LMFDB - Embedded newform 930.2.bg.h.121.2

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			121.2
Character	$\chi$	$=$	930.121
Dual form			930.2.bg.h.661.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.105382 - 0.0223997i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.105382 - 0.0223997i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(0.104528 + 0.994522i) q^{10} +(-3.84073 - 4.26556i) q^{11} +(-0.913545 - 0.406737i) q^{12} +(-0.151670 + 0.0675279i) q^{13} +(0.0720898 - 0.0800638i) q^{14} +(0.809017 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.0892976 - 0.0991750i) q^{17} +(-0.913545 + 0.406737i) q^{18} +(-5.58092 - 2.48479i) q^{19} +(0.669131 + 0.743145i) q^{20} +(-0.0112615 - 0.107146i) q^{21} +(-5.61444 - 1.19339i) q^{22} +(-1.59265 - 4.90166i) q^{23} +(-0.978148 + 0.207912i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.0830118 + 0.143781i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(0.0112615 - 0.107146i) q^{28} +(7.01739 - 5.09843i) q^{29} +1.00000 q^{30} +(4.39167 + 3.42246i) q^{31} -1.00000 q^{32} +(-4.64366 + 3.37381i) q^{33} +(0.0139497 - 0.132722i) q^{34} +(-0.0332924 + 0.102463i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.52412 + 2.63985i) q^{37} +(-5.97558 + 1.27015i) q^{38} +(0.0513041 + 0.157898i) q^{39} +(0.978148 + 0.207912i) q^{40} +(-0.710548 - 6.76041i) q^{41} +(-0.0720898 - 0.0800638i) q^{42} +(-7.82456 - 3.48372i) q^{43} +(-5.24364 + 2.33462i) q^{44} +(0.669131 - 0.743145i) q^{45} +(-4.16960 - 3.02939i) q^{46} +(-4.13220 - 3.00222i) q^{47} +(-0.669131 + 0.743145i) q^{48} +(-6.38421 + 2.84244i) q^{49} +(-0.913545 - 0.406737i) q^{50} +(-0.0892976 - 0.0991750i) q^{51} +(0.0173542 + 0.165114i) q^{52} +(11.1032 + 2.36005i) q^{53} +(0.309017 + 0.951057i) q^{54} +(5.61444 - 1.19339i) q^{55} +(-0.0538682 - 0.0933025i) q^{56} +(-3.05454 + 5.29062i) q^{57} +(2.68041 - 8.24944i) q^{58} +(-0.841758 + 8.00880i) q^{59} +(0.809017 - 0.587785i) q^{60} +8.18357 q^{61} +(5.56461 + 0.187469i) q^{62} -0.107736 q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.0173542 - 0.165114i) q^{65} +(-1.77372 + 5.45894i) q^{66} +(5.05897 - 8.76240i) q^{67} +(-0.0667266 - 0.115574i) q^{68} +(-5.04129 + 1.07156i) q^{69} +(0.0332924 + 0.102463i) q^{70} +(-1.10408 - 0.234680i) q^{71} +(0.104528 + 0.994522i) q^{72} +(2.62954 + 2.92040i) q^{73} +(2.78470 + 1.23983i) q^{74} +(-0.913545 + 0.406737i) q^{75} +(-4.08777 + 4.53993i) q^{76} +(-0.500291 - 0.363483i) q^{77} +(0.134316 + 0.0975862i) q^{78} +(-10.3013 + 11.4408i) q^{79} +(0.913545 - 0.406737i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-4.54852 - 5.05164i) q^{82} +(1.24301 + 11.8264i) q^{83} +(-0.105382 - 0.0223997i) q^{84} +(0.0412393 + 0.126922i) q^{85} +(-8.37788 + 1.78077i) q^{86} +(-4.33699 - 7.51188i) q^{87} +(-2.86994 + 4.97088i) q^{88} +(-1.03589 + 3.18814i) q^{89} +(0.104528 - 0.994522i) q^{90} +(-0.0144707 + 0.0105136i) q^{91} -5.15391 q^{92} +(3.86277 - 4.00987i) q^{93} -5.10768 q^{94} +(4.94235 - 3.59083i) q^{95} +(-0.104528 + 0.994522i) q^{96} +(1.82085 - 5.60400i) q^{97} +(-3.49420 + 6.05213i) q^{98} +(2.86994 + 4.97088i) 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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{15}\right)$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.104528	−	0.994522i	0.0603495	−	0.574187i
$3$	0.104528	−	0.994522i	0.0603495	−	0.574187i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−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
$7$	0.105382	−	0.0223997i	0.0398307	−	0.00846628i	−0.187953	−	0.982178i	$-0.560185\pi$
$7$	0.105382	−	0.0223997i	0.0398307	−	0.00846628i	0.227784	+	0.973712i	$0.426852\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−0.978148	−	0.207912i	−0.326049	−	0.0693039i
$10$	0.104528	+	0.994522i	0.0330548	+	0.314495i
$11$	−3.84073	−	4.26556i	−1.15802	−	1.28611i	−0.951492	−	0.307674i	$-0.900449\pi$
$11$	−3.84073	−	4.26556i	−1.15802	−	1.28611i	−0.206530	−	0.978440i	$-0.566217\pi$
$12$	−0.913545	−	0.406737i	−0.263718	−	0.117415i
$13$	−0.151670	+	0.0675279i	−0.0420657	+	0.0187289i	−0.427662	−	0.903939i	$-0.640663\pi$
$13$	−0.151670	+	0.0675279i	−0.0420657	+	0.0187289i	0.385596	+	0.922668i	$0.373996\pi$
$14$	0.0720898	−	0.0800638i	0.0192668	−	0.0213979i
$15$	0.809017	+	0.587785i	0.208887	+	0.151765i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	0.0892976	−	0.0991750i	0.0216578	−	0.0240535i	−0.732219	−	0.681070i	$-0.761515\pi$
$17$	0.0892976	−	0.0991750i	0.0216578	−	0.0240535i	0.753876	+	0.657016i	$0.228182\pi$
$18$	−0.913545	+	0.406737i	−0.215325	+	0.0958687i
$19$	−5.58092	−	2.48479i	−1.28035	−	0.570049i	−0.350011	−	0.936746i	$-0.613822\pi$
$19$	−5.58092	−	2.48479i	−1.28035	−	0.570049i	−0.930341	+	0.366697i	$0.880489\pi$
$20$	0.669131	+	0.743145i	0.149622	+	0.166172i
$21$	−0.0112615	−	0.107146i	−0.00245747	−	0.0233812i
$22$	−5.61444	−	1.19339i	−1.19700	−	0.254431i
$23$	−1.59265	−	4.90166i	−0.332090	−	1.02207i	−0.968138	−	0.250418i	$-0.919432\pi$
$23$	−1.59265	−	4.90166i	−0.332090	−	1.02207i	0.636048	−	0.771650i	$-0.280568\pi$
$24$	−0.978148	+	0.207912i	−0.199664	+	0.0424398i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.0830118	+	0.143781i	−0.0162799	+	0.0281977i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	0.0112615	−	0.107146i	0.00212823	−	0.0202487i
$29$	7.01739	−	5.09843i	1.30310	−	0.946756i	0.303116	−	0.952954i	$-0.401973\pi$
$29$	7.01739	−	5.09843i	1.30310	−	0.946756i	0.999981	+	0.00619803i	$0.00197291\pi$
$30$	1.00000			0.182574
$31$	4.39167	+	3.42246i	0.788767	+	0.614692i
$31$	4.39167	+	3.42246i	0.788767	+	0.614692i
$32$	−1.00000			−0.176777
$33$	−4.64366	+	3.37381i	−0.808357	+	0.587305i
$34$	0.0139497	−	0.132722i	0.00239235	−	0.0227617i
$35$	−0.0332924	+	0.102463i	−0.00562744	+	0.0173195i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	1.52412	+	2.63985i	0.250563	+	0.433988i	0.963681	−	0.267056i	$-0.0860509\pi$
$37$	1.52412	+	2.63985i	0.250563	+	0.433988i	−0.713118	+	0.701044i	$0.752718\pi$
$38$	−5.97558	+	1.27015i	−0.969367	+	0.206045i
$39$	0.0513041	+	0.157898i	0.00821523	+	0.0252839i
$40$	0.978148	+	0.207912i	0.154659	+	0.0328737i
$41$	−0.710548	−	6.76041i	−0.110969	−	1.05580i	−0.898334	−	0.439313i	$-0.855222\pi$
$41$	−0.710548	−	6.76041i	−0.110969	−	1.05580i	0.787365	−	0.616487i	$-0.211445\pi$
$42$	−0.0720898	−	0.0800638i	−0.0111237	−	0.0123541i
$43$	−7.82456	−	3.48372i	−1.19323	−	0.531262i	−0.288600	−	0.957450i	$-0.593190\pi$
$43$	−7.82456	−	3.48372i	−1.19323	−	0.531262i	−0.904635	+	0.426188i	$0.859856\pi$
$44$	−5.24364	+	2.33462i	−0.790508	+	0.351957i
$45$	0.669131	−	0.743145i	0.0997481	−	0.110781i
$46$	−4.16960	−	3.02939i	−0.614775	−	0.446660i
$47$	−4.13220	−	3.00222i	−0.602743	−	0.437919i	0.244108	−	0.969748i	$-0.421505\pi$
$47$	−4.13220	−	3.00222i	−0.602743	−	0.437919i	−0.846852	+	0.531829i	$0.821505\pi$
$48$	−0.669131	+	0.743145i	−0.0965807	+	0.107264i
$49$	−6.38421	+	2.84244i	−0.912031	+	0.406062i
$50$	−0.913545	−	0.406737i	−0.129195	−	0.0575212i
$51$	−0.0892976	−	0.0991750i	−0.0125042	−	0.0138873i
$52$	0.0173542	+	0.165114i	0.00240659	+	0.0228972i
$53$	11.1032	+	2.36005i	1.52514	+	0.324178i	0.892779	−	0.450496i	$-0.148753\pi$
$53$	11.1032	+	2.36005i	1.52514	+	0.324178i	0.632361	+	0.774674i	$0.282086\pi$
$54$	0.309017	+	0.951057i	0.0420519	+	0.129422i
$55$	5.61444	−	1.19339i	0.757051	−	0.160916i
$56$	−0.0538682	−	0.0933025i	−0.00719844	−	0.0124681i
$57$	−3.05454	+	5.29062i	−0.404584	+	0.700759i
$58$	2.68041	−	8.24944i	0.351955	−	1.08320i
$59$	−0.841758	+	8.00880i	−0.109588	+	1.04266i	0.792136	+	0.610344i	$0.208969\pi$
$59$	−0.841758	+	8.00880i	−0.109588	+	1.04266i	−0.901724	+	0.432312i	$0.857698\pi$
$60$	0.809017	−	0.587785i	0.104444	−	0.0758827i
$61$	8.18357			1.04780			0.523899	−	0.851780i	$-0.324477\pi$
$61$	8.18357			1.04780			0.523899	+	0.851780i	$0.324477\pi$
$62$	5.56461	+	0.187469i	0.706706	+	0.0238086i
$63$	−0.107736			−0.0135735
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	0.0173542	−	0.165114i	0.00215252	−	0.0204799i
$66$	−1.77372	+	5.45894i	−0.218330	+	0.671950i
$67$	5.05897	−	8.76240i	0.618052	−	1.07050i	−0.371789	−	0.928317i	$-0.621256\pi$
$67$	5.05897	−	8.76240i	0.618052	−	1.07050i	0.989841	−	0.142180i	$-0.0454111\pi$
$68$	−0.0667266	−	0.115574i	−0.00809179	−	0.0140154i
$69$	−5.04129	+	1.07156i	−0.606900	+	0.129001i
$70$	0.0332924	+	0.102463i	0.00397920	+	0.0122467i
$71$	−1.10408	−	0.234680i	−0.131030	−	0.0278514i	0.141930	−	0.989877i	$-0.454669\pi$
$71$	−1.10408	−	0.234680i	−0.131030	−	0.0278514i	−0.272960	+	0.962025i	$0.588003\pi$
$72$	0.104528	+	0.994522i	0.0123188	+	0.117206i
$73$	2.62954	+	2.92040i	0.307764	+	0.341807i	0.877108	−	0.480292i	$-0.159469\pi$
$73$	2.62954	+	2.92040i	0.307764	+	0.341807i	−0.569344	+	0.822099i	$0.692803\pi$
$74$	2.78470	+	1.23983i	0.323715	+	0.144127i
$75$	−0.913545	+	0.406737i	−0.105487	+	0.0469659i
$76$	−4.08777	+	4.53993i	−0.468900	+	0.520766i
$77$	−0.500291	−	0.363483i	−0.0570134	−	0.0414227i
$78$	0.134316	+	0.0975862i	0.0152083	+	0.0110495i
$79$	−10.3013	+	11.4408i	−1.15899	+	1.28719i	−0.207943	+	0.978141i	$0.566677\pi$
$79$	−10.3013	+	11.4408i	−1.15899	+	1.28719i	−0.951047	+	0.309047i	$0.899990\pi$
$80$	0.913545	−	0.406737i	0.102137	−	0.0454745i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	−4.54852	−	5.05164i	−0.502300	−	0.557860i
