.805185	−	0.593023i	$-0.797934\pi$
$29$	1.04900	−	3.22848i	0.194794	−	0.599513i	0.999979	−	0.00648999i	$-0.00206584\pi$
$30$	1.00000			0.182574
$31$	5.07568	−	2.28855i	0.911619	−	0.411035i
$31$	5.07568	−	2.28855i	0.911619	−	0.411035i
$32$	−1.00000			−0.176777
$33$	−0.504553	+	1.55286i	−0.0878315	+	0.270318i
$34$	−0.200247	+	0.222397i	−0.0343421	+	0.0381408i
$35$	−1.71009	−	1.24245i	−0.289058	−	0.210013i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	1.67877	+	2.90771i	0.275987	+	0.478024i	0.970384	−	0.241568i	$-0.0776618\pi$
$37$	1.67877	+	2.90771i	0.275987	+	0.478024i	−0.694396	+	0.719593i	$0.744329\pi$
$38$	0.610943	−	5.81274i	0.0991081	−	0.942950i
$39$	2.67759	−	1.94538i	0.428757	−	0.311510i
$40$	0.104528	+	0.994522i	0.0165274	+	0.157248i
$41$	−6.41896	−	7.12898i	−1.00247	−	1.11336i	−0.993549	−	0.113399i	$-0.963826\pi$
$41$	−6.41896	−	7.12898i	−1.00247	−	1.11336i	−0.00892384	−	0.999960i	$-0.502841\pi$
$42$	1.93104	−	0.859754i	0.297966	−	0.132663i
$43$	2.22633	−	0.473220i	0.339511	−	0.0721654i	−0.0350010	−	0.999387i	$-0.511143\pi$
$43$	2.22633	−	0.473220i	0.339511	−	0.0721654i	0.374512	+	0.927222i	$0.377810\pi$
$44$	−1.59709	−	0.339472i	−0.240770	−	0.0511773i
$45$	0.913545	+	0.406737i	0.136183	+	0.0606327i
$46$	−2.71175	−	8.34590i	−0.399825	−	1.23054i
$47$	−3.64105	−	11.2060i	−0.531101	−	1.63456i	−0.751925	−	0.659248i	$-0.770875\pi$
$47$	−3.64105	−	11.2060i	−0.531101	−	1.63456i	0.220824	−	0.975314i	$-0.429125\pi$
$48$	−0.913545	−	0.406737i	−0.131859	−	0.0587074i
$49$	2.47658	+	0.526413i	0.353797	+	0.0752019i
$50$	0.978148	−	0.207912i	0.138331	−	0.0294032i
$51$	−0.273392	+	0.121722i	−0.0382825	+	0.0170445i
$52$	2.21461	+	2.45957i	0.307111	+	0.341081i
$53$	−0.744581	−	7.08421i	−0.102276	−	0.973091i	−0.918517	−	0.395380i	$-0.870613\pi$
$53$	−0.744581	−	7.08421i	−0.102276	−	0.973091i	0.816241	−	0.577711i	$-0.196054\pi$
$54$	−0.809017	+	0.587785i	−0.110093	+	0.0799874i
$55$	−0.170671	+	1.62382i	−0.0230133	+	0.218956i
$56$	1.05689	+	1.83059i	0.141233	+	0.244623i
$57$	2.92238	−	5.06171i	0.387078	−	0.670439i
$58$	2.74631	+	1.99531i	0.360608	+	0.261997i
$59$	1.07573	−	1.19472i	0.140049	−	0.155540i	−0.669040	−	0.743226i	$-0.733295\pi$
$59$	1.07573	−	1.19472i	0.140049	−	0.155540i	0.809089	+	0.587687i	$0.199961\pi$
$60$	−0.309017	+	0.951057i	−0.0398939	+	0.122781i
$61$	−4.00470			−0.512750			−0.256375	−	0.966577i	$-0.582528\pi$
$61$	−4.00470			−0.512750			−0.256375	+	0.966577i	$0.582528\pi$
$62$	0.608066	+	5.53446i	0.0772245	+	0.702877i
$63$	2.11379			0.266312
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	2.21461	−	2.45957i	0.274688	−	0.305072i
$66$	−1.32094	−	0.959718i	−0.162596	−	0.118133i
$67$	−6.30798	+	10.9257i	−0.770642	+	1.33479i	0.166570	+	0.986030i	$0.446731\pi$
$67$	−6.30798	+	10.9257i	−0.770642	+	1.33479i	−0.937212	+	0.348761i	$0.886602\pi$
$68$	−0.149632	−	0.259171i	−0.0181456	−	0.0314291i
$69$	0.917279	−	8.72733i	0.110427	−	1.05065i
$70$	1.71009	−	1.24245i	0.204395	−	0.148501i
$71$	−0.776214	−	7.38518i	−0.0921197	−	0.876460i	−0.938824	−	0.344397i	$-0.888083\pi$
$71$	−0.776214	−	7.38518i	−0.0921197	−	0.876460i	0.846705	−	0.532063i	$-0.178583\pi$
$72$	−0.669131	−	0.743145i	−0.0788578	−	0.0875805i
$73$	−5.59443	+	2.49080i	−0.654779	+	0.291526i	−0.707110	−	0.707104i	$-0.750001\pi$
$73$	−5.59443	+	2.49080i	−0.654779	+	0.291526i	0.0523314	+	0.998630i	$0.483335\pi$
$74$	−3.28416	+	0.698070i	−0.381776	+	0.0811490i
$75$	0.978148	+	0.207912i	0.112947	+	0.0240076i
$76$	5.33945	+	2.37728i	0.612477	+	0.272692i
$77$	1.06652	+	3.28241i	0.121541	+	0.374065i
$78$	1.02275	+	3.14769i	0.115803	+	0.356406i
$79$	−7.74339	−	3.44758i	−0.871200	−	0.387883i	−0.0780786	−	0.996947i	$-0.524879\pi$
$79$	−7.74339	−	3.44758i	−0.871200	−	0.387883i	−0.793121	+	0.609064i	$0.791545\pi$
$80$	−0.978148	−	0.207912i	−0.109360	−	0.0232452i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	8.76363	−	3.90182i	0.967781	−	0.430884i
$83$	−1.43988	−	1.59915i	−0.158048	−	0.175530i	0.658920	−	0.752213i	$-0.271013\pi$
$83$	−1.43988	−	1.59915i	−0.158048	−	0.175530i	−0.816968	+	0.576683i	$0.804347\pi$
$84$	0.220951	+	2.10221i	0.0241077	+	0.229370i
$85$	−0.242110	+	0.175903i	−0.0262606	+	0.0190794i
$86$	−0.237913	+	2.26359i	−0.0256549	+	0.244090i
$87$	1.69731	+	2.93983i	0.181971	+	0.315183i
$88$	0.816385	−	1.41402i	0.0870269	−	0.150735i
$89$	−13.5560	−	9.84899i	−1.43693	−	1.04399i	−0.988673	−	0.150087i	$-0.952045\pi$
$89$	−13.5560	−	9.84899i	−1.43693	−	1.04399i	−0.448258	−	0.893904i	$-0.647955\pi$
$90$	−0.669131	+	0.743145i	−0.0705326	+	0.0783343i
$91$	2.16187	−	6.65355i	0.226626	−	0.697482i
$92$	8.77540			0.914899
$93$	−1.69557	+	5.30330i	−0.175823	+	0.549927i
$94$	11.7827			1.21529
$95$	1.80613	−	5.55869i	0.185305	−	0.570310i
$96$	0.669131	−	0.743145i	0.0682929	−	0.0758469i
$97$	3.88922	+	2.82569i	0.394891	+	0.286905i	0.767457	−	0.641101i	$-0.221522\pi$
$97$	3.88922	+	2.82569i	0.394891	+	0.286905i	−0.372566	+	0.928006i	$0.621522\pi$
$98$	−1.26595	+	2.19270i	−0.127881	+	0.221496i
$99$	−0.816385	−	1.41402i	−0.0820497	−	0.142114i
$100$	−0.104528	+	0.994522i	−0.0104528	+	0.0994522i
$101$	5.18387	−	3.76630i	0.515814	−	0.374761i	−0.299210	−	0.954187i	$-0.596723\pi$
$101$	5.18387	−	3.76630i	0.515814	−	0.374761i	0.815025	+	0.579426i	$0.196723\pi$
$102$	−0.0312817	−	0.297625i	−0.00309735	−	0.0294693i
$103$	3.87392	+	4.30242i	0.381709	+	0.423930i	0.903129	−	0.429370i	$-0.141264\pi$
$103$	3.87392	+	4.30242i	0.381709	+	0.423930i	−0.521420	+	0.853300i	$0.674598\pi$
$104$	−3.02354	+	1.34617i	−0.296483	+	0.132003i
$105$	2.06760	−	0.439481i	0.201777	−	0.0428889i
$106$	6.96757	+	1.48100i	0.676751	+	0.143848i
$107$	14.7015	+	6.54553i	1.42125	+	0.632780i	0.966225	−	0.257700i	$-0.0829646\pi$
$107$	14.7015	+	6.54553i	1.42125	+	0.632780i	0.455022	+	0.890480i	$0.349631\pi$
$108$	−0.309017	−	0.951057i	−0.0297352	−	0.0915155i
$109$	2.25447	+	6.93854i	0.215939	+	0.664592i	0.999086	+	0.0427546i	$0.0136134\pi$
$109$	2.25447	+	6.93854i	0.215939	+	0.664592i	−0.783147	+	0.621837i	$0.786387\pi$
$110$	−1.49161	−	0.664107i	−0.142219	−	0.0633201i
$111$	−3.28416	−	0.698070i	−0.311719	−	0.0662579i
$112$	−2.06760	+	0.439481i	−0.195369	+	0.0415270i
$113$	−9.93080	+	4.42148i	−0.934211	+	0.415937i	−0.816653	−	0.577129i	$-0.804173\pi$
$113$	−9.93080	+	4.42148i	−0.934211	+	0.415937i	−0.117558	+	0.993066i	$0.537506\pi$
$114$	3.91090	+	4.34350i	0.366290	+	0.406806i
$115$	−0.917279	−	8.72733i	−0.0855367	−	0.813828i
$116$	−2.74631	+	1.99531i	−0.254988	+	0.185260i
$117$	−0.345956	+	3.29155i	−0.0319836	+	0.304304i
$118$	0.803829	+	1.39227i	0.0739985	+	0.128169i
$119$	−0.316291	+	0.547832i	−0.0289943	+	0.0502197i
$120$	−0.809017	−	0.587785i	−0.0738528	−	0.0536572i
$121$	−5.57658	+	6.19342i	−0.506962	+	0.563038i
$122$	1.23752	−	3.80870i	0.112040	−	0.344823i
$123$	9.59299			0.864971
$124$	−5.45149	−	1.13194i	−0.489558	−	0.101651i
$125$	1.00000			0.0894427
$126$	−0.653196	+	2.01033i	−0.0581913	+	0.179094i
$127$	−2.42236	+	2.69030i	−0.214950	+	0.238726i	−0.840971	−	0.541080i	$-0.818016\pi$
$127$	−2.42236	+	2.69030i	−0.214950	+	0.238726i	0.626021	+	0.779806i	$0.284682\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−1.13803	+	1.97113i	−0.100198	+	0.173548i
$130$	1.65484	+	2.86627i	0.145139	+	0.251388i
$131$	−2.31587	+	22.0340i	−0.202338	+	1.92512i	0.148936	+	0.988847i	$0.452415\pi$
$131$	−2.31587	+	22.0340i	−0.202338	+	1.92512i	−0.351274	+	0.936273i	$0.614251\pi$
$132$	1.32094	−	0.959718i	0.114973	−	0.0835327i
$133$	−1.29140	−	12.2869i	−0.111979	−	1.06541i
$134$	−8.44172	−	9.37548i	−0.729254	−	0.809918i
$135$	−0.913545	+	0.406737i	−0.0786255	+	0.0350063i
$136$	0.292725	−	0.0622207i	0.0251010	−	0.00533538i
$137$	3.15648	+	0.670931i	0.269676	+	0.0573215i	0.340765	−	0.940149i	$-0.389314\pi$
$137$	3.15648	+	0.670931i	0.269676	+	0.0573215i	−0.0710886	+	0.997470i	$0.522647\pi$
$138$	8.01673	+	3.56928i	0.682429	+	0.303837i
$139$	1.52416	+	4.69088i	0.129277	+	0.397875i	0.994656	−	0.103243i	$-0.0329221\pi$
$139$	1.52416	+	4.69088i	0.129277	+	0.397875i	−0.865379	+	0.501119i	$0.832922\pi$
$140$	0.653196	+	2.01033i	0.0552051	+	0.169904i
$141$	10.7640	+	4.79245i	0.906493	+	0.403597i
$142$	7.26359	+	1.54392i	0.609547	+	0.129563i
$143$	−5.28585	+	1.12354i	−0.442025	+	0.0939554i
$144$	0.913545	−	0.406737i	0.0761288	−	0.0338947i
$145$	2.27145	+	2.52270i	0.188633	+	0.209499i
$146$	−0.640118	−	6.09032i	−0.0529766	−	0.504038i
$147$	−2.04836	+	1.48822i	−0.168946	+	0.122746i
$148$	0.350958	−	3.33914i	0.0288485	−	0.274476i
$149$	−8.02886	−	13.9064i	−0.657750	−	1.13926i	−0.981197	−	0.193010i	$-0.938175\pi$
$149$	−8.02886	−	13.9064i	−0.657750	−	1.13926i	0.323447	−	0.946246i	$-0.395158\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	14.4150	+	10.4731i	1.17308	+	0.852291i	0.991374	−	0.131063i	$-0.0418389\pi$
