LMFDB - Embedded newform 930.2.bg.d.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 21x^{14} + 167x^{12} + 653x^{10} + 1350x^{8} + 1472x^{6} + 777x^{4} + 149x^{2} + 1 $ x^16 + 21x^14 + 167x^12 + 653x^10 + 1350x^8 + 1472x^6 + 777x^4 + 149*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			121.1
Root			$-1.94768i$ of defining polynomial
Character	$\chi$	$=$	930.121
Dual form			930.2.bg.d.661.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.12135 - 0.238351i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(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} +(1.12135 - 0.238351i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(0.104528 + 0.994522i) q^{10} +(-2.99498 - 3.32626i) q^{11} +(0.913545 + 0.406737i) q^{12} +(-0.205713 + 0.0915895i) q^{13} +(-0.767096 + 0.851946i) q^{14} +(0.809017 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.86128 - 2.06716i) q^{17} +(0.913545 - 0.406737i) q^{18} +(-0.936877 - 0.417124i) q^{19} +(-0.669131 - 0.743145i) q^{20} +(0.119832 + 1.14013i) q^{21} +(4.37811 + 0.930596i) q^{22} +(-2.29085 - 7.05052i) q^{23} +(-0.978148 + 0.207912i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.112591 - 0.195013i) q^{26} +(0.309017 - 0.951057i) q^{27} +(0.119832 - 1.14013i) q^{28} +(-2.29345 + 1.66629i) q^{29} -1.00000 q^{30} +(-3.07150 + 4.64391i) q^{31} +1.00000 q^{32} +(3.62110 - 2.63088i) q^{33} +(-0.290761 + 2.76640i) q^{34} +(0.354259 - 1.09030i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-4.17943 - 7.23899i) q^{37} +(1.00313 - 0.213222i) q^{38} +(-0.0695848 - 0.214160i) q^{39} +(0.978148 + 0.207912i) q^{40} +(-0.598588 - 5.69518i) q^{41} +(-0.767096 - 0.851946i) q^{42} +(4.33531 + 1.93020i) q^{43} +(-4.08896 + 1.82052i) q^{44} +(-0.669131 + 0.743145i) q^{45} +(5.99753 + 4.35746i) q^{46} +(-8.06615 - 5.86040i) q^{47} +(0.669131 - 0.743145i) q^{48} +(-5.19419 + 2.31260i) q^{49} +(0.913545 + 0.406737i) q^{50} +(1.86128 + 2.06716i) q^{51} +(0.0235378 + 0.223948i) q^{52} +(6.10240 + 1.29710i) q^{53} +(0.309017 + 0.951057i) q^{54} +(-4.37811 + 0.930596i) q^{55} +(0.573203 + 0.992817i) q^{56} +(0.512770 - 0.888143i) q^{57} +(0.876022 - 2.69612i) q^{58} +(0.699405 - 6.65439i) q^{59} +(0.809017 - 0.587785i) q^{60} +6.58814 q^{61} +(-0.244725 - 5.56238i) q^{62} -1.14641 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.0235378 + 0.223948i) q^{65} +(-1.38314 + 4.25685i) q^{66} +(4.83920 - 8.38174i) q^{67} +(-1.39082 - 2.40897i) q^{68} +(7.25136 - 1.54132i) q^{69} +(0.354259 + 1.09030i) q^{70} +(5.30226 + 1.12703i) q^{71} +(-0.104528 - 0.994522i) q^{72} +(5.63767 + 6.26127i) q^{73} +(7.63620 + 3.39986i) q^{74} +(0.913545 - 0.406737i) q^{75} +(-0.686220 + 0.762124i) q^{76} +(-4.15125 - 3.01606i) q^{77} +(0.182175 + 0.132358i) q^{78} +(5.87313 - 6.52277i) q^{79} +(-0.913545 + 0.406737i) q^{80} +(0.913545 + 0.406737i) q^{81} +(3.83181 + 4.25566i) q^{82} +(-0.927358 - 8.82322i) q^{83} +(1.12135 + 0.238351i) q^{84} +(-0.859575 - 2.64550i) q^{85} +(-4.64188 + 0.986663i) q^{86} +(-1.41743 - 2.45507i) q^{87} +(2.23796 - 3.87626i) q^{88} +(-0.556227 + 1.71189i) q^{89} +(0.104528 - 0.994522i) q^{90} +(-0.208847 + 0.151736i) q^{91} -7.41336 q^{92} +(-4.29741 - 3.54010i) q^{93} +9.97031 q^{94} +(-0.829679 + 0.602797i) q^{95} +(-0.104528 + 0.994522i) q^{96} +(-0.298153 + 0.917621i) q^{97} +(2.84288 - 4.92401i) q^{98} +(2.23796 + 3.87626i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 20 q^{13} - 4 q^{14} + 4 q^{15} - 4 q^{16} - 12 q^{17} + 2 q^{18} - 7 q^{19} - 2 q^{20} - 4 q^{21} + 11 q^{22} + 11 q^{23} + 2 q^{24} - 8 q^{25} + 5 q^{26} - 4 q^{27} - 4 q^{28} + 23 q^{29} - 16 q^{30} - 17 q^{31} + 16 q^{32} - 2 q^{33} - 2 q^{34} + 7 q^{35} - 8 q^{36} + 17 q^{37} - 2 q^{38} - 5 q^{39} - 2 q^{40} + 8 q^{41} - 4 q^{42} + 32 q^{43} + q^{44} - 2 q^{45} + 11 q^{46} - 7 q^{47} + 2 q^{48} - q^{49} + 2 q^{50} - 12 q^{51} + 10 q^{52} + 54 q^{53} - 4 q^{54} - 11 q^{55} + q^{56} + 18 q^{57} - 22 q^{58} - 38 q^{59} + 4 q^{60} - 28 q^{61} - 27 q^{62} - 2 q^{63} - 4 q^{64} - 10 q^{65} - 7 q^{66} + q^{67} - 2 q^{68} - 13 q^{69} + 7 q^{70} - 11 q^{71} + 2 q^{72} + 53 q^{73} + 2 q^{74} + 2 q^{75} - 2 q^{76} + 44 q^{77} + 10 q^{78} + 48 q^{79} - 2 q^{80} + 2 q^{81} + 8 q^{82} + 56 q^{83} + 11 q^{84} - 24 q^{85} - 13 q^{86} + q^{87} - 9 q^{88} - 43 q^{89} - 2 q^{90} - 50 q^{91} - 44 q^{92} - 22 q^{93} - 72 q^{94} - 14 q^{95} + 2 q^{96} + 17 q^{97} + 29 q^{98} - 9 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 20 * q^13 - 4 * q^14 + 4 * q^15 - 4 * q^16 - 12 * q^17 + 2 * q^18 - 7 * q^19 - 2 * q^20 - 4 * q^21 + 11 * q^22 + 11 * q^23 + 2 * q^24 - 8 * q^25 + 5 * q^26 - 4 * q^27 - 4 * q^28 + 23 * q^29 - 16 * q^30 - 17 * q^31 + 16 * q^32 - 2 * q^33 - 2 * q^34 + 7 * q^35 - 8 * q^36 + 17 * q^37 - 2 * q^38 - 5 * q^39 - 2 * q^40 + 8 * q^41 - 4 * q^42 + 32 * q^43 + q^44 - 2 * q^45 + 11 * q^46 - 7 * q^47 + 2 * q^48 - q^49 + 2 * q^50 - 12 * q^51 + 10 * q^52 + 54 * q^53 - 4 * q^54 - 11 * q^55 + q^56 + 18 * q^57 - 22 * q^58 - 38 * q^59 + 4 * q^60 - 28 * q^61 - 27 * q^62 - 2 * q^63 - 4 * q^64 - 10 * q^65 - 7 * q^66 + q^67 - 2 * q^68 - 13 * q^69 + 7 * q^70 - 11 * q^71 + 2 * q^72 + 53 * q^73 + 2 * q^74 + 2 * q^75 - 2 * q^76 + 44 * q^77 + 10 * q^78 + 48 * q^79 - 2 * q^80 + 2 * q^81 + 8 * q^82 + 56 * q^83 + 11 * q^84 - 24 * q^85 - 13 * q^86 + q^87 - 9 * q^88 - 43 * q^89 - 2 * q^90 - 50 * q^91 - 44 * q^92 - 22 * q^93 - 72 * q^94 - 14 * q^95 + 2 * q^96 + 17 * q^97 + 29 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$7$	1.12135	−	0.238351i	0.423832	−	0.0900883i	0.00894247	−	0.999960i	$-0.497153\pi$
$7$	1.12135	−	0.238351i	0.423832	−	0.0900883i	0.414890	+	0.909872i	$0.363820\pi$
$8$	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
$11$	−2.99498	−	3.32626i	−0.903019	−	1.00290i	−0.999971	−	0.00761529i	$-0.997576\pi$
$11$	−2.99498	−	3.32626i	−0.903019	−	1.00290i	0.0969519	−	0.995289i	$-0.469091\pi$
$12$	0.913545	+	0.406737i	0.263718	+	0.117415i
$13$	−0.205713	+	0.0915895i	−0.0570546	+	0.0254023i	−0.435066	−	0.900399i	$-0.643275\pi$
$13$	−0.205713	+	0.0915895i	−0.0570546	+	0.0254023i	0.378011	+	0.925801i	$0.376608\pi$
$14$	−0.767096	+	0.851946i	−0.205015	+	0.227692i
$15$	0.809017	+	0.587785i	0.208887	+	0.151765i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.86128	−	2.06716i	0.451427	−	0.501361i	−0.473875	−	0.880592i	$-0.657145\pi$
$17$	1.86128	−	2.06716i	0.451427	−	0.501361i	0.925302	+	0.379232i	$0.123812\pi$
$18$	0.913545	−	0.406737i	0.215325	−	0.0958687i
$19$	−0.936877	−	0.417124i	−0.214934	−	0.0956949i	0.296445	−	0.955050i	$-0.404199\pi$
$19$	−0.936877	−	0.417124i	−0.214934	−	0.0956949i	−0.511380	+	0.859355i	$0.670865\pi$
$20$	−0.669131	−	0.743145i	−0.149622	−	0.166172i
$21$	0.119832	+	1.14013i	0.0261495	+	0.248796i
$22$	4.37811	+	0.930596i	0.933416	+	0.198404i
$23$	−2.29085	−	7.05052i	−0.477676	−	1.47014i	−0.842315	−	0.538986i	$-0.818807\pi$
$23$	−2.29085	−	7.05052i	−0.477676	−	1.47014i	0.364639	−	0.931149i	$-0.381193\pi$
$24$	−0.978148	+	0.207912i	−0.199664	+	0.0424398i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.112591	−	0.195013i	0.0220808	−	0.0382451i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	0.119832	−	1.14013i	0.0226461	−	0.215464i
$29$	−2.29345	+	1.66629i	−0.425884	+	0.309423i	−0.780001	−	0.625778i	$-0.784781\pi$
$29$	−2.29345	+	1.66629i	−0.425884	+	0.309423i	0.354117	+	0.935201i	$0.384781\pi$
$30$	−1.00000			−0.182574
$31$	−3.07150	+	4.64391i	−0.551658	+	0.834071i
$31$	−3.07150	+	4.64391i	−0.551658	+	0.834071i
$32$	1.00000			0.176777
$33$	3.62110	−	2.63088i	0.630352	−	0.457977i
$34$	−0.290761	+	2.76640i	−0.0498651	+	0.474434i
$35$	0.354259	−	1.09030i	0.0598807	−	0.184294i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−4.17943	−	7.23899i	−0.687094	−	1.19008i	−0.972774	−	0.231757i	$-0.925553\pi$
$37$	−4.17943	−	7.23899i	−0.687094	−	1.19008i	0.285679	−	0.958325i	$-0.407781\pi$
$38$	1.00313	−	0.213222i	0.162729	−	0.0345891i
$39$	−0.0695848	−	0.214160i	−0.0111425	−	0.0342931i
$40$	0.978148	+	0.207912i	0.154659	+	0.0328737i
$41$	−0.598588	−	5.69518i	−0.0934837	−	0.889438i	−0.936292	−	0.351224i	$-0.885766\pi$
$41$	−0.598588	−	5.69518i	−0.0934837	−	0.889438i	0.842808	−	0.538215i	$-0.180901\pi$
$42$	−0.767096	−	0.851946i	−0.118365	−	0.131458i
$43$	4.33531	+	1.93020i	0.661129	+	0.294353i	0.709739	−	0.704464i	$-0.248813\pi$
$43$	4.33531	+	1.93020i	0.661129	+	0.294353i	−0.0486108	+	0.998818i	$0.515479\pi$
$44$	−4.08896	+	1.82052i	−0.616433	+	0.274454i
$45$	−0.669131	+	0.743145i	−0.0997481	+	0.110781i
$46$	5.99753	+	4.35746i	0.884288	+	0.642473i
$47$	−8.06615	−	5.86040i	−1.17657	−	0.854827i	−0.184788	−	0.982778i	$-0.559160\pi$
$47$	−8.06615	−	5.86040i	−1.17657	−	0.854827i	−0.991780	+	0.127951i	$0.959160\pi$
$48$	0.669131	−	0.743145i	0.0965807	−	0.107264i
$49$	−5.19419	+	2.31260i	−0.742028	+	0.330372i
$50$	0.913545	+	0.406737i	0.129195	+	0.0575212i
$51$	1.86128	+	2.06716i	0.260632	+	0.289461i
$52$	0.0235378	+	0.223948i	0.00326411	+	0.0310560i
$53$	6.10240	+	1.29710i	0.838229	+	0.178171i	0.606974	−	0.794722i	$-0.292383\pi$
$53$	6.10240	+	1.29710i	0.838229	+	0.178171i	0.231255	+	0.972893i	$0.425717\pi$
$54$	0.309017	+	0.951057i	0.0420519	+	0.129422i
$55$	−4.37811	+	0.930596i	−0.590344	+	0.125482i
$56$	0.573203	+	0.992817i	0.0765975	+	0.132671i
$57$	0.512770	−	0.888143i	0.0679180	−	0.117637i
$58$	0.876022	−	2.69612i	0.115027	−	0.354018i
$59$	0.699405	−	6.65439i	0.0910548	−	0.866328i	−0.849706	−	0.527257i	$-0.823221\pi$
$59$	0.699405	−	6.65439i	0.0910548	−	0.866328i	0.940761	−	0.339071i	$-0.110113\pi$
$60$	0.809017	−	0.587785i	0.104444	−	0.0758827i
$61$	6.58814			0.843525			0.421763	−	0.906706i	$-0.361412\pi$
$61$	6.58814			0.843525			0.421763	+	0.906706i	$0.361412\pi$