$83$	1.24301	+	11.8264i	0.136438	+	1.29812i	0.821741	+	0.569861i	$0.193003\pi$
$83$	1.24301	+	11.8264i	0.136438	+	1.29812i	−0.685303	+	0.728258i	$0.740330\pi$
$84$	−0.105382	−	0.0223997i	−0.0114981	−	0.00244400i
$85$	0.0412393	+	0.126922i	0.00447303	+	0.0137666i
$86$	−8.37788	+	1.78077i	−0.903410	+	0.192026i
$87$	−4.33699	−	7.51188i	−0.464974	−	0.805358i
$88$	−2.86994	+	4.97088i	−0.305936	+	0.529897i
$89$	−1.03589	+	3.18814i	−0.109804	+	0.337943i	−0.990828	−	0.135129i	$-0.956855\pi$
$89$	−1.03589	+	3.18814i	−0.109804	+	0.337943i	0.881024	+	0.473072i	$0.156855\pi$
$90$	0.104528	−	0.994522i	0.0110183	−	0.104832i
$91$	−0.0144707	+	0.0105136i	−0.00151694	+	0.00110212i
$92$	−5.15391			−0.537333
$93$	3.86277	−	4.00987i	0.400550	−	0.415804i
$94$	−5.10768			−0.526817
$95$	4.94235	−	3.59083i	0.507074	−	0.368411i
$96$	−0.104528	+	0.994522i	−0.0106684	+	0.101503i
$97$	1.82085	−	5.60400i	0.184879	−	0.569000i	−0.815067	−	0.579367i	$-0.803300\pi$
$97$	1.82085	−	5.60400i	0.184879	−	0.569000i	0.999946	+	0.0103669i	$0.00329995\pi$
$98$	−3.49420	+	6.05213i	−0.352967	+	0.611357i
$99$	2.86994	+	4.97088i	0.288440	+	0.499592i
$100$	−0.978148	+	0.207912i	−0.0978148	+	0.0207912i
$101$	−0.787019	−	2.42220i	−0.0783113	−	0.241017i	0.904235	−	0.427035i	$-0.140442\pi$
$101$	−0.787019	−	2.42220i	−0.0783113	−	0.241017i	−0.982546	+	0.186018i	$0.940442\pi$
$102$	−0.130537	−	0.0277465i	−0.0129251	−	0.00274731i
$103$	0.482873	+	4.59423i	0.0475789	+	0.452683i	0.992213	+	0.124556i	$0.0397506\pi$
$103$	0.482873	+	4.59423i	0.0475789	+	0.452683i	−0.944634	+	0.328127i	$0.893583\pi$
$104$	0.111091	+	0.123380i	0.0108934	+	0.0120984i
$105$	0.0984221	+	0.0438204i	0.00960502	+	0.00427643i
$106$	10.3699	−	4.61696i	1.00721	−	0.448439i
$107$	9.83965	−	10.9280i	0.951235	−	1.05645i	−0.0471065	−	0.998890i	$-0.515000\pi$
$107$	9.83965	−	10.9280i	0.951235	−	1.05645i	0.998342	−	0.0575640i	$-0.0183333\pi$
$108$	0.809017	+	0.587785i	0.0778477	+	0.0565597i
$109$	13.5544	+	9.84784i	1.29827	+	0.943252i	0.999937	−	0.0112086i	$-0.00356788\pi$
$109$	13.5544	+	9.84784i	1.29827	+	0.943252i	0.298338	+	0.954460i	$0.403568\pi$
$110$	3.84073	−	4.26556i	0.366199	−	0.406705i
$111$	2.78470	−	1.23983i	0.264312	−	0.117679i
$112$	−0.0984221	−	0.0438204i	−0.00930002	−	0.00414064i
$113$	−12.5791	−	13.9705i	−1.18334	−	1.31423i	−0.938748	−	0.344605i	$-0.888013\pi$
$113$	−12.5791	−	13.9705i	−1.18334	−	1.31423i	−0.244591	−	0.969626i	$-0.578654\pi$
$114$	0.638573	+	6.07561i	0.0598078	+	0.569033i
$115$	5.04129	+	1.07156i	0.470103	+	0.0999234i
$116$	−2.68041	−	8.24944i	−0.248869	−	0.765941i
$117$	0.162396	−	0.0345182i	0.0150135	−	0.00319121i
$118$	4.02646	+	6.97403i	0.370665	+	0.642011i
$119$	0.00718889	−	0.0124515i	0.000659004	−	0.00114143i
$120$	0.309017	−	0.951057i	0.0282093	−	0.0868192i
$121$	−2.29400	+	21.8259i	−0.208545	+	1.98418i
$122$	6.62064	−	4.81018i	0.599405	−	0.435493i
$123$	−6.79765			−0.612924
$124$	4.61205	−	3.11913i	0.414175	−	0.280106i
$125$	1.00000			0.0894427
$126$	−0.0871606	+	0.0633259i	−0.00776489	+	0.00564152i
$127$	0.00824623	−	0.0784576i	0.000731735	−	0.00696199i	−0.994150	−	0.108009i	$-0.965553\pi$
$127$	0.00824623	−	0.0784576i	0.000731735	−	0.00696199i	0.994882	+	0.101047i	$0.0322192\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−4.28252	+	7.41755i	−0.377055	+	0.653079i
$130$	−0.0830118	−	0.143781i	−0.00728061	−	0.0126104i
$131$	18.6936	−	3.97345i	1.63327	−	0.347162i	0.702193	−	0.711987i	$-0.252205\pi$
$131$	18.6936	−	3.97345i	1.63327	−	0.347162i	0.931076	+	0.364825i	$0.118871\pi$
$132$	1.77372	+	5.45894i	0.154382	+	0.475140i
$133$	−0.643788	−	0.136841i	−0.0558235	−	0.0118656i
$134$	−1.05761	−	10.0625i	−0.0913639	−	0.869269i
$135$	−0.669131	−	0.743145i	−0.0575896	−	0.0639597i
$136$	−0.121916	−	0.0542803i	−0.0104542	−	0.00465450i
$137$	20.6205	−	9.18084i	1.76173	−	0.784372i	0.773047	−	0.634349i	$-0.218732\pi$
$137$	20.6205	−	9.18084i	1.76173	−	0.784372i	0.988682	−	0.150024i	$-0.0479349\pi$
$138$	−3.44864	+	3.83010i	−0.293568	+	0.326040i
$139$	10.2070	+	7.41580i	0.865744	+	0.629000i	0.929442	−	0.368969i	$-0.120289\pi$
$139$	10.2070	+	7.41580i	0.865744	+	0.629000i	−0.0636973	+	0.997969i	$0.520289\pi$
$140$	0.0871606	+	0.0633259i	0.00736642	+	0.00535202i
$141$	−3.41770	+	3.79575i	−0.287823	+	0.319659i
$142$	−1.03116	+	0.459103i	−0.0865332	+	0.0385271i
$143$	0.870567	+	0.387601i	0.0728005	+	0.0324129i
$144$	0.669131	+	0.743145i	0.0557609	+	0.0619287i
$145$	0.906677	+	8.62646i	0.0752954	+	0.716388i
$146$	3.84391	+	0.817048i	0.318124	+	0.0676194i
$147$	2.15953	+	6.64636i	0.178115	+	0.548182i
$148$	2.98162	−	0.633763i	0.245088	−	0.0520950i
$149$	−10.5600	−	18.2904i	−0.865105	−	1.49841i	−0.866943	−	0.498408i	$-0.833918\pi$
$149$	−10.5600	−	18.2904i	−0.865105	−	1.49841i	0.00183781	−	0.999998i	$-0.499415\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	4.80416	−	14.7857i	0.390957	−	1.20324i	−0.541109	−	0.840953i	$-0.681995\pi$
$151$	4.80416	−	14.7857i	0.390957	−	1.20324i	0.932066	−	0.362289i	$-0.118005\pi$
$152$	−0.638573	+	6.07561i	−0.0517951	+	0.492797i
$153$	−0.107966	+	0.0784418i	−0.00872852	+	0.00634164i
$154$	−0.618394			−0.0498316
$155$	−5.15977	+	2.09207i	−0.414443	+	0.168039i
$156$	0.166024			0.0132925
$157$	10.0461	−	7.29889i	0.801763	−	0.582515i	−0.109668	−	0.993968i	$-0.534979\pi$
$157$	10.0461	−	7.29889i	0.801763	−	0.582515i	0.911431	+	0.411454i	$0.134979\pi$
$158$	−1.60922	+	15.3108i	−0.128023	+	1.21806i
$159$	3.50772	−	10.7957i	0.278181	−	0.856152i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−0.277632	−	0.480873i	−0.0218805	−	0.0378981i
$162$	0.978148	−	0.207912i	0.0768505	−	0.0163351i
$163$	−4.44147	−	13.6694i	−0.347882	−	1.07067i	−0.960023	−	0.279923i	$-0.909691\pi$
$163$	−4.44147	−	13.6694i	−0.347882	−	1.07067i	0.612140	−	0.790749i	$-0.290309\pi$
$164$	−6.64911	−	1.41331i	−0.519208	−	0.110361i
$165$	−0.599980	−	5.70843i	−0.0467084	−	0.444401i
$166$	7.95701	+	8.83716i	0.617584	+	0.685896i
$167$	−14.7227	−	6.55496i	−1.13928	−	0.507238i	−0.251657	−	0.967817i	$-0.580975\pi$
$167$	−14.7227	−	6.55496i	−1.13928	−	0.507238i	−0.887619	+	0.460578i	$0.847642\pi$
$168$	−0.0984221	+	0.0438204i	−0.00759343	+	0.00338081i
$169$	−8.68025	+	9.64040i	−0.667712	+	0.741569i
$170$	0.107966	+	0.0784418i	0.00828061	+	0.00601621i
$171$	4.94235	+	3.59083i	0.377951	+	0.274597i
$172$	−5.73114	+	6.36507i	−0.436995	+	0.485332i
$173$	2.22767	−	0.991824i	0.169367	−	0.0754070i	−0.320302	−	0.947316i	$-0.603784\pi$
$173$	2.22767	−	0.991824i	0.169367	−	0.0754070i	0.489669	+	0.871909i	$0.337118\pi$
$174$	−7.92407	−	3.52802i	−0.600722	−	0.267459i
$175$	−0.0720898	−	0.0800638i	−0.00544947	−	0.00605225i
$176$	0.599980	+	5.70843i	0.0452252	+	0.430289i
$177$	7.87694	+	1.67429i	0.592067	+	0.125848i
$178$	1.03589	+	3.18814i	0.0776433	+	0.238962i
$179$	−0.471507	+	0.100222i	−0.0352421	+	0.00749094i	−0.225499	−	0.974243i	$-0.572401\pi$
$179$	−0.471507	+	0.100222i	−0.0352421	+	0.00749094i	0.190257	+	0.981734i	$0.439068\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	1.34373	−	2.32741i	0.0998786	−	0.172995i	−0.811756	−	0.583997i	$-0.801488\pi$
$181$	1.34373	−	2.32741i	0.0998786	−	0.172995i	0.911634	+	0.411002i	$0.134821\pi$
$182$	−0.00552732	+	0.0170113i	−0.000409712	+	0.00126096i
$183$	0.855416	−	8.13874i	0.0632341	−	0.601633i
$184$	−4.16960	+	3.02939i	−0.307387	+	0.223330i
$185$	−3.04823			−0.224110
$186$	0.768102	−	5.51453i	0.0563200	−	0.404345i
$187$	−0.766004			−0.0560158
$188$	−4.13220	+	3.00222i	−0.301372	+	0.218959i
$189$	−0.0112615	+	0.107146i	−0.000819155	+	0.00779374i
$190$	1.88781	−	5.81008i	0.136956	−	0.421507i
$191$	8.79824	−	15.2390i	0.636618	−	1.10265i	−0.349552	−	0.936917i	$-0.613666\pi$
$191$	8.79824	−	15.2390i	0.636618	−	1.10265i	0.986170	−	0.165738i	$-0.0530005\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	14.1057	−	2.99826i	1.01535	−	0.215820i	0.329961	−	0.943995i	$-0.392964\pi$
$193$	14.1057	−	2.99826i	1.01535	−	0.215820i	0.685391	+	0.728175i	$0.259631\pi$
$194$	−1.82085	−	5.60400i	−0.130729	−	0.402344i
$195$	−0.162396	−	0.0345182i	−0.0116294	−	0.00247190i
$196$	0.730486	+	6.95011i	0.0521776	+	0.496436i
$197$	9.01193	+	10.0088i	0.642073	+	0.713095i	0.973063	−	0.230540i	$-0.0740492\pi$
$197$	9.01193	+	10.0088i	0.642073	+	0.713095i	−0.330990	+	0.943634i	$0.607382\pi$
$198$	5.24364	+	2.33462i	0.372649	+	0.165914i
$199$	−18.3231	+	8.15797i	−1.29889	+	0.578303i	−0.935498	−	0.353333i	$-0.885048\pi$
$199$	−18.3231	+	8.15797i	−1.29889	+	0.578303i	−0.363393	+	0.931636i	$0.618382\pi$
$200$	−0.669131	+	0.743145i	−0.0473147	+	0.0525483i
$201$	−8.18559	−	5.94718i	−0.577367	−	0.419482i
$202$	−2.06044	−	1.49700i	−0.144972	−	0.105328i
$203$	0.625305	−	0.694471i	0.0438878	−	0.0487423i
$204$	−0.121916	+	0.0542803i	−0.00853579	+	0.00380038i
$205$	6.20996	+	2.76485i	0.433723	+	0.193106i
$206$	3.09107	+	3.43298i	0.215365	+	0.239187i
$207$	0.538731	+	5.12568i	0.0374444	+	0.356259i
$208$	0.162396	+	0.0345182i	0.0112601	+	0.00239341i
$209$	10.8358	+	33.3491i	0.749527	+	2.30681i
$210$	0.105382	−	0.0223997i	0.00727206	−	0.00154572i
$211$	10.4112	+	18.0327i	0.716736	+	1.24142i	0.962286	+	0.272040i	$0.0876983\pi$
$211$	10.4112	+	18.0327i	0.716736	+	1.24142i	−0.245549	+	0.969384i	$0.578968\pi$
$212$	5.67562	−	9.83046i	0.389803	−	0.675158i
