LMFDB - Embedded newform 930.2.bg.i.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:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			121.1
Character	$\chi$	$=$	930.121
Dual form			930.2.bg.i.661.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.78894 + 0.592807i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(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} +(-2.78894 + 0.592807i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(-0.104528 - 0.994522i) q^{10} +(-2.70362 - 3.00268i) q^{11} +(0.913545 + 0.406737i) q^{12} +(-5.36699 + 2.38954i) q^{13} +(-1.90786 + 2.11889i) q^{14} +(0.809017 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-5.07162 + 5.63261i) q^{17} +(-0.913545 + 0.406737i) q^{18} +(-0.852742 - 0.379665i) q^{19} +(-0.669131 - 0.743145i) q^{20} +(-0.298036 - 2.83563i) q^{21} +(-3.95220 - 0.840067i) q^{22} +(-0.646663 - 1.99022i) q^{23} +(0.978148 - 0.207912i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.93745 + 5.08781i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.298036 + 2.83563i) q^{28} +(7.71862 - 5.60791i) q^{29} +1.00000 q^{30} +(1.58731 + 5.33671i) q^{31} -1.00000 q^{32} +(3.26883 - 2.37495i) q^{33} +(-0.792265 + 7.53790i) q^{34} +(-0.881083 + 2.71170i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-1.17451 - 2.03431i) q^{37} +(-0.913045 + 0.194074i) q^{38} +(-1.81544 - 5.58736i) q^{39} +(-0.978148 - 0.207912i) q^{40} +(0.357944 + 3.40561i) q^{41} +(-1.90786 - 2.11889i) q^{42} +(-5.82991 - 2.59564i) q^{43} +(-3.69118 + 1.64342i) q^{44} +(-0.669131 + 0.743145i) q^{45} +(-1.69298 - 1.23003i) q^{46} +(6.85528 + 4.98065i) q^{47} +(0.669131 - 0.743145i) q^{48} +(1.03194 - 0.459451i) q^{49} +(-0.913545 - 0.406737i) q^{50} +(-5.07162 - 5.63261i) q^{51} +(0.614094 + 5.84272i) q^{52} +(-8.14085 - 1.73039i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-3.95220 + 0.840067i) q^{55} +(1.42562 + 2.46925i) q^{56} +(0.466721 - 0.808385i) q^{57} +(2.94825 - 9.07379i) q^{58} +(1.17362 - 11.1662i) q^{59} +(0.809017 - 0.587785i) q^{60} +2.20160 q^{61} +(4.42100 + 3.38449i) q^{62} +2.85125 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.614094 + 5.84272i) q^{65} +(1.24858 - 3.84274i) q^{66} +(3.87121 - 6.70512i) q^{67} +(3.78971 + 6.56397i) q^{68} +(2.04691 - 0.435085i) q^{69} +(0.881083 + 2.71170i) q^{70} +(-14.1517 - 3.00804i) q^{71} +(0.104528 + 0.994522i) q^{72} +(-3.02812 - 3.36307i) q^{73} +(-2.14593 - 0.955430i) q^{74} +(0.913545 - 0.406737i) q^{75} +(-0.624595 + 0.693683i) q^{76} +(9.32025 + 6.77155i) q^{77} +(-4.75289 - 3.45318i) q^{78} +(0.739059 - 0.820808i) q^{79} +(-0.913545 + 0.406737i) q^{80} +(0.913545 + 0.406737i) q^{81} +(2.29135 + 2.54480i) q^{82} +(0.689412 + 6.55931i) q^{83} +(-2.78894 - 0.592807i) q^{84} +(2.34217 + 7.20846i) q^{85} +(-6.24218 + 1.32682i) q^{86} +(4.77037 + 8.26253i) q^{87} +(-2.02025 + 3.49917i) q^{88} +(-2.31514 + 7.12528i) q^{89} +(-0.104528 + 0.994522i) q^{90} +(13.5517 - 9.84586i) q^{91} -2.09264 q^{92} +(-5.47339 + 1.02077i) q^{93} +8.47359 q^{94} +(-0.755171 + 0.548664i) q^{95} +(0.104528 - 0.994522i) q^{96} +(-1.48185 + 4.56066i) q^{97} +(0.564802 - 0.978265i) q^{98} +(2.02025 + 3.49917i) 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} - 7 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 - 7 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9} + 3 q^{10} - 13 q^{11} + 3 q^{12} + 11 q^{13} - 8 q^{14} + 6 q^{15} - 6 q^{16} - 29 q^{17} - 3 q^{18} + 9 q^{19} - 3 q^{20} - 2 q^{21} - 17 q^{22} - 5 q^{23} - 3 q^{24} - 12 q^{25} + 9 q^{26} - 6 q^{27} - 2 q^{28} + 13 q^{29} + 24 q^{30} + 57 q^{31} - 24 q^{32} + 16 q^{33} + 29 q^{34} + q^{35} - 12 q^{36} - 24 q^{37} + 6 q^{38} - 17 q^{39} + 3 q^{40} + 32 q^{41} - 8 q^{42} + 49 q^{43} - 8 q^{44} - 3 q^{45} + 28 q^{47} + 3 q^{48} + 12 q^{49} - 3 q^{50} - 29 q^{51} - 19 q^{52} - 36 q^{53} + 6 q^{54} - 17 q^{55} - 3 q^{56} - 6 q^{57} + 2 q^{58} + 6 q^{60} + 33 q^{62} - 6 q^{63} - 6 q^{64} + 19 q^{65} + 4 q^{66} - 5 q^{67} + 11 q^{68} + 10 q^{69} - q^{70} - 11 q^{71} - 3 q^{72} - 13 q^{73} + 9 q^{74} + 3 q^{75} - 6 q^{76} + 4 q^{77} - 8 q^{78} - 68 q^{79} - 3 q^{80} + 3 q^{81} - 2 q^{82} + 10 q^{83} - 7 q^{84} + 2 q^{85} - 34 q^{86} + 11 q^{87} - 12 q^{88} + 55 q^{89} + 3 q^{90} + 38 q^{91} + 10 q^{92} + 19 q^{93} + 42 q^{94} + 18 q^{95} - 3 q^{96} - q^{97} + 63 q^{98} + 12 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9 + 3 * q^10 - 13 * q^11 + 3 * q^12 + 11 * q^13 - 8 * q^14 + 6 * q^15 - 6 * q^16 - 29 * q^17 - 3 * q^18 + 9 * q^19 - 3 * q^20 - 2 * q^21 - 17 * q^22 - 5 * q^23 - 3 * q^24 - 12 * q^25 + 9 * q^26 - 6 * q^27 - 2 * q^28 + 13 * q^29 + 24 * q^30 + 57 * q^31 - 24 * q^32 + 16 * q^33 + 29 * q^34 + q^35 - 12 * q^36 - 24 * q^37 + 6 * q^38 - 17 * q^39 + 3 * q^40 + 32 * q^41 - 8 * q^42 + 49 * q^43 - 8 * q^44 - 3 * q^45 + 28 * q^47 + 3 * q^48 + 12 * q^49 - 3 * q^50 - 29 * q^51 - 19 * q^52 - 36 * q^53 + 6 * q^54 - 17 * q^55 - 3 * q^56 - 6 * q^57 + 2 * q^58 + 6 * q^60 + 33 * q^62 - 6 * q^63 - 6 * q^64 + 19 * q^65 + 4 * q^66 - 5 * q^67 + 11 * q^68 + 10 * q^69 - q^70 - 11 * q^71 - 3 * q^72 - 13 * q^73 + 9 * q^74 + 3 * q^75 - 6 * q^76 + 4 * q^77 - 8 * q^78 - 68 * q^79 - 3 * q^80 + 3 * q^81 - 2 * q^82 + 10 * q^83 - 7 * q^84 + 2 * q^85 - 34 * q^86 + 11 * q^87 - 12 * q^88 + 55 * q^89 + 3 * q^90 + 38 * q^91 + 10 * q^92 + 19 * q^93 + 42 * q^94 + 18 * q^95 - 3 * q^96 - q^97 + 63 * q^98 + 12 * 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
$7$	−2.78894	+	0.592807i	−1.05412	+	0.224060i	−0.702207	−	0.711973i	$-0.747802\pi$
$7$	−2.78894	+	0.592807i	−1.05412	+	0.224060i	−0.351913	+	0.936033i	$0.614469\pi$
$8$	−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