$62$	−0.244725	−	5.56238i	−0.0310800	−	0.706423i
$63$	−1.14641			−0.144434
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−0.0235378	+	0.223948i	−0.00291951	+	0.0277773i
$66$	−1.38314	+	4.25685i	−0.170252	+	0.523982i
$67$	4.83920	−	8.38174i	0.591202	−	1.02399i	−0.402868	−	0.915258i	$-0.631987\pi$
$67$	4.83920	−	8.38174i	0.591202	−	1.02399i	0.994071	−	0.108735i	$-0.0346799\pi$
$68$	−1.39082	−	2.40897i	−0.168662	−	0.292131i
$69$	7.25136	−	1.54132i	0.872961	−	0.185554i
$70$	0.354259	+	1.09030i	0.0423421	+	0.130315i
$71$	5.30226	+	1.12703i	0.629262	+	0.133754i	0.511493	−	0.859287i	$-0.329092\pi$
$71$	5.30226	+	1.12703i	0.629262	+	0.133754i	0.117769	+	0.993041i	$0.462426\pi$
$72$	−0.104528	−	0.994522i	−0.0123188	−	0.117206i
$73$	5.63767	+	6.26127i	0.659840	+	0.732826i	0.976453	−	0.215728i	$-0.0692126\pi$
$73$	5.63767	+	6.26127i	0.659840	+	0.732826i	−0.316614	+	0.948555i	$0.602546\pi$
$74$	7.63620	+	3.39986i	0.887691	+	0.395225i
$75$	0.913545	−	0.406737i	0.105487	−	0.0469659i
$76$	−0.686220	+	0.762124i	−0.0787148	+	0.0874216i
$77$	−4.15125	−	3.01606i	−0.473079	−	0.343712i
$78$	0.182175	+	0.132358i	0.0206273	+	0.0149866i
$79$	5.87313	−	6.52277i	0.660779	−	0.733869i	−0.315848	−	0.948810i	$-0.602289\pi$
$79$	5.87313	−	6.52277i	0.660779	−	0.733869i	0.976627	+	0.214941i	$0.0689558\pi$
$80$	−0.913545	+	0.406737i	−0.102137	+	0.0454745i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	3.83181	+	4.25566i	0.423153	+	0.469959i
$83$	−0.927358	−	8.82322i	−0.101791	−	0.968474i	−0.919566	−	0.392936i	$-0.871459\pi$
$83$	−0.927358	−	8.82322i	−0.101791	−	0.968474i	0.817775	−	0.575538i	$-0.195207\pi$
$84$	1.12135	+	0.238351i	0.122350	+	0.0260063i
$85$	−0.859575	−	2.64550i	−0.0932340	−	0.286945i
$86$	−4.64188	+	0.986663i	−0.500547	+	0.106395i
$87$	−1.41743	−	2.45507i	−0.151965	−	0.263211i
$88$	2.23796	−	3.87626i	0.238567	−	0.413211i
$89$	−0.556227	+	1.71189i	−0.0589599	+	0.181460i	−0.976199	−	0.216878i	$-0.930413\pi$
$89$	−0.556227	+	1.71189i	−0.0589599	+	0.181460i	0.917239	+	0.398338i	$0.130413\pi$
$90$	0.104528	−	0.994522i	0.0110183	−	0.104832i
$91$	−0.208847	+	0.151736i	−0.0218931	+	0.0159063i
$92$	−7.41336			−0.772896
$93$	−4.29741	−	3.54010i	−0.445621	−	0.367091i
$94$	9.97031			1.02836
$95$	−0.829679	+	0.602797i	−0.0851232	+	0.0618457i
$96$	−0.104528	+	0.994522i	−0.0106684	+	0.101503i
$97$	−0.298153	+	0.917621i	−0.0302729	+	0.0931703i	−0.965051	−	0.262061i	$-0.915598\pi$
$97$	−0.298153	+	0.917621i	−0.0302729	+	0.0931703i	0.934778	+	0.355231i	$0.115598\pi$
$98$	2.84288	−	4.92401i	0.287174	−	0.497400i
$99$	2.23796	+	3.87626i	0.224923	+	0.389579i
$100$	−0.978148	+	0.207912i	−0.0978148	+	0.0207912i
$101$	0.125284	+	0.385584i	0.0124662	+	0.0383670i	0.957096	−	0.289771i	$-0.0935790\pi$
$101$	0.125284	+	0.385584i	0.0124662	+	0.0383670i	−0.944630	+	0.328138i	$0.893579\pi$
$102$	−2.72086	−	0.578336i	−0.269405	−	0.0572638i
$103$	0.811519	+	7.72109i	0.0799614	+	0.760782i	0.958880	+	0.283811i	$0.0915987\pi$
$103$	0.811519	+	7.72109i	0.0799614	+	0.760782i	−0.878919	+	0.476971i	$0.841735\pi$
$104$	−0.150676	−	0.167342i	−0.0147750	−	0.0164093i
$105$	1.04729	+	0.466285i	0.102205	+	0.0455048i
$106$	−5.69936	+	2.53752i	−0.553571	+	0.246466i
$107$	1.60246	−	1.77971i	0.154915	−	0.172051i	−0.660691	−	0.750658i	$-0.729737\pi$
$107$	1.60246	−	1.77971i	0.154915	−	0.172051i	0.815607	+	0.578607i	$0.196403\pi$
$108$	−0.809017	−	0.587785i	−0.0778477	−	0.0565597i
$109$	15.4574	+	11.2305i	1.48055	+	1.07569i	0.977377	+	0.211502i	$0.0678356\pi$
$109$	15.4574	+	11.2305i	1.48055	+	1.07569i	0.503177	+	0.864183i	$0.332164\pi$
$110$	2.99498	−	3.32626i	0.285560	−	0.317146i
$111$	7.63620	−	3.39986i	0.724796	−	0.322700i
$112$	−1.04729	−	0.466285i	−0.0989600	−	0.0440598i
$113$	6.43511	+	7.14691i	0.605364	+	0.672325i	0.965448	−	0.260595i	$-0.0839188\pi$
$113$	6.43511	+	7.14691i	0.605364	+	0.672325i	−0.360084	+	0.932920i	$0.617252\pi$
$114$	0.107198	+	1.01992i	0.0100400	+	0.0955244i
$115$	−7.25136	−	1.54132i	−0.676193	−	0.143729i
$116$	0.876022	+	2.69612i	0.0813366	+	0.250328i
$117$	0.220260	−	0.0468178i	0.0203631	−	0.00432831i
$118$	3.34552	+	5.79462i	0.307980	+	0.533438i
$119$	1.59445	−	2.76166i	0.146163	−	0.253161i
$120$	−0.309017	+	0.951057i	−0.0282093	+	0.0868192i
$121$	−0.944296	+	8.98438i	−0.0858451	+	0.816762i
$122$	−5.32992	+	3.87241i	−0.482548	+	0.350592i
$123$	5.72655			0.516346
$124$	3.46747	+	4.35622i	0.311388	+	0.391200i
$125$	−1.00000			−0.0894427
$126$	0.927462	−	0.673841i	0.0826249	−	0.0600305i
$127$	2.20521	−	20.9811i	0.195680	−	1.86177i	−0.252193	−	0.967677i	$-0.581152\pi$
$127$	2.20521	−	20.9811i	0.195680	−	1.86177i	0.447873	−	0.894097i	$-0.352182\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−2.37279	+	4.10980i	−0.208913	+	0.361848i
$130$	−0.112591	−	0.195013i	−0.00987485	−	0.0171037i
$131$	−3.92347	+	0.833959i	−0.342795	+	0.0728634i	−0.376093	−	0.926582i	$-0.622733\pi$
$131$	−3.92347	+	0.833959i	−0.342795	+	0.0728634i	0.0332973	+	0.999445i	$0.489399\pi$
$132$	−1.38314	−	4.25685i	−0.120387	−	0.370512i
$133$	−1.14999	−	0.244439i	−0.0997171	−	0.0211955i
$134$	1.01167	+	9.62538i	0.0873948	+	0.831506i
$135$	−0.669131	−	0.743145i	−0.0575896	−	0.0639597i
$136$	2.54116	+	1.13140i	0.217902	+	0.0970164i
$137$	−10.7268	+	4.77590i	−0.916456	+	0.408033i	−0.810098	−	0.586295i	$-0.800586\pi$
$137$	−10.7268	+	4.77590i	−0.916456	+	0.408033i	−0.106359	+	0.994328i	$0.533919\pi$
$138$	−4.96050	+	5.50920i	−0.422266	+	0.468974i
$139$	−5.59859	−	4.06762i	−0.474867	−	0.345011i	0.324468	−	0.945897i	$-0.394815\pi$
$139$	−5.59859	−	4.06762i	−0.474867	−	0.345011i	−0.799335	+	0.600886i	$0.794815\pi$
$140$	−0.927462	−	0.673841i	−0.0783849	−	0.0569499i
$141$	6.67144	−	7.40938i	0.561836	−	0.623982i
$142$	−4.95207	+	2.20480i	−0.415568	+	0.185023i
$143$	0.920756	+	0.409947i	0.0769975	+	0.0342815i
$144$	0.669131	+	0.743145i	0.0557609	+	0.0619287i
$145$	0.296324	+	2.81934i	0.0246084	+	0.234133i
$146$	−8.24125	−	1.75173i	−0.682051	−	0.144974i
$147$	−1.75699	−	5.40747i	−0.144914	−	0.446001i
$148$	−8.17620	+	1.73791i	−0.672080	+	0.142855i
$149$	−5.29544	−	9.17197i	−0.433819	−	0.751397i	0.563379	−	0.826198i	$-0.309501\pi$
$149$	−5.29544	−	9.17197i	−0.433819	−	0.751397i	−0.997198	+	0.0748014i	$0.976168\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	−7.41707	+	22.8274i	−0.603593	+	1.85767i	−0.0974053	+	0.995245i	$0.531054\pi$
$151$	−7.41707	+	22.8274i	−0.603593	+	1.85767i	−0.506188	+	0.862423i	$0.668946\pi$
$152$	0.107198	−	1.01992i	0.00869491	−	0.0827265i
$153$	−2.25040	+	1.63501i	−0.181934	+	0.132183i
$154$	5.13122			0.413486
$155$	2.48599	+	4.98195i	0.199680	+	0.400160i
$156$	−0.225181			−0.0180289
$157$	11.1271	−	8.08433i	0.888041	−	0.645200i	−0.0473255	−	0.998880i	$-0.515070\pi$
$157$	11.1271	−	8.08433i	0.888041	−	0.645200i	0.935366	+	0.353680i	$0.115070\pi$
$158$	−0.917473	+	8.72917i	−0.0729902	+	0.694456i
$159$	−1.92787	+	5.93339i	−0.152890	+	0.470548i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−4.24936	−	7.36011i	−0.334896	−	0.580058i
$162$	−0.978148	+	0.207912i	−0.0768505	+	0.0163351i
$163$	−1.12267	−	3.45522i	−0.0879341	−	0.270633i	0.897414	−	0.441190i	$-0.145443\pi$
$163$	−1.12267	−	3.45522i	−0.0879341	−	0.270633i	−0.985348	+	0.170556i	$0.945443\pi$
$164$	−5.60142	−	1.19062i	−0.437397	−	0.0929716i
$165$	−0.467861	−	4.45140i	−0.0364229	−	0.346541i
$166$	5.93641	+	6.59305i	0.460754	+	0.511720i
$167$	−22.3593	−	9.95499i	−1.73021	−	0.770340i	−0.995792	−	0.0916447i	$-0.970788\pi$
$167$	−22.3593	−	9.95499i	−1.73021	−	0.770340i	−0.734420	−	0.678695i	$-0.762546\pi$
$168$	−1.04729	+	0.466285i	−0.0808005	+	0.0359747i
$169$	−8.66477	+	9.62320i	−0.666521	+	0.740246i
$170$	2.25040	+	1.63501i	0.172597	+	0.125399i
$171$	0.829679	+	0.602797i	0.0634471	+	0.0460970i
$172$	3.17542	−	3.52666i	0.242123	−	0.268905i
$173$	0.0888985	−	0.0395802i	0.00675883	−	0.00300922i	−0.403354	−	0.915044i	$-0.632156\pi$
$173$	0.0888985	−	0.0395802i	0.00675883	−	0.00300922i	0.410113	+	0.912035i	$0.365489\pi$
$174$	2.58978	+	1.15304i	0.196331	+	0.0874120i
$175$	−0.767096	−	0.851946i	−0.0579870	−	0.0644011i
$176$	0.467861	+	4.45140i	0.0352664	+	0.335537i
$177$	6.54483	+	1.39115i	0.491940	+	0.104565i
$178$	−0.556227	−	1.71189i	−0.0416909	−	0.128312i
$179$	−15.9450	+	3.38921i	−1.19178	+	0.253322i	−0.760769	−	0.649023i	$-0.775178\pi$
$179$	−15.9450	+	3.38921i	−1.19178	+	0.253322i	−0.431016	+	0.902345i	$0.641845\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	5.77158	−	9.99667i	0.428998	−	0.743047i	−0.567786	−	0.823176i	$-0.692200\pi$
$181$	5.77158	−	9.99667i	0.428998	−	0.743047i	0.996784	+	0.0801294i	$0.0255333\pi$
$182$	0.0797725	−	0.245514i	0.00591313	−	0.0181987i
$183$	−0.688648	+	6.55205i	−0.0509063	+	0.484342i
$184$	5.99753	−	4.35746i	0.442144	−	0.321236i
$185$	−8.35886			−0.614556
$186$	5.55749	+	0.338043i	0.407495	+	0.0247866i
$187$	−12.4504			−0.910464
$188$	−8.06615	+	5.86040i	−0.588284	+	0.427413i
$189$	0.119832	−	1.14013i	0.00871650	−	0.0829320i
$190$	0.316909	−	0.975346i	0.0229910	−	0.0707590i
$191$	−2.88144	+	4.99080i	−0.208493	+	0.361121i	−0.951240	−	0.308451i	$-0.900189\pi$
$191$	−2.88144	+	4.99080i	−0.208493	+	0.361121i	0.742747	+	0.669573i	$0.233523\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	8.61231	−	1.83060i	0.619928	−	0.131770i	0.112767	−	0.993621i	$-0.464029\pi$
$193$	8.61231	−	1.83060i	0.619928	−	0.131770i	0.507160	+	0.861852i	$0.330695\pi$
$194$	−0.298153	−	0.917621i	−0.0214061	−	0.0658813i
$195$	−0.220260	−	0.0468178i	−0.0157732	−	0.00335269i
$196$	0.594323	+	5.65461i	0.0424516	+	0.403900i
$197$	1.73815	+	1.93041i	0.123838	+	0.137536i	0.801875	−	0.597492i	$-0.203836\pi$
$197$	1.73815	+	1.93041i	0.123838	+	0.137536i	−0.678037	+	0.735028i	$0.737169\pi$