$213$	−0.348802	+	1.07350i	−0.0238995	+	0.0735552i
$214$	1.53710	−	14.6246i	0.105074	−	0.999715i
$215$	6.92927	−	5.03441i	0.472572	−	0.343344i
$216$	1.00000			0.0680414
$217$	0.539466	+	0.262294i	0.0366213	+	0.0178057i
$218$	16.7541			1.13473
$219$	3.17926	−	2.30987i	0.214835	−	0.156087i
$220$	0.599980	−	5.70843i	0.0404507	−	0.384862i
$221$	−0.00684669	+	0.0210720i	−0.000460559	+	0.00141745i
$222$	1.52412	−	2.63985i	0.102292	−	0.177175i
$223$	−7.89890	−	13.6813i	−0.528950	−	0.916168i	−0.999430	−	0.0337572i	$-0.989253\pi$
$223$	−7.89890	−	13.6813i	−0.528950	−	0.916168i	0.470480	−	0.882410i	$-0.344081\pi$
$224$	−0.105382	+	0.0223997i	−0.00704114	+	0.00149664i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	−18.3883	−	3.90856i	−1.22317	−	0.259993i
$227$	−1.45521	−	13.8454i	−0.0965855	−	0.918950i	−0.930311	−	0.366771i	$-0.880463\pi$
$227$	−1.45521	−	13.8454i	−0.0965855	−	0.918950i	0.833726	−	0.552179i	$-0.186203\pi$
$228$	4.08777	+	4.53993i	0.270719	+	0.300664i
$229$	−11.5528	−	5.14363i	−0.763430	−	0.339901i	−0.0121861	−	0.999926i	$-0.503879\pi$
$229$	−11.5528	−	5.14363i	−0.763430	−	0.339901i	−0.751244	+	0.660025i	$0.770546\pi$
$230$	4.70833	−	2.09629i	0.310458	−	0.138225i
$231$	−0.413786	+	0.459556i	−0.0272251	+	0.0302366i
$232$	−7.01739	−	5.09843i	−0.460714	−	0.334729i
$233$	−4.00882	−	2.91258i	−0.262627	−	0.190810i	0.448678	−	0.893694i	$-0.351895\pi$
$233$	−4.00882	−	2.91258i	−0.262627	−	0.190810i	−0.711304	+	0.702884i	$0.751895\pi$
$234$	0.111091	−	0.123380i	0.00726228	−	0.00806557i
$235$	4.66610	−	2.07748i	0.304383	−	0.135520i
$236$	7.35670	+	3.27541i	0.478880	+	0.213211i
$237$	10.3013	+	11.4408i	0.669143	+	0.743159i
$238$	−0.00150289	−	0.0142990i	−9.74176e−5	−	0.000926867i
$239$	−3.27988	−	0.697160i	−0.212158	−	0.0450955i	0.100607	−	0.994926i	$-0.467922\pi$
$239$	−3.27988	−	0.697160i	−0.212158	−	0.0450955i	−0.312764	+	0.949831i	$0.601255\pi$
$240$	−0.309017	−	0.951057i	−0.0199470	−	0.0613904i
$241$	−6.68759	+	1.42149i	−0.430786	+	0.0915664i	−0.418201	−	0.908354i	$-0.637339\pi$
$241$	−6.68759	+	1.42149i	−0.430786	+	0.0915664i	−0.0125847	+	0.999921i	$0.504006\pi$
$242$	10.9731	+	19.0059i	0.705376	+	1.22175i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	2.52886	−	7.78303i	0.161894	−	0.498258i
$245$	0.730486	−	6.95011i	0.0466690	−	0.444026i
$246$	−5.49942	+	3.99556i	−0.350630	+	0.254748i
$247$	1.01425			0.0645352
$248$	1.89785	−	5.23433i	0.120514	−	0.332380i
$249$	11.8916			0.753597
$250$	0.809017	−	0.587785i	0.0511667	−	0.0371748i
$251$	1.25637	−	11.9536i	0.0793016	−	0.754504i	−0.880542	−	0.473968i	$-0.842821\pi$
$251$	1.25637	−	11.9536i	0.0793016	−	0.754504i	0.959844	−	0.280536i	$-0.0905122\pi$
$252$	−0.0332924	+	0.102463i	−0.00209722	+	0.00645459i
$253$	−14.7914	+	25.6195i	−0.929928	+	1.61068i
$254$	−0.0394449	−	0.0683206i	−0.00247499	−	0.00428681i
$255$	0.130537	−	0.0277465i	0.00817454	−	0.00173755i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−0.356629	−	0.0758039i	−0.0222459	−	0.00472852i	0.196775	−	0.980449i	$-0.436953\pi$
$257$	−0.356629	−	0.0758039i	−0.0222459	−	0.00472852i	−0.219021	+	0.975720i	$0.570286\pi$
$258$	0.895291	+	8.51813i	0.0557384	+	0.530316i
$259$	0.219746	+	0.244053i	0.0136544	+	0.0151647i
$260$	−0.151670	−	0.0675279i	−0.00940618	−	0.00418790i
$261$	−7.92407	+	3.52802i	−0.490488	+	0.218379i
$262$	12.7879	−	14.2024i	0.790040	−	0.877428i
$263$	−0.841858	−	0.611646i	−0.0519112	−	0.0377157i	0.561527	−	0.827458i	$-0.310214\pi$
$263$	−0.841858	−	0.611646i	−0.0519112	−	0.0377157i	−0.613438	+	0.789743i	$0.710214\pi$
$264$	4.64366	+	3.37381i	0.285797	+	0.207644i
$265$	−7.59546	+	8.43561i	−0.466585	+	0.518195i
$266$	−0.601269	+	0.267702i	−0.0368661	+	0.0164139i
$267$	3.06240	+	1.36347i	0.187416	+	0.0834429i
$268$	−6.77023	−	7.51910i	−0.413557	−	0.459302i
$269$	1.35239	+	12.8671i	0.0824567	+	0.784523i	0.955124	+	0.296207i	$0.0957220\pi$
$269$	1.35239	+	12.8671i	0.0824567	+	0.784523i	−0.872667	+	0.488316i	$0.837611\pi$
$270$	−0.978148	−	0.207912i	−0.0595282	−	0.0126531i
$271$	8.03802	+	24.7385i	0.488275	+	1.50276i	0.827181	+	0.561936i	$0.189943\pi$
$271$	8.03802	+	24.7385i	0.488275	+	1.50276i	−0.338906	+	0.940820i	$0.610057\pi$
$272$	−0.130537	+	0.0277465i	−0.00791496	+	0.00168238i
$273$	0.00894339	+	0.0154904i	0.000541279	+	0.000937522i
$274$	11.2860	−	19.5479i	0.681811	−	1.18093i
$275$	−1.77372	+	5.45894i	−0.106959	+	0.329187i
$276$	−0.538731	+	5.12568i	−0.0324278	+	0.308530i
$277$	10.5255	−	7.64721i	0.632415	−	0.459476i	−0.224821	−	0.974400i	$-0.572180\pi$
$277$	10.5255	−	7.64721i	0.632415	−	0.459476i	0.857236	+	0.514924i	$0.172180\pi$
$278$	12.6165			0.756688
$279$	−3.58413	−	4.26075i	−0.214576	−	0.255084i
$280$	0.107736			0.00643848
$281$	−4.60326	+	3.34446i	−0.274607	+	0.199514i	−0.716562	−	0.697524i	$-0.754285\pi$
$281$	−4.60326	+	3.34446i	−0.274607	+	0.199514i	0.441955	+	0.897037i	$0.354285\pi$
$282$	−0.533898	+	5.07970i	−0.0317932	+	0.302492i
$283$	1.73515	−	5.34025i	0.103144	−	0.317445i	−0.886146	−	0.463406i	$-0.846627\pi$
$283$	1.73515	−	5.34025i	0.103144	−	0.317445i	0.989290	+	0.145961i	$0.0466273\pi$
$284$	−0.564374	+	0.977524i	−0.0334894	+	0.0580054i
$285$	−3.05454	−	5.29062i	−0.180935	−	0.313389i
$286$	0.932130	−	0.198130i	0.0551180	−	0.0117157i
$287$	−0.226310	−	0.696511i	−0.0133587	−	0.0411137i
$288$	0.978148	+	0.207912i	0.0576379	+	0.0122513i
$289$	1.77512	+	16.8892i	0.104419	+	0.993480i
$290$	5.80402	+	6.44602i	0.340824	+	0.378523i
$291$	−5.38297	−	2.39665i	−0.315555	−	0.140494i
$292$	3.59004	−	1.59839i	0.210091	−	0.0935385i
$293$	−12.6613	+	14.0618i	−0.739680	+	0.821498i	−0.989154	−	0.146883i	$-0.953076\pi$
$293$	−12.6613	+	14.0618i	−0.739680	+	0.821498i	0.249473	+	0.968382i	$0.419742\pi$
$294$	5.65373	+	4.10767i	0.329732	+	0.239564i
$295$	−6.51494	−	4.73338i	−0.379315	−	0.275588i
$296$	2.03967	−	2.26528i	0.118553	−	0.131667i
$297$	5.24364	−	2.33462i	0.304267	−	0.135468i
$298$	−19.2940	−	8.59024i	−1.11767	−	0.497619i
$299$	0.572556	+	0.635888i	0.0331118	+	0.0367743i
$300$	0.104528	+	0.994522i	0.00603495	+	0.0574187i
$301$	−0.902603	−	0.191854i	−0.0520252	−	0.0110583i
$302$	−4.80416	−	14.7857i	−0.276448	−	0.850821i
$303$	−2.49119	+	0.529519i	−0.143115	+	0.0304201i
$304$	3.05454	+	5.29062i	0.175190	+	0.303438i
$305$	−4.09178	+	7.08718i	−0.234295	+	0.405811i
$306$	−0.0412393	+	0.126922i	−0.00235749	+	0.00725562i
$307$	−1.41842	+	13.4953i	−0.0809532	+	0.770218i	0.876456	+	0.481483i	$0.159902\pi$
$307$	−1.41842	+	13.4953i	−0.0809532	+	0.770218i	−0.957409	+	0.288736i	$0.906765\pi$
$308$	−0.500291	+	0.363483i	−0.0285067	+	0.0207113i
$309$	4.61953			0.262796
$310$	−2.94466	+	4.72536i	−0.167245	+	0.268382i
$311$	18.8070			1.06645			0.533223	−	0.845975i	$-0.320981\pi$
$311$	18.8070			1.06645			0.533223	+	0.845975i	$0.320981\pi$
$312$	0.134316	−	0.0975862i	0.00760414	−	0.00552473i
$313$	0.542965	−	5.16597i	0.0306902	−	0.291998i	−0.968402	−	0.249395i	$-0.919768\pi$
$313$	0.542965	−	5.16597i	0.0306902	−	0.291998i	0.999092	−	0.0426029i	$-0.0135650\pi$
$314$	3.83725	−	11.8098i	0.216549	−	0.666468i
$315$	0.0538682	−	0.0933025i	0.00303513	−	0.00525700i
$316$	7.69754	+	13.3325i	0.433021	+	0.750014i
$317$	−9.52694	+	2.02501i	−0.535086	+	0.113736i	−0.467526	−	0.883979i	$-0.654855\pi$
$317$	−9.52694	+	2.02501i	−0.535086	+	0.113736i	−0.0675598	+	0.997715i	$0.521521\pi$
$318$	−3.50772	−	10.7957i	−0.196703	−	0.605391i
$319$	−48.6995	−	10.3514i	−2.72665	−	0.579568i
$320$	−0.104528	−	0.994522i	−0.00584332	−	0.0555955i
$321$	−9.83965	−	10.9280i	−0.549196	−	0.609944i
$322$	−0.507259	−	0.225846i	−0.0282685	−	0.0125859i
$323$	−0.744792	+	0.331603i	−0.0414413	+	0.0184509i
$324$	0.669131	−	0.743145i	0.0371739	−	0.0412858i
$325$	0.134316	+	0.0975862i	0.00745050	+	0.00541311i
$326$	−11.6279	−	8.44817i	−0.644010	−	0.467901i
$327$	11.2107	−	12.4508i	0.619954	−	0.688528i
$328$	−6.20996	+	2.76485i	−0.342888	+	0.152664i
$329$	−0.502709	−	0.223820i	−0.0277152	−	0.0123396i
$330$	−3.84073	−	4.26556i	−0.211425	−	0.234811i
$331$	0.0635930	+	0.605047i	0.00349538	+	0.0332564i	0.996131	−	0.0878857i	$-0.0280110\pi$
$331$	0.0635930	+	0.605047i	0.00349538	+	0.0332564i	−0.992635	+	0.121142i	$0.961344\pi$
$332$	11.6317	+	2.47240i	0.638373	+	0.135690i
$333$	−0.941955	−	2.89904i	−0.0516188	−	0.158866i
$334$	−15.7638	+	3.35070i	−0.862558	+	0.183342i
$335$	5.05897	+	8.76240i	0.276401	+	0.478741i
$336$	−0.0538682	+	0.0933025i	−0.00293875	+	0.00509007i
$337$	−6.40777	+	19.7211i	−0.349054	+	1.07428i	0.610324	+	0.792152i	$0.291039\pi$
$337$	−6.40777	+	19.7211i	−0.349054	+	1.07428i	−0.959378	+	0.282125i	$0.908961\pi$
$338$	−1.35599	+	12.9014i	−0.0737561	+	0.701742i
$339$	−15.2088	+	11.0498i	−0.826029	+	0.600145i
$340$	0.133453			0.00723751
$341$	−2.26850	−	31.8777i	−0.122846	−	1.72627i
$342$	6.10908			0.330341
$343$	−1.21924	+	0.885828i	−0.0658326	+	0.0478302i
$344$	−0.895291	+	8.51813i	−0.0482709	+	0.459267i
$345$	1.59265	−	4.90166i	0.0857452	−	0.263897i
$346$	1.21925	−	2.11180i	0.0655471	−	0.113531i
$347$	−2.06361	−	3.57428i	−0.110781	−	0.191878i	0.805305	−	0.592861i	$-0.202002\pi$
$347$	−2.06361	−	3.57428i	−0.110781	−	0.191878i	−0.916085	+	0.400984i	$0.868668\pi$
$348$	−8.48443	+	1.80342i	−0.454813	+	0.0966735i
$349$	4.11242	+	12.6567i	0.220133	+	0.677499i	0.998749	+	0.0499987i	$0.0159217\pi$