$151$	14.4150	+	10.4731i	1.17308	+	0.852291i	0.181704	+	0.983353i	$0.441839\pi$
$152$	−3.91090	+	4.34350i	−0.317216	+	0.352304i
$153$	0.0924779	−	0.284618i	0.00747640	−	0.0230100i
$154$	−3.45133			−0.278116
$155$	−0.555900	+	5.53994i	−0.0446510	+	0.444979i
$156$	−3.30968			−0.264986
$157$	2.29293	−	7.05693i	0.182996	−	0.563204i	−0.816912	−	0.576762i	$-0.804316\pi$
$157$	2.29293	−	7.05693i	0.182996	−	0.563204i	0.999908	+	0.0135583i	$0.00431588\pi$
$158$	5.67168	−	6.29904i	0.451215	−	0.501125i
$159$	5.76282	+	4.18693i	0.457021	+	0.332045i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−9.27466	−	16.0642i	−0.730946	−	1.26604i
$162$	0.104528	−	0.994522i	0.00821253	−	0.0781370i
$163$	−16.3912	+	11.9089i	−1.28386	+	0.932777i	−0.999662	−	0.0259896i	$-0.991726\pi$
$163$	−16.3912	+	11.9089i	−1.28386	+	0.932777i	−0.284195	+	0.958766i	$0.591726\pi$
$164$	1.00274	+	9.54044i	0.0783009	+	0.744983i
$165$	−1.09254	−	1.21338i	−0.0850538	−	0.0944618i
$166$	1.96583	−	0.875244i	0.152578	−	0.0679321i
$167$	20.3156	−	4.31821i	1.57207	−	0.334153i	0.662289	−	0.749249i	$-0.269585\pi$
$167$	20.3156	−	4.31821i	1.57207	−	0.334153i	0.909778	+	0.415096i	$0.136252\pi$
$168$	−2.06760	−	0.439481i	−0.159518	−	0.0339067i
$169$	−1.86913	−	0.832190i	−0.143779	−	0.0640146i
$170$	−0.0924779	−	0.284618i	−0.00709273	−	0.0218292i
$171$	1.80613	+	5.55869i	0.138118	+	0.425084i
$172$	−2.07929	−	0.925758i	−0.158544	−	0.0705884i
$173$	−19.2337	−	4.08824i	−1.46231	−	0.310823i	−0.593043	−	0.805170i	$-0.702074\pi$
$173$	−19.2337	−	4.08824i	−1.46231	−	0.310823i	−0.869264	+	0.494347i	$0.835407\pi$
$174$	−3.32044	+	0.705782i	−0.251722	+	0.0535052i
$175$	1.93104	−	0.859754i	0.145973	−	0.0649913i
$176$	1.09254	+	1.21338i	0.0823530	+	0.0914623i
$177$	0.168046	+	1.59885i	0.0126311	+	0.120177i
$178$	13.5560	−	9.84899i	1.01606	−	0.738213i
$179$	−1.38501	+	13.1775i	−0.103521	+	0.984933i	0.812271	+	0.583280i	$0.198231\pi$
$179$	−1.38501	+	13.1775i	−0.103521	+	0.984933i	−0.915792	+	0.401653i	$0.868436\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	−0.124276	+	0.215253i	−0.00923738	+	0.0159996i	−0.870607	−	0.491979i	$-0.836274\pi$
$181$	−0.124276	+	0.215253i	−0.00923738	+	0.0159996i	0.861370	+	0.507978i	$0.169607\pi$
$182$	5.65985	+	4.11212i	0.419536	+	0.304811i
$183$	2.67967	−	2.97607i	0.198087	−	0.219998i
$184$	−2.71175	+	8.34590i	−0.199913	+	0.615268i
$185$	−3.35753			−0.246851
$186$	−4.51978	−	3.25140i	−0.331406	−	0.238404i
$187$	0.488630			0.0357322
$188$	−3.64105	+	11.2060i	−0.265551	+	0.817281i
$189$	−1.41440	+	1.57085i	−0.102882	+	0.114262i
$190$	4.72851	+	3.43546i	0.343042	+	0.249235i
$191$	−10.5575	+	18.2862i	−0.763917	+	1.32314i	0.176900	+	0.984229i	$0.443393\pi$
$191$	−10.5575	+	18.2862i	−0.763917	+	1.32314i	−0.940817	+	0.338915i	$0.889940\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−1.69197	+	16.0980i	−0.121791	+	1.15876i	0.747432	+	0.664339i	$0.231287\pi$
$193$	−1.69197	+	16.0980i	−0.121791	+	1.15876i	−0.869222	+	0.494422i	$0.835380\pi$
$194$	−3.88922	+	2.82569i	−0.279230	+	0.202872i
$195$	0.345956	+	3.29155i	0.0247744	+	0.235713i
$196$	−1.69418	−	1.88157i	−0.121013	−	0.134398i
$197$	−12.5809	+	5.60136i	−0.896349	+	0.399080i	−0.802601	−	0.596516i	$-0.796551\pi$
$197$	−12.5809	+	5.60136i	−0.896349	+	0.399080i	−0.0937476	+	0.995596i	$0.529885\pi$
$198$	1.59709	−	0.339472i	0.113500	−	0.0241252i
$199$	−10.5255	−	2.23727i	−0.746136	−	0.158596i	−0.180872	−	0.983507i	$-0.557892\pi$
$199$	−10.5255	−	2.23727i	−0.746136	−	0.158596i	−0.565263	+	0.824910i	$0.691225\pi$
$200$	−0.913545	−	0.406737i	−0.0645974	−	0.0287606i
$201$	−3.89854	−	11.9985i	−0.274982	−	0.846308i
$202$	1.98006	+	6.09401i	0.139317	+	0.428773i
$203$	6.55515	+	2.91854i	0.460082	+	0.204841i
$204$	0.292725	+	0.0622207i	0.0204949	+	0.00435632i
$205$	9.38336	−	1.99449i	0.655362	−	0.139302i
$206$	−5.28895	+	2.35479i	−0.368499	+	0.164066i
$207$	5.87189	+	6.52139i	0.408124	+	0.453268i
$208$	−0.345956	−	3.29155i	−0.0239877	−	0.228228i
$209$	−7.72056	+	5.60931i	−0.534042	+	0.388004i
$210$	−0.220951	+	2.10221i	−0.0152471	+	0.145066i
$211$	−0.428015	−	0.741343i	−0.0294658	−	0.0510362i	0.850916	−	0.525301i	$-0.176047\pi$
$211$	−0.428015	−	0.741343i	−0.0294658	−	0.0510362i	−0.880382	+	0.474265i	$0.842714\pi$
$212$	−3.56162	+	6.16890i	−0.244613	+	0.423682i
$213$	6.00765	+	4.36481i	0.411637	+	0.299072i
$214$	−10.7682	+	11.9593i	−0.736098	+	0.817519i
$215$	−0.703342	+	2.16466i	−0.0479675	+	0.147629i
$216$	1.00000			0.0680414
$217$	3.68952	+	11.1758i	0.250461	+	0.758662i
$218$	−7.29561			−0.494121
$219$	1.89238	−	5.82414i	0.127875	−	0.393559i
$220$	1.09254	−	1.21338i	0.0736588	−	0.0818063i
$221$	−0.801308	−	0.582184i	−0.0539018	−	0.0391620i
$222$	1.67877	−	2.90771i	0.112671	−	0.195153i
$223$	−1.04328	−	1.80701i	−0.0698631	−	0.121006i	0.828978	−	0.559281i	$-0.188923\pi$
$223$	−1.04328	−	1.80701i	−0.0698631	−	0.121006i	−0.898841	+	0.438275i	$0.855590\pi$
$224$	0.220951	−	2.10221i	0.0147629	−	0.140460i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	−1.13629	−	10.8111i	−0.0755848	−	0.719141i
$227$	14.4942	+	16.0975i	0.962015	+	1.06843i	0.997613	+	0.0690595i	$0.0219998\pi$
$227$	14.4942	+	16.0975i	0.962015	+	1.06843i	−0.0355977	+	0.999366i	$0.511334\pi$
$228$	−5.33945	+	2.37728i	−0.353614	+	0.157439i
$229$	−14.9914	+	3.18652i	−0.990660	+	0.210571i	−0.674613	−	0.738172i	$-0.735689\pi$
$229$	−14.9914	+	3.18652i	−0.990660	+	0.210571i	−0.316048	+	0.948743i	$0.602356\pi$
$230$	8.58364	+	1.82451i	0.565988	+	0.120305i
$231$	−3.15294	−	1.40378i	−0.207448	−	0.0923620i
$232$	−1.04900	−	3.22848i	−0.0688700	−	0.211960i
$233$	1.69025	+	5.20206i	0.110732	+	0.340799i	0.991033	−	0.133617i	$-0.0426593\pi$
$233$	1.69025	+	5.20206i	0.110732	+	0.340799i	−0.880301	+	0.474416i	$0.842659\pi$
$234$	−3.02354	−	1.34617i	−0.197655	−	0.0880018i
$235$	11.5252	+	2.44976i	0.751821	+	0.159804i
$236$	−1.57253	+	0.334251i	−0.102363	+	0.0217579i
$237$	7.74339	−	3.44758i	0.502987	−	0.223944i
$238$	−0.423280	−	0.470100i	−0.0274372	−	0.0304721i
$239$	−0.718047	−	6.83176i	−0.0464466	−	0.441910i	−0.992890	−	0.119039i	$-0.962019\pi$
$239$	−0.718047	−	6.83176i	−0.0464466	−	0.441910i	0.946443	−	0.322871i	$-0.104648\pi$
$240$	0.809017	−	0.587785i	0.0522218	−	0.0379414i
$241$	2.42089	−	23.0333i	0.155944	−	1.48370i	−0.584395	−	0.811469i	$-0.698668\pi$
$241$	2.42089	−	23.0333i	0.155944	−	1.48370i	0.740338	−	0.672234i	$-0.234665\pi$
$242$	−4.16703	−	7.21751i	−0.267867	−	0.463959i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	3.23987	+	2.35391i	0.207412	+	0.150693i
$245$	−1.69418	+	1.88157i	−0.108237	+	0.120209i
$246$	−2.96440	+	9.12347i	−0.189003	+	0.581691i
$247$	19.3443			1.23085
$248$	2.76114	−	4.83489i	0.175332	−	0.307016i
$249$	2.15187			0.136369
$250$	−0.309017	+	0.951057i	−0.0195440	+	0.0601501i
$251$	−14.1884	+	15.7578i	−0.895562	+	0.994623i	0.104438	+	0.994531i	$0.466696\pi$
$251$	−14.1884	+	15.7578i	−0.895562	+	0.994623i	−1.00000		9.12325e-5i	$0.999971\pi$
$252$	−1.71009	−	1.24245i	−0.107725	−	0.0782671i
$253$	−7.16410	+	12.4086i	−0.450403	+	0.780121i
$254$	−1.81008	−	3.13515i	−0.113575	−	0.196717i
$255$	0.0312817	−	0.297625i	0.00195894	−	0.0186380i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−1.16313	−	11.0664i	−0.0725538	−	0.690303i	−0.968985	−	0.247120i	$-0.920516\pi$
$257$	−1.16313	−	11.0664i	−0.0725538	−	0.690303i	0.896431	−	0.443183i	$-0.146151\pi$
$258$	−1.52298	−	1.69144i	−0.0948168	−	0.105305i
$259$	−6.48353	+	2.88665i	−0.402867	+	0.179368i
$260$	−3.23736	+	0.688121i	−0.200772	+	0.0426755i
$261$	−3.32044	−	0.705782i	−0.205530	−	0.0436868i
$262$	−20.2399	−	9.01140i	−1.25043	−	0.556726i
$263$	−7.05510	−	21.7134i	−0.435036	−	1.33890i	−0.893050	−	0.449958i	$-0.851439\pi$
$263$	−7.05510	−	21.7134i	−0.435036	−	1.33890i	0.458014	−	0.888945i	$-0.348561\pi$
$264$	0.504553	+	1.55286i	0.0310531	+	0.0955717i
$265$	6.50740	+	2.89728i	0.399746	+	0.177978i
$266$	12.0846	+	2.56866i	0.740954	+	0.157495i
$267$	16.3899	−	3.48379i	1.00305	−	0.213205i
$268$	11.5252	−	5.13137i	0.704016	−	0.313448i
$269$	5.47829	+	6.08426i	0.334017	+	0.370964i	0.886634	−	0.462472i	$-0.153037\pi$
$269$	5.47829	+	6.08426i	0.334017	+	0.370964i	−0.552617	+	0.833435i	$0.686371\pi$
$270$	−0.104528	−	0.994522i	−0.00636140	−	0.0605247i
$271$	8.26020	−	6.00139i	0.501771	−	0.364558i	−0.307922	−	0.951412i	$-0.599634\pi$
$271$	8.26020	−	6.00139i	0.501771	−	0.364558i	0.809693	+	0.586853i	$0.199634\pi$
$272$	−0.0312817	+	0.297625i	−0.00189673	+	0.0180462i
$273$	3.49798	+	6.05868i	0.211707	+	0.366688i
$274$	−1.61350	+	2.79466i	−0.0974750	+	0.168832i
$275$	−1.32094	−	0.959718i	−0.0796556	−	0.0578732i
$276$	−5.87189	+	6.52139i	−0.353446	+	0.392542i
$277$	−4.61428	+	14.2013i	−0.277245	+	0.853273i	0.711371	+	0.702816i	$0.248074\pi$
$277$	−4.61428	+	14.2013i	−0.277245	+	0.853273i	−0.988617	+	0.150457i	$0.951926\pi$