$198$	−4.08896	−	1.82052i	−0.290590	−	0.129379i
$199$	−17.5347	+	7.80696i	−1.24300	+	0.553421i	−0.919606	−	0.392842i	$-0.871492\pi$
$199$	−17.5347	+	7.80696i	−1.24300	+	0.553421i	−0.323398	+	0.946263i	$0.604825\pi$
$200$	0.669131	−	0.743145i	0.0473147	−	0.0525483i
$201$	7.82999	+	5.68882i	0.552285	+	0.401258i
$202$	−0.327997	−	0.238304i	−0.0230778	−	0.0167670i
$203$	−2.17461	+	2.41515i	−0.152628	+	0.169510i
$204$	2.54116	−	1.13140i	0.177917	−	0.0792136i
$205$	−5.23147	−	2.32920i	−0.365382	−	0.162678i
$206$	−5.19488	−	5.76949i	−0.361944	−	0.401980i
$207$	0.774907	+	7.37275i	0.0538598	+	0.512441i
$208$	0.220260	+	0.0468178i	0.0152723	+	0.00324623i
$209$	1.41846	+	4.36557i	0.0981169	+	0.301973i
$210$	−1.12135	+	0.238351i	−0.0773808	+	0.0164478i
$211$	−1.05418	−	1.82589i	−0.0725725	−	0.125699i	0.827456	−	0.561531i	$-0.189788\pi$
$211$	−1.05418	−	1.82589i	−0.0725725	−	0.125699i	−0.900028	+	0.435832i	$0.856454\pi$
$212$	3.11937	−	5.40290i	0.214239	−	0.371073i
$213$	−1.67509	+	5.15540i	−0.114775	+	0.353243i
$214$	−0.250328	+	2.38171i	−0.0171121	+	0.162811i
$215$	3.83926	−	2.78939i	0.261835	−	0.190235i
$216$	1.00000			0.0680414
$217$	−2.33736	+	5.93956i	−0.158670	+	0.403204i
$218$	−19.1064			−1.29405
$219$	−6.81627	+	4.95231i	−0.460601	+	0.334646i
$220$	−0.467861	+	4.45140i	−0.0315432	+	0.300113i
$221$	−0.193560	+	0.595717i	−0.0130203	+	0.0400722i
$222$	−4.17943	+	7.23899i	−0.280505	+	0.485849i
$223$	−4.51215	−	7.81528i	−0.302156	−	0.523350i	0.674468	−	0.738304i	$-0.264373\pi$
$223$	−4.51215	−	7.81528i	−0.302156	−	0.523350i	−0.976624	+	0.214954i	$0.931040\pi$
$224$	1.12135	−	0.238351i	0.0749237	−	0.0159255i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	−9.40696	−	1.99951i	−0.625741	−	0.133005i
$227$	−0.808775	−	7.69498i	−0.0536803	−	0.510734i	−0.988017	−	0.154343i	$-0.950674\pi$
$227$	−0.808775	−	7.69498i	−0.0536803	−	0.510734i	0.934337	−	0.356391i	$-0.115993\pi$
$228$	−0.686220	−	0.762124i	−0.0454460	−	0.0504729i
$229$	2.34900	+	1.04584i	0.155226	+	0.0691111i	0.482879	−	0.875687i	$-0.339591\pi$
$229$	2.34900	+	1.04584i	0.155226	+	0.0691111i	−0.327653	+	0.944798i	$0.606258\pi$
$230$	6.77244	−	3.01528i	0.446561	−	0.198822i
$231$	3.43346	−	3.81324i	0.225905	−	0.250893i
$232$	−2.29345	−	1.66629i	−0.150573	−	0.109397i
$233$	18.2316	+	13.2461i	1.19439	+	0.867778i	0.993722	−	0.111881i	$-0.0356874\pi$
$233$	18.2316	+	13.2461i	1.19439	+	0.867778i	0.200672	+	0.979658i	$0.435687\pi$
$234$	−0.150676	+	0.167342i	−0.00984998	+	0.0109395i
$235$	−9.10833	+	4.05529i	−0.594162	+	0.264538i
$236$	−6.11258	−	2.72149i	−0.397895	−	0.177154i
$237$	5.87313	+	6.52277i	0.381501	+	0.423700i
$238$	0.333330	+	3.17142i	0.0216066	+	0.205573i
$239$	15.1536	+	3.22099i	0.980204	+	0.208349i	0.670032	−	0.742332i	$-0.266280\pi$
$239$	15.1536	+	3.22099i	0.980204	+	0.208349i	0.310171	+	0.950681i	$0.399614\pi$
$240$	−0.309017	−	0.951057i	−0.0199470	−	0.0613904i
$241$	−12.6719	+	2.69349i	−0.816268	+	0.173503i	−0.597082	−	0.802180i	$-0.703673\pi$
$241$	−12.6719	+	2.69349i	−0.816268	+	0.173503i	−0.219186	+	0.975683i	$0.570340\pi$
$242$	−4.51693	−	7.82356i	−0.290360	−	0.502917i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	2.03585	−	6.26569i	0.130332	−	0.401120i
$245$	−0.594323	+	5.65461i	−0.0379699	+	0.361259i
$246$	−4.63288	+	3.36598i	−0.295382	+	0.214607i
$247$	0.230932			0.0146939
$248$	−5.36577	−	1.48612i	−0.340726	−	0.0943690i
$249$	8.87182			0.562229
$250$	0.809017	−	0.587785i	0.0511667	−	0.0371748i
$251$	−2.49620	+	23.7498i	−0.157559	+	1.49907i	0.574878	+	0.818239i	$0.305049\pi$
$251$	−2.49620	+	23.7498i	−0.157559	+	1.49907i	−0.732437	+	0.680834i	$0.761617\pi$
$252$	−0.354259	+	1.09030i	−0.0223162	+	0.0686823i
$253$	−16.5908	+	28.7361i	−1.04305	+	1.80662i
$254$	10.5483	+	18.2703i	0.661862	+	1.14638i
$255$	2.72086	−	0.578336i	0.170387	−	0.0362168i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	6.45407	+	1.37185i	0.402594	+	0.0855739i	0.404758	−	0.914424i	$-0.367356\pi$
$257$	6.45407	+	1.37185i	0.402594	+	0.0855739i	−0.00216463	+	0.999998i	$0.500689\pi$
$258$	−0.496049	−	4.71959i	−0.0308827	−	0.293829i
$259$	−6.41205	−	7.12130i	−0.398425	−	0.442496i
$260$	0.205713	+	0.0915895i	0.0127578	+	0.00568014i
$261$	2.58978	−	1.15304i	0.160303	−	0.0713716i
$262$	2.68397	−	2.98085i	0.165816	−	0.184157i
$263$	23.1569	+	16.8245i	1.42792	+	1.03744i	0.990400	+	0.138234i	$0.0441427\pi$
$263$	23.1569	+	16.8245i	1.42792	+	1.03744i	0.437519	+	0.899209i	$0.355857\pi$
$264$	3.62110	+	2.63088i	0.222863	+	0.161919i
$265$	4.17453	−	4.63628i	0.256439	−	0.284804i
$266$	1.07404	−	0.478194i	0.0658537	−	0.0293200i
$267$	−1.64437	−	0.732121i	−0.100634	−	0.0448051i
$268$	−6.47611	−	7.19245i	−0.395592	−	0.439349i
$269$	1.24400	+	11.8358i	0.0758477	+	0.721643i	0.964683	+	0.263415i	$0.0848489\pi$
$269$	1.24400	+	11.8358i	0.0758477	+	0.721643i	−0.888835	+	0.458228i	$0.848484\pi$
$270$	0.978148	+	0.207912i	0.0595282	+	0.0126531i
$271$	0.256164	+	0.788391i	0.0155608	+	0.0478913i	0.958535	−	0.284973i	$-0.0919848\pi$
$271$	0.256164	+	0.788391i	0.0155608	+	0.0478913i	−0.942975	+	0.332865i	$0.891985\pi$
$272$	−2.72086	+	0.578336i	−0.164976	+	0.0350668i
$273$	−0.129075	−	0.223564i	−0.00781195	−	0.0135307i
$274$	5.87100	−	10.1689i	0.354680	−	0.614324i
$275$	−1.38314	+	4.25685i	−0.0834062	+	0.256698i
$276$	0.774907	−	7.37275i	0.0466439	−	0.443787i
$277$	−1.20031	+	0.872076i	−0.0721196	+	0.0523980i	−0.623261	−	0.782014i	$-0.714193\pi$
$277$	−1.20031	+	0.872076i	−0.0721196	+	0.0523980i	0.551141	+	0.834412i	$0.314193\pi$
$278$	6.92024			0.415049
$279$	3.96990	−	3.90383i	0.237672	−	0.233716i
$280$	1.14641			0.0685109
$281$	0.662332	−	0.481213i	0.0395114	−	0.0287067i	−0.567854	−	0.823129i	$-0.692226\pi$
$281$	0.662332	−	0.481213i	0.0395114	−	0.0287067i	0.607366	+	0.794422i	$0.292226\pi$
$282$	−1.04218	+	9.91569i	−0.0620610	+	0.590471i
$283$	−7.00363	+	21.5550i	−0.416323	+	1.28131i	0.494740	+	0.869041i	$0.335263\pi$
$283$	−7.00363	+	21.5550i	−0.416323	+	1.28131i	−0.911063	+	0.412268i	$0.864737\pi$
$284$	2.71036	−	4.69448i	0.160830	−	0.278566i
$285$	−0.512770	−	0.888143i	−0.0303739	−	0.0526091i
$286$	−0.985869	+	0.209553i	−0.0582956	+	0.0123911i
$287$	−2.02868	−	6.24365i	−0.119749	−	0.368551i
$288$	−0.978148	−	0.207912i	−0.0576379	−	0.0122513i
$289$	0.968191	+	9.21173i	0.0569524	+	0.541866i
$290$	−1.89690	−	2.10672i	−0.111390	−	0.123711i
$291$	−0.881428	−	0.392437i	−0.0516702	−	0.0230051i
$292$	7.69696	−	3.42691i	0.450430	−	0.200544i
$293$	−2.72522	+	3.02666i	−0.159209	+	0.176820i	−0.817472	−	0.575969i	$-0.804625\pi$
$293$	−2.72522	+	3.02666i	−0.159209	+	0.176820i	0.658263	+	0.752788i	$0.271292\pi$
$294$	4.59987	+	3.34200i	0.268270	+	0.194909i
$295$	−5.41317	−	3.93290i	−0.315167	−	0.228982i
$296$	5.59317	−	6.21185i	0.325097	−	0.361056i
$297$	−4.08896	+	1.82052i	−0.237265	+	0.105637i
$298$	9.67525	+	4.30770i	0.560472	+	0.249538i
$299$	1.11701	+	1.24057i	0.0645985	+	0.0717439i
$300$	−0.104528	−	0.994522i	−0.00603495	−	0.0574187i
$301$	5.32149	+	1.13112i	0.306725	+	0.0651965i
$302$	−7.41707	−	22.8274i	−0.426805	−	1.31357i
$303$	−0.396567	+	0.0842930i	−0.0227822	+	0.00484251i
$304$	0.512770	+	0.888143i	0.0294094	+	0.0509385i
$305$	3.29407	−	5.70550i	0.188618	−	0.326696i
$306$	0.859575	−	2.64550i	0.0491386	−	0.151233i
$307$	0.468532	−	4.45778i	0.0267405	−	0.254419i	−0.972982	−	0.230879i	$-0.925840\pi$
$307$	0.468532	−	4.45778i	0.0267405	−	0.254419i	0.999723	−	0.0235397i	$-0.00749360\pi$
$308$	−4.15125	+	3.01606i	−0.236539	+	0.171856i
$309$	−7.76362			−0.441657
$310$	−4.93953	−	2.56925i	−0.280546	−	0.145924i
$311$	−19.0008			−1.07743			−0.538717	−	0.842487i	$-0.681091\pi$
$311$	−19.0008			−1.07743			−0.538717	+	0.842487i	$0.681091\pi$
$312$	0.182175	−	0.132358i	0.0103137	−	0.00749331i
$313$	2.33189	−	22.1865i	0.131806	−	1.25405i	−0.706049	−	0.708163i	$-0.749524\pi$
$313$	2.33189	−	22.1865i	0.131806	−	1.25405i	0.837856	−	0.545892i	$-0.183809\pi$
$314$	−4.25018	+	13.0807i	−0.239852	+	0.738188i
$315$	−0.573203	+	0.992817i	−0.0322963	+	0.0559389i
$316$	−4.38863	−	7.60133i	−0.246880	−	0.427608i
$317$	8.48399	−	1.80333i	0.476508	−	0.101285i	0.0366044	−	0.999330i	$-0.488346\pi$
$317$	8.48399	−	1.80333i	0.476508	−	0.101285i	0.439904	+	0.898045i	$0.355013\pi$
$318$	−1.92787	−	5.93339i	−0.108110	−	0.332728i
$319$	12.4114	+	2.63812i	0.694903	+	0.147706i
$320$	0.104528	+	0.994522i	0.00584332	+	0.0555955i
$321$	1.60246	+	1.77971i	0.0894404	+	0.0993336i
$322$	7.76397	+	3.45674i	0.432669	+	0.192637i
$323$	−2.60606	+	1.16029i	−0.145005	+	0.0645603i
$324$	0.669131	−	0.743145i	0.0371739	−	0.0412858i
$325$	0.182175	+	0.132358i	0.0101053	+	0.00734191i
$326$	2.93918	+	2.13544i	0.162786	+	0.118271i
$327$	−12.7847	+	14.1989i	−0.706996	+	0.785199i
$328$	5.23147	−	2.32920i	0.288859	−	0.128609i
$329$	−10.4418	−	4.64901i	−0.575677	−	0.256308i
$330$	2.99498	+	3.32626i	0.164868	+	0.183104i
$331$	−1.61811	−	15.3953i	−0.0889395	−	0.846203i	−0.944502	−	0.328504i	$-0.893455\pi$
$331$	−1.61811	−	15.3953i	−0.0889395	−	0.846203i	0.855563	−	0.517699i	$-0.173211\pi$
$332$	−8.67795	−	1.84455i	−0.476264	−	0.101233i
$333$	2.58303	+	7.94975i	0.141549	+	0.435644i
$334$	23.9404	−	5.08869i	1.30996	−	0.278441i
$335$	−4.83920	−	8.38174i	−0.264394	−	0.457943i
$336$	0.573203	−	0.992817i	0.0312708	−	0.0541626i
$337$	−3.17298	+	9.76543i	−0.172843	+	0.531957i	−0.999528	−	0.0307079i	$-0.990224\pi$
$337$	−3.17298	+	9.76543i	−0.172843	+	0.531957i	0.826685	+	0.562665i	$0.190224\pi$
$338$	1.35357	−	12.8784i	0.0736245	−	0.700490i
$339$	−7.78041	+	5.65280i	−0.422574	+	0.307018i
$340$	−2.78164			−0.150856
$341$	24.6459	−	3.69179i	1.33465	−	0.199922i
$342$	−1.02554			−0.0554548
$343$	−11.7656	+	8.54818i	−0.635280	+	0.461558i