$349$	4.11242	+	12.6567i	0.220133	+	0.677499i	−0.778617	+	0.627500i	$0.784078\pi$
$350$	−0.105382	−	0.0223997i	−0.00563291	−	0.00119731i
$351$	−0.0173542	−	0.165114i	−0.000926298	−	0.00881314i
$352$	3.84073	+	4.26556i	0.204711	+	0.227355i
$353$	−13.1266	−	5.84435i	−0.698659	−	0.311063i	0.0264955	−	0.999649i	$-0.491565\pi$
$353$	−13.1266	−	5.84435i	−0.698659	−	0.311063i	−0.725155	+	0.688586i	$0.758232\pi$
$354$	7.35670	−	3.27541i	0.391004	−	0.174086i
$355$	0.755279	−	0.838823i	0.0400861	−	0.0445201i
$356$	2.71200	+	1.97038i	0.143736	+	0.104430i
$357$	−0.0116319	−	0.00845104i	−0.000615623	−	0.000447277i
$358$	−0.322548	+	0.358226i	−0.0170472	+	0.0189328i
$359$	−1.09483	+	0.487451i	−0.0577830	+	0.0257267i	−0.435425	−	0.900225i	$-0.643402\pi$
$359$	−1.09483	+	0.487451i	−0.0577830	+	0.0257267i	0.377642	+	0.925952i	$0.376735\pi$
$360$	−0.913545	−	0.406737i	−0.0481481	−	0.0214369i
$361$	12.2590	+	13.6150i	0.645213	+	0.716581i
$362$	−0.280916	−	2.67274i	−0.0147646	−	0.140476i
$363$	21.4666	+	4.56286i	1.12670	+	0.239488i
$364$	0.00552732	+	0.0170113i	0.000289710	+	0.000891637i
$365$	−3.84391	+	0.817048i	−0.201199	+	0.0427663i
$366$	−4.09178	−	7.08718i	−0.213881	−	0.370453i
$367$	16.4199	−	28.4401i	0.857112	−	1.48456i	−0.0175595	−	0.999846i	$-0.505590\pi$
$367$	16.4199	−	28.4401i	0.857112	−	1.48456i	0.874672	−	0.484716i	$-0.161077\pi$
$368$	−1.59265	+	4.90166i	−0.0830225	+	0.255517i
$369$	−0.710548	+	6.76041i	−0.0369897	+	0.351933i
$370$	−2.46607	+	1.79171i	−0.128205	+	0.0931463i
$371$	1.22294			0.0634920
$372$	−2.61995	−	4.91283i	−0.135838	−	0.254718i
$373$	1.72015			0.0890660			0.0445330	−	0.999008i	$-0.485820\pi$
$373$	1.72015			0.0890660			0.0445330	+	0.999008i	$0.485820\pi$
$374$	−0.619711	+	0.450246i	−0.0320445	+	0.0232817i
$375$	0.104528	−	0.994522i	0.00539783	−	0.0513569i
$376$	−1.57836	+	4.85769i	−0.0813977	+	0.250516i
$377$	−0.720042	+	1.24715i	−0.0370841	+	0.0642315i
$378$	0.0538682	+	0.0933025i	0.00277068	+	0.00479896i
$379$	−9.68424	+	2.05845i	−0.497446	+	0.105735i	−0.449801	−	0.893129i	$-0.648505\pi$
$379$	−9.68424	+	2.05845i	−0.497446	+	0.105735i	−0.0476453	+	0.998864i	$0.515172\pi$
$380$	−1.88781	−	5.81008i	−0.0968426	−	0.298051i
$381$	−0.0771659	−	0.0164021i	−0.00395333	−	0.000840306i
$382$	−1.83933	−	17.5001i	−0.0941084	−	0.895382i
$383$	17.6603	+	19.6138i	0.902401	+	1.00222i	0.999976	+	0.00698992i	$0.00222498\pi$
$383$	17.6603	+	19.6138i	0.902401	+	1.00222i	−0.0975743	+	0.995228i	$0.531108\pi$
$384$	0.913545	+	0.406737i	0.0466192	+	0.0207562i
$385$	0.564931	−	0.251523i	0.0287915	−	0.0128188i
$386$	9.64944	−	10.7168i	0.491143	−	0.545470i
$387$	6.92927	+	5.03441i	0.352235	+	0.255913i
$388$	−4.76705	−	3.46346i	−0.242010	−	0.175831i
$389$	3.93748	−	4.37301i	0.199638	−	0.221721i	−0.635010	−	0.772504i	$-0.719004\pi$
$389$	3.93748	−	4.37301i	0.199638	−	0.221721i	0.834648	+	0.550783i	$0.185671\pi$
$390$	−0.151670	+	0.0675279i	−0.00768011	+	0.00341941i
$391$	−0.628342	−	0.279756i	−0.0317766	−	0.0141479i
$392$	4.67615	+	5.19339i	0.236181	+	0.262306i
$393$	−1.99767	−	19.0065i	−0.100769	−	0.958753i
$394$	13.1738	+	2.80018i	0.663687	+	0.141071i
$395$	−4.75734	−	14.6416i	−0.239368	−	0.736699i
$396$	5.61444	−	1.19339i	0.282136	−	0.0599699i
$397$	−9.13061	−	15.8147i	−0.458252	−	0.793716i	0.540616	−	0.841269i	$-0.318191\pi$
$397$	−9.13061	−	15.8147i	−0.458252	−	0.793716i	−0.998869	+	0.0475529i	$0.984858\pi$
$398$	−10.0286	+	17.3700i	−0.502687	+	0.870679i
$399$	−0.203386	+	0.625957i	−0.0101820	+	0.0313371i
$400$	−0.104528	+	0.994522i	−0.00522642	+	0.0497261i
$401$	−27.0404	+	19.6460i	−1.35034	+	0.981076i	−0.351341	+	0.936248i	$0.614274\pi$
$401$	−27.0404	+	19.6460i	−1.35034	+	0.981076i	−0.998995	+	0.0448282i	$0.985726\pi$
$402$	−10.1179			−0.504637
$403$	−0.897196	−	0.222525i	−0.0446925	−	0.0110847i
$404$	−2.54685			−0.126710
$405$	−0.809017	+	0.587785i	−0.0402004	+	0.0292073i
$406$	0.0976822	−	0.929384i	0.00484789	−	0.0461246i
$407$	5.40671	−	16.6401i	0.268000	−	0.824821i
$408$	−0.0667266	+	0.115574i	−0.00330346	+	0.00572176i
$409$	1.27809	+	2.21372i	0.0631975	+	0.109461i	0.895893	−	0.444270i	$-0.146537\pi$
$409$	1.27809	+	2.21372i	0.0631975	+	0.109461i	−0.832696	+	0.553731i	$0.813204\pi$
$410$	6.64911	−	1.41331i	0.328376	−	0.0697985i
$411$	−6.97512	−	21.4672i	−0.344057	−	1.05890i
$412$	4.51859	+	0.960455i	0.222615	+	0.0473182i
$413$	0.0906881	+	0.862839i	0.00446247	+	0.0424575i
$414$	3.44864	+	3.83010i	0.169491	+	0.188239i
$415$	−10.8635	−	4.83674i	−0.533268	−	0.237426i
$416$	0.151670	−	0.0675279i	0.00743624	−	0.00331083i
$417$	8.44210	−	9.37590i	0.413411	−	0.459140i
$418$	28.3685	+	20.6109i	1.38755	+	1.00811i
$419$	−19.6379	−	14.2678i	−0.959374	−	0.697026i	−0.00636850	−	0.999980i	$-0.502027\pi$
$419$	−19.6379	−	14.2678i	−0.959374	−	0.697026i	−0.953005	+	0.302954i	$0.902027\pi$
$420$	0.0720898	−	0.0800638i	0.00351762	−	0.00390671i
$421$	−23.2792	+	10.3646i	−1.13456	+	0.505138i	−0.886095	−	0.463503i	$-0.846592\pi$
$421$	−23.2792	+	10.3646i	−1.13456	+	0.505138i	−0.248463	+	0.968641i	$0.579926\pi$
$422$	19.0222	+	8.46923i	0.925987	+	0.412276i
$423$	3.41770	+	3.79575i	0.166174	+	0.184555i
$424$	−1.18653	−	11.2890i	−0.0576228	−	0.548245i
$425$	−0.130537	−	0.0277465i	−0.00633197	−	0.00134590i
$426$	0.348802	+	1.07350i	0.0168995	+	0.0520114i
$427$	0.862402	−	0.183309i	0.0417345	−	0.00887095i
$428$	−7.35257	−	12.7350i	−0.355400	−	0.615570i
$429$	0.476477	−	0.825283i	0.0230045	−	0.0398450i
$430$	2.64675	−	8.14585i	0.127637	−	0.392828i
$431$	0.799846	−	7.61003i	0.0385272	−	0.366562i	−0.958224	−	0.286019i	$-0.907668\pi$
$431$	0.799846	−	7.61003i	0.0385272	−	0.366562i	0.996751	−	0.0805430i	$-0.0256654\pi$
$432$	0.809017	−	0.587785i	0.0389238	−	0.0282798i
$433$	12.6526			0.608047			0.304023	−	0.952665i	$-0.401670\pi$
$433$	12.6526			0.608047			0.304023	+	0.952665i	$0.401670\pi$
$434$	0.590610	−	0.104889i	0.0283502	−	0.00503486i
$435$	8.67397			0.415885
$436$	13.5544	−	9.84784i	0.649137	−	0.471626i
$437$	−3.29115	+	31.3132i	−0.157437	+	1.49791i
$438$	1.21437	−	3.73745i	0.0580249	−	0.178582i
$439$	10.6502	−	18.4467i	0.508306	−	0.880411i	−0.491648	−	0.870794i	$-0.663605\pi$
$439$	10.6502	−	18.4467i	0.508306	−	0.880411i	0.999954	−	0.00961735i	$-0.00306134\pi$
$440$	−2.86994	−	4.97088i	−0.136819	−	0.236977i
$441$	6.83568	−	1.45297i	0.325509	−	0.0691890i
$442$	0.00684669	+	0.0210720i	0.000325664	+	0.00100229i
$443$	−3.67030	−	0.780147i	−0.174381	−	0.0370659i	0.119893	−	0.992787i	$-0.461745\pi$
$443$	−3.67030	−	0.780147i	−0.174381	−	0.0370659i	−0.294275	+	0.955721i	$0.595078\pi$
$444$	−0.318627	−	3.03153i	−0.0151214	−	0.143870i
$445$	−2.24307	−	2.49118i	−0.106332	−	0.118093i
$446$	−14.4320	−	6.42555i	−0.683376	−	0.304258i
$447$	−19.2940	+	8.59024i	−0.912575	+	0.406304i
$448$	−0.0720898	+	0.0800638i	−0.00340592	+	0.00378266i
$449$	−0.908036	−	0.659727i	−0.0428529	−	0.0311344i	0.566153	−	0.824300i	$-0.308431\pi$
$449$	−0.908036	−	0.659727i	−0.0428529	−	0.0311344i	−0.609006	+	0.793166i	$0.708431\pi$
$450$	0.809017	+	0.587785i	0.0381374	+	0.0277085i
$451$	−26.1079	+	28.9958i	−1.22937	+	1.36536i
$452$	−17.1739	+	7.64629i	−0.807790	+	0.359651i
$453$	−14.2025	−	6.32337i	−0.667293	−	0.297098i
$454$	−9.31539	−	10.3458i	−0.437193	−	0.485552i
$455$	−0.00186968	−	0.0177888i	−8.76519e−5	−	0.000833952i
$456$	5.97558	+	1.27015i	0.279832	+	0.0594802i
$457$	−4.45255	−	13.7035i	−0.208281	−	0.641024i	−0.999563	−	0.0295720i	$-0.990586\pi$
$457$	−4.45255	−	13.7035i	−0.208281	−	0.641024i	0.791281	−	0.611452i	$-0.209414\pi$
$458$	−12.3698	+	2.62927i	−0.578001	+	0.122858i
$459$	0.0667266	+	0.115574i	0.00311453	+	0.00539452i
$460$	2.57696	−	4.46342i	0.120151	−	0.208108i
$461$	−1.88677	+	5.80687i	−0.0878754	+	0.270453i	−0.985332	−	0.170651i	$-0.945413\pi$
$461$	−1.88677	+	5.80687i	−0.0878754	+	0.270453i	0.897456	+	0.441104i	$0.145413\pi$
$462$	−0.0646397	+	0.615006i	−0.00300731	+	0.0286127i
$463$	13.8010	−	10.0270i	0.641387	−	0.465995i	−0.218940	−	0.975738i	$-0.570260\pi$
$463$	13.8010	−	10.0270i	0.641387	−	0.465995i	0.860326	+	0.509744i	$0.170260\pi$
$464$	−8.67397			−0.402679
$465$	1.54126	+	5.35019i	0.0714744	+	0.248109i
$466$	−4.95518			−0.229544
$467$	26.4648	−	19.2278i	1.22465	−	0.889757i	0.228168	−	0.973622i	$-0.426726\pi$
$467$	26.4648	−	19.2278i	1.22465	−	0.889757i	0.996477	+	0.0838645i	$0.0267263\pi$
$468$	0.0173542	−	0.165114i	0.000802198	−	0.00763240i
$469$	0.336851	−	1.03672i	0.0155543	−	0.0478713i
$470$	2.55384	−	4.42338i	0.117800	−	0.204035i
$471$	−6.20880	−	10.7540i	−0.286087	−	0.495517i
$472$	7.87694	−	1.67429i	0.362565	−	0.0770656i
$473$	15.1920	+	46.7561i	0.698528	+	2.14985i
$474$	15.0587	+	3.20082i	0.691668	+	0.147018i
$475$	0.638573	+	6.07561i	0.0292997	+	0.278768i
$476$	−0.00962061	−	0.0106848i	−0.000440960	−	0.000489735i
$477$	−10.3699	−	4.61696i	−0.474804	−	0.211396i
$478$	−3.06326	+	1.36385i	−0.140110	+	0.0623811i
$479$	−14.6455	+	16.2655i	−0.669172	+	0.743191i	−0.978155	−	0.207877i	$-0.933345\pi$
$479$	−14.6455	+	16.2655i	−0.669172	+	0.743191i	0.308983	+	0.951068i	$0.400011\pi$
$480$	−0.809017	−	0.587785i	−0.0369264	−	0.0268286i
$481$	−0.409426	−	0.297465i	−0.0186682	−	0.0135633i
$482$	−4.57485	+	5.08088i	−0.208379	+	0.231428i
$483$	−0.507259	+	0.225846i	−0.0230811	+	0.0102764i
$484$	20.0488	+	8.92630i	0.911309	+	0.405741i
$485$	3.94278	+	4.37890i	0.179032	+	0.198836i