$278$	−4.93228			−0.295819
$279$	−2.80656	−	4.80866i	−0.168025	−	0.287887i
$280$	−2.11379			−0.126323
$281$	−5.22626	+	16.0848i	−0.311772	+	0.959537i	0.665290	+	0.746585i	$0.268308\pi$
$281$	−5.22626	+	16.0848i	−0.311772	+	0.959537i	−0.977063	+	0.212952i	$0.931692\pi$
$282$	−7.88415	+	8.75624i	−0.469494	+	0.521426i
$283$	−0.119243	−	0.0866349i	−0.00708824	−	0.00514991i	0.584235	−	0.811584i	$-0.301394\pi$
$283$	−0.119243	−	0.0866349i	−0.00708824	−	0.00514991i	−0.591324	+	0.806434i	$0.701394\pi$
$284$	−3.71293	+	6.43099i	−0.220322	+	0.381609i
$285$	2.92238	+	5.06171i	0.173107	+	0.299830i
$286$	0.564866	−	5.37434i	0.0334012	−	0.317791i
$287$	16.4049	−	11.9188i	0.968348	−	0.703546i
$288$	0.104528	+	0.994522i	0.00615940	+	0.0586028i
$289$	−11.3153	−	12.5669i	−0.665605	−	0.739230i
$290$	−3.10114	+	1.38072i	−0.182105	+	0.0810785i
$291$	−4.70229	+	0.999503i	−0.275653	+	0.0585919i
$292$	5.99005	+	1.27322i	0.350541	+	0.0745098i
$293$	−6.51129	−	2.89901i	−0.380394	−	0.169362i	0.207627	−	0.978208i	$-0.433426\pi$
$293$	−6.51129	−	2.89901i	−0.380394	−	0.169362i	−0.588021	+	0.808846i	$0.700093\pi$
$294$	−0.782402	−	2.40799i	−0.0456306	−	0.140437i
$295$	0.496794	+	1.52897i	0.0289244	+	0.0890203i
$296$	3.06726	+	1.36563i	0.178281	+	0.0793757i
$297$	1.59709	+	0.339472i	0.0926725	+	0.0196982i
$298$	15.7068	−	3.33859i	0.909871	−	0.193399i
$299$	26.5328	−	11.8132i	1.53443	−	0.683173i
$300$	−0.669131	−	0.743145i	−0.0386323	−	0.0429055i
$301$	0.502898	+	4.78475i	0.0289866	+	0.275789i
$302$	−14.4150	+	10.4731i	−0.829491	+	0.602661i
$303$	−0.669778	+	6.37252i	−0.0384778	+	0.366091i
$304$	−2.92238	−	5.06171i	−0.167610	−	0.290309i
$305$	2.00235	−	3.46818i	0.114654	−	0.198587i
$306$	0.242110	+	0.175903i	0.0138405	+	0.0100557i
$307$	−14.9227	+	16.5734i	−0.851685	+	0.945892i	−0.999067	−	0.0431873i	$-0.986249\pi$
$307$	−14.9227	+	16.5734i	−0.851685	+	0.945892i	0.147382	+	0.989080i	$0.452915\pi$
$308$	1.06652	−	3.28241i	0.0607705	−	0.187032i
$309$	−5.78948			−0.329352
$310$	−5.09702	−	2.24063i	−0.289491	−	0.127259i
$311$	7.57760			0.429686			0.214843	−	0.976649i	$-0.431076\pi$
$311$	7.57760			0.429686			0.214843	+	0.976649i	$0.431076\pi$
$312$	1.02275	−	3.14769i	0.0579017	−	0.178203i
$313$	16.3841	−	18.1964i	0.926087	−	1.02852i	−0.0734257	−	0.997301i	$-0.523393\pi$
$313$	16.3841	−	18.1964i	0.926087	−	1.02852i	0.999512	−	0.0312228i	$-0.00994014\pi$
$314$	6.00298	+	4.36142i	0.338768	+	0.246129i
$315$	−1.05689	+	1.83059i	−0.0595492	+	0.103142i
$316$	4.23810	+	7.34060i	0.238412	+	0.412941i
$317$	−1.93595	+	18.4194i	−0.108734	+	1.03453i	0.795049	+	0.606545i	$0.207445\pi$
$317$	−1.93595	+	18.4194i	−0.108734	+	1.03453i	−0.903783	+	0.427990i	$0.859222\pi$
$318$	−5.76282	+	4.18693i	−0.323163	+	0.234791i
$319$	−0.579363	−	5.51227i	−0.0324381	−	0.308628i
$320$	0.669131	+	0.743145i	0.0374055	+	0.0415431i
$321$	−14.7015	+	6.54553i	−0.820558	+	0.365336i
$322$	18.1440	−	3.85662i	1.01112	−	0.214921i
$323$	−1.71091	−	0.363665i	−0.0951974	−	0.0202348i
$324$	0.913545	+	0.406737i	0.0507525	+	0.0225965i
$325$	1.02275	+	3.14769i	0.0567318	+	0.174603i
$326$	−6.26088	−	19.2690i	−0.346758	−	1.06721i
$327$	−6.66487	−	2.96739i	−0.368568	−	0.164097i
$328$	−9.38336	−	1.99449i	−0.518109	−	0.110128i
$329$	24.3618	−	5.17826i	1.34311	−	0.285487i
$330$	1.49161	−	0.664107i	0.0821104	−	0.0365579i
$331$	−10.7287	−	11.9154i	−0.589702	−	0.654930i	0.372255	−	0.928130i	$-0.378585\pi$
$331$	−10.7287	−	11.9154i	−0.589702	−	0.654930i	−0.961957	+	0.273200i	$0.911918\pi$
$332$	0.224932	+	2.14008i	0.0123447	+	0.117452i
$333$	2.71630	−	1.97351i	0.148852	−	0.108148i
$334$	−2.17100	+	20.6557i	−0.118792	+	1.13023i
$335$	−6.30798	−	10.9257i	−0.344642	−	0.596937i
$336$	1.05689	−	1.83059i	0.0576582	−	0.0998670i
$337$	12.9512	+	9.40962i	0.705498	+	0.512574i	0.881718	−	0.471776i	$-0.156387\pi$
$337$	12.9512	+	9.40962i	0.705498	+	0.512574i	−0.176220	+	0.984351i	$0.556387\pi$
$338$	1.36905	−	1.52049i	0.0744666	−	0.0827036i
$339$	3.35920	−	10.3386i	0.182447	−	0.561514i
$340$	0.299265			0.0162299
$341$	6.05109	−	6.78441i	0.327685	−	0.367397i
$342$	−5.84475			−0.316048
$343$	−6.22620	+	19.1623i	−0.336183	+	1.03467i
$344$	1.52298	−	1.69144i	0.0821138	−	0.0911966i
$345$	7.09945	+	5.15805i	0.382221	+	0.277700i
$346$	9.83167	−	17.0290i	0.528554	−	0.915483i
$347$	−7.22574	−	12.5153i	−0.387898	−	0.671859i	0.604269	−	0.796781i	$-0.293465\pi$
$347$	−7.22574	−	12.5153i	−0.387898	−	0.671859i	−0.992167	+	0.124922i	$0.960132\pi$
$348$	0.354835	−	3.37603i	0.0190211	−	0.180974i
$349$	7.13535	−	5.18414i	0.381947	−	0.277500i	−0.380201	−	0.924904i	$-0.624145\pi$
$349$	7.13535	−	5.18414i	0.381947	−	0.277500i	0.762147	+	0.647403i	$0.224145\pi$
$350$	0.220951	+	2.10221i	0.0118103	+	0.112368i
$351$	−2.21461	−	2.45957i	−0.118207	−	0.131282i
$352$	−1.49161	+	0.664107i	−0.0795030	+	0.0353970i
$353$	13.0047	−	2.76423i	0.692169	−	0.147125i	0.151622	−	0.988439i	$-0.451550\pi$
$353$	13.0047	−	2.76423i	0.692169	−	0.147125i	0.540547	+	0.841314i	$0.318217\pi$
$354$	−1.57253	−	0.334251i	−0.0835789	−	0.0177652i
$355$	6.78386	+	3.02037i	0.360050	+	0.160305i
$356$	5.17792	+	15.9360i	0.274429	+	0.844607i
$357$	−0.195479	−	0.601621i	−0.0103458	−	0.0318412i
$358$	−12.1046	−	5.38930i	−0.639746	−	0.284833i
$359$	23.5792	+	5.01192i	1.24447	+	0.264519i	0.782653	−	0.622458i	$-0.213866\pi$
$359$	23.5792	+	5.01192i	1.24447	+	0.264519i	0.461812	+	0.886978i	$0.347199\pi$
$360$	0.978148	−	0.207912i	0.0515529	−	0.0109579i
$361$	13.8504	−	6.16660i	0.728969	−	0.324558i
$362$	−0.166314	−	0.184711i	−0.00874128	−	0.00970817i
$363$	−0.871147	−	8.28841i	−0.0457234	−	0.435029i
$364$	−5.65985	+	4.11212i	−0.296657	+	0.215534i
$365$	0.640118	−	6.09032i	0.0335053	−	0.318782i
$366$	2.00235	+	3.46818i	0.104665	+	0.181284i
$367$	−0.469367	+	0.812967i	−0.0245008	+	0.0424366i	−0.878016	−	0.478632i	$-0.841133\pi$
$367$	−0.469367	+	0.812967i	−0.0245008	+	0.0424366i	0.853515	+	0.521068i	$0.174466\pi$
$368$	−7.09945	−	5.15805i	−0.370084	−	0.268882i
$369$	−6.41896	+	7.12898i	−0.334158	+	0.371120i
$370$	1.03753	−	3.19320i	0.0539388	−	0.166007i
$371$	15.0570			0.781720
$372$	4.48895	−	3.29383i	0.232741	−	0.170777i
$373$	−3.07859			−0.159403			−0.0797017	−	0.996819i	$-0.525397\pi$
$373$	−3.07859			−0.159403			−0.0797017	+	0.996819i	$0.525397\pi$
$374$	−0.150995	+	0.464715i	−0.00780777	+	0.0240299i
$375$	−0.669131	+	0.743145i	−0.0345538	+	0.0383758i
$376$	−9.53239	−	6.92568i	−0.491595	−	0.357165i
$377$	−5.61756	+	9.72990i	−0.289319	+	0.501115i
$378$	−1.05689	−	1.83059i	−0.0543607	−	0.0941555i
$379$	−2.76802	+	26.3360i	−0.142184	+	1.35279i	0.657993	+	0.753024i	$0.271405\pi$
$379$	−2.76802	+	26.3360i	−0.142184	+	1.35279i	−0.800177	+	0.599764i	$0.795261\pi$
$380$	−4.72851	+	3.43546i	−0.242567	+	0.176235i
$381$	−0.378410	−	3.60033i	−0.0193865	−	0.184450i
$382$	−14.1288	−	15.6916i	−0.722890	−	0.802851i
$383$	0.873550	−	0.388930i	0.0446363	−	0.0198734i	−0.384297	−	0.923209i	$-0.625556\pi$
$383$	0.873550	−	0.388930i	0.0446363	−	0.0198734i	0.428933	+	0.903336i	$0.358889\pi$
$384$	−0.978148	+	0.207912i	−0.0499159	+	0.0106099i
$385$	−3.37591	−	0.717571i	−0.172052	−	0.0365708i
$386$	−14.7873	−	6.58372i	−0.752652	−	0.335102i
$387$	−0.703342	−	2.16466i	−0.0357529	−	0.110036i
$388$	−1.48555	−	4.57206i	−0.0754174	−	0.232111i
$389$	1.93897	+	0.863285i	0.0983097	+	0.0437703i	0.455302	−	0.890337i	$-0.349531\pi$
$389$	1.93897	+	0.863285i	0.0983097	+	0.0437703i	−0.356993	+	0.934107i	$0.616198\pi$
$390$	−3.23736	−	0.688121i	−0.163930	−	0.0348444i
$391$	−2.56878	+	0.546011i	−0.129909	+	0.0276130i
$392$	2.31301	−	1.02982i	0.116825	−	0.0520137i
$393$	−14.8248	−	16.4646i	−0.747814	−	0.830532i
$394$	−1.43951	−	13.6960i	−0.0725215	−	0.689996i
$395$	6.85739	−	4.98218i	0.345033	−	0.250681i
$396$	−0.170671	+	1.62382i	−0.00857653	+	0.0816003i
$397$	−18.6101	−	32.2337i	−0.934015	−	1.61776i	−0.776382	−	0.630263i	$-0.782947\pi$
$397$	−18.6101	−	32.2337i	−0.934015	−	1.61776i	−0.157633	−	0.987498i	$-0.550386\pi$
$398$	5.38034	−	9.31903i	0.269692	−	0.467121i
$399$	9.99505	+	7.26183i	0.500378	+	0.363546i
$400$	0.669131	−	0.743145i	0.0334565	−	0.0371572i
$401$	−0.457333	+	1.40753i	−0.0228381	+	0.0702885i	−0.961826	−	0.273662i	$-0.911765\pi$
$401$	−0.457333	+	1.40753i	−0.0228381	+	0.0702885i	0.938988	+	0.343950i	$0.111765\pi$
$402$	12.6160			0.629227
$403$	−18.0066	+	3.91616i	−0.896972	+	0.195078i
$404$	−6.40762			−0.318791
$405$	0.309017	−	0.951057i	0.0153552	−	0.0472584i
$406$	−4.80135	+	5.33244i	−0.238287	+	0.264645i
$407$	4.43509	+	3.22228i	0.219839	+	0.159723i
$408$	−0.149632	+	0.259171i	−0.00740791	+	0.0128309i
$409$	1.34520	+	2.32995i	0.0665157	+	0.115209i	0.897365	−	0.441288i	$-0.145478\pi$
$409$	1.34520	+	2.32995i	0.0665157	+	0.115209i	−0.830850	+	0.556497i	$0.812145\pi$