$344$	−0.496049	+	4.71959i	−0.0267452	+	0.254463i
$345$	2.29085	−	7.05052i	0.123335	−	0.379587i
$346$	−0.0486558	+	0.0842742i	−0.00261575	+	0.00453061i
$347$	−6.83461	−	11.8379i	−0.366901	−	0.635492i	0.622178	−	0.782876i	$-0.286248\pi$
$347$	−6.83461	−	11.8379i	−0.366901	−	0.635492i	−0.989079	+	0.147384i	$0.952915\pi$
$348$	−2.77292	+	0.589402i	−0.148644	+	0.0315953i
$349$	0.587205	+	1.80723i	0.0314324	+	0.0967389i	0.965542	−	0.260248i	$-0.0838042\pi$
$349$	0.587205	+	1.80723i	0.0314324	+	0.0967389i	−0.934110	+	0.356987i	$0.883804\pi$
$350$	1.12135	+	0.238351i	0.0599389	+	0.0127404i
$351$	0.0235378	+	0.223948i	0.00125636	+	0.0119534i
$352$	−2.99498	−	3.32626i	−0.159633	−	0.177290i
$353$	4.44642	+	1.97967i	0.236659	+	0.105367i	0.521640	−	0.853166i	$-0.325321\pi$
$353$	4.44642	+	1.97967i	0.236659	+	0.105367i	−0.284981	+	0.958533i	$0.591987\pi$
$354$	−6.11258	+	2.72149i	−0.324880	+	0.144646i
$355$	3.62717	−	4.02838i	0.192510	−	0.213804i
$356$	1.45622	+	1.05801i	0.0771795	+	0.0560742i
$357$	2.57987	+	1.87438i	0.136541	+	0.0992029i
$358$	10.9076	−	12.1142i	0.576487	−	0.640253i
$359$	−4.92856	+	2.19434i	−0.260119	+	0.115813i	−0.532653	−	0.846334i	$-0.678805\pi$
$359$	−4.92856	+	2.19434i	−0.260119	+	0.115813i	0.272534	+	0.962146i	$0.412138\pi$
$360$	−0.913545	−	0.406737i	−0.0481481	−	0.0214369i
$361$	−12.0097	−	13.3382i	−0.632091	−	0.702009i
$362$	1.20659	+	11.4799i	0.0634169	+	0.603371i
$363$	−8.83646	−	1.87825i	−0.463794	−	0.0985824i
$364$	0.0797725	+	0.245514i	0.00418121	+	0.0128685i
$365$	8.24125	−	1.75173i	0.431367	−	0.0916899i
$366$	−3.29407	−	5.70550i	−0.172184	−	0.298231i
$367$	15.5700	−	26.9680i	0.812747	−	1.40772i	−0.0981880	−	0.995168i	$-0.531305\pi$
$367$	15.5700	−	26.9680i	0.812747	−	1.40772i	0.910935	−	0.412551i	$-0.135362\pi$
$368$	−2.29085	+	7.05052i	−0.119419	+	0.367534i
$369$	−0.598588	+	5.69518i	−0.0311612	+	0.296479i
$370$	6.76246	−	4.91322i	0.351564	−	0.255426i
$371$	7.15212			0.371320
$372$	−4.69480	+	2.99313i	−0.243414	+	0.155187i
$373$	−7.48991			−0.387813			−0.193906	−	0.981020i	$-0.562116\pi$
$373$	−7.48991			−0.387813			−0.193906	+	0.981020i	$0.562116\pi$
$374$	10.0726	−	7.31817i	0.520841	−	0.378413i
$375$	0.104528	−	0.994522i	0.00539783	−	0.0513569i
$376$	3.08099	−	9.48232i	0.158890	−	0.489014i
$377$	0.319179	−	0.552835i	0.0164386	−	0.0284724i
$378$	0.573203	+	0.992817i	0.0294824	+	0.0510650i
$379$	18.3878	−	3.90845i	0.944519	−	0.200764i	0.290186	−	0.956970i	$-0.406283\pi$
$379$	18.3878	−	3.90845i	0.944519	−	0.200764i	0.654333	+	0.756207i	$0.272949\pi$
$380$	0.316909	+	0.975346i	0.0162571	+	0.0500342i
$381$	20.6357	+	4.38625i	1.05720	+	0.224714i
$382$	−0.602384	−	5.73130i	−0.0308207	−	0.293239i
$383$	15.3380	+	17.0346i	0.783736	+	0.870427i	0.994241	−	0.107166i	$-0.0341776\pi$
$383$	15.3380	+	17.0346i	0.783736	+	0.870427i	−0.210505	+	0.977593i	$0.567511\pi$
$384$	0.913545	+	0.406737i	0.0466192	+	0.0207562i
$385$	−4.68761	+	2.08706i	−0.238903	+	0.106366i
$386$	−5.89150	+	6.54318i	−0.299870	+	0.333039i
$387$	−3.83926	−	2.78939i	−0.195161	−	0.141792i
$388$	0.780575	+	0.567121i	0.0396277	+	0.0287912i
$389$	18.2969	−	20.3207i	0.927689	−	1.03030i	−0.0717707	−	0.997421i	$-0.522865\pi$
$389$	18.2969	−	20.3207i	0.927689	−	1.03030i	0.999459	−	0.0328814i	$-0.0104684\pi$
$390$	0.205713	−	0.0915895i	0.0104167	−	0.00463781i
$391$	−18.8385	−	8.38744i	−0.952704	−	0.424171i
$392$	−3.80451	−	4.22534i	−0.192157	−	0.213412i
$393$	−0.419277	−	3.98915i	−0.0211497	−	0.201226i
$394$	−2.54086	−	0.540076i	−0.128007	−	0.0272087i
$395$	−2.71232	−	8.34767i	−0.136472	−	0.420017i
$396$	4.37811	−	0.930596i	0.220008	−	0.0467642i
$397$	10.6356	+	18.4214i	0.533785	+	0.924543i	0.999221	+	0.0394617i	$0.0125643\pi$
$397$	10.6356	+	18.4214i	0.533785	+	0.924543i	−0.465436	+	0.885082i	$0.654102\pi$
$398$	9.59708	−	16.6226i	0.481058	−	0.833217i
$399$	0.363307	−	1.11814i	0.0181881	−	0.0559771i
$400$	−0.104528	+	0.994522i	−0.00522642	+	0.0497261i
$401$	18.8840	−	13.7201i	0.943024	−	0.685147i	−0.00612259	−	0.999981i	$-0.501949\pi$
$401$	18.8840	−	13.7201i	0.943024	−	0.685147i	0.949147	+	0.314834i	$0.101949\pi$
$402$	−9.67840			−0.482715
$403$	0.206515	−	1.23663i	0.0102873	−	0.0616010i
$404$	0.405427			0.0201707
$405$	0.809017	−	0.587785i	0.0402004	−	0.0292073i
$406$	0.339708	−	3.23211i	0.0168594	−	0.160407i
$407$	−11.5614	+	35.5825i	−0.573079	+	1.76376i
$408$	−1.39082	+	2.40897i	−0.0688559	+	0.119262i
$409$	−12.6413	−	21.8954i	−0.625073	−	1.08266i	−0.988527	−	0.151045i	$-0.951736\pi$
$409$	−12.6413	−	21.8954i	−0.625073	−	1.08266i	0.363454	−	0.931612i	$-0.381597\pi$
$410$	5.60142	−	1.19062i	0.276634	−	0.0588004i
$411$	−3.62848	−	11.1673i	−0.178980	−	0.550842i
$412$	7.59397	+	1.61415i	0.374128	+	0.0795233i
$413$	−0.801802	−	7.62864i	−0.0394541	−	0.375381i
$414$	−4.96050	−	5.50920i	−0.243795	−	0.270762i
$415$	−8.10481	−	3.60849i	−0.397849	−	0.177134i
$416$	−0.205713	+	0.0915895i	−0.0100859	+	0.00449054i
$417$	4.63055	−	5.14274i	0.226759	−	0.251841i
$418$	−3.71358	−	2.69807i	−0.181637	−	0.131967i
$419$	23.6558	+	17.1869i	1.15566	+	0.839636i	0.989223	−	0.146416i	$-0.0467738\pi$
$419$	23.6558	+	17.1869i	1.15566	+	0.839636i	0.166437	+	0.986052i	$0.446774\pi$
$420$	0.767096	−	0.851946i	0.0374304	−	0.0415707i
$421$	1.86158	−	0.828827i	0.0907276	−	0.0403945i	−0.360871	−	0.932616i	$-0.617521\pi$
$421$	1.86158	−	0.828827i	0.0907276	−	0.0403945i	0.451599	+	0.892221i	$0.350854\pi$
$422$	1.92608	+	0.857545i	0.0937600	+	0.0417446i
$423$	6.67144	+	7.40938i	0.324376	+	0.360256i
$424$	0.652125	+	6.20455i	0.0316700	+	0.301320i
$425$	−2.72086	−	0.578336i	−0.131981	−	0.0280534i
$426$	−1.67509	−	5.15540i	−0.0811585	−	0.249780i
$427$	7.38764	−	1.57029i	0.357513	−	0.0759917i
$428$	−1.19742	−	2.07399i	−0.0578793	−	0.100250i
$429$	−0.503947	+	0.872861i	−0.0243308	+	0.0421421i
$430$	−1.46647	+	4.51332i	−0.0707193	+	0.217652i
$431$	−2.29587	+	21.8437i	−0.110588	+	1.05217i	0.788688	+	0.614794i	$0.210761\pi$
$431$	−2.29587	+	21.8437i	−0.110588	+	1.05217i	−0.899276	+	0.437381i	$0.855906\pi$
$432$	−0.809017	+	0.587785i	−0.0389238	+	0.0282798i
$433$	38.3080			1.84096			0.920482	−	0.390785i	$-0.127796\pi$
$433$	38.3080			1.84096			0.920482	+	0.390785i	$0.127796\pi$
$434$	−1.60022	−	6.17907i	−0.0768132	−	0.296605i
$435$	−2.83487			−0.135921
$436$	15.4574	−	11.2305i	0.740277	−	0.537843i
$437$	−0.794697	+	7.56104i	−0.0380155	+	0.361694i
$438$	2.60358	−	8.01300i	0.124404	−	0.382876i
$439$	−1.02352	+	1.77278i	−0.0488497	+	0.0846102i	−0.889416	−	0.457098i	$-0.848889\pi$
$439$	−1.02352	+	1.77278i	−0.0488497	+	0.0846102i	0.840567	+	0.541708i	$0.182222\pi$
$440$	−2.23796	−	3.87626i	−0.106691	−	0.184794i
$441$	5.56151	−	1.18213i	0.264834	−	0.0562921i
$442$	−0.193560	−	0.595717i	−0.00920672	−	0.0283354i
$443$	11.1010	+	2.35959i	0.527425	+	0.112108i	0.463925	−	0.885874i	$-0.346441\pi$
$443$	11.1010	+	2.35959i	0.527425	+	0.112108i	0.0634995	+	0.997982i	$0.479774\pi$
$444$	−0.873739	−	8.31307i	−0.0414658	−	0.394521i
$445$	1.20443	+	1.33765i	0.0570953	+	0.0634107i
$446$	8.24412	+	3.67052i	0.390370	+	0.173804i
$447$	9.67525	−	4.30770i	0.457624	−	0.203747i
$448$	−0.767096	+	0.851946i	−0.0362419	+	0.0402507i
$449$	−13.8490	−	10.0619i	−0.653575	−	0.474850i	0.210912	−	0.977505i	$-0.432357\pi$
$449$	−13.8490	−	10.0619i	−0.653575	−	0.474850i	−0.864487	+	0.502655i	$0.832357\pi$
$450$	−0.809017	−	0.587785i	−0.0381374	−	0.0277085i
$451$	−17.1509	+	19.0480i	−0.807604	+	0.896935i
$452$	8.78567	−	3.91163i	0.413243	−	0.183988i
$453$	−21.9271	−	9.76256i	−1.03022	−	0.458685i
$454$	5.17731	+	5.74999i	0.242983	+	0.269860i
$455$	0.0269839	+	0.256735i	0.00126503	+	0.0120359i
$456$	1.00313	+	0.213222i	0.0469758	+	0.00998502i
$457$	−9.51814	−	29.2938i	−0.445240	−	1.37031i	−0.882221	−	0.470836i	$-0.843952\pi$
$457$	−9.51814	−	29.2938i	−0.445240	−	1.37031i	0.436981	−	0.899471i	$-0.356048\pi$
$458$	−2.51511	+	0.534603i	−0.117523	+	0.0249803i
$459$	−1.39082	−	2.40897i	−0.0649180	−	0.112441i
$460$	−3.70668	+	6.42016i	−0.172825	+	0.299341i
$461$	6.72851	−	20.7082i	0.313378	−	0.964478i	−0.663039	−	0.748585i	$-0.730734\pi$
$461$	6.72851	−	20.7082i	0.313378	−	0.964478i	0.976417	−	0.215893i	$-0.0692664\pi$
$462$	−0.536359	+	5.10311i	−0.0249537	+	0.237418i
$463$	−5.70780	+	4.14696i	−0.265264	+	0.192726i	−0.712464	−	0.701708i	$-0.752421\pi$
$463$	−5.70780	+	4.14696i	−0.265264	+	0.192726i	0.447200	+	0.894434i	$0.352421\pi$
$464$	2.83487			0.131605
$465$	−5.21452	+	1.95162i	−0.241817	+	0.0905041i
$466$	−22.5355			−1.04394
$467$	−18.9574	+	13.7734i	−0.877244	+	0.637355i	−0.932521	−	0.361116i	$-0.882396\pi$
$467$	−18.9574	+	13.7734i	−0.877244	+	0.637355i	0.0552766	+	0.998471i	$0.482396\pi$
$468$	0.0235378	−	0.223948i	0.00108804	−	0.0103520i
$469$	3.42866	−	10.5523i	0.158321	−	0.487261i
$470$	4.98515	−	8.63454i	0.229948	−	0.398282i
$471$	6.87694	+	11.9112i	0.316873	+	0.548840i
$472$	6.54483	−	1.39115i	0.301250	−	0.0640327i
$473$	−6.56379	−	20.2013i	−0.301803	−	0.928855i
$474$	−8.58545	−	1.82489i	−0.394343	−	0.0838202i
$475$	0.107198	+	1.01992i	0.00491858	+	0.0467972i
$476$	−2.13379	−	2.36981i	−0.0978019	−	0.108620i
$477$	−5.69936	−	2.53752i	−0.260956	−	0.116185i
$478$	−14.1528	+	6.30121i	−0.647332	+	0.288211i
$479$	−25.9954	+	28.8708i	−1.18776	+	1.31914i	−0.251490	+	0.967860i	$0.580921\pi$
$479$	−25.9954	+	28.8708i	−1.18776	+	1.31914i	−0.936270	+	0.351281i	$0.885746\pi$
$480$	0.809017	+	0.587785i	0.0369264	+	0.0268286i
$481$	1.52278	+	1.10636i	0.0694328	+	0.0504459i
$482$	8.66857	−	9.62743i	0.394843	−	0.438517i
$483$	7.76397	−	3.45674i	0.353273	−	0.157287i
$484$	8.25285	+	3.67441i	0.375130	+	0.167018i
$485$	0.645606	+	0.717018i	0.0293155	+	0.0325581i
$486$	−0.104528	−	0.994522i	−0.00474151	−	0.0451124i