$486$	−0.104528	−	0.994522i	−0.00474151	−	0.0451124i
$487$	−36.5106	−	7.76057i	−1.65445	−	0.351665i	−0.716275	−	0.697818i	$-0.754154\pi$
$487$	−36.5106	−	7.76057i	−1.65445	−	0.351665i	−0.938178	+	0.346154i	$0.887488\pi$
$488$	−2.52886	−	7.78303i	−0.114476	−	0.352321i
$489$	−14.0588	+	2.98829i	−0.635761	+	0.135135i
$490$	−3.49420	−	6.05213i	−0.157852	−	0.273407i
$491$	−10.9554	+	18.9754i	−0.494412	+	0.856346i	−0.999979	−	0.00644078i	$-0.997950\pi$
$491$	−10.9554	+	18.9754i	−0.494412	+	0.856346i	0.505568	+	0.862787i	$0.331283\pi$
$492$	−2.10059	+	6.46495i	−0.0947019	+	0.291463i
$493$	0.120999	−	1.15123i	0.00544952	−	0.0518487i
$494$	0.820546	−	0.596162i	0.0369181	−	0.0268226i
$495$	−5.73987			−0.257988
$496$	−1.54126	−	5.35019i	−0.0692048	−	0.240230i
$497$	−0.121607			−0.00545483
$498$	9.62048	−	6.98969i	0.431104	−	0.313215i
$499$	1.83635	−	17.4717i	0.0822063	−	0.782140i	−0.873303	−	0.487178i	$-0.838026\pi$
$499$	1.83635	−	17.4717i	0.0822063	−	0.782140i	0.955509	−	0.294962i	$-0.0953071\pi$
$500$	0.309017	−	0.951057i	0.0138197	−	0.0425325i
$501$	−8.05799	+	13.9569i	−0.360005	+	0.623546i
$502$	−6.00972	−	10.4091i	−0.268227	−	0.464583i
$503$	−1.78324	+	0.379040i	−0.0795109	+	0.0169006i	−0.247495	−	0.968889i	$-0.579607\pi$
$503$	−1.78324	+	0.379040i	−0.0795109	+	0.0169006i	0.167984	+	0.985790i	$0.446274\pi$
$504$	0.0332924	+	0.102463i	0.00148296	+	0.00456408i
$505$	2.49119	+	0.529519i	0.110857	+	0.0235633i
$506$	3.09225	+	29.4208i	0.137467	+	1.30791i
$507$	8.68025	+	9.64040i	0.385504	+	0.428145i
$508$	−0.0720694	−	0.0320874i	−0.00319756	−	0.00142365i
$509$	−27.0706	+	12.0526i	−1.19988	+	0.534222i	−0.906676	−	0.421827i	$-0.861389\pi$
$509$	−27.0706	+	12.0526i	−1.19988	+	0.534222i	−0.293206	+	0.956049i	$0.594722\pi$
$510$	0.0892976	−	0.0991750i	0.00395416	−	0.00439154i
$511$	0.342522	+	0.248857i	0.0151523	+	0.0110088i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	4.08777	−	4.53993i	0.180480	−	0.200443i
$514$	−0.333075	+	0.148295i	−0.0146913	+	0.00654100i
$515$	−4.22015	−	1.87893i	−0.185962	−	0.0827957i
$516$	5.73114	+	6.36507i	0.252299	+	0.280207i
$517$	3.06451	+	29.1568i	0.134777	+	1.28232i
$518$	0.321229	+	0.0682794i	0.0141140	+	0.00300002i
$519$	−0.753535	−	2.31914i	−0.0330765	−	0.101799i
$520$	−0.162396	+	0.0345182i	−0.00712152	+	0.00151372i
$521$	−18.3987	−	31.8675i	−0.806061	−	1.39614i	−0.915572	−	0.402153i	$-0.868262\pi$
$521$	−18.3987	−	31.8675i	−0.806061	−	1.39614i	0.109511	−	0.993986i	$-0.465071\pi$
$522$	−4.33699	+	7.51188i	−0.189825	+	0.328786i
$523$	4.31229	−	13.2719i	0.188563	−	0.580338i	−0.811428	−	0.584452i	$-0.801309\pi$
$523$	4.31229	−	13.2719i	0.188563	−	0.580338i	0.999992	+	0.00411389i	$0.00130950\pi$
$524$	1.99767	−	19.0065i	0.0872686	−	0.830305i
$525$	−0.0871606	+	0.0633259i	−0.00380400	+	0.00276377i
$526$	−1.04059			−0.0453720
$527$	0.731588	−	0.129927i	0.0318685	−	0.00565969i
$528$	5.73987			0.249796
$529$	−2.88239	+	2.09418i	−0.125321	+	0.0910512i
$530$	−1.18653	+	11.2890i	−0.0515394	+	0.490365i
$531$	2.48849	−	7.65877i	0.107991	−	0.332362i
$532$	−0.329085	+	0.569992i	−0.0142677	+	0.0247123i
$533$	0.564285	+	0.977371i	0.0244419	+	0.0423346i
$534$	3.27896	−	0.696964i	0.141894	−	0.0301606i
$535$	4.54414	+	13.9854i	0.196460	+	0.604642i
$536$	−9.89684	−	2.10364i	−0.427478	−	0.0908634i
$537$	0.0503870	+	0.479400i	0.00217436	+	0.0206877i
$538$	8.65722	+	9.61482i	0.373239	+	0.414524i
$539$	36.6446	+	16.3152i	1.57839	+	0.702746i
$540$	−0.913545	+	0.406737i	−0.0393127	+	0.0175032i
$541$	21.0933	−	23.4265i	0.906873	−	1.00718i	−0.0930611	−	0.995660i	$-0.529665\pi$
$541$	21.0933	−	23.4265i	0.906873	−	1.00718i	0.999934	−	0.0115236i	$-0.00366815\pi$
$542$	21.0438	+	15.2892i	0.903909	+	0.656729i
$543$	−2.17420	−	1.57965i	−0.0933038	−	0.0677892i
$544$	−0.0892976	+	0.0991750i	−0.00382860	+	0.00425209i
$545$	−15.3057	+	6.81452i	−0.655623	+	0.291902i
$546$	0.0163404	+	0.00727521i	0.000699304	+	0.000311350i
$547$	−5.77003	−	6.40827i	−0.246709	−	0.273998i	0.607053	−	0.794661i	$-0.292351\pi$
$547$	−5.77003	−	6.40827i	−0.246709	−	0.273998i	−0.853762	+	0.520663i	$0.825685\pi$
$548$	−2.35941	−	22.4483i	−0.100789	−	0.958944i
$549$	−8.00474	−	1.70146i	−0.341634	−	0.0726165i
$550$	1.77372	+	5.45894i	0.0756316	+	0.232770i
$551$	−51.8320	+	11.0172i	−2.20812	+	0.469350i
$552$	2.57696	+	4.46342i	0.109683	+	0.189976i
$553$	−0.829306	+	1.43640i	−0.0352657	+	0.0610820i
$554$	4.02038	−	12.3734i	0.170809	−	0.525697i
$555$	−0.318627	+	3.03153i	−0.0135250	+	0.128681i
$556$	10.2070	−	7.41580i	0.432872	−	0.314500i
$557$	−27.5747			−1.16838			−0.584189	−	0.811617i	$-0.698587\pi$
$557$	−27.5747			−1.16838			−0.584189	+	0.811617i	$0.698587\pi$
$558$	−5.40403	−	1.34032i	−0.228771	−	0.0567402i
$559$	1.42200			0.0601442
$560$	0.0871606	−	0.0633259i	0.00368321	−	0.00267601i
$561$	−0.0800693	+	0.761808i	−0.00338053	+	0.0321636i
$562$	−1.75829	+	5.41145i	−0.0741689	+	0.228268i
$563$	1.44722	−	2.50665i	0.0609929	−	0.105643i	−0.833917	−	0.551890i	$-0.813907\pi$
$563$	1.44722	−	2.50665i	0.0609929	−	0.105643i	0.894909	+	0.446248i	$0.147240\pi$
$564$	2.55384	+	4.42338i	0.107536	+	0.186258i
$565$	18.3883	−	3.90856i	0.773602	−	0.164434i
$566$	−1.73515	−	5.34025i	−0.0729339	−	0.224468i
$567$	0.105382	+	0.0223997i	0.00442563	+	0.000940698i
$568$	0.117986	+	1.12256i	0.00495059	+	0.0471017i
$569$	4.15754	+	4.61742i	0.174293	+	0.193572i	0.823962	−	0.566645i	$-0.191759\pi$
$569$	4.15754	+	4.61742i	0.174293	+	0.193572i	−0.649669	+	0.760218i	$0.725092\pi$
$570$	−5.58092	−	2.48479i	−0.233759	−	0.104076i
$571$	−15.7719	+	7.02211i	−0.660034	+	0.293866i	−0.709287	−	0.704920i	$-0.750983\pi$
$571$	−15.7719	+	7.02211i	−0.660034	+	0.293866i	0.0492523	+	0.998786i	$0.484316\pi$
$572$	0.637651	−	0.708183i	0.0266615	−	0.0296106i
$573$	−14.2358	−	10.3429i	−0.594711	−	0.432083i
$574$	−0.592488	−	0.430467i	−0.0247300	−	0.0179674i
$575$	−3.44864	+	3.83010i	−0.143818	+	0.159726i
$576$	0.913545	−	0.406737i	0.0380644	−	0.0169474i
$577$	1.88541	+	0.839438i	0.0784906	+	0.0349463i	0.445606	−	0.895229i	$-0.352988\pi$
$577$	1.88541	+	0.839438i	0.0784906	+	0.0349463i	−0.367116	+	0.930175i	$0.619655\pi$
$578$	11.3633	+	12.6202i	0.472651	+	0.524932i
$579$	−1.50739	−	14.3419i	−0.0626450	−	0.596027i
$580$	8.48443	+	1.80342i	0.352297	+	0.0748830i
$581$	0.395899	+	1.21845i	0.0164246	+	0.0505499i
$582$	−5.76363	+	1.22510i	−0.238910	+	0.0507819i
$583$	−32.5773	−	56.4256i	−1.34921	−	2.33691i
$584$	1.96489	−	3.40329i	0.0813078	−	0.140829i
$585$	−0.0513041	+	0.157898i	−0.00212116	+	0.00652827i
$586$	−1.97789	+	18.8183i	−0.0817058	+	0.777379i
$587$	14.5526	−	10.5731i	0.600650	−	0.436398i	−0.245460	−	0.969407i	$-0.578939\pi$
$587$	14.5526	−	10.5731i	0.600650	−	0.436398i	0.846109	+	0.533009i	$0.178939\pi$
$588$	6.98839			0.288196
$589$	−16.0055	−	30.0128i	−0.659495	−	1.23666i
$590$	−8.05291			−0.331533
$591$	10.8959	−	7.91636i	0.448199	−	0.325636i
$592$	0.318627	−	3.03153i	0.0130955	−	0.124595i
$593$	11.0835	−	34.1115i	0.455145	−	1.40079i	−0.415820	−	0.909447i	$-0.636505\pi$
$593$	11.0835	−	34.1115i	0.455145	−	1.40079i	0.870965	−	0.491346i	$-0.163495\pi$
$594$	2.86994	−	4.97088i	0.117755	−	0.203958i
$595$	0.00718889	+	0.0124515i	0.000294716	+	0.000510462i
$596$	−20.6584	+	4.39108i	−0.846200	+	0.179865i
$597$	6.19799	+	19.0755i	0.253667	+	0.780707i
$598$	0.836973	+	0.177904i	0.0342264	+	0.00727504i
$599$	3.59026	+	34.1590i	0.146694	+	1.39570i	0.781922	+	0.623376i	$0.214239\pi$
$599$	3.59026	+	34.1590i	0.146694	+	1.39570i	−0.635228	+	0.772324i	$0.719094\pi$
$600$	0.669131	+	0.743145i	0.0273171	+	0.0303388i
$601$	6.62137	+	2.94802i	0.270091	+	0.120252i	0.537314	−	0.843382i	$-0.319439\pi$
$601$	6.62137	+	2.94802i	0.270091	+	0.120252i	−0.267222	+	0.963635i	$0.586106\pi$
$602$	−0.842991	+	0.375324i	−0.0343577	+	0.0152970i
$603$	−6.77023	+	7.51910i	−0.275705	+	0.306201i
$604$	−12.5775	−	9.13806i	−0.511769	−	0.371822i
$605$	−17.7548	−	12.8996i	−0.721836	−	0.524444i
$606$	−1.70417	+	1.89268i	−0.0692273	+	0.0768847i
$607$	−4.42458	+	1.96995i	−0.179588	+	0.0799578i	−0.494561	−	0.869143i	$-0.664671\pi$
$607$	−4.42458	+	1.96995i	−0.179588	+	0.0799578i	0.314973	+	0.949101i	$0.398005\pi$
$608$	5.58092	+	2.48479i	0.226336	+	0.100771i
$609$	−0.625305	−	0.694471i	−0.0253386	−	0.0281414i
$610$	0.855416	+	8.13874i	0.0346348	+	0.329528i
$611$	0.829464	+	0.176308i	0.0335565	+	0.00713266i
$612$	0.0412393	+	0.126922i	0.00166700	+	0.00513050i
$613$	8.72640	−	1.85485i	0.352456	−	0.0749168i	−0.0282816	−	0.999600i	$-0.509004\pi$
$613$	8.72640	−	1.85485i	0.352456	−	0.0749168i	0.380737	+	0.924683i	$0.375670\pi$
$614$	6.78483	+	11.7517i	0.273813	+	0.474259i
$615$	3.39883	−	5.88694i	0.137054	−	0.237384i
$616$	−0.191094	+	0.588127i	−0.00769940	+	0.0236963i
$617$	−3.91510	+	37.2497i	−0.157616	+	1.49962i	0.574537	+	0.818478i	$0.305182\pi$
$617$	−3.91510	+	37.2497i	−0.157616	+	1.49962i	−0.732154	+	0.681140i	$0.761485\pi$
$618$	3.73728	−	2.71529i	0.150335	−	0.109225i
$619$	44.3125			1.78107			0.890534	−	0.454917i	$-0.150331\pi$
$619$	44.3125			1.78107			0.890534	+	0.454917i	$0.150331\pi$
$620$	0.395218	+	5.55372i	0.0158723	+	0.223043i
$621$	5.15391			0.206819
$622$	15.2152	−	11.0545i	0.610073	−	0.443244i
$623$	−0.0377510	+	0.359177i	−0.00151246	+	0.0143901i