$11$	−2.70362	−	3.00268i	−0.815173	−	0.905341i	0.181781	−	0.983339i	$-0.441814\pi$
$11$	−2.70362	−	3.00268i	−0.815173	−	0.905341i	−0.996954	+	0.0779982i	$0.975147\pi$
$12$	0.913545	+	0.406737i	0.263718	+	0.117415i
$13$	−5.36699	+	2.38954i	−1.48853	+	0.662738i	−0.980126	−	0.198377i	$-0.936433\pi$
$13$	−5.36699	+	2.38954i	−1.48853	+	0.662738i	−0.508409	+	0.861116i	$0.669766\pi$
$14$	−1.90786	+	2.11889i	−0.509896	+	0.566297i
$15$	0.809017	+	0.587785i	0.208887	+	0.151765i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−5.07162	+	5.63261i	−1.23005	+	1.36611i	−0.322277	+	0.946645i	$0.604448\pi$
$17$	−5.07162	+	5.63261i	−1.23005	+	1.36611i	−0.907772	+	0.419463i	$0.862218\pi$
$18$	−0.913545	+	0.406737i	−0.215325	+	0.0958687i
$19$	−0.852742	−	0.379665i	−0.195632	−	0.0871012i	0.306582	−	0.951844i	$-0.400815\pi$
$19$	−0.852742	−	0.379665i	−0.195632	−	0.0871012i	−0.502215	+	0.864743i	$0.667481\pi$
$20$	−0.669131	−	0.743145i	−0.149622	−	0.166172i
$21$	−0.298036	−	2.83563i	−0.0650369	−	0.618784i
$22$	−3.95220	−	0.840067i	−0.842613	−	0.179103i
$23$	−0.646663	−	1.99022i	−0.134838	−	0.414990i	0.860726	−	0.509068i	$-0.170010\pi$
$23$	−0.646663	−	1.99022i	−0.134838	−	0.414990i	−0.995565	+	0.0940777i	$0.970010\pi$
$24$	0.978148	−	0.207912i	0.199664	−	0.0424398i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.93745	+	5.08781i	−0.576081	+	0.997802i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	−0.298036	+	2.83563i	−0.0563236	+	0.535883i
$29$	7.71862	−	5.60791i	1.43331	−	1.04136i	0.443924	−	0.896064i	$-0.353586\pi$
$29$	7.71862	−	5.60791i	1.43331	−	1.04136i	0.989388	−	0.145298i	$-0.0464141\pi$
$30$	1.00000			0.182574
$31$	1.58731	+	5.33671i	0.285089	+	0.958501i
$31$	1.58731	+	5.33671i	0.285089	+	0.958501i
$32$	−1.00000			−0.176777
$33$	3.26883	−	2.37495i	0.569031	−	0.413425i
$34$	−0.792265	+	7.53790i	−0.135872	+	1.29274i
$35$	−0.881083	+	2.71170i	−0.148930	+	0.458360i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−1.17451	−	2.03431i	−0.193088	−	0.334438i	0.753184	−	0.657810i	$-0.228517\pi$
$37$	−1.17451	−	2.03431i	−0.193088	−	0.334438i	−0.946272	+	0.323372i	$0.895184\pi$
$38$	−0.913045	+	0.194074i	−0.148115	+	0.0314829i
$39$	−1.81544	−	5.58736i	−0.290704	−	0.894694i
$40$	−0.978148	−	0.207912i	−0.154659	−	0.0328737i
$41$	0.357944	+	3.40561i	0.0559015	+	0.531867i	0.986258	+	0.165211i	$0.0528306\pi$
$41$	0.357944	+	3.40561i	0.0559015	+	0.531867i	−0.930357	+	0.366656i	$0.880503\pi$
$42$	−1.90786	−	2.11889i	−0.294389	−	0.326952i
$43$	−5.82991	−	2.59564i	−0.889053	−	0.395832i	−0.0891902	−	0.996015i	$-0.528428\pi$
$43$	−5.82991	−	2.59564i	−0.889053	−	0.395832i	−0.799863	+	0.600183i	$0.795095\pi$
$44$	−3.69118	+	1.64342i	−0.556466	+	0.247755i
$45$	−0.669131	+	0.743145i	−0.0997481	+	0.110781i
$46$	−1.69298	−	1.23003i	−0.249617	−	0.181357i