$487$	−6.15566	−	1.30843i	−0.278939	−	0.0592904i	0.0663177	−	0.997799i	$-0.478875\pi$
$487$	−6.15566	−	1.30843i	−0.278939	−	0.0592904i	−0.345257	+	0.938508i	$0.612208\pi$
$488$	2.03585	+	6.26569i	0.0921585	+	0.283635i
$489$	3.55364	−	0.755349i	0.160701	−	0.0341581i
$490$	−2.84288	−	4.92401i	−0.128428	−	0.222444i
$491$	20.1938	−	34.9767i	0.911334	−	1.57848i	0.0991522	−	0.995072i	$-0.468387\pi$
$491$	20.1938	−	34.9767i	0.911334	−	1.57848i	0.812182	−	0.583404i	$-0.198280\pi$
$492$	1.76960	−	5.44628i	0.0797798	−	0.245537i
$493$	−0.824268	+	7.84239i	−0.0371232	+	0.353203i
$494$	−0.186828	+	0.135739i	−0.00840579	+	0.00610717i
$495$	4.47592			0.201178
$496$	5.21452	−	1.95162i	0.234139	−	0.0876302i
$497$	6.21434			0.278751
$498$	−7.17745	+	5.21472i	−0.321629	+	0.233677i
$499$	3.71205	−	35.3178i	0.166174	−	1.58104i	−0.520362	−	0.853946i	$-0.674203\pi$
$499$	3.71205	−	35.3178i	0.166174	−	1.58104i	0.686536	−	0.727096i	$-0.259130\pi$
$500$	−0.309017	+	0.951057i	−0.0138197	+	0.0425325i
$501$	12.2376	−	21.1962i	0.546737	−	0.946976i
$502$	−11.9403	−	20.6812i	−0.532922	−	0.923048i
$503$	−0.811162	+	0.172418i	−0.0361679	+	0.00768773i	−0.225960	−	0.974137i	$-0.572552\pi$
$503$	−0.811162	+	0.172418i	−0.0361679	+	0.00768773i	0.189792	+	0.981824i	$0.439219\pi$
$504$	−0.354259	−	1.09030i	−0.0157800	−	0.0485657i
$505$	0.396567	+	0.0842930i	0.0176470	+	0.00375099i
$506$	−3.46842	−	32.9998i	−0.154190	−	1.46702i
$507$	−8.66477	−	9.62320i	−0.384816	−	0.427381i
$508$	−19.2728	−	8.58080i	−0.855092	−	0.380711i
$509$	22.3684	−	9.95907i	0.991463	−	0.441428i	0.154089	−	0.988057i	$-0.450756\pi$
$509$	22.3684	−	9.95907i	0.991463	−	0.441428i	0.837375	+	0.546629i	$0.184089\pi$
$510$	−1.86128	+	2.06716i	−0.0824190	+	0.0915355i
$511$	7.81421	+	5.67736i	0.345680	+	0.251151i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−0.686220	+	0.762124i	−0.0302973	+	0.0336486i
$514$	−6.02780	+	2.68375i	−0.265875	+	0.118375i
$515$	7.09242	+	3.15775i	0.312529	+	0.139147i
$516$	3.17542	+	3.52666i	0.139790	+	0.155252i
$517$	4.66472	+	44.3818i	0.205154	+	1.95191i
$518$	9.37325	+	1.99235i	0.411837	+	0.0875387i
$519$	0.0300709	+	0.0925488i	0.00131997	+	0.00406244i
$520$	−0.220260	+	0.0468178i	−0.00965906	+	0.00205310i
$521$	6.67736	+	11.5655i	0.292541	+	0.506695i	0.974410	−	0.224779i	$-0.0721660\pi$
$521$	6.67736	+	11.5655i	0.292541	+	0.506695i	−0.681869	+	0.731474i	$0.738833\pi$
$522$	−1.41743	+	2.45507i	−0.0620394	+	0.107455i
$523$	9.38921	−	28.8970i	0.410561	−	1.26358i	−0.505600	−	0.862768i	$-0.668729\pi$
$523$	9.38921	−	28.8970i	0.410561	−	1.26358i	0.916161	−	0.400810i	$-0.131271\pi$
$524$	−0.419277	+	3.98915i	−0.0183162	+	0.174267i
$525$	0.927462	−	0.673841i	0.0404778	−	0.0294088i
$526$	−28.6236			−1.24805
$527$	3.88279	+	14.9929i	0.169137	+	0.653102i
$528$	−4.47592			−0.194789
$529$	−25.8545	+	18.7844i	−1.12411	+	0.816711i
$530$	−0.652125	+	6.20455i	−0.0283265	+	0.269509i
$531$	−2.06765	+	6.36356i	−0.0897282	+	0.276155i
$532$	−0.587842	+	1.01817i	−0.0254862	+	0.0441434i
$533$	0.644756	+	1.11675i	0.0279275	+	0.0483718i
$534$	1.76065	−	0.374238i	0.0761909	−	0.0161949i
$535$	−0.740044	−	2.27762i	−0.0319949	−	0.0984702i
$536$	9.46690	+	2.01225i	0.408908	+	0.0869161i
$537$	−1.70394	−	16.2119i	−0.0735305	−	0.699596i
$538$	−7.96334	−	8.84418i	−0.343324	−	0.381300i
$539$	23.2488	+	10.3510i	1.00140	+	0.445851i
$540$	−0.913545	+	0.406737i	−0.0393127	+	0.0175032i
$541$	−28.5549	+	31.7134i	−1.22767	+	1.36347i	−0.318026	+	0.948082i	$0.603020\pi$
$541$	−28.5549	+	31.7134i	−1.22767	+	1.36347i	−0.909646	+	0.415385i	$0.863647\pi$
$542$	−0.670645	−	0.487252i	−0.0288067	−	0.0209293i
$543$	9.33861	+	6.78490i	0.400758	+	0.291168i
$544$	1.86128	−	2.06716i	0.0798018	−	0.0886289i
$545$	17.4546	−	7.77129i	0.747673	−	0.332886i
$546$	0.235831	+	0.104999i	0.0100926	+	0.00449353i
$547$	0.398354	+	0.442417i	0.0170324	+	0.0189164i	0.751601	−	0.659618i	$-0.229282\pi$
$547$	0.398354	+	0.442417i	0.0170324	+	0.0189164i	−0.734568	+	0.678535i	$0.762615\pi$
$548$	1.22737	+	11.6777i	0.0524308	+	0.498845i
$549$	−6.44417	−	1.36975i	−0.275031	−	0.0584596i
$550$	−1.38314	−	4.25685i	−0.0589771	−	0.181513i
$551$	2.84374	−	0.604455i	0.121147	−	0.0257506i
$552$	3.70668	+	6.42016i	0.157767	+	0.273260i
$553$	5.03115	−	8.71421i	0.213946	−	0.370566i
$554$	0.458477	−	1.41105i	0.0194788	−	0.0599497i
$555$	0.873739	−	8.31307i	0.0370882	−	0.352870i
$556$	−5.59859	+	4.06762i	−0.237433	+	0.172505i
$557$	23.5473			0.997733			0.498866	−	0.866679i	$-0.333750\pi$
$557$	23.5473			0.997733			0.498866	+	0.866679i	$0.333750\pi$
$558$	−0.917108	+	5.49171i	−0.0388243	+	0.232483i
$559$	−1.06862			−0.0451977
$560$	−0.927462	+	0.673841i	−0.0391924	+	0.0284750i
$561$	1.30142	−	12.3822i	0.0549461	−	0.522777i
$562$	−0.252988	+	0.778618i	−0.0106717	+	0.0328440i
$563$	11.1130	−	19.2482i	0.468355	−	0.811215i	−0.530991	−	0.847378i	$-0.678180\pi$
$563$	11.1130	−	19.2482i	0.468355	−	0.811215i	0.999346	+	0.0361625i	$0.0115134\pi$
$564$	−4.98515	−	8.63454i	−0.209913	−	0.363580i
$565$	9.40696	−	1.99951i	0.395754	−	0.0841200i
$566$	−7.00363	−	21.5550i	−0.294385	−	0.906022i
$567$	1.12135	+	0.238351i	0.0470925	+	0.0100098i
$568$	0.566619	+	5.39102i	0.0237748	+	0.226202i
$569$	−6.56003	−	7.28565i	−0.275011	−	0.305430i	0.589779	−	0.807565i	$-0.299215\pi$
$569$	−6.56003	−	7.28565i	−0.275011	−	0.305430i	−0.864790	+	0.502135i	$0.832548\pi$
$570$	0.936877	+	0.417124i	0.0392414	+	0.0174714i
$571$	−18.2833	+	8.14025i	−0.765132	+	0.340659i	−0.751920	−	0.659254i	$-0.770872\pi$
$571$	−18.2833	+	8.14025i	−0.765132	+	0.340659i	−0.0132119	+	0.999913i	$0.504206\pi$
$572$	0.674412	−	0.749011i	0.0281986	−	0.0313177i
$573$	−4.66226	−	3.38733i	−0.194769	−	0.141508i
$574$	5.31116	+	3.85879i	0.221684	+	0.161063i
$575$	−4.96050	+	5.50920i	−0.206867	+	0.229749i
$576$	0.913545	−	0.406737i	0.0380644	−	0.0169474i
$577$	16.6530	+	7.41440i	0.693274	+	0.308665i	0.722956	−	0.690894i	$-0.242783\pi$
$577$	16.6530	+	7.41440i	0.693274	+	0.308665i	−0.0296822	+	0.999559i	$0.509450\pi$
$578$	−6.19780	−	6.88335i	−0.257794	−	0.286310i
$579$	0.920343	+	8.75648i	0.0382482	+	0.363907i
$580$	2.77292	+	0.589402i	0.115139	+	0.0244736i
$581$	−3.14292	−	9.67292i	−0.130390	−	0.401300i
$582$	0.943759	−	0.200602i	0.0391201	−	0.00831523i
$583$	−13.9620	−	24.1829i	−0.578248	−	1.00156i
$584$	−4.21268	+	7.29658i	−0.174322	+	0.301935i
$585$	0.0695848	−	0.214160i	0.00287698	−	0.00885443i
$586$	0.425721	−	4.05047i	0.0175864	−	0.167323i
$587$	29.3966	−	21.3579i	1.21333	−	0.881535i	0.217800	−	0.975993i	$-0.430112\pi$
$587$	29.3966	−	21.3579i	1.21333	−	0.881535i	0.995529	+	0.0944586i	$0.0301120\pi$
$588$	−5.68575			−0.234476
$589$	4.81471	−	3.06957i	0.198386	−	0.126480i
$590$	6.69105			0.275466
$591$	−2.10152	+	1.52685i	−0.0864451	+	0.0628060i
$592$	−0.873739	+	8.31307i	−0.0359105	+	0.341665i
$593$	−2.58582	+	7.95834i	−0.106187	+	0.326810i	−0.990007	−	0.141017i	$-0.954963\pi$
$593$	−2.58582	+	7.95834i	−0.106187	+	0.326810i	0.883820	+	0.467827i	$0.154963\pi$
$594$	2.23796	−	3.87626i	0.0918246	−	0.159045i
$595$	−1.59445	−	2.76166i	−0.0653659	−	0.113217i
$596$	−10.3594	+	2.20197i	−0.424339	+	0.0901961i
$597$	−5.93132	−	18.2547i	−0.242753	−	0.747116i
$598$	−1.63287	−	0.347077i	−0.0667730	−	0.0141930i
$599$	−1.66258	−	15.8184i	−0.0679311	−	0.646321i	−0.974519	−	0.224304i	$-0.927989\pi$
$599$	−1.66258	−	15.8184i	−0.0679311	−	0.646321i	0.906588	−	0.422017i	$-0.138678\pi$
$600$	0.669131	+	0.743145i	0.0273171	+	0.0303388i
$601$	6.36575	+	2.83421i	0.259664	+	0.115610i	0.532440	−	0.846468i	$-0.321275\pi$
$601$	6.36575	+	2.83421i	0.259664	+	0.115610i	−0.272776	+	0.962078i	$0.587942\pi$
$602$	−4.97003	+	2.21280i	−0.202563	+	0.0901869i
$603$	−6.47611	+	7.19245i	−0.263728	+	0.292899i
$604$	19.4182	+	14.1081i	0.790113	+	0.574051i
$605$	7.30855	+	5.30997i	0.297135	+	0.215881i
$606$	0.271284	−	0.301291i	0.0110201	−	0.0122391i
$607$	28.0947	−	12.5086i	1.14033	−	0.507708i	0.252371	−	0.967630i	$-0.418790\pi$
$607$	28.0947	−	12.5086i	1.14033	−	0.507708i	0.887959	+	0.459923i	$0.152123\pi$
$608$	−0.936877	−	0.417124i	−0.0379954	−	0.0169166i
$609$	−2.17461	−	2.41515i	−0.0881198	−	0.0978669i
$610$	0.688648	+	6.55205i	0.0278826	+	0.265285i
$611$	2.19606	+	0.466788i	0.0888433	+	0.0188842i
$612$	0.859575	+	2.64550i	0.0347463	+	0.106938i
$613$	26.8203	−	5.70083i	1.08326	−	0.230254i	0.368503	−	0.929626i	$-0.379870\pi$
$613$	26.8203	−	5.70083i	1.08326	−	0.230254i	0.714758	+	0.699372i	$0.246537\pi$
$614$	2.24117	+	3.88182i	0.0904462	+	0.156657i
$615$	2.86328	−	4.95934i	0.115458	−	0.199980i
$616$	1.58564	−	4.88008i	0.0638871	−	0.196624i
$617$	−4.27878	+	40.7098i	−0.172257	+	1.63892i	0.477398	+	0.878687i	$0.341580\pi$
$617$	−4.27878	+	40.7098i	−0.172257	+	1.63892i	−0.649655	+	0.760229i	$0.725087\pi$
$618$	6.28090	−	4.56334i	0.252655	−	0.183565i
$619$	4.46646			0.179522			0.0897612	−	0.995963i	$-0.471390\pi$
$619$	4.46646			0.179522			0.0897612	+	0.995963i	$0.471390\pi$
$620$	5.50633	−	0.824811i	0.221140	−	0.0331252i
$621$	−7.41336			−0.297488
$622$	15.3719	−	11.1684i	0.616358	−	0.447811i
$623$	−0.215696	+	2.05221i	−0.00864169	+	0.0822202i
$624$	−0.0695848	+	0.214160i	−0.00278562	+	0.00857326i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	11.1543	+	19.3199i	0.445817	+	0.772178i
$627$	−4.48993	+	0.954363i	−0.179310	+	0.0381136i
$628$	−4.25018	−	13.0807i	−0.169601	−	0.521977i
$629$	−22.7433	−	4.83423i	−0.906834	−	0.192753i
$630$	−0.119832	−	1.14013i	−0.00477422	−	0.0454237i
$631$	11.7017	+	12.9961i	0.465839	+	0.517367i	0.929588	−	0.368600i	$-0.120163\pi$
$631$	11.7017	+	12.9961i	0.465839	+	0.517367i	−0.463749	+	0.885967i	$0.653496\pi$
$632$	8.01842	+	3.57003i	0.318956	+	0.142008i
$633$	1.92608	−	0.857545i	0.0765547	−	0.0340843i