$410$	−1.00274	+	9.54044i	−0.0495218	+	0.471169i
$411$	−2.61070	+	1.89678i	−0.128776	+	0.0935613i
$412$	−0.605166	−	5.75777i	−0.0298144	−	0.283665i
$413$	2.27387	+	2.52539i	0.111890	+	0.124266i
$414$	−8.01673	+	3.56928i	−0.394001	+	0.175420i
$415$	2.10485	−	0.447399i	0.103323	−	0.0219619i
$416$	3.23736	+	0.688121i	0.158724	+	0.0337379i
$417$	−4.50586	−	2.00614i	−0.220653	−	0.0982411i
$418$	−2.94899	−	9.07606i	−0.144240	−	0.443925i
$419$	3.63206	+	11.1783i	0.177438	+	0.546098i	0.999736	−	0.0229586i	$-0.00730859\pi$
$419$	3.63206	+	11.1783i	0.177438	+	0.546098i	−0.822298	+	0.569056i	$0.807309\pi$
$420$	−1.93104	−	0.859754i	−0.0942251	−	0.0419517i
$421$	13.1471	+	2.79449i	0.640748	+	0.136195i	0.516818	−	0.856096i	$-0.327117\pi$
$421$	13.1471	+	2.79449i	0.640748	+	0.136195i	0.123931	+	0.992291i	$0.460450\pi$
$422$	0.837323	−	0.177979i	0.0407603	−	0.00866386i
$423$	−10.7640	+	4.79245i	−0.523364	+	0.233017i
$424$	−4.76637	−	5.29359i	−0.231476	−	0.257080i
$425$	−0.0312817	−	0.297625i	−0.00151739	−	0.0144370i
$426$	−6.00765	+	4.36481i	−0.291072	+	0.211476i
$427$	0.884843	−	8.41872i	0.0428205	−	0.407410i
$428$	−8.04640	−	13.9368i	−0.388937	−	0.673659i
$429$	2.70197	−	4.67995i	0.130452	−	0.225950i
$430$	−1.84137	−	1.33784i	−0.0887989	−	0.0645162i
$431$	−2.44613	+	2.71671i	−0.117826	+	0.130859i	−0.799172	−	0.601102i	$-0.794728\pi$
$431$	−2.44613	+	2.71671i	−0.117826	+	0.130859i	0.681346	+	0.731962i	$0.261395\pi$
$432$	−0.309017	+	0.951057i	−0.0148676	+	0.0457577i
$433$	7.67687			0.368927			0.184463	−	0.982839i	$-0.440945\pi$
$433$	7.67687			0.368927			0.184463	+	0.982839i	$0.440945\pi$
$434$	−11.7689	+	0.0554375i	−0.564927	+	0.00266109i
$435$	−3.39462			−0.162760
$436$	2.25447	−	6.93854i	0.107969	−	0.332296i
$437$	34.3198	−	38.1159i	1.64174	−	1.82333i
$438$	4.95431	+	3.59952i	0.236726	+	0.171992i
$439$	17.0196	−	29.4789i	0.812303	−	1.40695i	−0.0989459	−	0.995093i	$-0.531547\pi$
$439$	17.0196	−	29.4789i	0.812303	−	1.40695i	0.911249	−	0.411857i	$-0.135120\pi$
$440$	0.816385	+	1.41402i	0.0389196	+	0.0674107i
$441$	0.264656	−	2.51804i	0.0126027	−	0.119907i
$442$	0.801308	−	0.582184i	0.0381143	−	0.0276917i
$443$	−0.726144	−	6.90880i	−0.0345001	−	0.328247i	−0.998136	−	0.0610282i	$-0.980562\pi$
$443$	−0.726144	−	6.90880i	−0.0345001	−	0.328247i	0.963636	−	0.267219i	$-0.0861046\pi$
$444$	2.24663	+	2.49513i	0.106620	+	0.118414i
$445$	15.3075	−	6.81532i	0.725643	−	0.323077i
$446$	2.04096	−	0.433820i	0.0966423	−	0.0205419i
$447$	15.7068	+	3.33859i	0.742907	+	0.157910i
$448$	1.93104	+	0.859754i	0.0912331	+	0.0406196i
$449$	−4.06541	−	12.5120i	−0.191858	−	0.590480i	−0.999999	−	0.00148973i	$-0.999526\pi$
$449$	−4.06541	−	12.5120i	−0.191858	−	0.590480i	0.808140	−	0.588990i	$-0.200474\pi$
$450$	−0.309017	−	0.951057i	−0.0145672	−	0.0448332i
$451$	−14.3090	−	6.37077i	−0.673784	−	0.299988i
$452$	10.6331	+	2.26013i	0.500137	+	0.106307i
$453$	−17.4286	+	3.70456i	−0.818866	+	0.174055i
$454$	−19.7885	+	8.81043i	−0.928723	+	0.413494i
$455$	4.68121	+	5.19901i	0.219458	+	0.243733i
$456$	−0.610943	−	5.81274i	−0.0286100	−	0.272206i
$457$	−23.1985	+	16.8547i	−1.08518	+	0.788428i	−0.978579	−	0.205874i	$-0.933996\pi$
$457$	−23.1985	+	16.8547i	−1.08518	+	0.788428i	−0.106600	+	0.994302i	$0.533996\pi$
$458$	1.60204	−	15.2424i	0.0748583	−	0.712229i
$459$	0.149632	+	0.259171i	0.00698424	+	0.0120971i
$460$	−4.38770	+	7.59972i	−0.204578	+	0.354339i
$461$	30.3088	+	22.0206i	1.41162	+	1.02560i	0.993085	+	0.117401i	$0.0374564\pi$
$461$	30.3088	+	22.0206i	1.41162	+	1.02560i	0.418535	+	0.908200i	$0.362544\pi$
$462$	2.30939	−	2.56483i	0.107442	−	0.119327i
$463$	4.31490	−	13.2799i	0.200530	−	0.617169i	−0.799337	−	0.600883i	$-0.794816\pi$
$463$	4.31490	−	13.2799i	0.200530	−	0.617169i	0.999867	−	0.0162862i	$-0.00518428\pi$
$464$	3.39462			0.157591
$465$	−3.74501	−	4.12006i	−0.173671	−	0.191063i
$466$	−5.46977			−0.253382
$467$	6.59891	−	20.3093i	0.305361	−	0.939805i	−0.674181	−	0.738566i	$-0.735503\pi$
$467$	6.59891	−	20.3093i	0.305361	−	0.939805i	0.979542	−	0.201239i	$-0.0644967\pi$
$468$	2.21461	−	2.45957i	0.102370	−	0.113694i
$469$	−21.5744	−	15.6747i	−0.996213	−	0.723791i
$470$	−5.89134	+	10.2041i	−0.271747	+	0.470680i
$471$	3.71005	+	6.42599i	0.170950	+	0.296094i
$472$	0.168046	−	1.59885i	0.00773494	−	0.0735931i
$473$	3.00654	−	2.18438i	0.138241	−	0.100438i
$474$	0.886004	+	8.42976i	0.0406955	+	0.387192i
$475$	3.91090	+	4.34350i	0.179445	+	0.199293i
$476$	0.577892	−	0.257294i	0.0264877	−	0.0117931i
$477$	−6.96757	+	1.48100i	−0.319023	+	0.0678105i
$478$	6.71928	+	1.42823i	0.307333	+	0.0653256i
$479$	4.94707	+	2.20258i	0.226037	+	0.100638i	0.516631	−	0.856208i	$-0.327186\pi$
$479$	4.94707	+	2.20258i	0.226037	+	0.100638i	−0.290593	+	0.956847i	$0.593853\pi$
$480$	0.309017	+	0.951057i	0.0141046	+	0.0434096i
$481$	−3.43391	−	10.5685i	−0.156573	−	0.481881i
$482$	21.1579	+	9.42008i	0.963714	+	0.429073i
$483$	18.1440	+	3.85662i	0.825579	+	0.175482i
$484$	8.15195	−	1.73275i	0.370543	−	0.0787613i
$485$	−4.39173	+	1.95532i	−0.199418	+	0.0887866i
$486$	0.669131	+	0.743145i	0.0303524	+	0.0337097i
$487$	1.92801	+	18.3438i	0.0873667	+	0.831238i	0.947196	+	0.320656i	$0.103903\pi$
$487$	1.92801	+	18.3438i	0.0873667	+	0.831238i	−0.859829	+	0.510582i	$0.829430\pi$
$488$	−3.23987	+	2.35391i	−0.146662	+	0.106556i
$489$	2.11781	−	20.1496i	0.0957708	−	0.911198i
$490$	−1.26595	−	2.19270i	−0.0571900	−	0.0990559i
$491$	−7.23025	+	12.5232i	−0.326297	+	0.565162i	−0.981774	−	0.190053i	$-0.939134\pi$
$491$	−7.23025	+	12.5232i	−0.326297	+	0.565162i	0.655477	+	0.755215i	$0.272467\pi$
$492$	−7.76089	−	5.63862i	−0.349888	−	0.254208i
$493$	0.679764	−	0.754954i	0.0306150	−	0.0340014i
$494$	−5.97771	+	18.3975i	−0.268950	+	0.827742i
$495$	1.63277			0.0733875
$496$	3.74501	+	4.12006i	0.168156	+	0.184996i
$497$	15.6967			0.704093
$498$	−0.664964	+	2.04655i	−0.0297978	+	0.0917081i
$499$	4.35264	−	4.83410i	0.194851	−	0.216404i	−0.637800	−	0.770202i	$-0.720155\pi$
$499$	4.35264	−	4.83410i	0.194851	−	0.216404i	0.832651	+	0.553798i	$0.186822\pi$
$500$	−0.809017	−	0.587785i	−0.0361803	−	0.0262866i
$501$	−10.3847	+	17.9869i	−0.463955	+	0.803594i
$502$	−10.6021	−	18.3634i	−0.473195	−	0.819597i
$503$	−1.57997	+	15.0324i	−0.0704476	+	0.670264i	0.901131	+	0.433547i	$0.142738\pi$
$503$	−1.57997	+	15.0324i	−0.0704476	+	0.670264i	−0.971579	+	0.236717i	$0.923929\pi$
$504$	1.71009	−	1.24245i	0.0761734	−	0.0553432i
$505$	0.669778	+	6.37252i	0.0298047	+	0.283573i
$506$	−9.58744	−	10.6479i	−0.426214	−	0.473358i
$507$	1.86913	−	0.832190i	0.0830110	−	0.0369589i
$508$	3.54105	−	0.752673i	0.157109	−	0.0333945i
$509$	−17.0450	−	3.62302i	−0.755506	−	0.160588i	−0.185971	−	0.982555i	$-0.559543\pi$
$509$	−17.0450	−	3.62302i	−0.755506	−	0.160588i	−0.569534	+	0.821967i	$0.692876\pi$
$510$	0.273392	+	0.121722i	0.0121060	+	0.00538994i
$511$	−4.00009	−	12.3110i	−0.176953	−	0.544606i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−5.33945	−	2.37728i	−0.235742	−	0.104959i
$514$	10.8842	+	2.31351i	0.480081	+	0.102044i
$515$	−5.66297	+	1.20370i	−0.249540	+	0.0530414i
$516$	2.07929	−	0.925758i	0.0915355	−	0.0407542i
$517$	−12.8730	−	14.2969i	−0.566154	−	0.628777i
$518$	−0.741850	−	7.05823i	−0.0325950	−	0.310121i
$519$	15.9080	−	11.5578i	0.698283	−	0.507332i
$520$	0.345956	−	3.29155i	0.0151712	−	0.144344i
$521$	−11.2472	−	19.4808i	−0.492751	−	0.853469i	0.507215	−	0.861820i	$-0.330675\pi$
$521$	−11.2472	−	19.4808i	−0.492751	−	0.853469i	−0.999965	+	0.00835073i	$0.997342\pi$
$522$	1.69731	−	2.93983i	0.0742893	−	0.128673i
$523$	24.4355	+	17.7534i	1.06849	+	0.776304i	0.975640	−	0.219376i	$-0.0704023\pi$
$523$	24.4355	+	17.7534i	1.06849	+	0.776304i	0.0928501	+	0.995680i	$0.470402\pi$
$524$	14.8248	−	16.4646i	0.647626	−	0.719261i
$525$	−0.653196	+	2.01033i	−0.0285078	+	0.0877380i
$526$	22.8308			0.995469
$527$	1.66622	−	0.00784871i	0.0725816	−	0.000341895i
$528$	−1.63277			−0.0710572
$529$	16.6893	−	51.3643i	0.725621	−	2.23323i
$530$	−4.76637	+	5.29359i	−0.207038	+	0.229939i
$531$	−1.30062	−	0.944958i	−0.0564422	−	0.0410077i
$532$	−6.17728	+	10.6994i	−0.267819	+	0.463876i
$533$	15.8749	+	27.4961i	0.687617	+	1.19099i
$534$	−1.75149	+	16.6643i	−0.0757944	+	0.721135i
$535$	−13.0193	+	9.45911i	−0.562875	+	0.408953i
$536$	1.31873	+	12.5468i	0.0569603	+	0.541941i
$537$	−8.86604	−	9.84674i	−0.382598	−	0.424918i
$538$	−7.47936	+	3.33002i	−0.322458	+	0.143568i
$539$	4.04368	−	0.859511i	0.174174	−	0.0370218i
$540$	0.978148	+	0.207912i	0.0420928	+	0.00894709i
$541$	18.7335	+	8.34069i	0.805416	+	0.358594i	0.767793	−	0.640698i	$-0.221355\pi$
$541$	18.7335	+	8.34069i	0.805416	+	0.358594i	0.0376229	+	0.999292i	$0.488021\pi$
$542$	3.15512	+	9.71045i	0.135524	+	0.417099i
$543$	−0.0768070	−	0.236388i	−0.00329610	−	0.0101444i
$544$	−0.273392	−	0.121722i	−0.0117216	−	0.00521879i