$624$	0.0513041	−	0.157898i	0.00205381	−	0.00632097i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−2.59721	−	4.49850i	−0.103805	−	0.179796i
$627$	34.2991	−	7.29049i	1.36977	−	0.291154i
$628$	−3.83725	−	11.8098i	−0.153123	−	0.471264i
$629$	0.397907	+	0.0845777i	0.0158656	+	0.00337233i
$630$	−0.0112615	−	0.107146i	−0.000448670	−	0.00426881i
$631$	2.18675	+	2.42863i	0.0870532	+	0.0966824i	0.785097	−	0.619372i	$-0.212613\pi$
$631$	2.18675	+	2.42863i	0.0870532	+	0.0966824i	−0.698044	+	0.716055i	$0.745946\pi$
$632$	14.0641	+	6.26175i	0.559440	+	0.249079i
$633$	19.0222	−	8.46923i	0.756065	−	0.336622i
$634$	−6.51718	+	7.23806i	−0.258830	+	0.287460i
$635$	0.0638232	+	0.0463703i	0.00253275	+	0.00184015i
$636$	−9.18334	−	6.67209i	−0.364143	−	0.264565i
$637$	0.776351	−	0.862225i	0.0307601	−	0.0341626i
$638$	−45.4832	+	20.2504i	−1.80070	+	0.801721i
$639$	1.03116	+	0.459103i	0.0407921	+	0.0181618i
$640$	−0.669131	−	0.743145i	−0.0264497	−	0.0293754i
$641$	−1.26095	−	11.9972i	−0.0498047	−	0.473860i	−0.990789	−	0.135411i	$-0.956764\pi$
$641$	−1.26095	−	11.9972i	−0.0498047	−	0.473860i	0.940985	−	0.338449i	$-0.109902\pi$
$642$	−14.3838	−	3.05737i	−0.567683	−	0.120665i
$643$	12.1711	+	37.4588i	0.479982	+	1.47723i	0.839120	+	0.543947i	$0.183071\pi$
$643$	12.1711	+	37.4588i	0.479982	+	1.47723i	−0.359138	+	0.933284i	$0.616929\pi$
$644$	−0.543131	+	0.115446i	−0.0214023	+	0.00454921i
$645$	−4.28252	−	7.41755i	−0.168624	−	0.292066i
$646$	−0.407638	+	0.706050i	−0.0160383	+	0.0277792i
$647$	−4.36199	+	13.4248i	−0.171488	+	0.527785i	−0.999456	−	0.0329907i	$-0.989497\pi$
$647$	−4.36199	+	13.4248i	−0.171488	+	0.527785i	0.827968	+	0.560775i	$0.189497\pi$
$648$	0.104528	−	0.994522i	0.00410627	−	0.0390685i
$649$	37.3949	−	27.1690i	1.46788	−	1.06648i
$650$	0.166024			0.00651198
$651$	0.317247	−	0.509093i	0.0124339	−	0.0199529i
$652$	−14.3729			−0.562886
$653$	−24.1698	+	17.5604i	−0.945838	+	0.687191i	−0.949819	−	0.312801i	$-0.898733\pi$
$653$	−24.1698	+	17.5604i	−0.945838	+	0.687191i	0.00398102	+	0.999992i	$0.498733\pi$
$654$	1.75128	−	16.6624i	0.0684807	−	0.651550i
$655$	−5.90570	+	18.1759i	−0.230755	+	0.710190i
$656$	−3.39883	+	5.88694i	−0.132702	+	0.229846i
$657$	−1.96489	−	3.40329i	−0.0766577	−	0.132775i
$658$	−0.538258	+	0.114410i	−0.0209835	+	0.00446018i
$659$	−11.1959	−	34.4574i	−0.436130	−	1.34227i	−0.891924	−	0.452185i	$-0.850645\pi$
$659$	−11.1959	−	34.4574i	−0.436130	−	1.34227i	0.455794	−	0.890085i	$-0.349355\pi$
$660$	−5.61444	−	1.19339i	−0.218542	−	0.0464525i
$661$	−1.47543	−	14.0378i	−0.0573876	−	0.546006i	−0.985011	−	0.172490i	$-0.944819\pi$
$661$	−1.47543	−	14.0378i	−0.0573876	−	0.546006i	0.927624	−	0.373516i	$-0.121848\pi$
$662$	0.407085	+	0.452114i	0.0158218	+	0.0175719i
$663$	0.0202409	+	0.00901181i	0.000786090	+	0.000349990i
$664$	10.8635	−	4.83674i	0.421585	−	0.187702i
$665$	0.440402	−	0.489116i	0.0170781	−	0.0189671i
$666$	−2.46607	−	1.79171i	−0.0955583	−	0.0694272i
$667$	−36.1670	−	26.2769i	−1.40039	−	1.01745i
$668$	−10.7837	+	11.9765i	−0.417234	+	0.463385i
$669$	−14.4320	+	6.42555i	−0.557974	+	0.248426i
$670$	9.24320	+	4.11534i	0.357096	+	0.158989i
$671$	−31.4308	−	34.9075i	−1.21337	−	1.34759i
$672$	0.0112615	+	0.107146i	0.000434423	+	0.00413326i
$673$	−9.33319	−	1.98383i	−0.359768	−	0.0764711i	0.0244816	−	0.999700i	$-0.492206\pi$
$673$	−9.33319	−	1.98383i	−0.359768	−	0.0764711i	−0.384250	+	0.923229i	$0.625540\pi$
$674$	6.40777	+	19.7211i	0.246818	+	0.759628i
$675$	0.978148	−	0.207912i	0.0376489	−	0.00800252i
$676$	6.48622	+	11.2345i	0.249470	+	0.432095i
$677$	−2.13314	+	3.69470i	−0.0819832	+	0.141999i	−0.904102	−	0.427317i	$-0.859459\pi$
$677$	−2.13314	+	3.69470i	−0.0819832	+	0.141999i	0.822119	+	0.569316i	$0.192792\pi$
$678$	−5.80925	+	17.8790i	−0.223103	+	0.686640i
$679$	0.0663573	−	0.631348i	0.00254656	−	0.0242289i
$680$	0.107966	−	0.0784418i	0.00414030	−	0.00300811i
$681$	−13.9216			−0.533478
$682$	−20.5725	−	24.4562i	−0.787761	−	0.936475i
$683$	42.6174			1.63071			0.815354	−	0.578963i	$-0.196542\pi$
$683$	42.6174			1.63071			0.815354	+	0.578963i	$0.196542\pi$
$684$	4.94235	−	3.59083i	0.188975	−	0.137299i
$685$	−2.35941	+	22.4483i	−0.0901485	+	0.857706i
$686$	−0.465707	+	1.43330i	−0.0177808	+	0.0547236i
$687$	−6.32305	+	10.9518i	−0.241239	+	0.417839i
$688$	4.28252	+	7.41755i	0.163270	+	0.282791i
$689$	−1.84339	+	0.391825i	−0.0702275	+	0.0149273i
$690$	−1.59265	−	4.90166i	−0.0606310	−	0.186603i
$691$	45.5246	+	9.67655i	1.73184	+	0.368113i	0.962616	−	0.270869i	$-0.0873111\pi$
$691$	45.5246	+	9.67655i	1.73184	+	0.368113i	0.769221	+	0.638983i	$0.220644\pi$
$692$	−0.254892	−	2.42513i	−0.00968953	−	0.0921897i
$693$	0.413786	+	0.459556i	0.0157184	+	0.0174571i
$694$	−3.77041	−	1.67869i	−0.143123	−	0.0637223i
$695$	−11.5258	+	5.13160i	−0.437197	+	0.194653i
$696$	−5.80402	+	6.44602i	−0.220001	+	0.244336i
$697$	−0.733914	−	0.533220i	−0.0277990	−	0.0201972i
$698$	10.7664	+	7.82228i	0.407516	+	0.296078i
$699$	−3.31566	+	3.68242i	−0.125410	+	0.139282i
$700$	−0.0984221	+	0.0438204i	−0.00372001	+	0.00165625i
$701$	−15.0279	−	6.69085i	−0.567596	−	0.252710i	0.102814	−	0.994701i	$-0.467215\pi$
$701$	−15.0279	−	6.69085i	−0.567596	−	0.252710i	−0.670410	+	0.741991i	$0.733882\pi$
$702$	−0.111091	−	0.123380i	−0.00419288	−	0.00465666i
$703$	−1.94652	−	18.5199i	−0.0734143	−	0.698490i
$704$	5.61444	+	1.19339i	0.211602	+	0.0449775i
$705$	−1.57836	−	4.85769i	−0.0594445	−	0.182951i
$706$	−14.0549	+	2.98746i	−0.528962	+	0.112434i
$707$	−0.137194	−	0.237627i	−0.00515972	−	0.00893689i
$708$	4.02646	−	6.97403i	0.151323	−	0.262100i
$709$	15.1145	−	46.5176i	0.567636	−	1.74700i	−0.0923511	−	0.995727i	$-0.529438\pi$
$709$	15.1145	−	46.5176i	0.567636	−	1.74700i	0.659987	−	0.751277i	$-0.270562\pi$
$710$	0.117986	−	1.12256i	0.00442794	−	0.0421291i
$711$	12.4549	−	9.04901i	0.467095	−	0.339364i
$712$	3.35221			0.125630
$713$	9.78136	−	26.9773i	0.366315	−	1.01031i
$714$	−0.0143778			−0.000538075
$715$	−0.770956	+	0.560132i	−0.0288321	+	0.0209478i
$716$	−0.0503870	+	0.479400i	−0.00188305	+	0.0179160i
$717$	−1.03618	+	3.18904i	−0.0386969	+	0.119097i
$718$	−0.599221	+	1.03788i	−0.0223627	+	0.0387334i
$719$	23.5984	+	40.8736i	0.880071	+	1.52433i	0.851261	+	0.524743i	$0.175838\pi$
$719$	23.5984	+	40.8736i	0.880071	+	1.52433i	0.0288099	+	0.999585i	$0.490828\pi$
$720$	−0.978148	+	0.207912i	−0.0364534	+	0.00774841i
$721$	0.153795	+	0.473333i	0.00572764	+	0.0176279i
$722$	17.9205	+	3.80912i	0.666932	+	0.141761i
$723$	0.714661	+	6.79955i	0.0265785	+	0.252878i
$724$	−1.79826	−	1.99717i	−0.0668318	−	0.0742243i
$725$	−7.92407	−	3.52802i	−0.294293	−	0.131027i
$726$	20.0488	−	8.92630i	0.744081	−	0.331286i
$727$	12.6061	−	14.0005i	0.467536	−	0.519251i	−0.462550	−	0.886593i	$-0.653065\pi$
$727$	12.6061	−	14.0005i	0.467536	−	0.519251i	0.930086	+	0.367342i	$0.119732\pi$
$728$	0.0144707	+	0.0105136i	0.000536320	+	0.000389660i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−2.62954	+	2.92040i	−0.0973236	+	0.108089i
$731$	−1.04421	+	0.464913i	−0.0386216	+	0.0171954i
$732$	−7.47606	−	3.32856i	−0.276323	−	0.123027i
$733$	6.24376	+	6.93439i	0.230618	+	0.256128i	0.847336	−	0.531056i	$-0.178205\pi$
$733$	6.24376	+	6.93439i	0.230618	+	0.256128i	−0.616718	+	0.787184i	$0.711538\pi$
$734$	−3.43270	−	32.6599i	−0.126703	−	1.20550i
$735$	−6.83568	−	1.45297i	−0.252138	−	0.0535936i
$736$	1.59265	+	4.90166i	0.0587057	+	0.180678i
$737$	−56.8066	+	12.0746i	−2.09250	+	0.444774i
$738$	3.39883	+	5.88694i	0.125113	+	0.216701i
$739$	−8.97634	+	15.5475i	−0.330200	+	0.571923i	−0.982551	−	0.185994i	$-0.940450\pi$
$739$	−8.97634	+	15.5475i	−0.330200	+	0.571923i	0.652351	+	0.757917i	$0.273783\pi$
$740$	−0.941955	+	2.89904i	−0.0346270	+	0.106571i
$741$	0.106018	−	1.00869i	0.00389467	−	0.0370553i
$742$	0.989380	−	0.718827i	0.0363213	−	0.0263890i
$743$	−3.04809			−0.111824			−0.0559118	−	0.998436i	$-0.517807\pi$
$743$	−3.04809			−0.111824			−0.0559118	+	0.998436i	$0.517807\pi$
$744$	−5.00727	−	2.43459i	−0.183575	−	0.0892564i
$745$	21.1199			0.773773
$746$	1.39163	−	1.01108i	0.0509512	−	0.0370182i
$747$	1.24301	−	11.8264i	0.0454793	−	0.432706i
$748$	−0.236708	+	0.728513i	−0.00865491	+	0.0266371i
$749$	0.792139	−	1.37203i	0.0289441	−	0.0501327i
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	20.8929	−	4.44093i	0.762394	−	0.162052i	0.189724	−	0.981838i	$-0.439241\pi$
$751$	20.8929	−	4.44093i	0.762394	−	0.162052i	0.572671	+	0.819786i	$0.305907\pi$
$752$	1.57836	+	4.85769i	0.0575569	+	0.177142i
$753$	−11.7568	−	2.49898i	−0.428441	−	0.0910680i
$754$	0.150530	+	1.43220i	0.00548197	+	0.0521575i
$755$	10.4027	+	11.5534i	0.378593	+	0.420470i
$756$	0.0984221	+	0.0438204i	0.00357958	+	0.00159373i
$757$	7.13205	−	3.17539i	0.259219	−	0.115412i	−0.273013	−	0.962010i	$-0.588020\pi$
$757$	7.13205	−	3.17539i	0.259219	−	0.115412i	0.532232	+	0.846599i	$0.321354\pi$
$758$	−6.62479	+	7.35758i	−0.240623	+	0.267239i
$759$	23.9330	+	17.3883i	0.868713	+	0.631157i
$760$	−4.94235	−	3.59083i	−0.179278	−	0.130253i
$761$	16.8214	−	18.6821i	0.609776	−	0.677225i	−0.356630	−	0.934246i	$-0.616074\pi$
$761$	16.8214	−	18.6821i	0.609776	−	0.677225i	0.966406	+	0.257021i	$0.0827408\pi$
$762$	−0.0720694	+	0.0320874i	−0.00261080	+	0.00116240i
$763$	1.64898	+	0.734173i	0.0596970	+	0.0265788i
$764$	−11.7743	−	13.0767i	−0.425981	−	0.473099i
$765$	−0.0139497	−	0.132722i	−0.000504351	−	0.00479858i