$634$	−5.80372	+	6.44568i	−0.230495	+	0.255991i
$635$	−17.0676	−	12.4003i	−0.677307	−	0.492092i
$636$	5.04724	+	3.66703i	0.200136	+	0.145407i
$637$	0.856705	−	0.951467i	0.0339439	−	0.0376985i
$638$	−11.5916	+	5.16093i	−0.458918	+	0.204323i
$639$	−4.95207	−	2.20480i	−0.195901	−	0.0872207i
$640$	−0.669131	−	0.743145i	−0.0264497	−	0.0293754i
$641$	−0.417437	−	3.97165i	−0.0164878	−	0.156871i	0.983180	−	0.182638i	$-0.0584637\pi$
$641$	−0.417437	−	3.97165i	−0.0164878	−	0.156871i	−0.999668	+	0.0257675i	$0.991797\pi$
$642$	−2.34250	−	0.497914i	−0.0924511	−	0.0196511i
$643$	−3.18382	−	9.79878i	−0.125558	−	0.386426i	0.868445	−	0.495786i	$-0.165120\pi$
$643$	−3.18382	−	9.79878i	−0.125558	−	0.386426i	−0.994002	+	0.109360i	$0.965120\pi$
$644$	−8.31300	+	1.76698i	−0.327578	+	0.0696289i
$645$	2.37279	+	4.10980i	0.0934287	+	0.161823i
$646$	1.42634	−	2.47050i	0.0561187	−	0.0972004i
$647$	−14.3601	+	44.1959i	−0.564554	+	1.73752i	0.104717	+	0.994502i	$0.466606\pi$
$647$	−14.3601	+	44.1959i	−0.564554	+	1.73752i	−0.669272	+	0.743018i	$0.733394\pi$
$648$	−0.104528	+	0.994522i	−0.00410627	+	0.0390685i
$649$	−24.2289	+	17.6033i	−0.951068	+	0.690992i
$650$	−0.225181			−0.00883233
$651$	−5.66271	−	2.94541i	−0.221939	−	0.115440i
$652$	−3.63303			−0.142280
$653$	−7.72902	+	5.61546i	−0.302460	+	0.219750i	−0.728654	−	0.684882i	$-0.759854\pi$
$653$	−7.72902	+	5.61546i	−0.302460	+	0.219750i	0.426195	+	0.904632i	$0.359854\pi$
$654$	1.99717	−	19.0018i	0.0780954	−	0.743028i
$655$	−1.23951	+	3.81480i	−0.0484315	+	0.149057i
$656$	−2.86328	+	4.95934i	−0.111792	+	0.193630i
$657$	−4.21268	−	7.29658i	−0.164352	−	0.284667i
$658$	11.1802	−	2.37644i	0.435851	−	0.0926431i
$659$	−9.03240	−	27.7989i	−0.351852	−	1.08289i	−0.957812	−	0.287395i	$-0.907211\pi$
$659$	−9.03240	−	27.7989i	−0.351852	−	1.08289i	0.605960	−	0.795495i	$-0.292789\pi$
$660$	−4.37811	−	0.930596i	−0.170418	−	0.0362234i
$661$	2.63005	+	25.0233i	0.102297	+	0.973293i	0.918471	+	0.395487i	$0.129424\pi$
$661$	2.63005	+	25.0233i	0.102297	+	0.973293i	−0.816174	+	0.577806i	$0.803909\pi$
$662$	10.3582	+	11.5040i	0.402584	+	0.447114i
$663$	−0.572221	−	0.254769i	−0.0222232	−	0.00989441i
$664$	8.10481	−	3.60849i	0.314528	−	0.140037i
$665$	−0.786687	+	0.873704i	−0.0305064	+	0.0338808i
$666$	−6.76246	−	4.91322i	−0.262040	−	0.190383i
$667$	17.0022	+	12.3528i	0.658328	+	0.478303i
$668$	−16.3771	+	18.1887i	−0.633651	+	0.703741i
$669$	8.24412	−	3.67052i	0.318736	−	0.141910i
$670$	8.84166	+	3.93656i	0.341583	+	0.152083i
$671$	−19.7313	−	21.9139i	−0.761719	−	0.845975i
$672$	0.119832	+	1.14013i	0.00462262	+	0.0439813i
$673$	−6.99573	−	1.48699i	−0.269665	−	0.0573192i	0.0710942	−	0.997470i	$-0.477351\pi$
$673$	−6.99573	−	1.48699i	−0.269665	−	0.0573192i	−0.340760	+	0.940150i	$0.610684\pi$
$674$	−3.17298	−	9.76543i	−0.122219	−	0.376150i
$675$	−0.978148	+	0.207912i	−0.0376489	+	0.00800252i
$676$	6.47465	+	11.2144i	0.249025	+	0.431324i
$677$	−15.5447	+	26.9243i	−0.597433	+	1.03478i	0.395765	+	0.918352i	$0.370479\pi$
$677$	−15.5447	+	26.9243i	−0.597433	+	1.03478i	−0.993199	+	0.116433i	$0.962854\pi$
$678$	2.97185	−	9.14642i	0.114133	−	0.351266i
$679$	−0.115619	+	1.10004i	−0.00443706	+	0.0422158i
$680$	2.25040	−	1.63501i	0.0862987	−	0.0626997i
$681$	7.73737			0.296497
$682$	−17.7690	+	17.4732i	−0.680409	+	0.669084i
$683$	10.9389			0.418566			0.209283	−	0.977855i	$-0.432887\pi$
$683$	10.9389			0.418566			0.209283	+	0.977855i	$0.432887\pi$
$684$	0.829679	−	0.602797i	0.0317236	−	0.0230485i
$685$	−1.22737	+	11.6777i	−0.0468955	+	0.446181i
$686$	4.49404	−	13.8312i	0.171583	−	0.528079i
$687$	−1.28565	+	2.22681i	−0.0490506	+	0.0849581i
$688$	−2.37279	−	4.10980i	−0.0904619	−	0.156685i
$689$	−1.37415	+	0.292084i	−0.0523508	+	0.0111275i
$690$	2.29085	+	7.05052i	0.0872113	+	0.268409i
$691$	−27.9123	−	5.93294i	−1.06183	−	0.225700i	−0.356297	−	0.934373i	$-0.615961\pi$
$691$	−27.9123	−	5.93294i	−1.06183	−	0.225700i	−0.705537	+	0.708673i	$0.749294\pi$
$692$	−0.0101718	−	0.0967784i	−0.000386675	−	0.00367896i
$693$	3.43346	+	3.81324i	0.130426	+	0.144853i
$694$	12.4875	+	5.55977i	0.474017	+	0.211046i
$695$	−6.32196	+	2.81472i	−0.239806	+	0.106768i
$696$	1.89690	−	2.10672i	0.0719016	−	0.0798549i
$697$	−12.8870	−	9.36296i	−0.488130	−	0.354648i
$698$	−1.53732	−	1.11693i	−0.0581885	−	0.0422764i
$699$	−15.0792	+	16.7472i	−0.570348	+	0.633436i
$700$	−1.04729	+	0.466285i	−0.0395840	+	0.0176239i
$701$	31.1495	+	13.8686i	1.17650	+	0.523811i	0.899441	−	0.437042i	$-0.143974\pi$
$701$	31.1495	+	13.8686i	1.17650	+	0.523811i	0.277058	+	0.960853i	$0.410641\pi$
$702$	−0.150676	−	0.167342i	−0.00568689	−	0.00631593i
$703$	0.896054	+	8.52538i	0.0337953	+	0.321541i
$704$	4.37811	+	0.930596i	0.165006	+	0.0350732i
$705$	−3.08099	−	9.48232i	−0.116037	−	0.357125i
$706$	−4.76085	+	1.01195i	−0.179177	+	0.0380853i
$707$	0.232392	+	0.402515i	0.00874000	+	0.0151381i
$708$	3.34552	−	5.79462i	0.125732	−	0.217775i
$709$	−4.69343	+	14.4449i	−0.176266	+	0.542490i	−0.999689	−	0.0249377i	$-0.992061\pi$
$709$	−4.69343	+	14.4449i	−0.176266	+	0.542490i	0.823423	+	0.567427i	$0.192061\pi$
$710$	−0.566619	+	5.39102i	−0.0212648	+	0.202321i
$711$	−7.10095	+	5.15914i	−0.266306	+	0.193483i
$712$	−1.79999			−0.0674574
$713$	39.7783	+	11.0172i	1.48971	+	0.412596i
$714$	−3.18889			−0.119341
$715$	0.815403	−	0.592425i	0.0304943	−	0.0221554i
$716$	−1.70394	+	16.2119i	−0.0636792	+	0.605867i
$717$	−4.78733	+	14.7339i	−0.178786	+	0.550247i
$718$	2.69749	−	4.67219i	0.100669	−	0.174365i
$719$	−5.22629	−	9.05219i	−0.194908	−	0.337590i	0.751963	−	0.659206i	$-0.229107\pi$
$719$	−5.22629	−	9.05219i	−0.194908	−	0.337590i	−0.946870	+	0.321616i	$0.895774\pi$
$720$	0.978148	−	0.207912i	0.0364534	−	0.00774841i
$721$	2.75033	+	8.46465i	0.102428	+	0.315240i
$722$	17.5561	+	3.73165i	0.653369	+	0.138878i
$723$	−1.35416	−	12.8840i	−0.0503619	−	0.479162i
$724$	−7.72388	−	8.57824i	−0.287056	−	0.318808i
$725$	2.58978	+	1.15304i	0.0961820	+	0.0428230i
$726$	8.25285	−	3.67441i	0.306292	−	0.136370i
$727$	7.55444	−	8.39006i	0.280179	−	0.311170i	−0.586586	−	0.809887i	$-0.699529\pi$
$727$	7.55444	−	8.39006i	0.280179	−	0.311170i	0.866765	+	0.498717i	$0.166195\pi$
$728$	−0.208847	−	0.151736i	−0.00774039	−	0.00562372i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−5.63767	+	6.26127i	−0.208660	+	0.231740i
$731$	12.0593	−	5.36914i	0.446029	−	0.198585i
$732$	6.01857	+	2.67964i	0.222453	+	0.0990423i
$733$	2.65812	+	2.95214i	0.0981797	+	0.109040i	0.790232	−	0.612808i	$-0.209960\pi$
$733$	2.65812	+	2.95214i	0.0981797	+	0.109040i	−0.692052	+	0.721847i	$0.743293\pi$
$734$	3.25501	+	30.9694i	0.120145	+	1.14310i
$735$	−5.56151	−	1.18213i	−0.205139	−	0.0436037i
$736$	−2.29085	−	7.05052i	−0.0844420	−	0.259886i
$737$	−42.3731	+	9.00668i	−1.56083	+	0.331765i
$738$	−2.86328	−	4.95934i	−0.105399	−	0.182556i
$739$	5.19128	−	8.99156i	0.190964	−	0.330760i	−0.754606	−	0.656178i	$-0.772172\pi$
$739$	5.19128	−	8.99156i	0.190964	−	0.330760i	0.945570	+	0.325419i	$0.105505\pi$
$740$	−2.58303	+	7.94975i	−0.0949541	+	0.292239i
$741$	−0.0241390	+	0.229667i	−0.000886768	+	0.00843703i
$742$	−5.78619	+	4.20391i	−0.212418	+	0.154330i
$743$	11.2085			0.411200			0.205600	−	0.978636i	$-0.434085\pi$
$743$	11.2085			0.411200			0.205600	+	0.978636i	$0.434085\pi$
$744$	2.03886	−	5.18103i	0.0747482	−	0.189946i
$745$	−10.5909			−0.388020
$746$	6.05946	−	4.40246i	0.221853	−	0.161185i
$747$	−0.927358	+	8.82322i	−0.0339302	+	0.322825i
$748$	−3.84739	+	11.8410i	−0.140674	+	0.432951i
$749$	1.37273	−	2.37763i	0.0501583	−	0.0868768i
$750$	0.500000	+	0.866025i	0.0182574	+	0.0316228i
$751$	−15.4240	+	3.27846i	−0.562828	+	0.119633i	−0.480535	−	0.876975i	$-0.659558\pi$
$751$	−15.4240	+	3.27846i	−0.562828	+	0.119633i	−0.0822928	+	0.996608i	$0.526224\pi$
$752$	3.08099	+	9.48232i	0.112352	+	0.345785i
$753$	−23.3588	−	4.96506i	−0.851241	−	0.180937i
$754$	0.0667267	+	0.634862i	0.00243004	+	0.0231203i
$755$	16.0606	+	17.8371i	0.584504	+	0.649158i
$756$	−1.04729	−	0.466285i	−0.0380897	−	0.0169586i
$757$	36.3214	−	16.1713i	1.32012	−	0.587757i	0.378868	−	0.925451i	$-0.376313\pi$
$757$	36.3214	−	16.1713i	1.32012	−	0.587757i	0.941256	+	0.337693i	$0.109647\pi$
$758$	−12.5787	+	13.9701i	−0.456880	+	0.507417i
$759$	−26.8445	−	19.5037i	−0.974393	−	0.707938i
$760$	−0.829679	−	0.602797i	−0.0300956	−	0.0218657i
$761$	14.1027	−	15.6627i	0.511224	−	0.567772i	−0.431172	−	0.902270i	$-0.641900\pi$
$761$	14.1027	−	15.6627i	0.511224	−	0.567772i	0.942397	+	0.334498i	$0.108567\pi$
$762$	−19.2728	+	8.58080i	−0.698180	+	0.310850i
$763$	20.0101	+	8.90906i	0.724413	+	0.322530i
$764$	3.85612	+	4.28265i	0.139509	+	0.154941i
$765$	0.290761	+	2.76640i	0.0105125	+	0.100020i
$766$	−22.4214	−	4.76581i	−0.810118	−	0.172196i
$767$	0.465595	+	1.43296i	0.0168117	+	0.0517410i
$768$	−0.978148	+	0.207912i	−0.0352959	+	0.00750237i
$769$	−11.6164	−	20.1202i	−0.418897	−	0.725552i	0.576931	−	0.816793i	$-0.304250\pi$
$769$	−11.6164	−	20.1202i	−0.418897	−	0.725552i	−0.995829	+	0.0912409i	$0.970917\pi$
$770$	2.56561	−	4.44377i	0.0924582	−	0.160142i
$771$	−2.03897	+	6.27531i	−0.0734318	+	0.226000i
$772$	0.920343	−	8.75648i	0.0331239	−	0.315153i
$773$	11.1800	−	8.12271i	0.402115	−	0.292154i	−0.368287	−	0.929712i	$-0.620056\pi$
$773$	11.1800	−	8.12271i	0.402115	−	0.292154i	0.770402	+	0.637559i	$0.220056\pi$
$774$	4.74559			0.170577
$775$	5.55749	+	0.338043i	0.199631	+	0.0121429i
$776$	−0.964844			−0.0346359
$777$	7.75253	−	5.63254i	0.278121	−	0.202066i
$778$	−2.85825	+	27.1945i	−0.102473	+	0.974969i
$779$	−1.81480	+	5.58537i	−0.0650219	+	0.200117i
$780$	−0.112591	+	0.195013i	−0.00403139	+	0.00698257i
$781$	−12.1313	−	21.0121i	−0.434094	−	0.751872i
$782$	20.1707	−	4.28741i	0.721302	−	0.153318i