$545$	−7.13619	−	1.51684i	−0.305681	−	0.0649744i
$546$	−6.84308	+	1.45454i	−0.292857	+	0.0622486i
$547$	−22.7711	+	10.1384i	−0.973623	+	0.433485i	−0.830988	−	0.556291i	$-0.812224\pi$
$547$	−22.7711	+	10.1384i	−0.973623	+	0.433485i	−0.142635	+	0.989775i	$0.545558\pi$
$548$	−2.15928	−	2.39813i	−0.0922400	−	0.102443i
$549$	0.418606	+	3.98277i	0.0178656	+	0.169980i
$550$	1.32094	−	0.959718i	0.0563250	−	0.0409225i
$551$	−2.07392	+	19.7321i	−0.0883520	+	0.840614i
$552$	−4.38770	−	7.59972i	−0.186753	−	0.323466i
$553$	8.95843	−	15.5165i	0.380951	−	0.659827i
$554$	−12.0803	−	8.77688i	−0.513245	−	0.372894i
$555$	2.24663	−	2.49513i	0.0953640	−	0.105912i
$556$	1.52416	−	4.69088i	0.0646387	−	0.198938i
$557$	−24.7086			−1.04694			−0.523469	−	0.852045i	$-0.675363\pi$
$557$	−24.7086			−1.04694			−0.523469	+	0.852045i	$0.675363\pi$
$558$	5.44058	−	1.18324i	0.230318	−	0.0500907i
$559$	−7.53304			−0.318614
$560$	0.653196	−	2.01033i	0.0276026	−	0.0849520i
$561$	−0.326958	+	0.363123i	−0.0138042	+	0.0153311i
$562$	−13.6825	−	9.94093i	−0.577162	−	0.419333i
$563$	−11.1413	+	19.2973i	−0.469551	+	0.813286i	−0.999394	−	0.0348099i	$-0.988917\pi$
$563$	−11.1413	+	19.2973i	−0.469551	+	0.813286i	0.529843	+	0.848096i	$0.322251\pi$
$564$	−5.89134	−	10.2041i	−0.248070	−	0.429670i
$565$	1.13629	−	10.8111i	0.0478040	−	0.454825i
$566$	0.119243	−	0.0866349i	0.00501214	−	0.00364153i
$567$	−0.220951	−	2.10221i	−0.00927906	−	0.0882844i
$568$	−4.96887	−	5.51849i	−0.208489	−	0.231551i
$569$	−15.5428	+	6.92009i	−0.651587	+	0.290105i	−0.705786	−	0.708425i	$-0.749406\pi$
$569$	−15.5428	+	6.92009i	−0.651587	+	0.290105i	0.0541990	+	0.998530i	$0.482739\pi$
$570$	−5.71703	+	1.21519i	−0.239460	+	0.0508988i
$571$	−9.02307	−	1.91791i	−0.377604	−	0.0802622i	0.0152000	−	0.999884i	$-0.495162\pi$
$571$	−9.02307	−	1.91791i	−0.377604	−	0.0802622i	−0.392804	+	0.919622i	$0.628495\pi$
$572$	4.93675	+	2.19798i	0.206416	+	0.0919022i
$573$	−6.52492	−	20.0817i	−0.272583	−	0.838923i
$574$	6.26610	+	19.2851i	0.261542	+	0.804943i
$575$	8.01673	+	3.56928i	0.334321	+	0.148849i
$576$	−0.978148	−	0.207912i	−0.0407562	−	0.00866299i
$577$	4.12822	−	0.877481i	0.171860	−	0.0365300i	−0.121178	−	0.992631i	$-0.538667\pi$
$577$	4.12822	−	0.877481i	0.171860	−	0.0365300i	0.293038	+	0.956101i	$0.405334\pi$
$578$	15.4485	−	6.87810i	0.642571	−	0.286091i
$579$	−10.8310	−	12.0290i	−0.450121	−	0.499910i
$580$	−0.354835	−	3.37603i	−0.0147337	−	0.140182i
$581$	3.67989	−	2.67360i	0.152667	−	0.110919i
$582$	0.502504	−	4.78101i	0.0208295	−	0.198179i
$583$	−5.81530	−	10.0724i	−0.240845	−	0.417156i
$584$	−3.06193	+	5.30342i	−0.126704	+	0.219457i
$585$	−2.67759	−	1.94538i	−0.110705	−	0.0804316i
$586$	4.76923	−	5.29676i	0.197015	−	0.218807i
$587$	10.4353	−	32.1165i	0.430711	−	1.32559i	−0.466708	−	0.884411i	$-0.654560\pi$
$587$	10.4353	−	32.1165i	0.430711	−	1.32559i	0.897419	−	0.441180i	$-0.145440\pi$
$588$	2.53191			0.104414
$589$	−26.2368	+	19.2516i	−1.08107	+	0.793250i
$590$	−1.60766			−0.0661862
$591$	4.25562	−	13.0974i	0.175053	−	0.538757i
$592$	−2.24663	+	2.49513i	−0.0923358	+	0.102549i
$593$	−30.0615	−	21.8409i	−1.23448	−	0.896900i	−0.237260	−	0.971446i	$-0.576249\pi$
$593$	−30.0615	−	21.8409i	−1.23448	−	0.896900i	−0.997218	+	0.0745461i	$0.976249\pi$
$594$	−0.816385	+	1.41402i	−0.0334967	+	0.0580179i
$595$	−0.316291	−	0.547832i	−0.0129667	−	0.0224589i
$596$	−1.67849	+	15.9697i	−0.0687536	+	0.654146i
$597$	8.70558	−	6.32497i	0.356296	−	0.258864i
$598$	3.03590	+	28.8847i	0.124147	+	1.18118i
$599$	−19.8437	−	22.0387i	−0.810794	−	0.900477i	0.185830	−	0.982582i	$-0.440503\pi$
$599$	−19.8437	−	22.0387i	−0.810794	−	0.900477i	−0.996624	+	0.0821044i	$0.973836\pi$
$600$	0.913545	−	0.406737i	0.0372953	−	0.0166050i
$601$	23.0333	−	4.89589i	0.939550	−	0.199707i	0.287411	−	0.957807i	$-0.407205\pi$
$601$	23.0333	−	4.89589i	0.939550	−	0.199707i	0.652138	+	0.758100i	$0.273872\pi$
$602$	−4.70598	−	1.00029i	−0.191801	−	0.0407686i
$603$	11.5252	+	5.13137i	0.469344	+	0.208966i
$604$	−5.50605	−	16.9459i	−0.224038	−	0.689518i
$605$	−2.57537	−	7.92617i	−0.104704	−	0.322244i
$606$	−5.85365	−	2.60621i	−0.237788	−	0.105870i
$607$	−42.1775	−	8.96510i	−1.71193	−	0.363882i	−0.755344	−	0.655328i	$-0.772530\pi$
$607$	−42.1775	−	8.96510i	−1.71193	−	0.363882i	−0.956587	+	0.291446i	$0.905864\pi$
$608$	5.71703	−	1.21519i	0.231856	−	0.0492826i
$609$	−6.55515	+	2.91854i	−0.265628	+	0.118265i
$610$	2.67967	+	2.97607i	0.108497	+	0.120498i
$611$	4.07629	+	38.7833i	0.164909	+	1.56900i
$612$	−0.242110	+	0.175903i	−0.00978673	+	0.00711048i
$613$	−1.68968	+	16.0762i	−0.0682454	+	0.649312i	0.905916	+	0.423458i	$0.139184\pi$
$613$	−1.68968	+	16.0762i	−0.0682454	+	0.649312i	−0.974161	+	0.225854i	$0.927483\pi$
$614$	−11.1508	−	19.3138i	−0.450011	−	0.779442i
$615$	−4.79649	+	8.30777i	−0.193413	+	0.335002i
$616$	2.79218	+	2.02864i	0.112500	+	0.0817362i
$617$	10.2844	−	11.4220i	0.414034	−	0.459831i	−0.499668	−	0.866217i	$-0.666545\pi$
$617$	10.2844	−	11.4220i	0.414034	−	0.459831i	0.913701	+	0.406386i	$0.133211\pi$
$618$	1.78905	−	5.50612i	0.0719661	−	0.221489i
$619$	33.9115			1.36302			0.681509	−	0.731809i	$-0.261324\pi$
$619$	33.9115			1.36302			0.681509	+	0.731809i	$0.261324\pi$
$620$	3.70603	−	4.15516i	0.148838	−	0.166875i
$621$	−8.77540			−0.352145
$622$	−2.34161	+	7.20672i	−0.0938899	+	0.288963i
$623$	23.6998	−	26.3213i	0.949513	−	1.05454i
$624$	2.67759	+	1.94538i	0.107189	+	0.0778776i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	12.2429	+	21.2053i	0.489323	+	0.847533i
$627$	0.997529	−	9.49086i	0.0398375	−	0.379028i
$628$	−6.00298	+	4.36142i	−0.239545	+	0.174040i
$629$	0.105029	+	0.999287i	0.00418779	+	0.0398442i
$630$	−1.41440	−	1.57085i	−0.0563510	−	0.0625841i
$631$	6.86841	−	3.05801i	0.273427	−	0.121738i	−0.265443	−	0.964127i	$-0.585518\pi$
$631$	6.86841	−	3.05801i	0.273427	−	0.121738i	0.538870	+	0.842389i	$0.318851\pi$
$632$	−8.29097	+	1.76230i	−0.329797	+	0.0701005i
$633$	0.837323	+	0.177979i	0.0332806	+	0.00707401i
$634$	−16.9196	−	7.53310i	−0.671964	−	0.299178i
$635$	−1.11869	−	3.44298i	−0.0443939	−	0.136630i
$636$	−2.20120	−	6.77460i	−0.0872833	−	0.268630i
$637$	−7.65533	−	3.40837i	−0.303315	−	0.135045i
$638$	5.42152	+	1.15238i	0.214640	+	0.0456231i
$639$	−7.26359	+	1.54392i	−0.287343	+	0.0610767i
$640$	−0.913545	+	0.406737i	−0.0361111	+	0.0160777i
$641$	22.6663	+	25.1735i	0.895266	+	0.994294i	1.00000		0.000206752i	$-6.58111e-5\pi$
$641$	22.6663	+	25.1735i	0.895266	+	0.994294i	−0.104734	+	0.994500i	$0.533399\pi$
$642$	−1.68216	−	16.0046i	−0.0663894	−	0.631653i
$643$	−13.2130	+	9.59983i	−0.521071	+	0.378580i	−0.817007	−	0.576627i	$-0.804368\pi$
$643$	−13.2130	+	9.59983i	−0.521071	+	0.378580i	0.295936	+	0.955208i	$0.404368\pi$
$644$	−1.93893	+	18.4477i	−0.0764046	+	0.726941i
$645$	−1.13803	−	1.97113i	−0.0448099	−	0.0776131i
$646$	0.874565	−	1.51479i	0.0344093	−	0.0595987i
$647$	−10.7854	−	7.83607i	−0.424019	−	0.308068i	0.355234	−	0.934777i	$-0.384401\pi$
$647$	−10.7854	−	7.83607i	−0.424019	−	0.308068i	−0.779253	+	0.626710i	$0.784401\pi$
$648$	−0.669131	+	0.743145i	−0.0262859	+	0.0291935i
$649$	0.811149	−	2.49646i	0.0318404	−	0.0979947i
$650$	−3.30968			−0.129816
$651$	−10.7740	−	4.73621i	−0.422267	−	0.185627i
$652$	20.2606			0.793467
$653$	−1.65127	+	5.08210i	−0.0646194	+	0.198878i	−0.978153	−	0.207884i	$-0.933342\pi$
$653$	−1.65127	+	5.08210i	−0.0646194	+	0.198878i	0.913534	+	0.406762i	$0.133342\pi$
$654$	4.88172	−	5.42170i	0.190890	−	0.212005i
$655$	−17.9241	−	13.0226i	−0.700351	−	0.508835i
$656$	4.79649	−	8.30777i	0.187272	−	0.324364i
$657$	3.06193	+	5.30342i	0.119457	+	0.206906i
$658$	−2.60339	+	24.7696i	−0.101491	+	0.965620i
$659$	35.9988	−	26.1547i	1.40231	−	1.01884i	0.407929	−	0.913014i	$-0.366251\pi$
$659$	35.9988	−	26.1547i	1.40231	−	1.01884i	0.994385	−	0.105827i	$-0.0337490\pi$
$660$	0.170671	+	1.62382i	0.00664335	+	0.0632073i
$661$	−4.08254	−	4.53412i	−0.158792	−	0.176357i	0.658499	−	0.752582i	$-0.271192\pi$
$661$	−4.08254	−	4.53412i	−0.158792	−	0.176357i	−0.817291	+	0.576225i	$0.804525\pi$
$662$	14.6476	−	6.52152i	0.569294	−	0.253466i
$663$	0.968827	−	0.205931i	0.0376261	−	0.00799768i
$664$	−2.10485	−	0.447399i	−0.0816839	−	0.0173624i
$665$	11.2865	+	5.02505i	0.437670	+	0.194863i
$666$	1.03753	+	3.19320i	0.0402036	+	0.123734i
$667$	9.20536	+	28.3312i	0.356433	+	1.09699i
$668$	−18.9738	−	8.44769i	−0.734119	−	0.326851i
$669$	2.04096	+	0.433820i	0.0789081	+	0.0167724i
$670$	12.3403	−	2.62300i	0.476746	−	0.101335i
$671$	−5.97345	+	2.65955i	−0.230603	+	0.102671i
$672$	1.41440	+	1.57085i	0.0545616	+	0.0605968i
$673$	0.662233	+	6.30072i	0.0255272	+	0.242875i	0.999843	+	0.0176913i	$0.00563160\pi$
$673$	0.662233	+	6.30072i	0.0255272	+	0.242875i	−0.974316	+	0.225184i	$0.927702\pi$
$674$	−12.9512	+	9.40962i	−0.498863	+	0.362445i
$675$	0.104528	−	0.994522i	0.00402330	−	0.0382792i