$766$	25.8162	+	5.48741i	0.932778	+	0.198268i
$767$	−0.413147	−	1.27154i	−0.0149179	−	0.0459125i
$768$	0.978148	−	0.207912i	0.0352959	−	0.00750237i
$769$	10.1283	+	17.5428i	0.365236	+	0.632608i	0.988814	−	0.149153i	$-0.0476548\pi$
$769$	10.1283	+	17.5428i	0.365236	+	0.632608i	−0.623578	+	0.781761i	$0.714321\pi$
$770$	0.309197	−	0.535545i	0.0111427	−	0.0192997i
$771$	−0.112667	+	0.346752i	−0.00405759	+	0.0124880i
$772$	1.50739	−	14.3419i	0.0542522	−	0.516175i
$773$	−0.424780	+	0.308621i	−0.0152783	+	0.0111003i	−0.595398	−	0.803431i	$-0.703006\pi$
$773$	−0.424780	+	0.308621i	−0.0152783	+	0.0111003i	0.580120	+	0.814531i	$0.303006\pi$
$774$	8.56505			0.307864
$775$	0.768102	−	5.51453i	0.0275910	−	0.198088i
$776$	−5.89239			−0.211525
$777$	0.265686	−	0.193032i	0.00953142	−	0.00692499i
$778$	0.615095	−	5.85224i	0.0220522	−	0.209813i
$779$	−12.8327	+	39.4949i	−0.459778	+	1.41505i
$780$	−0.0830118	+	0.143781i	−0.00297230	+	0.00514817i
$781$	3.23943	+	5.61086i	0.115916	+	0.200772i
$782$	−0.672776	+	0.143003i	−0.0240584	+	0.00511377i
$783$	2.68041	+	8.24944i	0.0957899	+	0.294811i
$784$	6.83568	+	1.45297i	0.244131	+	0.0518917i
$785$	1.29799	+	12.3496i	0.0463274	+	0.440776i
$786$	−12.7879	−	14.2024i	−0.456130	−	0.506584i
$787$	−35.2060	−	15.6747i	−1.25496	−	0.558743i	−0.331868	−	0.943326i	$-0.607679\pi$
$787$	−35.2060	−	15.6747i	−1.25496	−	0.558743i	−0.923091	+	0.384583i	$0.874345\pi$
$788$	12.3037	−	5.47798i	0.438302	−	0.195145i
$789$	−0.696293	+	0.773312i	−0.0247887	+	0.0275306i
$790$	−12.4549	−	9.04901i	−0.443125	−	0.321949i
$791$	−1.63854	−	1.19047i	−0.0582599	−	0.0423283i
$792$	3.84073	−	4.26556i	0.136474	−	0.151570i
$793$	−1.24120	+	0.552619i	−0.0440764	+	0.0196241i
$794$	−16.6825	−	7.42751i	−0.592038	−	0.263592i
$795$	7.59546	+	8.43561i	0.269383	+	0.299180i
$796$	2.09654	+	19.9473i	0.0743099	+	0.707012i
$797$	30.7563	+	6.53745i	1.08944	+	0.231568i	0.717410	−	0.696651i	$-0.245327\pi$
$797$	30.7563	+	6.53745i	1.08944	+	0.231568i	0.372033	+	0.928219i	$0.378661\pi$
$798$	0.203386	+	0.625957i	0.00719978	+	0.0221586i
$799$	−0.666741	+	0.141720i	−0.0235876	+	0.00501370i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	1.67611	−	2.90310i	0.0592223	−	0.102576i
$802$	−10.3285	+	31.7879i	−0.364713	+	1.12247i
$803$	2.35779	−	22.4329i	0.0832047	−	0.791640i
$804$	−8.18559	+	5.94718i	−0.288683	+	0.209741i
$805$	0.555264			0.0195705
$806$	−0.856644	+	0.347333i	−0.0301740	+	0.0122343i
$807$	12.9380			0.455440
$808$	−2.06044	+	1.49700i	−0.0724861	+	0.0526642i
$809$	−2.25229	+	21.4291i	−0.0791862	+	0.753407i	0.880824	+	0.473443i	$0.156989\pi$
$809$	−2.25229	+	21.4291i	−0.0791862	+	0.753407i	−0.960011	+	0.279964i	$0.909678\pi$
$810$	−0.309017	+	0.951057i	−0.0108578	+	0.0334167i
$811$	−9.03862	+	15.6554i	−0.317389	+	0.549734i	−0.979942	−	0.199281i	$-0.936139\pi$
$811$	−9.03862	+	15.6554i	−0.317389	+	0.549734i	0.662553	+	0.749015i	$0.269473\pi$
$812$	−0.467252	−	0.809304i	−0.0163973	−	0.0284010i
$813$	25.4432	−	5.40811i	0.892331	−	0.189671i
$814$	−5.40671	−	16.6401i	−0.189505	−	0.583236i
$815$	14.0588	+	2.98829i	0.492458	+	0.104675i
$816$	0.0139497	+	0.132722i	0.000488336	+	0.00464620i
$817$	35.0120	+	38.8847i	1.22491	+	1.36040i
$818$	2.33519	+	1.03969i	0.0816479	+	0.0363520i
$819$	0.0163404	−	0.00727521i	0.000570980	−	0.000254216i
$820$	4.54852	−	5.05164i	0.158841	−	0.176411i
$821$	−3.62380	−	2.63284i	−0.126471	−	0.0918869i	0.522751	−	0.852485i	$-0.324906\pi$
$821$	−3.62380	−	2.63284i	−0.126471	−	0.0918869i	−0.649223	+	0.760598i	$0.724906\pi$
$822$	−18.2611	−	13.2675i	−0.636929	−	0.462756i
$823$	−6.00828	+	6.67287i	−0.209435	+	0.232602i	−0.838706	−	0.544585i	$-0.816687\pi$
$823$	−6.00828	+	6.67287i	−0.209435	+	0.232602i	0.629270	+	0.777187i	$0.283354\pi$
$824$	4.22015	−	1.87893i	0.147016	−	0.0654558i
$825$	5.24364	+	2.33462i	0.182560	+	0.0812809i
$826$	0.580532	+	0.644747i	0.0201993	+	0.0224336i
$827$	2.99129	+	28.4602i	0.104017	+	0.989658i	0.914689	+	0.404157i	$0.132435\pi$
$827$	2.99129	+	28.4602i	0.104017	+	0.989658i	−0.810672	+	0.585500i	$0.800898\pi$
$828$	5.04129	+	1.07156i	0.175197	+	0.0372392i
$829$	2.52462	+	7.76997i	0.0876836	+	0.269862i	0.985278	−	0.170960i	$-0.0546869\pi$
$829$	2.52462	+	7.76997i	0.0876836	+	0.269862i	−0.897594	+	0.440822i	$0.854687\pi$
$830$	−11.6317	+	2.47240i	−0.403742	+	0.0858181i
$831$	−6.50510	−	11.2672i	−0.225660	−	0.390854i
$832$	0.0830118	−	0.143781i	0.00287792	−	0.00498470i
$833$	−0.288196	+	0.886977i	−0.00998541	+	0.0307319i
$834$	1.31878	−	12.5474i	0.0456658	−	0.434481i
$835$	13.0381	−	9.47274i	0.451202	−	0.327818i
$836$	35.0653			1.21276
$837$	−4.61205	+	3.11913i	−0.159416	+	0.107813i
$838$	−24.2738			−0.838523
$839$	7.02351	−	5.10288i	0.242478	−	0.176171i	−0.459908	−	0.887966i	$-0.652118\pi$
$839$	7.02351	−	5.10288i	0.242478	−	0.176171i	0.702387	+	0.711796i	$0.252118\pi$
$840$	0.0112615	−	0.107146i	0.000388560	−	0.00369690i
$841$	14.2883	−	43.9748i	0.492699	−	1.51637i
$842$	−12.7411	+	22.0683i	−0.439088	+	0.760523i
$843$	2.84497	+	4.92763i	0.0979860	+	0.169717i
$844$	20.3674	−	4.32922i	0.701074	−	0.149018i
$845$	−4.00870	−	12.3375i	−0.137904	−	0.424424i
$846$	4.99606	+	1.06195i	0.171768	+	0.0365105i
$847$	0.247147	+	2.35145i	0.00849208	+	0.0807967i
$848$	−7.59546	−	8.43561i	−0.260829	−	0.289680i
$849$	−5.12963	−	2.28386i	−0.176048	−	0.0783818i
$850$	−0.121916	+	0.0542803i	−0.00418167	+	0.00186180i
$851$	10.5123	−	11.6750i	0.360356	−	0.400215i
$852$	0.913176	+	0.663461i	0.0312849	+	0.0227298i
$853$	42.4894	+	30.8704i	1.45481	+	1.05698i	0.984677	+	0.174386i	$0.0557940\pi$
$853$	42.4894	+	30.8704i	1.45481	+	1.05698i	0.470133	+	0.882596i	$0.344206\pi$
$854$	0.589951	−	0.655207i	0.0201877	−	0.0224207i
$855$	−5.58092	+	2.48479i	−0.190863	+	0.0849779i
$856$	−13.4338	−	5.98112i	−0.459158	−	0.204430i
$857$	−12.7964	−	14.2119i	−0.437117	−	0.485468i	0.483826	−	0.875164i	$-0.339247\pi$
$857$	−12.7964	−	14.2119i	−0.437117	−	0.485468i	−0.920943	+	0.389696i	$0.872580\pi$
$858$	−0.0996108	−	0.947734i	−0.00340066	−	0.0323551i
$859$	30.9192	+	6.57208i	1.05495	+	0.224236i	0.702565	−	0.711619i	$-0.252038\pi$
$859$	30.9192	+	6.57208i	1.05495	+	0.224236i	0.352384	+	0.935856i	$0.385371\pi$
$860$	−2.64675	−	8.14585i	−0.0902533	−	0.277771i
$861$	−0.716351	+	0.152265i	−0.0244132	+	0.00518918i
$862$	−3.82597	−	6.62678i	−0.130313	−	0.225709i
$863$	18.2805	−	31.6627i	0.622274	−	1.07781i	−0.366787	−	0.930305i	$-0.619542\pi$
$863$	18.2805	−	31.6627i	0.622274	−	1.07781i	0.989061	−	0.147505i	$-0.0471244\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$	−0.254892	+	2.42513i	−0.00866658	+	0.0824570i
$866$	10.2362	−	7.43703i	0.347840	−	0.252721i
$867$	16.9822			0.576745
$868$	0.416161	−	0.432009i	0.0141254	−	0.0146633i
$869$	88.3659			2.99761
$870$	7.01739	−	5.09843i	0.237912	−	0.172853i
$871$	−0.175589	+	1.67061i	−0.00594960	+	0.0566066i
$872$	5.17731	−	15.9341i	0.175326	−	0.539598i
$873$	−2.94620	+	5.10296i	−0.0997136	+	0.172709i
$874$	15.7428	+	27.2674i	0.532509	+	0.922333i
$875$	0.105382	−	0.0223997i	0.00356257	−	0.000757247i
$876$	−1.21437	−	3.73745i	−0.0410298	−	0.126277i
$877$	−29.3759	−	6.24404i	−0.991954	−	0.210846i	−0.316775	−	0.948501i	$-0.602600\pi$
$877$	−29.3759	−	6.24404i	−0.991954	−	0.210846i	−0.675179	+	0.737654i	$0.735933\pi$
$878$	−2.22650	−	21.1837i	−0.0751406	−	0.714915i
$879$	12.6613	+	14.0618i	0.427055	+	0.474292i
$880$	−5.24364	−	2.33462i	−0.176763	−	0.0786999i
$881$	−22.4755	+	10.0067i	−0.757218	+	0.337135i	−0.748771	−	0.662829i	$-0.769356\pi$
$881$	−22.4755	+	10.0067i	−0.757218	+	0.337135i	−0.00844740	+	0.999964i	$0.502689\pi$
$882$	4.67615	−	5.19339i	0.157454	−	0.174870i
$883$	−25.2412	−	18.3388i	−0.849435	−	0.617151i	0.0755549	−	0.997142i	$-0.475927\pi$
$883$	−25.2412	−	18.3388i	−0.849435	−	0.617151i	−0.924990	+	0.379991i	$0.875927\pi$
$884$	0.0179249	+	0.0130232i	0.000602879	+	0.000438017i
$885$	−5.38845	+	5.98448i	−0.181131	+	0.201166i
$886$	−3.42790	+	1.52620i	−0.115162	+	0.0512736i
$887$	5.82017	+	2.59131i	0.195422	+	0.0870075i	0.502114	−	0.864801i	$-0.332556\pi$
$887$	5.82017	+	2.59131i	0.195422	+	0.0870075i	−0.306692	+	0.951809i	$0.599222\pi$
$888$	−2.03967	−	2.26528i	−0.0684467	−	0.0760177i
$889$	−0.000888419	−	0.00845275i	−2.97966e−5	−	0.000283496i
$890$	−3.27896	−	0.696964i	−0.109911	−	0.0233623i
$891$	−1.77372	−	5.45894i	−0.0594218	−	0.182882i
$892$	−15.4526	+	3.28455i	−0.517391	+	0.109975i
$893$	15.6016	+	27.0228i	0.522088	+	0.904283i
$894$	−10.5600	+	18.2904i	−0.353178	+	0.611722i
$895$	0.148959	−	0.458448i	0.00497915	−	0.0153242i
$896$	−0.0112615	+	0.107146i	−0.000376221	+	0.00357951i
$897$	0.692252	−	0.502951i	0.0231136	−	0.0167930i
$898$	−1.12239			−0.0374548
$899$	48.2673	+	1.62610i	1.60980	+	0.0542335i
$900$	1.00000			0.0333333
$901$	1.22555	−	0.890411i	0.0408288	−	0.0296639i
$902$	−4.07846	+	38.8039i	−0.135798	+	1.29203i
$903$	−0.285151	+	0.877605i	−0.00948923	+	0.0292048i
$904$	−9.39956	+	16.2805i	−0.312625	+	0.541482i
$905$	1.34373	+	2.32741i	0.0446671	+	0.0773656i
$906$	−15.2069	+	3.23232i	−0.505214	+	0.107387i
$907$	−0.439917	−	1.35393i	−0.0146072	−	0.0449564i	0.943487	−	0.331409i	$-0.107524\pi$
$907$	−0.439917	−	1.35393i	−0.0146072	−	0.0449564i	−0.958094	+	0.286452i	$0.907524\pi$
$908$	−13.6174	−	2.89447i	−0.451910	−	0.0960564i