$783$	0.876022	+	2.69612i	0.0313065	+	0.0963514i
$784$	5.56151	+	1.18213i	0.198625	+	0.0422191i
$785$	−1.43767	−	13.6785i	−0.0513127	−	0.488208i
$786$	2.68397	+	2.98085i	0.0957339	+	0.106323i
$787$	8.51271	+	3.79010i	0.303445	+	0.135103i	0.552811	−	0.833307i	$-0.313555\pi$
$787$	8.51271	+	3.79010i	0.303445	+	0.135103i	−0.249365	+	0.968410i	$0.580222\pi$
$788$	2.37305	−	1.05655i	0.0845363	−	0.0376380i
$789$	−19.1529	+	21.2714i	−0.681861	+	0.757284i
$790$	7.10095	+	5.15914i	0.252640	+	0.183554i
$791$	8.91951	+	6.48040i	0.317141	+	0.230417i
$792$	−2.99498	+	3.32626i	−0.106422	+	0.118193i
$793$	−1.35527	+	0.603404i	−0.0481270	+	0.0214275i
$794$	−19.4322	−	8.65178i	−0.689623	−	0.307040i
$795$	4.17453	+	4.63628i	0.148055	+	0.164432i
$796$	2.00634	+	19.0890i	0.0711127	+	0.676592i
$797$	−51.7016	−	10.9895i	−1.83137	−	0.389269i	−0.842575	−	0.538579i	$-0.818961\pi$
$797$	−51.7016	−	10.9895i	−1.83137	−	0.389269i	−0.988790	+	0.149310i	$0.952295\pi$
$798$	0.363307	+	1.11814i	0.0128609	+	0.0395818i
$799$	−27.1278	+	5.76619i	−0.959712	+	0.203993i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	0.899994	−	1.55883i	0.0317997	−	0.0550787i
$802$	−7.21306	+	22.1995i	−0.254702	+	0.783892i
$803$	3.94190	−	37.5047i	0.139107	−	1.32351i
$804$	7.82999	−	5.68882i	0.276142	−	0.200629i
$805$	−8.49872			−0.299541
$806$	0.559799	+	1.12184i	0.0197181	+	0.0395152i
$807$	−11.9010			−0.418936
$808$	−0.327997	+	0.238304i	−0.0115389	+	0.00838350i
$809$	−1.23554	+	11.7554i	−0.0434393	+	0.413298i	0.951096	+	0.308896i	$0.0999594\pi$
$809$	−1.23554	+	11.7554i	−0.0434393	+	0.413298i	−0.994535	+	0.104402i	$0.966707\pi$
$810$	−0.309017	+	0.951057i	−0.0108578	+	0.0334167i
$811$	16.7320	−	28.9806i	0.587539	−	1.01765i	−0.407015	−	0.913422i	$-0.633430\pi$
$811$	16.7320	−	28.9806i	0.587539	−	1.01765i	0.994554	−	0.104226i	$-0.0332365\pi$
$812$	1.62495	+	2.81450i	0.0570247	+	0.0987697i
$813$	−0.810848	+	0.172351i	−0.0284377	+	0.00604462i
$814$	−11.5614	−	35.5825i	−0.405228	−	1.24716i
$815$	−3.55364	−	0.755349i	−0.124479	−	0.0264587i
$816$	−0.290761	−	2.76640i	−0.0101787	−	0.0968435i
$817$	−3.25652	−	3.61673i	−0.113931	−	0.126533i
$818$	23.0968	+	10.2834i	0.807562	+	0.359550i
$819$	0.235831	−	0.104999i	0.00824060	−	0.00366895i
$820$	−3.83181	+	4.25566i	−0.133813	+	0.148614i
$821$	0.349354	+	0.253821i	0.0121925	+	0.00885840i	0.593865	−	0.804565i	$-0.297601\pi$
$821$	0.349354	+	0.253821i	0.0121925	+	0.00885840i	−0.581672	+	0.813423i	$0.697601\pi$
$822$	9.49947	+	6.90177i	0.331332	+	0.240727i
$823$	16.5123	−	18.3387i	0.575581	−	0.639248i	−0.383108	−	0.923704i	$-0.625146\pi$
$823$	16.5123	−	18.3387i	0.575581	−	0.639248i	0.958689	+	0.284456i	$0.0918129\pi$
$824$	−7.09242	+	3.15775i	−0.247076	+	0.110005i
$825$	−4.08896	−	1.82052i	−0.142359	−	0.0633824i
$826$	5.13267	+	5.70041i	0.178589	+	0.198343i
$827$	5.13042	+	48.8127i	0.178402	+	1.69738i	0.607656	+	0.794200i	$0.292110\pi$
$827$	5.13042	+	48.8127i	0.178402	+	1.69738i	−0.429254	+	0.903184i	$0.641223\pi$
$828$	7.25136	+	1.54132i	0.252002	+	0.0535647i
$829$	15.8520	+	48.7874i	0.550562	+	1.69446i	0.707384	+	0.706829i	$0.249875\pi$
$829$	15.8520	+	48.7874i	0.550562	+	1.69446i	−0.156822	+	0.987627i	$0.550125\pi$
$830$	8.67795	−	1.84455i	0.301216	−	0.0640254i
$831$	−0.741832	−	1.28489i	−0.0257339	−	0.0445724i
$832$	0.112591	−	0.195013i	0.00390338	−	0.00676085i
$833$	−4.88733	+	15.0417i	−0.169336	+	0.521162i
$834$	−0.723362	+	6.88233i	−0.0250480	+	0.238316i
$835$	−19.8009	+	14.3862i	−0.685239	+	0.497855i
$836$	4.59023			0.158757
$837$	3.46747	+	4.35622i	0.119853	+	0.150573i
$838$	−29.2401			−1.01008
$839$	−34.7427	+	25.2421i	−1.19945	+	0.871453i	−0.994231	−	0.107262i	$-0.965791\pi$
$839$	−34.7427	+	25.2421i	−1.19945	+	0.871453i	−0.205222	+	0.978716i	$0.565791\pi$
$840$	−0.119832	+	1.14013i	−0.00413460	+	0.0393381i
$841$	−6.47809	+	19.9375i	−0.223382	+	0.687500i
$842$	−1.01887	+	1.76474i	−0.0351127	+	0.0608170i
$843$	0.409344	+	0.709004i	0.0140986	+	0.0244194i
$844$	−2.06228	+	0.438351i	−0.0709867	+	0.0150887i
$845$	4.00155	+	12.3155i	0.137658	+	0.423666i
$846$	−9.75243	−	2.07294i	−0.335295	−	0.0712693i
$847$	1.08255	+	10.2997i	0.0371968	+	0.353904i
$848$	−4.17453	−	4.63628i	−0.143354	−	0.159211i
$849$	−20.7048	−	9.21837i	−0.710587	−	0.316374i
$850$	2.54116	−	1.13140i	0.0871610	−	0.0388066i
$851$	−41.4642	+	46.0506i	−1.42137	+	1.57860i
$852$	4.38545	+	3.18622i	0.150243	+	0.109158i
$853$	−19.4569	−	14.1362i	−0.666190	−	0.484015i	0.202558	−	0.979270i	$-0.435075\pi$
$853$	−19.4569	−	14.1362i	−0.666190	−	0.484015i	−0.868748	+	0.495255i	$0.835075\pi$
$854$	−5.05373	+	5.61274i	−0.172935	+	0.192064i
$855$	0.936877	−	0.417124i	0.0320405	−	0.0142654i
$856$	2.18779	+	0.974067i	0.0747771	+	0.0332929i
$857$	0.862082	+	0.957439i	0.0294482	+	0.0327055i	0.757689	−	0.652616i	$-0.226328\pi$
$857$	0.862082	+	0.957439i	0.0294482	+	0.0327055i	−0.728241	+	0.685321i	$0.759662\pi$
$858$	−0.105354	−	1.00237i	−0.00359671	−	0.0342204i
$859$	22.9611	+	4.88053i	0.783423	+	0.166522i	0.582224	−	0.813029i	$-0.302183\pi$
$859$	22.9611	+	4.88053i	0.783423	+	0.166522i	0.201199	+	0.979550i	$0.435516\pi$
$860$	−1.46647	−	4.51332i	−0.0500061	−	0.153903i
$861$	6.42150	−	1.36493i	0.218844	−	0.0465167i
$862$	−10.9820	−	19.0214i	−0.374049	−	0.647872i
$863$	8.35653	−	14.4739i	0.284460	−	0.492699i	−0.688018	−	0.725693i	$-0.741519\pi$
$863$	8.35653	−	14.4739i	0.284460	−	0.492699i	0.972478	+	0.232995i	$0.0748525\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$	0.0101718	−	0.0967784i	0.000345852	−	0.00329057i
$866$	−30.9918	+	22.5169i	−1.05314	+	0.765154i
$867$	−9.26247			−0.314570
$868$	4.92658	+	4.05839i	0.167219	+	0.137751i
$869$	−39.2863			−1.33270
$870$	2.29345	−	1.66629i	0.0777554	−	0.0564926i
$871$	−0.227809	+	2.16746i	−0.00771900	+	0.0734414i
$872$	−5.90422	+	18.1713i	−0.199942	+	0.615358i
$873$	0.482422	−	0.835579i	0.0163275	−	0.0282801i
$874$	−3.80134	−	6.58412i	−0.128582	−	0.222711i
$875$	−1.12135	+	0.238351i	−0.0379087	+	0.00805774i
$876$	2.60358	+	8.01300i	0.0879669	+	0.270734i
$877$	53.2384	+	11.3162i	1.79773	+	0.382120i	0.980863	−	0.194700i	$-0.0623732\pi$
$877$	53.2384	+	11.3162i	1.79773	+	0.382120i	0.816871	+	0.576820i	$0.195707\pi$
$878$	−0.213973	−	2.03582i	−0.00722124	−	0.0687055i
$879$	−2.72522	−	3.02666i	−0.0919194	−	0.102087i
$880$	4.08896	+	1.82052i	0.137839	+	0.0613698i
$881$	21.2172	−	9.44653i	0.714827	−	0.318262i	−0.0169018	−	0.999857i	$-0.505380\pi$
$881$	21.2172	−	9.44653i	0.714827	−	0.318262i	0.731729	+	0.681596i	$0.238714\pi$
$882$	−3.80451	+	4.22534i	−0.128105	+	0.142275i
$883$	7.15993	+	5.20199i	0.240951	+	0.175061i	0.701707	−	0.712466i	$-0.252422\pi$
$883$	7.15993	+	5.20199i	0.240951	+	0.175061i	−0.460756	+	0.887527i	$0.652422\pi$
$884$	0.506747	+	0.368173i	0.0170437	+	0.0123830i
$885$	4.47718	−	4.97242i	0.150499	−	0.167146i
$886$	−10.3678	+	4.61606i	−0.348314	+	0.155080i
$887$	5.59966	+	2.49313i	0.188018	+	0.0837110i	0.498586	−	0.866840i	$-0.333853\pi$
$887$	5.59966	+	2.49313i	0.188018	+	0.0837110i	−0.310568	+	0.950551i	$0.600519\pi$
$888$	5.59317	+	6.21185i	0.187695	+	0.208456i
$889$	−2.52806	−	24.0529i	−0.0847885	−	0.806708i
$890$	−1.76065	−	0.374238i	−0.0590172	−	0.0125445i
$891$	−1.38314	−	4.25685i	−0.0463368	−	0.142610i
$892$	−8.82710	+	1.87626i	−0.295553	+	0.0628218i
$893$	5.11247	+	8.85506i	0.171082	+	0.296323i
$894$	−5.29544	+	9.17197i	−0.177106	+	0.306757i
$895$	−5.03735	+	15.5034i	−0.168380	+	0.518221i
$896$	0.119832	−	1.14013i	0.00400331	−	0.0380889i
$897$	−1.35053	+	0.981219i	−0.0450929	+	0.0327619i
$898$	17.1183			0.571245
$899$	−0.693761	−	15.7686i	−0.0231382	−	0.525913i
$900$	1.00000			0.0333333
$901$	14.0396	−	10.2004i	0.467727	−	0.339824i
$902$	2.67923	−	25.4912i	0.0892087	−	0.848764i
$903$	−1.68117	+	5.17410i	−0.0559457	+	0.172183i
$904$	−4.80856	+	8.32867i	−0.159930	+	0.277007i
$905$	−5.77158	−	9.99667i	−0.191854	−	0.332301i
$906$	23.4777	−	4.99033i	0.779993	−	0.165793i
$907$	−10.2953	−	31.6857i	−0.341850	−	1.05211i	−0.963249	−	0.268612i	$-0.913435\pi$
$907$	−10.2953	−	31.6857i	−0.341850	−	1.05211i	0.621398	−	0.783495i	$-0.286565\pi$
$908$	−7.56829	−	1.60869i	−0.251162	−	0.0533862i
$909$	−0.0423787	−	0.403206i	−0.00140561	−	0.0133735i
$910$	−0.172736	−	0.191842i	−0.00572613	−	0.00635951i
$911$	40.9124	+	18.2154i	1.35549	+	0.603503i	0.950473	−	0.310807i	$-0.100599\pi$
$911$	40.9124	+	18.2154i	1.35549	+	0.603503i	0.405016	+	0.914310i	$0.367266\pi$
$912$	−0.936877	+	0.417124i	−0.0310231	+	0.0138124i
$913$	−26.5709	+	29.5100i	−0.879368	+	0.976637i
$914$	24.9188	+	18.1046i	0.824241	+	0.598846i
$915$	5.32992	+	3.87241i	0.176202	+	0.128018i
$916$	1.72053	−	1.91085i	0.0568480	−	0.0631361i
$917$	−4.20083	+	1.87033i	−0.138724	+	0.0617637i
$918$	2.54116	+	1.13140i	0.0838707	+	0.0373416i
$919$	−23.7060	−	26.3281i	−0.781987	−	0.868485i	0.212080	−	0.977252i	$-0.431976\pi$
$919$	−23.7060	−	26.3281i	−0.781987	−	0.868485i	−0.994067	+	0.108767i	$0.965310\pi$
$920$	−0.774907	−	7.37275i	−0.0255479	−	0.243072i
$921$	4.38439	+	0.931930i	0.144470	+	0.0307081i
$922$	6.72851	+	20.7082i	0.221592	+	0.681989i
$923$	−1.19397	+	0.253786i	−0.0393000	+	0.00835347i
$924$	−2.56561	−	4.44377i	−0.0844024	−	0.146189i
$925$	−4.17943	+	7.23899i	−0.137419	+	0.238017i
$926$	2.18019	−	6.70992i	0.0716454	−	0.220502i
$927$	0.811519	−	7.72109i	0.0266538	−	0.253594i
$928$	−2.29345	+	1.66629i	−0.0752863	+	0.0546987i
$929$	14.6159			0.479533			0.239766	−	0.970831i	$-0.422929\pi$
$929$	14.6159			0.479533			0.239766	+	0.970831i	$0.422929\pi$
$930$	3.07150	−	4.64391i	0.100718	−	0.152280i
$931$	5.83096			0.191102
$932$	18.2316	−	13.2461i	0.597197	−	0.433889i
$933$	1.98612	−	18.8967i	0.0650226	−	0.618649i
$934$	7.24109	−	22.2858i	0.236936	−	0.729213i