$676$	1.02301	+	1.77190i	0.0393465	+	0.0681501i
$677$	2.40492	−	4.16545i	0.0924287	−	0.160091i	−0.816104	−	0.577905i	$-0.803870\pi$
$677$	2.40492	−	4.16545i	0.0924287	−	0.160091i	0.908533	+	0.417814i	$0.137204\pi$
$678$	8.79451	+	6.38959i	0.337751	+	0.245391i
$679$	−6.79950	+	7.55161i	−0.260941	+	0.289804i
$680$	−0.0924779	+	0.284618i	−0.00354637	+	0.0109146i
$681$	−21.6613			−0.830061
$682$	4.58247	+	7.85143i	0.175472	+	0.300647i
$683$	20.3631			0.779172			0.389586	−	0.920990i	$-0.372618\pi$
$683$	20.3631			0.779172			0.389586	+	0.920990i	$0.372618\pi$
$684$	1.80613	−	5.55869i	0.0690591	−	0.212542i
$685$	−2.15928	+	2.39813i	−0.0825020	+	0.0916277i
$686$	−16.3004	−	11.8429i	−0.622353	−	0.452166i
$687$	7.66316	−	13.2730i	0.292368	−	0.506396i
$688$	1.13803	+	1.97113i	0.0433870	+	0.0751486i
$689$	−2.46432	+	23.4465i	−0.0938833	+	0.893240i
$690$	−7.09945	+	5.15805i	−0.270271	+	0.196364i
$691$	2.46090	+	23.4139i	0.0936170	+	0.890706i	0.936041	+	0.351891i	$0.114461\pi$
$691$	2.46090	+	23.4139i	0.0936170	+	0.890706i	−0.842424	+	0.538815i	$0.818872\pi$
$692$	13.1573	+	14.6127i	0.500167	+	0.555492i
$693$	3.15294	−	1.40378i	0.119770	−	0.0533252i
$694$	14.1357	−	3.00463i	0.536583	−	0.114054i
$695$	−4.82450	−	1.02548i	−0.183004	−	0.0388986i
$696$	3.10114	+	1.38072i	0.117549	+	0.0523360i
$697$	−0.887140	−	2.73034i	−0.0336028	−	0.103419i
$698$	2.72546	+	8.38811i	0.103160	+	0.317495i
$699$	−4.99689	−	2.22476i	−0.189000	−	0.0841481i
$700$	−2.06760	−	0.439481i	−0.0781477	−	0.0166108i
$701$	−4.09886	+	0.871240i	−0.154812	+	0.0329063i	−0.284666	−	0.958627i	$-0.591883\pi$
$701$	−4.09886	+	0.871240i	−0.154812	+	0.0329063i	0.129854	+	0.991533i	$0.458549\pi$
$702$	3.02354	−	1.34617i	0.114116	−	0.0508078i
$703$	−13.1310	−	14.5834i	−0.495245	−	0.550025i
$704$	−0.170671	−	1.62382i	−0.00643240	−	0.0612002i
$705$	−9.53239	+	6.92568i	−0.359010	+	0.260836i
$706$	−1.38973	+	13.2224i	−0.0523031	+	0.497631i
$707$	6.77217	+	11.7297i	0.254694	+	0.441142i
$708$	0.803829	−	1.39227i	0.0302097	−	0.0523248i
$709$	15.5842	+	11.3226i	0.585277	+	0.425228i	0.840623	−	0.541621i	$-0.182189\pi$
$709$	15.5842	+	11.3226i	0.585277	+	0.425228i	−0.255346	+	0.966850i	$0.582189\pi$
$710$	−4.96887	+	5.51849i	−0.186478	+	0.207105i
$711$	−2.61929	+	8.06134i	−0.0982310	+	0.302324i
$712$	−16.7561			−0.627962
$713$	−24.2301	+	42.4281i	−0.907424	+	1.58894i
$714$	0.632582			0.0236738
$715$	1.66991	−	5.13946i	0.0624511	−	0.192205i
$716$	8.86604	−	9.84674i	0.331340	−	0.367990i
$717$	5.55745	+	4.03773i	0.207547	+	0.150792i
$718$	−12.0530	+	20.8764i	−0.449814	+	0.779101i
$719$	20.7820	+	35.9954i	0.775036	+	1.34240i	0.934774	+	0.355243i	$0.115602\pi$
$719$	20.7820	+	35.9954i	0.775036	+	1.34240i	−0.159738	+	0.987160i	$0.551065\pi$
$720$	−0.104528	+	0.994522i	−0.00389555	+	0.0370636i
$721$	−9.90053	+	7.19316i	−0.368715	+	0.267887i
$722$	1.58477	+	15.0781i	0.0589791	+	0.561149i
$723$	15.4972	+	17.2113i	0.576346	+	0.640097i
$724$	0.227064	−	0.101095i	0.00843877	−	0.00375718i
$725$	−3.32044	+	0.705782i	−0.123318	+	0.0262121i
$726$	8.15195	+	1.73275i	0.302547	+	0.0643084i
$727$	−34.7076	−	15.4528i	−1.28723	−	0.573114i	−0.354965	−	0.934879i	$-0.615507\pi$
$727$	−34.7076	−	15.4528i	−1.28723	−	0.573114i	−0.932269	+	0.361766i	$0.882174\pi$
$728$	−2.16187	−	6.65355i	−0.0801242	−	0.246597i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	5.59443	+	2.49080i	0.207059	+	0.0921887i
$731$	0.666261	+	0.141618i	0.0246426	+	0.00523794i
$732$	−3.91719	+	0.832625i	−0.144784	+	0.0307747i
$733$	−12.7950	+	5.69669i	−0.472593	+	0.210412i	−0.629192	−	0.777250i	$-0.716614\pi$
$733$	−12.7950	+	5.69669i	−0.472593	+	0.210412i	0.156598	+	0.987662i	$0.449947\pi$
$734$	−0.628136	−	0.697615i	−0.0231849	−	0.0257495i
$735$	−0.264656	−	2.51804i	−0.00976200	−	0.0928792i
$736$	7.09945	−	5.15805i	0.261689	−	0.190128i
$737$	−2.15318	+	20.4861i	−0.0793132	+	0.754615i
$738$	−4.79649	−	8.30777i	−0.176561	−	0.305813i
$739$	26.7061	−	46.2564i	0.982401	−	1.70157i	0.329441	−	0.944176i	$-0.393140\pi$
$739$	26.7061	−	46.2564i	0.982401	−	1.70157i	0.652960	−	0.757393i	$-0.273527\pi$
$740$	2.71630	+	1.97351i	0.0998532	+	0.0725476i
$741$	−12.9438	+	14.3756i	−0.475504	+	0.528101i
$742$	−4.65287	+	14.3201i	−0.170812	+	0.525706i
$743$	41.5574			1.52459			0.762297	−	0.647228i	$-0.224072\pi$
$743$	41.5574			1.52459			0.762297	+	0.647228i	$0.224072\pi$
$744$	1.74546	+	5.28710i	0.0639916	+	0.193834i
$745$	16.0577			0.588309
$746$	0.951337	−	2.92791i	0.0348309	−	0.107199i
$747$	−1.43988	+	1.59915i	−0.0526825	+	0.0585099i
$748$	−0.395310	−	0.287210i	−0.0144540	−	0.0105014i
$749$	−17.0084	+	29.4594i	−0.621472	+	1.07642i
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	−1.56016	+	14.8440i	−0.0569311	+	0.541664i	0.928469	+	0.371410i	$0.121125\pi$
$751$	−1.56016	+	14.8440i	−0.0569311	+	0.541664i	−0.985400	+	0.170254i	$0.945541\pi$
$752$	9.53239	−	6.92568i	0.347610	−	0.252554i
$753$	−2.21644	−	21.0880i	−0.0807716	−	0.768491i
$754$	−7.51776	−	8.34932i	−0.273781	−	0.304064i
$755$	−16.2775	+	7.24721i	−0.592399	+	0.263753i
$756$	2.06760	−	0.439481i	0.0751977	−	0.0159838i
$757$	−7.50347	−	1.59491i	−0.272718	−	0.0579681i	0.0695223	−	0.997580i	$-0.477852\pi$
$757$	−7.50347	−	1.59491i	−0.272718	−	0.0579681i	−0.342241	+	0.939612i	$0.611186\pi$
$758$	−24.1916	−	10.7708i	−0.878679	−	0.391213i
$759$	−4.42766	−	13.6269i	−0.160714	−	0.494626i
$760$	−1.80613	−	5.55869i	−0.0655152	−	0.201635i
$761$	21.9636	+	9.77881i	0.796179	+	0.354482i	0.764177	−	0.645006i	$-0.223145\pi$
$761$	21.9636	+	9.77881i	0.796179	+	0.354482i	0.0320013	+	0.999488i	$0.489812\pi$
$762$	3.54105	+	0.752673i	0.128279	+	0.0272665i
$763$	−15.0844	+	3.20628i	−0.546091	+	0.116075i
$764$	19.2896	−	8.58828i	0.697873	−	0.310713i
$765$	0.200247	+	0.222397i	0.00723996	+	0.00804079i
$766$	0.0999522	+	0.950981i	0.00361142	+	0.0343604i
$767$	−4.30464	+	3.12751i	−0.155432	+	0.112928i
$768$	0.104528	−	0.994522i	0.00377185	−	0.0358867i
$769$	11.0168	+	19.0817i	0.397277	+	0.688103i	0.993389	−	0.114798i	$-0.0366220\pi$
$769$	11.0168	+	19.0817i	0.397277	+	0.688103i	−0.596112	+	0.802901i	$0.703289\pi$
$770$	1.72566	−	2.98894i	0.0621886	−	0.107714i
$771$	9.00222	+	6.54049i	0.324207	+	0.235550i
$772$	10.8310	−	12.0290i	0.389816	−	0.432935i
$773$	−1.34900	+	4.15181i	−0.0485203	+	0.149330i	−0.972381	−	0.233398i	$-0.925015\pi$
$773$	−1.34900	+	4.15181i	−0.0485203	+	0.149330i	0.923861	+	0.382728i	$0.125015\pi$
$774$	2.27606			0.0818114
$775$	−4.51978	−	3.25140i	−0.162355	−	0.116794i
$776$	4.80734			0.172574
$777$	2.19313	−	6.74975i	0.0786780	−	0.242146i
$778$	−1.42021	+	1.57730i	−0.0509169	+	0.0565490i
$779$	45.3605	+	32.9563i	1.62521	+	1.18078i
$780$	1.65484	−	2.86627i	0.0592528	−	0.102629i
$781$	−6.06236	−	10.5003i	−0.216928	−	0.375731i
$782$	0.274509	−	2.61178i	0.00981644	−	0.0933972i
$783$	2.74631	−	1.99531i	0.0981450	−	0.0713065i
$784$	0.264656	+	2.51804i	0.00945201	+	0.0899299i
$785$	4.96501	+	5.51420i	0.177209	+	0.196810i
$786$	20.2399	−	9.01140i	0.721935	−	0.321426i
$787$	19.8975	−	4.22934i	0.709268	−	0.150760i	0.160868	−	0.986976i	$-0.448571\pi$
$787$	19.8975	−	4.22934i	0.709268	−	0.150760i	0.548400	+	0.836216i	$0.315237\pi$
$788$	13.4705	+	2.86325i	0.479868	+	0.101999i
$789$	20.8570	+	9.28612i	0.742527	+	0.330594i
$790$	2.61929	+	8.06134i	0.0931901	+	0.286810i
$791$	−7.10064	−	21.8535i	−0.252470	−	0.777022i
$792$	−1.49161	−	0.664107i	−0.0530020	−	0.0235980i
$793$	12.9647	+	2.75572i	0.460388	+	0.0978585i
$794$	36.4069	−	7.73852i	1.29203	−	0.274630i
$795$	−6.50740	+	2.89728i	−0.230794	+	0.102756i
$796$	7.20031	+	7.99675i	0.255208	+	0.283437i
$797$	−1.26373	−	12.0236i	−0.0447638	−	0.425899i	−0.993838	−	0.110845i	$-0.964644\pi$
$797$	−1.26373	−	12.0236i	−0.0447638	−	0.425899i	0.949074	−	0.315054i	$-0.102022\pi$
$798$	−9.99505	+	7.26183i	−0.353821	+	0.257066i
$799$	0.368582	−	3.50682i	0.0130395	−	0.124063i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	−8.37805	+	14.5112i	−0.296024	+	0.512729i
$802$	−1.19731	−	0.869899i	−0.0422786	−	0.0307172i
$803$	−6.69054	+	7.43060i	−0.236104	+	0.262220i
$804$	−3.89854	+	11.9985i	−0.137491	+	0.423154i
$805$	18.5493			0.653778
$806$	1.83985	−	18.3354i	0.0648060	−	0.645838i
$807$	−8.18718			−0.288202
$808$	1.98006	−	6.09401i	0.0696584	−	0.214386i
$809$	23.6104	−	26.2220i	0.830098	−	0.921918i	−0.167858	−	0.985811i	$-0.553685\pi$
$809$	23.6104	−	26.2220i	0.830098	−	0.921918i	0.997957	+	0.0638934i	$0.0203518\pi$
$810$	0.809017	+	0.587785i	0.0284260	+	0.0206527i
$811$	−27.2930	+	47.2728i	−0.958386	+	1.65997i	−0.231964	+	0.972724i	$0.574515\pi$
$811$	−27.2930	+	47.2728i	−0.958386	+	1.65997i	−0.726422	+	0.687249i	$0.758818\pi$
$812$	−3.58775	−	6.21417i	−0.125905	−	0.218075i
$813$	−1.06725	+	10.1542i	−0.0374302	+	0.356125i
$814$	−4.43509	+	3.22228i	−0.155450	+	0.112941i