$47$	6.85528	+	4.98065i	0.999945	+	0.726503i	0.962076	−	0.272780i	$-0.0879431\pi$
$47$	6.85528	+	4.98065i	0.999945	+	0.726503i	0.0378687	+	0.999283i	$0.487943\pi$
$48$	0.669131	−	0.743145i	0.0965807	−	0.107264i
$49$	1.03194	−	0.459451i	0.147421	−	0.0656359i
$50$	−0.913545	−	0.406737i	−0.129195	−	0.0575212i
$51$	−5.07162	−	5.63261i	−0.710169	−	0.788723i
$52$	0.614094	+	5.84272i	0.0851596	+	0.810239i
$53$	−8.14085	−	1.73039i	−1.11823	−	0.237687i	−0.388518	−	0.921441i	$-0.627013\pi$
$53$	−8.14085	−	1.73039i	−1.11823	−	0.237687i	−0.729713	+	0.683754i	$0.760346\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	−3.95220	+	0.840067i	−0.532915	+	0.113275i
$56$	1.42562	+	2.46925i	0.190507	+	0.329968i
$57$	0.466721	−	0.808385i	0.0618187	−	0.107073i
$58$	2.94825	−	9.07379i	0.387124	−	1.19145i
$59$	1.17362	−	11.1662i	0.152792	−	1.45372i	−0.602390	−	0.798202i	$-0.705785\pi$
$59$	1.17362	−	11.1662i	0.152792	−	1.45372i	0.755181	−	0.655516i	$-0.227549\pi$
$60$	0.809017	−	0.587785i	0.104444	−	0.0758827i
$61$	2.20160			0.281886			0.140943	−	0.990018i	$-0.454987\pi$
$61$	2.20160			0.281886			0.140943	+	0.990018i	$0.454987\pi$
$62$	4.42100	+	3.38449i	0.561467	+	0.429831i
$63$	2.85125			0.359223
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−0.614094	+	5.84272i	−0.0761690	+	0.724700i
$66$	1.24858	−	3.84274i	0.153690	−	0.473009i
$67$	3.87121	−	6.70512i	0.472943	−	0.819161i	−0.526577	−	0.850127i	$-0.676525\pi$
$67$	3.87121	−	6.70512i	0.472943	−	0.819161i	0.999520	+	0.0309658i	$0.00985830\pi$
$68$	3.78971	+	6.56397i	0.459570	+	0.795999i
$69$	2.04691	−	0.435085i	0.246420	−	0.0523781i
$70$	0.881083	+	2.71170i	0.105310	+	0.324110i
$71$	−14.1517	−	3.00804i	−1.67950	−	0.356988i	−0.733132	−	0.680087i	$-0.761942\pi$
$71$	−14.1517	−	3.00804i	−1.67950	−	0.356988i	−0.946365	+	0.323098i	$0.895276\pi$
$72$	0.104528	+	0.994522i	0.0123188	+	0.117206i
$73$	−3.02812	−	3.36307i	−0.354415	−	0.393618i	0.539403	−	0.842048i	$-0.318650\pi$
$73$	−3.02812	−	3.36307i	−0.354415	−	0.393618i	−0.893818	+	0.448430i	$0.851983\pi$
$74$	−2.14593	−	0.955430i	−0.249460	−	0.111067i
$75$	0.913545	−	0.406737i	0.105487	−	0.0469659i
$76$	−0.624595	+	0.693683i	−0.0716460	+	0.0795709i
$77$	9.32025	+	6.77155i	1.06214	+	0.771690i
$78$	−4.75289	−	3.45318i	−0.538159	−	0.390996i
$79$	0.739059	−	0.820808i	0.0831506	−	0.0923481i	−0.700134	−	0.714012i	$-0.746876\pi$
$79$	0.739059	−	0.820808i	0.0831506	−	0.0923481i	0.783284	+	0.621664i	$0.213543\pi$
$80$	−0.913545	+	0.406737i	−0.102137	+	0.0454745i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	2.29135	+	2.54480i	0.253037	+	0.281026i
$83$	0.689412	+	6.55931i	0.0756728	+	0.719978i	0.964919	+	0.262549i	$0.0845631\pi$
$83$	0.689412	+	6.55931i	0.0756728	+	0.719978i	−0.889246	+	0.457429i	$0.848770\pi$
$84$	−2.78894	−	0.592807i	−0.304298	−	0.0646806i
$85$	2.34217	+	7.20846i	0.254044	+	0.781867i