$909$	0.266218	+	2.53289i	0.00882989	+	0.0840108i
$910$	−0.0119686	−	0.0132925i	−0.000396755	−	0.000440641i
$911$	14.2715	+	6.35407i	0.472835	+	0.210520i	0.629298	−	0.777164i	$-0.283343\pi$
$911$	14.2715	+	6.35407i	0.472835	+	0.210520i	−0.156463	+	0.987684i	$0.550009\pi$
$912$	5.58092	−	2.48479i	0.184803	−	0.0822795i
$913$	45.6722	−	50.7242i	1.51153	−	1.67872i
$914$	−11.6569	−	8.46925i	−0.385577	−	0.280138i
$915$	6.62064	+	4.81018i	0.218872	+	0.159020i
$916$	−8.46190	+	9.39789i	−0.279589	+	0.310515i
$917$	1.88097	−	0.837461i	0.0621151	−	0.0276554i
$918$	0.121916	+	0.0542803i	0.00402381	+	0.00179152i
$919$	−0.200270	−	0.222423i	−0.00660631	−	0.00733705i	0.739833	−	0.672791i	$-0.234905\pi$
$919$	−0.200270	−	0.222423i	−0.00660631	−	0.00733705i	−0.746439	+	0.665454i	$0.768238\pi$
$920$	−0.538731	−	5.12568i	−0.0177614	−	0.168989i
$921$	13.2731	+	2.82129i	0.437364	+	0.0929647i
$922$	1.88677	+	5.80687i	0.0621373	+	0.191239i
$923$	0.183304	−	0.0389624i	0.00603351	−	0.00128246i
$924$	0.309197	+	0.535545i	0.0101718	+	0.0176181i
$925$	1.52412	−	2.63985i	0.0501126	−	0.0867976i
$926$	5.27151	−	16.2240i	0.173233	−	0.533155i
$927$	0.482873	−	4.59423i	0.0158596	−	0.150894i
$928$	−7.01739	+	5.09843i	−0.230357	+	0.167364i
$929$	8.58264			0.281587			0.140794	−	0.990039i	$-0.455035\pi$
$929$	8.58264			0.281587			0.140794	+	0.990039i	$0.455035\pi$
$930$	4.39167	+	3.42246i	0.144009	+	0.112227i
$931$	42.6926			1.39919
$932$	−4.00882	+	2.91258i	−0.131313	+	0.0954048i
$933$	1.96586	−	18.7040i	0.0643595	−	0.612340i
$934$	10.1087	−	31.1113i	0.330765	−	1.01799i
$935$	0.383002	−	0.663379i	0.0125255	−	0.0216948i
$936$	−0.0830118	−	0.143781i	−0.00271332	−	0.00469962i
$937$	18.8213	−	4.00058i	0.614864	−	0.130693i	0.110056	−	0.993925i	$-0.464897\pi$
$937$	18.8213	−	4.00058i	0.614864	−	0.130693i	0.504807	+	0.863232i	$0.331564\pi$
$938$	−0.336851	−	1.03672i	−0.0109986	−	0.0338501i
$939$	−5.08091	−	1.07998i	−0.165809	−	0.0352438i
$940$	−0.533898	−	5.07970i	−0.0174138	−	0.165682i
$941$	25.4349	+	28.2483i	0.829152	+	0.920867i	0.997899	−	0.0647924i	$-0.0206385\pi$
$941$	25.4349	+	28.2483i	0.829152	+	0.920867i	−0.168746	+	0.985660i	$0.553972\pi$
$942$	−11.3440	−	5.05070i	−0.369609	−	0.164561i
$943$	−32.0056	+	14.2498i	−1.04225	+	0.464038i
$944$	5.38845	−	5.98448i	0.175379	−	0.194778i
$945$	−0.0871606	−	0.0633259i	−0.00283534	−	0.00205999i
$946$	39.7731	+	28.8969i	1.29314	+	0.939518i
$947$	−36.3487	+	40.3693i	−1.18117	+	1.31183i	−0.241240	+	0.970466i	$0.577554\pi$
$947$	−36.3487	+	40.3693i	−1.18117	+	1.31183i	−0.939933	+	0.341359i	$0.889113\pi$
$948$	14.0641	−	6.26175i	0.456781	−	0.203372i
$949$	−0.596031	−	0.265370i	−0.0193480	−	0.00861427i
$950$	4.08777	+	4.53993i	0.132625	+	0.147295i
$951$	1.01808	+	9.68642i	0.0330136	+	0.314104i
$952$	−0.0140636	−	0.00298931i	−0.000455803	−	9.68840e-5i
$953$	11.6299	+	35.7932i	0.376730	+	1.15945i	0.942304	+	0.334757i	$0.108654\pi$
$953$	11.6299	+	35.7932i	0.376730	+	1.15945i	−0.565575	+	0.824697i	$0.691346\pi$
$954$	−11.1032	+	2.36005i	−0.359479	+	0.0764096i
$955$	8.79824	+	15.2390i	0.284704	+	0.493122i
$956$	−1.67658	+	2.90392i	−0.0542244	+	0.0939194i
$957$	−15.3852	+	47.3507i	−0.497333	+	1.53063i
$958$	−2.28786	+	21.7675i	−0.0739174	+	0.703277i
$959$	1.96739	−	1.42939i	0.0635302	−	0.0461574i
$960$	−1.00000			−0.0322749
$961$	7.57354	+	30.0606i	0.244308	+	0.969698i
$962$	−0.506078			−0.0163166
$963$	−11.8967	+	8.64346i	−0.383366	+	0.278532i
$964$	−0.714661	+	6.79955i	−0.0230177	+	0.218999i
$965$	−4.45629	+	13.7150i	−0.143453	+	0.441503i
$966$	−0.277632	+	0.480873i	−0.00893267	+	0.0154718i
$967$	−4.77169	−	8.26482i	−0.153447	−	0.265779i	0.779045	−	0.626968i	$-0.215704\pi$
$967$	−4.77169	−	8.26482i	−0.153447	−	0.265779i	−0.932493	+	0.361189i	$0.882371\pi$
$968$	21.4666	−	4.56286i	0.689962	−	0.146656i
$969$	0.251934	+	0.775374i	0.00809329	+	0.0249086i
$970$	5.76363	+	1.22510i	0.185059	+	0.0393355i
$971$	4.98789	+	47.4566i	0.160069	+	1.52296i	0.719742	+	0.694242i	$0.244260\pi$
$971$	4.98789	+	47.4566i	0.160069	+	1.52296i	−0.559673	+	0.828714i	$0.689073\pi$
$972$	−0.669131	−	0.743145i	−0.0214624	−	0.0238364i
$973$	1.24174	+	0.552860i	0.0398085	+	0.0177239i
$974$	−34.0992	+	15.1820i	−1.09261	+	0.486461i
$975$	0.111091	−	0.123380i	0.00355777	−	0.00395131i
$976$	−6.62064	−	4.81018i	−0.211922	−	0.153970i
$977$	−25.2605	−	18.3528i	−0.808154	−	0.587158i	0.105141	−	0.994457i	$-0.466471\pi$
$977$	−25.2605	−	18.3528i	−0.808154	−	0.587158i	−0.913295	+	0.407299i	$0.866471\pi$
$978$	−9.61734	+	10.6811i	−0.307529	+	0.341545i
$979$	17.5778	−	7.82614i	0.561789	−	0.250124i
$980$	−6.38421	−	2.84244i	−0.203936	−	0.0907983i
$981$	−11.2107	−	12.4508i	−0.357930	−	0.397522i
$982$	2.29031	+	21.7908i	0.0730867	+	0.695373i
$983$	18.7774	+	3.99127i	0.598907	+	0.127302i	0.497382	−	0.867531i	$-0.334295\pi$
$983$	18.7774	+	3.99127i	0.598907	+	0.127302i	0.101525	+	0.994833i	$0.467628\pi$
$984$	2.10059	+	6.46495i	0.0669644	+	0.206095i
$985$	−13.1738	+	2.80018i	−0.419752	+	0.0892211i
$986$	−0.578785	−	1.00248i	−0.0184323	−	0.0319256i
$987$	−0.275142	+	0.476559i	−0.00875785	+	0.0151690i
$988$	0.313421	−	0.964610i	0.00997124	−	0.0306883i
$989$	−4.61425	+	43.9017i	−0.146725	+	1.39599i
$990$	−4.64366	+	3.37381i	−0.147585	+	0.107227i
$991$	−32.4113			−1.02958			−0.514789	−	0.857317i	$-0.672130\pi$
$991$	−32.4113			−1.02958			−0.514789	+	0.857317i	$0.672130\pi$
$992$	−4.39167	−	3.42246i	−0.139436	−	0.108663i
$993$	0.608379			0.0193063
$994$	−0.0983823	+	0.0714789i	−0.00312050	+	0.00226717i
$995$	2.09654	−	19.9473i	0.0664648	−	0.632371i
$996$	3.67470	−	11.3096i	0.116437	−	0.358357i
$997$	26.8794	−	46.5565i	0.851279	−	1.47446i	−0.0287747	−	0.999586i	$-0.509161\pi$
$997$	26.8794	−	46.5565i	0.851279	−	1.47446i	0.880054	−	0.474873i	$-0.157506\pi$
$998$	−8.78396	−	15.2143i	−0.278052	−	0.481599i
$999$	−2.98162	+	0.633763i	−0.0943343	+	0.0200514i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.h.121.2	✓	24
31.10	even	15	inner	930.2.bg.h.661.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.h.121.2	✓	24	1.1	even	1	trivial
930.2.bg.h.661.2	yes	24	31.10	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)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.105382 - 0.0223997i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.105382 - 0.0223997i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(0.104528 + 0.994522i) q^{10} +(-3.84073 - 4.26556i) q^{11} +(-0.913545 - 0.406737i) q^{12} +(-0.151670 + 0.0675279i) q^{13} +(0.0720898 - 0.0800638i) q^{14} +(0.809017 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.0892976 - 0.0991750i) q^{17} +(-0.913545 + 0.406737i) q^{18} +(-5.58092 - 2.48479i) q^{19} +(0.669131 + 0.743145i) q^{20} +(-0.0112615 - 0.107146i) q^{21} +(-5.61444 - 1.19339i) q^{22} +(-1.59265 - 4.90166i) q^{23} +(-0.978148 + 0.207912i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.0830118 + 0.143781i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(0.0112615 - 0.107146i) q^{28} +(7.01739 - 5.09843i) q^{29} +1.00000 q^{30} +(4.39167 + 3.42246i) q^{31} -1.00000 q^{32} +(-4.64366 + 3.37381i) q^{33} +(0.0139497 - 0.132722i) q^{34} +(-0.0332924 + 0.102463i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.52412 + 2.63985i) q^{37} +(-5.97558 + 1.27015i) q^{38} +(0.0513041 + 0.157898i) q^{39} +(0.978148 + 0.207912i) q^{40} +(-0.710548 - 6.76041i) q^{41} +(-0.0720898 - 0.0800638i) q^{42} +(-7.82456 - 3.48372i) q^{43} +(-5.24364 + 2.33462i) q^{44} +(0.669131 - 0.743145i) q^{45} +(-4.16960 - 3.02939i) q^{46} +(-4.13220 - 3.00222i) q^{47} +(-0.669131 + 0.743145i) q^{48} +(-6.38421 + 2.84244i) q^{49} +(-0.913545 - 0.406737i) q^{50} +(-0.0892976 - 0.0991750i) q^{51} +(0.0173542 + 0.165114i) q^{52} +(11.1032 + 2.36005i) q^{53} +(0.309017 + 0.951057i) q^{54} +(5.61444 - 1.19339i) q^{55} +(-0.0538682 - 0.0933025i) q^{56} +(-3.05454 + 5.29062i) q^{57} +(2.68041 - 8.24944i) q^{58} +(-0.841758 + 8.00880i) q^{59} +(0.809017 - 0.587785i) q^{60} +8.18357 q^{61} +(5.56461 + 0.187469i) q^{62} -0.107736 q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.0173542 - 0.165114i) q^{65} +(-1.77372 + 5.45894i) q^{66} +(5.05897 - 8.76240i) q^{67} +(-0.0667266 - 0.115574i) q^{68} +(-5.04129 + 1.07156i) q^{69} +(0.0332924 + 0.102463i) q^{70} +(-1.10408 - 0.234680i) q^{71} +(0.104528 + 0.994522i) q^{72} +(2.62954 + 2.92040i) q^{73} +(2.78470 + 1.23983i) q^{74} +(-0.913545 + 0.406737i) q^{75} +(-4.08777 + 4.53993i) q^{76} +(-0.500291 - 0.363483i) q^{77} +(0.134316 + 0.0975862i) q^{78} +(-10.3013 + 11.4408i) q^{79} +(0.913545 - 0.406737i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-4.54852 - 5.05164i) q^{82} +(1.24301 + 11.8264i) q^{83} +(-0.105382 - 0.0223997i) q^{84} +(0.0412393 + 0.126922i) q^{85} +(-8.37788 + 1.78077i) q^{86} +(-4.33699 - 7.51188i) q^{87} +(-2.86994 + 4.97088i) q^{88} +(-1.03589 + 3.18814i) q^{89} +(0.104528 - 0.994522i) q^{90} +(-0.0144707 + 0.0105136i) q^{91} -5.15391 q^{92} +(3.86277 - 4.00987i) q^{93} -5.10768 q^{94} +(4.94235 - 3.59083i) q^{95} +(-0.104528 + 0.994522i) q^{96} +(1.82085 - 5.60400i) q^{97} +(-3.49420 + 6.05213i) q^{98} +(2.86994 + 4.97088i) 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

Varieties

Fields

Representations

Groups

Database

Properties

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