$815$	−2.11781	−	20.1496i	−0.0741837	−	0.705811i
$816$	−0.200247	−	0.222397i	−0.00701006	−	0.00778546i
$817$	−12.1529	+	5.41083i	−0.425177	+	0.189301i
$818$	−2.63160	+	0.559364i	−0.0920118	+	0.0195577i
$819$	−6.84308	−	1.45454i	−0.239117	−	0.0508258i
$820$	−8.76363	−	3.90182i	−0.306039	−	0.136257i
$821$	−12.2029	−	37.5567i	−0.425885	−	1.31074i	−0.902144	−	0.431434i	$-0.858008\pi$
$821$	−12.2029	−	37.5567i	−0.425885	−	1.31074i	0.476260	−	0.879305i	$-0.341992\pi$
$822$	−0.997197	−	3.06906i	−0.0347812	−	0.107046i
$823$	−33.9085	−	15.0970i	−1.18198	−	0.526249i	−0.280826	−	0.959759i	$-0.590608\pi$
$823$	−33.9085	−	15.0970i	−1.18198	−	0.526249i	−0.901149	+	0.433509i	$0.857275\pi$
$824$	5.66297	+	1.20370i	0.197279	+	0.0419329i
$825$	1.59709	−	0.339472i	0.0556035	−	0.0118189i
$826$	−3.10445	+	1.38219i	−0.108018	+	0.0480926i
$827$	−34.7998	−	38.6491i	−1.21011	−	1.34396i	−0.922397	−	0.386243i	$-0.873773\pi$
$827$	−34.7998	−	38.6491i	−1.21011	−	1.34396i	−0.287710	−	0.957718i	$-0.592894\pi$
$828$	−0.917279	−	8.72733i	−0.0318777	−	0.303296i
$829$	−12.8051	+	9.30345i	−0.444740	+	0.323122i	−0.787515	−	0.616295i	$-0.788633\pi$
$829$	−12.8051	+	9.30345i	−0.444740	+	0.323122i	0.342776	+	0.939417i	$0.388633\pi$
$830$	−0.224932	+	2.14008i	−0.00780749	+	0.0742833i
$831$	−7.46606	−	12.9316i	−0.258995	−	0.448592i
$832$	−1.65484	+	2.86627i	−0.0573713	+	0.0993699i
$833$	0.613001	+	0.445371i	0.0212392	+	0.0154312i
$834$	3.30034	−	3.66540i	0.114281	−	0.126922i
$835$	−6.41811	+	19.7529i	−0.222108	+	0.683578i
$836$	9.54314			0.330056
$837$	5.45149	+	1.13194i	0.188431	+	0.0391255i
$838$	−11.7536			−0.406022
$839$	−0.629256	+	1.93665i	−0.0217243	+	0.0668606i	−0.961331	−	0.275396i	$-0.911191\pi$
$839$	−0.629256	+	1.93665i	−0.0217243	+	0.0668606i	0.939607	+	0.342256i	$0.111191\pi$
$840$	1.41440	−	1.57085i	0.0488014	−	0.0541995i
$841$	14.1388	+	10.2724i	0.487545	+	0.354222i
$842$	−6.72039	+	11.6400i	−0.231600	+	0.401143i
$843$	−8.45626	−	14.6467i	−0.291249	−	0.504458i
$844$	−0.0894795	+	0.851340i	−0.00308001	+	0.0293043i
$845$	1.65526	−	1.20262i	0.0569428	−	0.0413713i
$846$	−1.23163	−	11.7181i	−0.0423441	−	0.402878i
$847$	−11.7877	−	13.0916i	−0.405030	−	0.449831i
$848$	6.50740	−	2.89728i	0.223465	−	0.0994930i
$849$	0.144171	−	0.0306445i	0.00494794	−	0.00105172i
$850$	0.292725	+	0.0622207i	0.0100404	+	0.00213415i
$851$	−26.9164	−	11.9840i	−0.922683	−	0.410805i
$852$	−2.29472	−	7.06242i	−0.0786157	−	0.241954i
$853$	5.96511	+	18.3587i	0.204241	+	0.628590i	0.999744	+	0.0226397i	$0.00720705\pi$
$853$	5.96511	+	18.3587i	0.204241	+	0.628590i	−0.795502	+	0.605950i	$0.792793\pi$
$854$	7.73324	+	3.44306i	0.264626	+	0.117819i
$855$	−5.71703	−	1.21519i	−0.195518	−	0.0415587i
$856$	15.7411	−	3.34588i	0.538021	−	0.114360i
$857$	−25.7205	+	11.4515i	−0.878597	+	0.391177i	−0.795921	−	0.605400i	$-0.793013\pi$
$857$	−25.7205	+	11.4515i	−0.878597	+	0.391177i	−0.0826755	+	0.996577i	$0.526347\pi$
$858$	3.61594	+	4.01591i	0.123446	+	0.137101i
$859$	5.02764	+	47.8348i	0.171541	+	1.63210i	0.654219	+	0.756305i	$0.272997\pi$
$859$	5.02764	+	47.8348i	0.171541	+	1.63210i	−0.482678	+	0.875798i	$0.660336\pi$
$860$	1.84137	−	1.33784i	0.0627903	−	0.0456198i
$861$	−2.11958	+	20.1664i	−0.0722350	+	0.687271i
$862$	−1.82785	−	3.16592i	−0.0622567	−	0.107832i
$863$	6.30310	−	10.9173i	0.214560	−	0.371629i	−0.738576	−	0.674170i	$-0.764502\pi$
$863$	6.30310	−	10.9173i	0.214560	−	0.371629i	0.953136	+	0.302541i	$0.0978349\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$	13.1573	−	14.6127i	0.447363	−	0.496847i
$866$	−2.37228	+	7.30114i	−0.0806134	+	0.248103i
$867$	16.9104			0.574309
$868$	3.58408	−	11.2101i	0.121651	−	0.380494i
$869$	−13.8397			−0.469479
$870$	1.04900	−	3.22848i	0.0355643	−	0.109456i
$871$	27.9394	−	31.0298i	0.946690	−	1.05141i
$872$	5.90227	+	4.28825i	0.199876	+	0.145219i
$873$	2.40367	−	4.16328i	0.0813520	−	0.140906i
$874$	25.6450	+	44.4185i	0.867456	+	1.50248i
$875$	−0.220951	+	2.10221i	−0.00746950	+	0.0710676i
$876$	−4.95431	+	3.59952i	−0.167391	+	0.121616i
$877$	5.23690	+	49.8258i	0.176837	+	1.68250i	0.618867	+	0.785496i	$0.287592\pi$
$877$	5.23690	+	49.8258i	0.176837	+	1.68250i	−0.442030	+	0.897000i	$0.645741\pi$
$878$	22.7767	+	25.2961i	0.768677	+	0.853702i
$879$	6.51129	−	2.89901i	0.219620	−	0.0977813i
$880$	−1.59709	+	0.339472i	−0.0538379	+	0.0114436i
$881$	6.97862	+	1.48335i	0.235116	+	0.0499754i	0.323963	−	0.946070i	$-0.394985\pi$
$881$	6.97862	+	1.48335i	0.235116	+	0.0499754i	−0.0888468	+	0.996045i	$0.528318\pi$
$882$	2.31301	+	1.02982i	0.0778832	+	0.0346758i
$883$	11.0803	+	34.1015i	0.372880	+	1.14761i	0.944898	+	0.327366i	$0.106161\pi$
$883$	11.0803	+	34.1015i	0.372880	+	1.14761i	−0.572018	+	0.820241i	$0.693839\pi$
$884$	0.306072	+	0.941994i	0.0102943	+	0.0316827i
$885$	−1.46867	−	0.653893i	−0.0493688	−	0.0219804i
$886$	6.79505	+	1.44433i	0.228284	+	0.0485233i
$887$	−17.0656	+	3.62740i	−0.573006	+	0.121796i	−0.485296	−	0.874350i	$-0.661288\pi$
$887$	−17.0656	+	3.62740i	−0.573006	+	0.121796i	−0.0877101	+	0.996146i	$0.527955\pi$
$888$	−3.06726	+	1.36563i	−0.102930	+	0.0458276i
$889$	−5.12035	−	5.68673i	−0.171731	−	0.190727i
$890$	1.75149	+	16.6643i	0.0587101	+	0.558589i
$891$	−1.32094	+	0.959718i	−0.0442531	+	0.0321518i
$892$	−0.218105	+	2.07513i	−0.00730268	+	0.0694804i
$893$	34.4334	+	59.6404i	1.15227	+	1.99579i
$894$	−8.02886	+	13.9064i	−0.268525	+	0.465099i
$895$	−10.7195	−	7.78821i	−0.358315	−	0.260331i
$896$	−1.41440	+	1.57085i	−0.0472518	+	0.0524784i
$897$	−8.97502	+	27.6223i	−0.299667	+	0.922281i
$898$	13.1559			0.439019
$899$	−2.06416	−	18.7874i	−0.0688435	−	0.626595i
$900$	1.00000			0.0333333
$901$	0.658742	−	2.02740i	0.0219459	−	0.0675425i
$902$	10.4807	−	11.6400i	0.348969	−	0.387569i
$903$	−3.89227	−	2.82790i	−0.129527	−	0.0941066i
$904$	−5.43531	+	9.41423i	−0.180776	+	0.313112i
$905$	−0.124276	−	0.215253i	−0.00413108	−	0.00715525i
$906$	1.86248	−	17.7203i	0.0618768	−	0.588719i
$907$	−5.85850	+	4.25645i	−0.194528	+	0.141333i	−0.680786	−	0.732482i	$-0.738362\pi$
$907$	−5.85850	+	4.25645i	−0.194528	+	0.141333i	0.486258	+	0.873815i	$0.338362\pi$
$908$	−2.26422	−	21.5426i	−0.0751407	−	0.714916i
$909$	−4.28753	−	4.76179i	−0.142208	−	0.157939i
$910$	−6.39112	+	2.84551i	−0.211864	+	0.0943278i
$911$	−38.6265	+	8.21031i	−1.27975	+	0.272020i	−0.797130	−	0.603808i	$-0.793649\pi$
$911$	−38.6265	+	8.21031i	−1.27975	+	0.272020i	−0.482623	+	0.875828i	$0.660316\pi$
$912$	5.71703	+	1.21519i	0.189310	+	0.0402391i
$913$	−3.20975	−	1.42907i	−0.106227	−	0.0472954i
$914$	−8.86102	−	27.2714i	−0.293097	−	0.902059i
$915$	1.23752	+	3.80870i	0.0409112	+	0.125912i
$916$	14.0013	+	6.23378i	0.462616	+	0.205970i
$917$	−45.8083	−	9.73686i	−1.51272	−	0.321539i
$918$	−0.292725	+	0.0622207i	−0.00966137	+	0.00205359i
$919$	−43.5901	+	19.4076i	−1.43790	+	0.640197i	−0.969894	−	0.243526i	$-0.921696\pi$
$919$	−43.5901	+	19.4076i	−1.43790	+	0.640197i	−0.468011	+	0.883723i	$0.655029\pi$
$920$	−5.87189	−	6.52139i	−0.193590	−	0.215004i
$921$	−2.33116	−	22.1795i	−0.0768143	−	0.730839i
$922$	−30.3088	+	22.0206i	−0.998166	+	0.725210i
$923$	−2.56902	+	24.4426i	−0.0845603	+	0.804538i
$924$	1.72566	+	2.98894i	0.0567701	+	0.0983288i
$925$	1.67877	−	2.90771i	0.0551975	−	0.0956049i
$926$	11.2966	+	8.20743i	0.371228	+	0.269713i
$927$	3.87392	−	4.30242i	0.127236	−	0.141310i
$928$	−1.04900	+	3.22848i	−0.0344350	+	0.105980i
$929$	−5.26567			−0.172761			−0.0863804	−	0.996262i	$-0.527530\pi$
$929$	−5.26567			−0.172761			−0.0863804	+	0.996262i	$0.527530\pi$
$930$	5.07568	−	2.28855i	0.166438	−	0.0750444i
$931$	−14.7984			−0.484997
$932$	1.69025	−	5.20206i	0.0553661	−	0.170399i
$933$	−5.07040	+	5.63125i	−0.165998	+	0.184359i
$934$	17.2762	+	12.5519i	0.565293	+	0.410710i
$935$	−0.244315	+	0.423166i	−0.00798996	+	0.0138390i
$936$	1.65484	+	2.86627i	0.0540901	+	0.0936869i
$937$	−4.40946	+	41.9532i	−0.144051	+	1.37055i	0.648719	+	0.761028i	$0.275305\pi$
$937$	−4.40946	+	41.9532i	−0.144051	+	1.37055i	−0.792769	+	0.609522i	$0.791361\pi$
$938$	21.5744	−	15.6747i	0.704429	−	0.511798i
$939$	2.55945	+	24.3516i	0.0835247	+	0.794684i
$940$	−7.88415	−	8.75624i	−0.257153	−	0.285597i
$941$	10.4044	−	4.63235i	0.339175	−	0.151010i	−0.230080	−	0.973172i	$-0.573899\pi$
$941$	10.4044	−	4.63235i	0.339175	−	0.151010i	0.569254	+	0.822162i	$0.307232\pi$
$942$	−7.25794	+	1.54272i	−0.236477	+	0.0502647i
$943$	82.3427	+	17.5025i	2.68145	+	0.569959i
$944$	1.46867	+	0.653893i	0.0478011	+	0.0212824i
$945$	−0.653196	−	2.01033i	−0.0212485	−	0.0653960i
$946$	1.14840	+	3.53440i	0.0373376	+	0.114913i
$947$	−31.5354	−	14.0404i	−1.02476	−	0.456253i	−0.175642	−	0.984454i	$-0.556200\pi$
$947$	−31.5354	−	14.0404i	−1.02476	−	0.456253i	−0.849119	+	0.528201i	$0.822867\pi$
$948$	−8.29097	−	1.76230i	−0.269278	−	0.0572369i