$86$	−6.24218	+	1.32682i	−0.673111	+	0.143074i
$87$	4.77037	+	8.26253i	0.511437	+	0.885836i
$88$	−2.02025	+	3.49917i	−0.215359	+	0.373013i
$89$	−2.31514	+	7.12528i	−0.245405	+	0.755278i	0.750165	+	0.661251i	$0.229974\pi$
$89$	−2.31514	+	7.12528i	−0.245405	+	0.755278i	−0.995570	+	0.0940272i	$0.970026\pi$
$90$	−0.104528	+	0.994522i	−0.0110183	+	0.104832i
$91$	13.5517	−	9.84586i	1.42060	−	1.03213i
$92$	−2.09264			−0.218173
$93$	−5.47339	+	1.02077i	−0.567564	+	0.105849i
$94$	8.47359			0.873984
$95$	−0.755171	+	0.548664i	−0.0774789	+	0.0562917i
$96$	0.104528	−	0.994522i	0.0106684	−	0.101503i
$97$	−1.48185	+	4.56066i	−0.150459	+	0.463065i	−0.997673	−	0.0681875i	$-0.978278\pi$
$97$	−1.48185	+	4.56066i	−0.150459	+	0.463065i	0.847214	+	0.531252i	$0.178278\pi$
$98$	0.564802	−	0.978265i	0.0570536	−	0.0988197i
$99$	2.02025	+	3.49917i	0.203043	+	0.351680i
$100$	−0.978148	+	0.207912i	−0.0978148	+	0.0207912i
$101$	3.18891	+	9.81447i	0.317309	+	0.976576i	0.974794	+	0.223108i	$0.0716203\pi$
$101$	3.18891	+	9.81447i	0.317309	+	0.976576i	−0.657485	+	0.753468i	$0.728380\pi$
$102$	−7.41379	−	1.57585i	−0.734075	−	0.156032i
$103$	−1.84270	−	17.5321i	−0.181566	−	1.72749i	−0.583754	−	0.811931i	$-0.698417\pi$
$103$	−1.84270	−	17.5321i	−0.181566	−	1.72749i	0.402187	−	0.915557i	$-0.368250\pi$
$104$	3.93108	+	4.36590i	0.385474	+	0.428112i
$105$	−2.60474	−	1.15971i	−0.254197	−	0.113176i
$106$	−7.60318	+	3.38515i	−0.738486	+	0.328795i
$107$	3.38803	−	3.76279i	0.327533	−	0.363762i	−0.556777	−	0.830662i	$-0.687962\pi$
$107$	3.38803	−	3.76279i	0.327533	−	0.363762i	0.884310	+	0.466899i	$0.154629\pi$
$108$	−0.809017	−	0.587785i	−0.0778477	−	0.0565597i
$109$	−2.70798	−	1.96746i	−0.259377	−	0.188449i	0.450495	−	0.892779i	$-0.351247\pi$
$109$	−2.70798	−	1.96746i	−0.259377	−	0.188449i	−0.709873	+	0.704330i	$0.751247\pi$
$110$	−2.70362	+	3.00268i	−0.257780	+	0.286294i
$111$	2.14593	−	0.955430i	0.203683	−	0.0906854i
$112$	2.60474	+	1.15971i	0.246125	+	0.109582i
$113$	8.92626	+	9.91362i	0.839712	+	0.932595i	0.998502	−	0.0547177i	$-0.0174259\pi$
$113$	8.92626	+	9.91362i	0.839712	+	0.932595i	−0.158790	+	0.987312i	$0.550759\pi$
$114$	−0.0975713	−	0.928329i	−0.00913839	−	0.0869460i
$115$	−2.04691	−	0.435085i	−0.190876	−	0.0405719i
$116$	−2.94825	−	9.07379i	−0.273738	−	0.842480i
$117$	5.74652	−	1.22146i	0.531266	−	0.112924i
$118$	−5.61386	−	9.72350i	−0.516798	−	0.895120i
$119$	10.8054	−	18.7155i	0.990529	−	1.71565i
$120$	0.309017	−	0.951057i	0.0282093	−	0.0868192i
$121$	−0.556680	+	5.29646i	−0.0506073	+	0.481496i
$122$	1.78113	−	1.29407i	0.161256	−	0.117159i
$123$	−3.42437			−0.308765
$124$	5.56602	+	0.139514i	0.499843	+	0.0125287i
$125$	−1.00000			−0.0894427
$126$	2.30671	−	1.67592i	0.205498	−	0.149303i
$127$	0.944148	−	8.98297i	0.0837796	−	0.797109i	−0.869279	−	0.494322i	$-0.835416\pi$