$935$	−6.22521	+	10.7824i	−0.203586	+	0.352621i
$936$	0.112591	+	0.195013i	0.00368014	+	0.00637419i
$937$	4.13163	−	0.878204i	0.134974	−	0.0286897i	−0.139929	−	0.990162i	$-0.544687\pi$
$937$	4.13163	−	0.878204i	0.134974	−	0.0286897i	0.274903	+	0.961472i	$0.411354\pi$
$938$	3.42866	+	10.5523i	0.111950	+	0.344546i
$939$	21.8212	+	4.63824i	0.712108	+	0.151363i
$940$	1.04218	+	9.91569i	0.0339922	+	0.323414i
$941$	−16.8255	−	18.6866i	−0.548496	−	0.609167i	0.403611	−	0.914931i	$-0.367755\pi$
$941$	−16.8255	−	18.6866i	−0.548496	−	0.609167i	−0.952107	+	0.305764i	$0.901088\pi$
$942$	−12.5648	−	5.59421i	−0.409383	−	0.182269i
$943$	−38.7827	+	17.2672i	−1.26294	+	0.562297i
$944$	−4.47718	+	4.97242i	−0.145720	+	0.161838i
$945$	−0.927462	−	0.673841i	−0.0301703	−	0.0219200i
$946$	17.1842	+	12.4851i	0.558707	+	0.405925i
$947$	7.07257	−	7.85489i	0.229828	−	0.255250i	−0.617190	−	0.786814i	$-0.711729\pi$
$947$	7.07257	−	7.85489i	0.229828	−	0.255250i	0.847018	+	0.531565i	$0.178396\pi$
$948$	8.01842	−	3.57003i	0.260426	−	0.115949i
$949$	−1.73321	−	0.771675i	−0.0562624	−	0.0250496i
$950$	−0.686220	−	0.762124i	−0.0222639	−	0.0247266i
$951$	0.906630	+	8.62601i	0.0293995	+	0.279718i
$952$	3.11921	+	0.663008i	0.101094	+	0.0214882i
$953$	−15.4273	−	47.4802i	−0.499738	−	1.53804i	−0.809440	−	0.587202i	$-0.800229\pi$
$953$	−15.4273	−	47.4802i	−0.499738	−	1.53804i	0.309702	−	0.950834i	$-0.399771\pi$
$954$	6.10240	−	1.29710i	0.197572	−	0.0419953i
$955$	2.88144	+	4.99080i	0.0932411	+	0.161498i
$956$	7.74606	−	13.4166i	0.250526	−	0.433923i
$957$	−3.92100	+	12.0676i	−0.126748	+	0.390090i
$958$	4.06088	−	38.6367i	0.131201	−	1.24829i
$959$	−10.8903	+	7.91223i	−0.351665	+	0.255499i
$960$	−1.00000			−0.0322749
$961$	−12.1318	−	28.5275i	−0.391347	−	0.920243i
$962$	−1.88226			−0.0606865
$963$	−1.93746	+	1.40765i	−0.0624338	+	0.0453608i
$964$	−1.35416	+	12.8840i	−0.0436147	+	0.414966i
$965$	2.72081	−	8.37378i	0.0875859	−	0.269562i
$966$	−4.24936	+	7.36011i	−0.136721	+	0.236808i
$967$	−9.52307	−	16.4944i	−0.306241	−	0.530425i	0.671296	−	0.741190i	$-0.265738\pi$
$967$	−9.52307	−	16.4944i	−0.306241	−	0.530425i	−0.977537	+	0.210764i	$0.932405\pi$
$968$	−8.83646	+	1.87825i	−0.284014	+	0.0603691i
$969$	−0.881528	−	2.71306i	−0.0283187	−	0.0871561i
$970$	−0.943759	−	0.200602i	−0.0303023	−	0.00644095i
$971$	−3.50726	−	33.3694i	−0.112553	−	1.07087i	−0.894359	−	0.447351i	$-0.852368\pi$
$971$	−3.50726	−	33.3694i	−0.112553	−	1.07087i	0.781805	−	0.623523i	$-0.214299\pi$
$972$	0.669131	+	0.743145i	0.0214624	+	0.0238364i
$973$	−7.24753	−	3.22681i	−0.232345	−	0.103447i
$974$	5.74910	−	2.55967i	0.184213	−	0.0820170i
$975$	−0.150676	+	0.167342i	−0.00482548	+	0.00535924i
$976$	−5.32992	−	3.87241i	−0.170607	−	0.123953i
$977$	4.34569	+	3.15733i	0.139031	+	0.101012i	0.655127	−	0.755519i	$-0.272615\pi$
$977$	4.34569	+	3.15733i	0.139031	+	0.101012i	−0.516096	+	0.856531i	$0.672615\pi$
$978$	−2.43097	+	2.69987i	−0.0777339	+	0.0863322i
$979$	7.36007	−	3.27691i	0.235229	−	0.104731i
$980$	5.19419	+	2.31260i	0.165922	+	0.0738734i
$981$	−12.7847	−	14.1989i	−0.408184	−	0.453335i
$982$	4.22166	+	40.1664i	0.134718	+	1.28176i
$983$	−50.2031	−	10.6710i	−1.60123	−	0.340352i	−0.681169	−	0.732126i	$-0.738528\pi$
$983$	−50.2031	−	10.6710i	−1.60123	−	0.340352i	−0.920061	+	0.391774i	$0.871861\pi$
$984$	1.76960	+	5.44628i	0.0564129	+	0.173621i
$985$	2.54086	−	0.540076i	0.0809585	−	0.0172083i
$986$	−3.94279	−	6.82912i	−0.125564	−	0.217483i
$987$	5.71501	−	9.89869i	0.181911	−	0.315079i
$988$	0.0713620	−	0.219630i	0.00227033	−	0.00698735i
$989$	3.67739	−	34.9880i	0.116934	−	1.11255i
$990$	−3.62110	+	2.63088i	−0.115086	+	0.0836149i
$991$	−5.47853			−0.174031			−0.0870156	−	0.996207i	$-0.527733\pi$
$991$	−5.47853			−0.174031			−0.0870156	+	0.996207i	$0.527733\pi$
$992$	−3.07150	+	4.64391i	−0.0975202	+	0.147444i
$993$	15.4801			0.491247
$994$	−5.02751	+	3.65270i	−0.159463	+	0.115857i
$995$	−2.00634	+	19.0890i	−0.0636051	+	0.605162i
$996$	2.74154	−	8.43760i	0.0868691	−	0.267356i
$997$	−18.0695	+	31.2973i	−0.572267	+	0.991195i	0.424066	+	0.905631i	$0.360602\pi$
$997$	−18.0695	+	31.2973i	−0.572267	+	0.991195i	−0.996333	+	0.0855637i	$0.972731\pi$
$998$	17.7562	+	30.7546i	0.562062	+	0.973519i
$999$	−8.17620	+	1.73791i	−0.258684	+	0.0549849i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.d.121.1	✓	16
31.10	even	15	inner	930.2.bg.d.661.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.d.121.1	✓	16	1.1	even	1	trivial
930.2.bg.d.661.1	yes	16	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)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.12135 - 0.238351i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(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} +(1.12135 - 0.238351i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(0.104528 + 0.994522i) q^{10} +(-2.99498 - 3.32626i) q^{11} +(0.913545 + 0.406737i) q^{12} +(-0.205713 + 0.0915895i) q^{13} +(-0.767096 + 0.851946i) q^{14} +(0.809017 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.86128 - 2.06716i) q^{17} +(0.913545 - 0.406737i) q^{18} +(-0.936877 - 0.417124i) q^{19} +(-0.669131 - 0.743145i) q^{20} +(0.119832 + 1.14013i) q^{21} +(4.37811 + 0.930596i) q^{22} +(-2.29085 - 7.05052i) q^{23} +(-0.978148 + 0.207912i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.112591 - 0.195013i) q^{26} +(0.309017 - 0.951057i) q^{27} +(0.119832 - 1.14013i) q^{28} +(-2.29345 + 1.66629i) q^{29} -1.00000 q^{30} +(-3.07150 + 4.64391i) q^{31} +1.00000 q^{32} +(3.62110 - 2.63088i) q^{33} +(-0.290761 + 2.76640i) q^{34} +(0.354259 - 1.09030i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-4.17943 - 7.23899i) q^{37} +(1.00313 - 0.213222i) q^{38} +(-0.0695848 - 0.214160i) q^{39} +(0.978148 + 0.207912i) q^{40} +(-0.598588 - 5.69518i) q^{41} +(-0.767096 - 0.851946i) q^{42} +(4.33531 + 1.93020i) q^{43} +(-4.08896 + 1.82052i) q^{44} +(-0.669131 + 0.743145i) q^{45} +(5.99753 + 4.35746i) q^{46} +(-8.06615 - 5.86040i) q^{47} +(0.669131 - 0.743145i) q^{48} +(-5.19419 + 2.31260i) q^{49} +(0.913545 + 0.406737i) q^{50} +(1.86128 + 2.06716i) q^{51} +(0.0235378 + 0.223948i) q^{52} +(6.10240 + 1.29710i) q^{53} +(0.309017 + 0.951057i) q^{54} +(-4.37811 + 0.930596i) q^{55} +(0.573203 + 0.992817i) q^{56} +(0.512770 - 0.888143i) q^{57} +(0.876022 - 2.69612i) q^{58} +(0.699405 - 6.65439i) q^{59} +(0.809017 - 0.587785i) q^{60} +6.58814 q^{61} +(-0.244725 - 5.56238i) q^{62} -1.14641 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.0235378 + 0.223948i) q^{65} +(-1.38314 + 4.25685i) q^{66} +(4.83920 - 8.38174i) q^{67} +(-1.39082 - 2.40897i) q^{68} +(7.25136 - 1.54132i) q^{69} +(0.354259 + 1.09030i) q^{70} +(5.30226 + 1.12703i) q^{71} +(-0.104528 - 0.994522i) q^{72} +(5.63767 + 6.26127i) q^{73} +(7.63620 + 3.39986i) q^{74} +(0.913545 - 0.406737i) q^{75} +(-0.686220 + 0.762124i) q^{76} +(-4.15125 - 3.01606i) q^{77} +(0.182175 + 0.132358i) q^{78} +(5.87313 - 6.52277i) q^{79} +(-0.913545 + 0.406737i) q^{80} +(0.913545 + 0.406737i) q^{81} +(3.83181 + 4.25566i) q^{82} +(-0.927358 - 8.82322i) q^{83} +(1.12135 + 0.238351i) q^{84} +(-0.859575 - 2.64550i) q^{85} +(-4.64188 + 0.986663i) q^{86} +(-1.41743 - 2.45507i) q^{87} +(2.23796 - 3.87626i) q^{88} +(-0.556227 + 1.71189i) q^{89} +(0.104528 - 0.994522i) q^{90} +(-0.208847 + 0.151736i) q^{91} -7.41336 q^{92} +(-4.29741 - 3.54010i) q^{93} +9.97031 q^{94} +(-0.829679 + 0.602797i) q^{95} +(-0.104528 + 0.994522i) q^{96} +(-0.298153 + 0.917621i) q^{97} +(2.84288 - 4.92401i) q^{98} +(2.23796 + 3.87626i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 20 q^{13} - 4 q^{14} + 4 q^{15} - 4 q^{16} - 12 q^{17} + 2 q^{18} - 7 q^{19} - 2 q^{20} - 4 q^{21} + 11 q^{22} + 11 q^{23} + 2 q^{24} - 8 q^{25} + 5 q^{26} - 4 q^{27} - 4 q^{28} + 23 q^{29} - 16 q^{30} - 17 q^{31} + 16 q^{32} - 2 q^{33} - 2 q^{34} + 7 q^{35} - 8 q^{36} + 17 q^{37} - 2 q^{38} - 5 q^{39} - 2 q^{40} + 8 q^{41} - 4 q^{42} + 32 q^{43} + q^{44} - 2 q^{45} + 11 q^{46} - 7 q^{47} + 2 q^{48} - q^{49} + 2 q^{50} - 12 q^{51} + 10 q^{52} + 54 q^{53} - 4 q^{54} - 11 q^{55} + q^{56} + 18 q^{57} - 22 q^{58} - 38 q^{59} + 4 q^{60} - 28 q^{61} - 27 q^{62} - 2 q^{63} - 4 q^{64} - 10 q^{65} - 7 q^{66} + q^{67} - 2 q^{68} - 13 q^{69} + 7 q^{70} - 11 q^{71} + 2 q^{72} + 53 q^{73} + 2 q^{74} + 2 q^{75} - 2 q^{76} + 44 q^{77} + 10 q^{78} + 48 q^{79} - 2 q^{80} + 2 q^{81} + 8 q^{82} + 56 q^{83} + 11 q^{84} - 24 q^{85} - 13 q^{86} + q^{87} - 9 q^{88} - 43 q^{89} - 2 q^{90} - 50 q^{91} - 44 q^{92} - 22 q^{93} - 72 q^{94} - 14 q^{95} + 2 q^{96} + 17 q^{97} + 29 q^{98} - 9 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 20 * q^13 - 4 * q^14 + 4 * q^15 - 4 * q^16 - 12 * q^17 + 2 * q^18 - 7 * q^19 - 2 * q^20 - 4 * q^21 + 11 * q^22 + 11 * q^23 + 2 * q^24 - 8 * q^25 + 5 * q^26 - 4 * q^27 - 4 * q^28 + 23 * q^29 - 16 * q^30 - 17 * q^31 + 16 * q^32 - 2 * q^33 - 2 * q^34 + 7 * q^35 - 8 * q^36 + 17 * q^37 - 2 * q^38 - 5 * q^39 - 2 * q^40 + 8 * q^41 - 4 * q^42 + 32 * q^43 + q^44 - 2 * q^45 + 11 * q^46 - 7 * q^47 + 2 * q^48 - q^49 + 2 * q^50 - 12 * q^51 + 10 * q^52 + 54 * q^53 - 4 * q^54 - 11 * q^55 + q^56 + 18 * q^57 - 22 * q^58 - 38 * q^59 + 4 * q^60 - 28 * q^61 - 27 * q^62 - 2 * q^63 - 4 * q^64 - 10 * q^65 - 7 * q^66 + q^67 - 2 * q^68 - 13 * q^69 + 7 * q^70 - 11 * q^71 + 2 * q^72 + 53 * q^73 + 2 * q^74 + 2 * q^75 - 2 * q^76 + 44 * q^77 + 10 * q^78 + 48 * q^79 - 2 * q^80 + 2 * q^81 + 8 * q^82 + 56 * q^83 + 11 * q^84 - 24 * q^85 - 13 * q^86 + q^87 - 9 * q^88 - 43 * q^89 - 2 * q^90 - 50 * q^91 - 44 * q^92 - 22 * q^93 - 72 * q^94 - 14 * q^95 + 2 * q^96 + 17 * q^97 + 29 * q^98 - 9 * q^99

Introduction

L-functions

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