$949$	19.8251	−	4.21396i	0.643551	−	0.136791i
$950$	−5.33945	+	2.37728i	−0.173235	+	0.0771290i
$951$	−12.3929	−	13.7637i	−0.401866	−	0.446317i
$952$	0.0661228	+	0.629117i	0.00214305	+	0.0203898i
$953$	−8.64486	+	6.28086i	−0.280035	+	0.203457i	−0.718932	−	0.695080i	$-0.755369\pi$
$953$	−8.64486	+	6.28086i	−0.280035	+	0.203457i	0.438898	+	0.898537i	$0.355369\pi$
$954$	0.744581	−	7.08421i	0.0241067	−	0.229360i
$955$	−10.5575	−	18.2862i	−0.341634	−	0.591728i
$956$	−3.43469	+	5.94907i	−0.111086	+	0.192407i
$957$	4.48409	+	3.25788i	0.144950	+	0.105312i
$958$	−3.62350	+	4.02431i	−0.117070	+	0.130019i
$959$	−2.10786	+	6.48733i	−0.0680664	+	0.209487i
$960$	−1.00000			−0.0322749
$961$	20.5251	−	23.2319i	0.662100	−	0.749416i
$962$	11.1124			0.358277
$963$	4.97295	−	15.3052i	0.160251	−	0.493202i
$964$	−15.4972	+	17.2113i	−0.499130	+	0.554340i
$965$	−13.0953	−	9.51429i	−0.421553	−	0.306276i
$966$	−9.27466	+	16.0642i	−0.298407	+	0.516857i
$967$	−6.59631	−	11.4251i	−0.212123	−	0.367408i	0.740256	−	0.672325i	$-0.234704\pi$
$967$	−6.59631	−	11.4251i	−0.212123	−	0.367408i	−0.952379	+	0.304918i	$0.901371\pi$
$968$	−0.871147	+	8.28841i	−0.0279997	+	0.266400i
$969$	1.41508	−	1.02811i	0.0454588	−	0.0330277i
$970$	−0.502504	−	4.78101i	−0.0161344	−	0.153509i
$971$	−0.0730887	−	0.0811733i	−0.00234553	−	0.00260497i	0.741971	−	0.670432i	$-0.233891\pi$
$971$	−0.0730887	−	0.0811733i	−0.00234553	−	0.00260497i	−0.744316	+	0.667827i	$0.767225\pi$
$972$	−0.913545	+	0.406737i	−0.0293020	+	0.0130461i
$973$	−10.1980	+	2.16764i	−0.326932	+	0.0694915i
$974$	−18.0418	−	3.83490i	−0.578097	−	0.122878i
$975$	−3.02354	−	1.34617i	−0.0968309	−	0.0431119i
$976$	−1.23752	−	3.80870i	−0.0396121	−	0.121913i
$977$	−8.74692	−	26.9202i	−0.279839	−	0.861255i	−0.987898	−	0.155102i	$-0.950429\pi$
$977$	−8.74692	−	26.9202i	−0.279839	−	0.861255i	0.708060	−	0.706153i	$-0.249571\pi$
$978$	18.5090	+	8.24074i	0.591853	+	0.263510i
$979$	−26.7610	−	5.68823i	−0.855285	−	0.181796i
$980$	2.47658	−	0.526413i	0.0791114	−	0.0168157i
$981$	6.66487	−	2.96739i	0.212793	−	0.0947416i
$982$	−9.67596	−	10.7462i	−0.308772	−	0.342926i
$983$	−0.596084	−	5.67136i	−0.0190121	−	0.180888i	0.980895	−	0.194539i	$-0.0623212\pi$
$983$	−0.596084	−	5.67136i	−0.0190121	−	0.180888i	−0.999907	+	0.0136511i	$0.995655\pi$
$984$	7.76089	−	5.63862i	0.247408	−	0.179753i
$985$	1.43951	−	13.6960i	0.0458666	−	0.436392i
$986$	0.507946	+	0.879788i	0.0161763	+	0.0280182i
$987$	−12.4530	+	21.5693i	−0.396384	+	0.686558i
$988$	−15.6498	−	11.3703i	−0.497888	−	0.361737i
$989$	−13.3648	+	14.8431i	−0.424976	+	0.471983i
$990$	−0.504553	+	1.55286i	−0.0160358	+	0.0493530i
$991$	20.8897			0.663584			0.331792	−	0.943353i	$-0.392347\pi$
$991$	20.8897			0.663584			0.331792	+	0.943353i	$0.392347\pi$
$992$	−5.07568	+	2.28855i	−0.161153	+	0.0726615i
$993$	16.0338			0.508816
$994$	−4.85054	+	14.9284i	−0.153850	+	0.473501i
$995$	7.20031	−	7.99675i	0.228265	−	0.253514i
$996$	−1.74090	−	1.26484i	−0.0551625	−	0.0400779i
$997$	1.61027	−	2.78906i	0.0509977	−	0.0883305i	−0.839400	−	0.543515i	$-0.817093\pi$
$997$	1.61027	−	2.78906i	0.0509977	−	0.0883305i	0.890397	+	0.455184i	$0.150427\pi$
$998$	3.25246	+	5.63342i	0.102955	+	0.178323i
$999$	−0.350958	+	3.33914i	−0.0111038	+	0.105646i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.h.541.1	yes	24
31.20	even	15	inner	930.2.bg.h.361.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.h.361.1	✓	24	31.20	even	15	inner
930.2.bg.h.541.1	yes	24	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.220951 + 2.10221i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(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} +(-0.220951 + 2.10221i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-0.669131 - 0.743145i) q^{10} +(1.49161 - 0.664107i) q^{11} +(0.978148 - 0.207912i) q^{12} +(-3.23736 - 0.688121i) q^{13} +(-1.93104 - 0.859754i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.273392 + 0.121722i) q^{17} +(0.978148 + 0.207912i) q^{18} +(-5.71703 + 1.21519i) q^{19} +(0.913545 - 0.406737i) q^{20} +(-1.41440 - 1.57085i) q^{21} +(0.170671 + 1.62382i) q^{22} +(-7.09945 + 5.15805i) q^{23} +(-0.104528 + 0.994522i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.65484 - 2.86627i) q^{26} +(0.809017 + 0.587785i) q^{27} +(1.41440 - 1.57085i) q^{28} +(1.04900 - 3.22848i) q^{29} +1.00000 q^{30} +(5.07568 - 2.28855i) q^{31} -1.00000 q^{32} +(-0.504553 + 1.55286i) q^{33} +(-0.200247 + 0.222397i) q^{34} +(-1.71009 - 1.24245i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.67877 + 2.90771i) q^{37} +(0.610943 - 5.81274i) q^{38} +(2.67759 - 1.94538i) q^{39} +(0.104528 + 0.994522i) q^{40} +(-6.41896 - 7.12898i) q^{41} +(1.93104 - 0.859754i) q^{42} +(2.22633 - 0.473220i) q^{43} +(-1.59709 - 0.339472i) q^{44} +(0.913545 + 0.406737i) q^{45} +(-2.71175 - 8.34590i) q^{46} +(-3.64105 - 11.2060i) q^{47} +(-0.913545 - 0.406737i) q^{48} +(2.47658 + 0.526413i) q^{49} +(0.978148 - 0.207912i) q^{50} +(-0.273392 + 0.121722i) q^{51} +(2.21461 + 2.45957i) q^{52} +(-0.744581 - 7.08421i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(-0.170671 + 1.62382i) q^{55} +(1.05689 + 1.83059i) q^{56} +(2.92238 - 5.06171i) q^{57} +(2.74631 + 1.99531i) q^{58} +(1.07573 - 1.19472i) q^{59} +(-0.309017 + 0.951057i) q^{60} -4.00470 q^{61} +(0.608066 + 5.53446i) q^{62} +2.11379 q^{63} +(0.309017 - 0.951057i) q^{64} +(2.21461 - 2.45957i) q^{65} +(-1.32094 - 0.959718i) q^{66} +(-6.30798 + 10.9257i) q^{67} +(-0.149632 - 0.259171i) q^{68} +(0.917279 - 8.72733i) q^{69} +(1.71009 - 1.24245i) q^{70} +(-0.776214 - 7.38518i) q^{71} +(-0.669131 - 0.743145i) q^{72} +(-5.59443 + 2.49080i) q^{73} +(-3.28416 + 0.698070i) q^{74} +(0.978148 + 0.207912i) q^{75} +(5.33945 + 2.37728i) q^{76} +(1.06652 + 3.28241i) q^{77} +(1.02275 + 3.14769i) q^{78} +(-7.74339 - 3.44758i) q^{79} +(-0.978148 - 0.207912i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(8.76363 - 3.90182i) q^{82} +(-1.43988 - 1.59915i) q^{83} +(0.220951 + 2.10221i) q^{84} +(-0.242110 + 0.175903i) q^{85} +(-0.237913 + 2.26359i) q^{86} +(1.69731 + 2.93983i) q^{87} +(0.816385 - 1.41402i) q^{88} +(-13.5560 - 9.84899i) q^{89} +(-0.669131 + 0.743145i) q^{90} +(2.16187 - 6.65355i) q^{91} +8.77540 q^{92} +(-1.69557 + 5.30330i) q^{93} +11.7827 q^{94} +(1.80613 - 5.55869i) q^{95} +(0.669131 - 0.743145i) q^{96} +(3.88922 + 2.82569i) q^{97} +(-1.26595 + 2.19270i) q^{98} +(-0.816385 - 1.41402i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 - 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 11 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9} - 3 q^{10} - 5 q^{11} - 3 q^{12} - 13 q^{13} - 4 q^{14} + 6 q^{15} - 6 q^{16} + 31 q^{17} - 3 q^{18} - 3 q^{19} + 3 q^{20} - 4 q^{21} + 5 q^{22} - 9 q^{23} + 3 q^{24} - 12 q^{25} + 3 q^{26} + 6 q^{27} + 4 q^{28} + 11 q^{29} + 24 q^{30} + 17 q^{31} - 24 q^{32} + 10 q^{33} + 9 q^{34} + 7 q^{35} - 12 q^{36} + 8 q^{37} - 2 q^{38} - q^{39} - 3 q^{40} + 12 q^{41} + 4 q^{42} - 7 q^{43} - 10 q^{44} + 3 q^{45} - 6 q^{46} - 46 q^{47} - 3 q^{48} + 20 q^{49} - 3 q^{50} - 31 q^{51} + 17 q^{52} + 48 q^{53} - 6 q^{54} - 5 q^{55} + q^{56} - 2 q^{57} + 14 q^{58} + 12 q^{59} + 6 q^{60} - 4 q^{61} + 13 q^{62} + 2 q^{63} - 6 q^{64} + 17 q^{65} + 10 q^{66} - 33 q^{67} + q^{68} - 12 q^{69} - 7 q^{70} - 35 q^{71} - 3 q^{72} + 19 q^{73} + 7 q^{74} - 3 q^{75} + 2 q^{76} + 26 q^{77} - 4 q^{78} - 12 q^{79} + 3 q^{80} + 3 q^{81} - 12 q^{82} + 11 q^{84} - 2 q^{85} - 48 q^{86} + 3 q^{87} + 21 q^{89} - 3 q^{90} + 72 q^{91} + 6 q^{92} + 19 q^{93} - 14 q^{94} + 6 q^{95} + 3 q^{96} - 35 q^{97} - 5 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 - 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 11 * q^7 + 6 * q^8 + 3 * q^9 - 3 * q^10 - 5 * q^11 - 3 * q^12 - 13 * q^13 - 4 * q^14 + 6 * q^15 - 6 * q^16 + 31 * q^17 - 3 * q^18 - 3 * q^19 + 3 * q^20 - 4 * q^21 + 5 * q^22 - 9 * q^23 + 3 * q^24 - 12 * q^25 + 3 * q^26 + 6 * q^27 + 4 * q^28 + 11 * q^29 + 24 * q^30 + 17 * q^31 - 24 * q^32 + 10 * q^33 + 9 * q^34 + 7 * q^35 - 12 * q^36 + 8 * q^37 - 2 * q^38 - q^39 - 3 * q^40 + 12 * q^41 + 4 * q^42 - 7 * q^43 - 10 * q^44 + 3 * q^45 - 6 * q^46 - 46 * q^47 - 3 * q^48 + 20 * q^49 - 3 * q^50 - 31 * q^51 + 17 * q^52 + 48 * q^53 - 6 * q^54 - 5 * q^55 + q^56 - 2 * q^57 + 14 * q^58 + 12 * q^59 + 6 * q^60 - 4 * q^61 + 13 * q^62 + 2 * q^63 - 6 * q^64 + 17 * q^65 + 10 * q^66 - 33 * q^67 + q^68 - 12 * q^69 - 7 * q^70 - 35 * q^71 - 3 * q^72 + 19 * q^73 + 7 * q^74 - 3 * q^75 + 2 * q^76 + 26 * q^77 - 4 * q^78 - 12 * q^79 + 3 * q^80 + 3 * q^81 - 12 * q^82 + 11 * q^84 - 2 * q^85 - 48 * q^86 + 3 * q^87 + 21 * q^89 - 3 * q^90 + 72 * q^91 + 6 * q^92 + 19 * q^93 - 14 * q^94 + 6 * q^95 + 3 * q^96 - 35 * q^97 - 5 * q^98

Introduction

L-functions

Modular forms

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