$127$	0.944148	−	8.98297i	0.0837796	−	0.797109i	0.953058	−	0.302787i	$-0.0979171\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	3.19082	−	5.52666i	0.280936	−	0.486595i
$130$	2.93745	+	5.08781i	0.257631	+	0.446231i
$131$	9.05224	−	1.92411i	0.790898	−	0.168111i	0.205286	−	0.978702i	$-0.434188\pi$
$131$	9.05224	−	1.92411i	0.790898	−	0.168111i	0.585612	+	0.810591i	$0.300854\pi$
$132$	−1.24858	−	3.84274i	−0.108675	−	0.334468i
$133$	2.60331	+	0.553352i	0.225736	+	0.0479817i
$134$	−0.809302	−	7.70000i	−0.0699131	−	0.665178i
$135$	−0.669131	−	0.743145i	−0.0575896	−	0.0639597i
$136$	6.92415	+	3.08283i	0.593741	+	0.264350i
$137$	−11.7859	+	5.24743i	−1.00694	+	0.448318i	−0.842862	−	0.538129i	$-0.819131\pi$
$137$	−11.7859	+	5.24743i	−1.00694	+	0.448318i	−0.164077	+	0.986447i	$0.552465\pi$
$138$	1.40025	−	1.55514i	0.119197	−	0.132382i
$139$	−14.8218	−	10.7687i	−1.25717	−	0.913387i	−0.258555	−	0.965997i	$-0.583246\pi$
$139$	−14.8218	−	10.7687i	−1.25717	−	0.913387i	−0.998615	+	0.0526091i	$0.983246\pi$
$140$	2.30671	+	1.67592i	0.194952	+	0.141641i
$141$	−5.66994	+	6.29710i	−0.477495	+	0.530312i
$142$	−13.2170	+	5.88461i	−1.10915	+	0.493825i
$143$	21.6853	+	9.65492i	1.81342	+	0.807385i
$144$	0.669131	+	0.743145i	0.0557609	+	0.0619287i
$145$	−0.997279	−	9.48848i	−0.0828195	−	0.787975i
$146$	−4.42657	−	0.940896i	−0.366345	−	0.0778691i
$147$	0.349067	+	1.07432i	0.0287905	+	0.0886082i
$148$	−2.29768	+	0.488388i	−0.188868	+	0.0401452i
$149$	6.76585	+	11.7188i	0.554280	+	0.960041i	0.997959	+	0.0638552i	$0.0203396\pi$
$149$	6.76585	+	11.7188i	0.554280	+	0.960041i	−0.443679	+	0.896186i	$0.646327\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	−1.96900	+	6.05995i	−0.160235	+	0.493152i	−0.998654	−	0.0518745i	$-0.983480\pi$
$151$	−1.96900	+	6.05995i	−0.160235	+	0.493152i	0.838419	+	0.545027i	$0.183480\pi$
$152$	−0.0975713	+	0.928329i	−0.00791408	+	0.0752974i
$153$	6.13188	−	4.45507i	0.495733	−	0.360171i
$154$	11.5205			0.928345
$155$	5.41538	+	1.29371i	0.434974	+	0.103913i
$156$	−5.87490			−0.470368
$157$	−17.6945	+	12.8558i	−1.41217	+	1.02601i	−0.419173	+	0.907906i	$0.637680\pi$
$157$	−17.6945	+	12.8558i	−1.41217	+	1.02601i	−0.993002	+	0.118099i	$0.962320\pi$
$158$	0.115452	−	1.09846i	0.00918490	−	0.0873885i
$159$	2.57186	−	7.91537i	0.203962	−	0.627730i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	2.98332	+	5.16726i	0.235119	+	0.407237i
$162$	0.978148	−	0.207912i	0.0768505	−	0.0163351i
$163$	−3.26060	−	10.0351i	−0.255390	−	0.786009i	−0.993753	−	0.111605i	$-0.964401\pi$
$163$	−3.26060	−	10.0351i	−0.255390	−	0.786009i	0.738363	−	0.674404i	$-0.235599\pi$
$164$	3.34954	+	0.711967i	0.261555	+	0.0555953i
$165$	−0.422347	−	4.01836i	−0.0328797	−	0.312829i
$166$	4.41321	+	4.90137i	0.342532	+	0.380420i
$167$	−11.4377	−	5.09240i	−0.885077	−	0.394061i	−0.0867103	−	0.996234i	$-0.527635\pi$
$167$	−11.4377	−	5.09240i	−0.885077	−	0.394061i	−0.798366	+	0.602172i	$0.794302\pi$
$168$	−2.60474	+	1.15971i	−0.200960	+	0.0894733i
$169$	14.3960	−	15.9884i	1.10738	−	1.22987i
$170$	6.13188	+	4.45507i	0.470294	+	0.341689i
$171$	0.755171	+	0.548664i	0.0577494	+	0.0419574i
$172$	−4.27015	+	4.74248i	−0.325596	+	0.361611i
$173$	9.40548	−	4.18759i	0.715086	−	0.318377i	−0.0167482	−	0.999860i	$-0.505331\pi$
$173$	9.40548	−	4.18759i	0.715086	−	0.318377i	0.731834	+	0.681483i	$0.238665\pi$
$174$	8.71590	+	3.88057i	0.660751	+	0.294185i
$175$	1.90786	+	2.11889i	0.144220	+	0.160173i
$176$	0.422347	+	4.01836i	0.0318356	+	0.302896i
$177$	10.9824	+	2.33438i	0.825486	+	0.175462i
$178$	2.31514	+	7.12528i	0.173527	+	0.534062i
$179$	10.4310	−	2.21718i	0.779649	−	0.165720i	0.199138	−	0.979972i	$-0.436186\pi$
$179$	10.4310	−	2.21718i	0.779649	−	0.165720i	0.580512	+	0.814252i	$0.302853\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	−6.31895	+	10.9447i	−0.469684	+	0.813517i	−0.999399	−	0.0346590i	$-0.988965\pi$
$181$	−6.31895	+	10.9447i	−0.469684	+	0.813517i	0.529715	+	0.848176i	$0.322299\pi$
$182$	5.17628	−	15.9309i	0.383691	−	1.18088i
$183$	−0.230129	+	2.18954i	−0.0170117	+	0.161855i
$184$	−1.69298	+	1.23003i	−0.124808	+	0.0906787i
$185$	−2.34901			−0.172703
$186$	−3.82807	+	4.04300i	−0.280688	+	0.296447i
$187$	30.6247			2.23950
$188$	6.85528	−	4.98065i	0.499973	−	0.363251i
$189$	−0.298036	+	2.83563i	−0.0216790	+	0.206261i
$190$	−0.288450	+	0.887757i	−0.0209263	+	0.0644046i
$191$	−10.4262	+	18.0587i	−0.754411	+	1.30668i	0.191255	+	0.981540i	$0.438744\pi$
$191$	−10.4262	+	18.0587i	−0.754411	+	1.30668i	−0.945666	+	0.325138i	$0.894589\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	16.5945	−	3.52727i	1.19450	−	0.253899i	0.432595	−	0.901588i	$-0.357598\pi$
$193$	16.5945	−	3.52727i	1.19450	−	0.253899i	0.761904	+	0.647690i	$0.224265\pi$
$194$	1.48185	+	4.56066i	0.106391	+	0.327436i
$195$	−5.74652	−	1.22146i	−0.411517	−	0.0874706i
$196$	−0.118076	−	1.12342i	−0.00843398	−	0.0802440i
$197$	2.47363	+	2.74725i	0.176239	+	0.195733i	0.824792	−	0.565436i	$-0.191292\pi$
$197$	2.47363	+	2.74725i	0.176239	+	0.195733i	−0.648553	+	0.761170i	$0.724626\pi$
$198$	3.69118	+	1.64342i	0.262321	+	0.116793i
$199$	6.40460	−	2.85151i	0.454010	−	0.202138i	−0.166974	−	0.985961i	$-0.553400\pi$
$199$	6.40460	−	2.85151i	0.454010	−	0.202138i	0.620985	+	0.783823i	$0.286733\pi$
$200$	−0.669131	+	0.743145i	−0.0473147	+	0.0525483i
$201$	6.26374	+	4.55088i	0.441810	+	0.320994i
$202$	8.34868	+	6.06567i	0.587411	+	0.426779i
$203$	−18.2024	+	20.2158i	−1.27756	+	1.41887i
$204$	−6.92415	+	3.08283i	−0.484787	+	0.215841i
$205$	3.12832	+	1.39282i	0.218491	+	0.0972785i
$206$	−11.7959	−	13.1006i	−0.821858	−	0.912766i
$207$	0.218741	+	2.08118i	0.0152035	+	0.144652i
$208$	5.74652	+	1.22146i	0.398449	+	0.0846930i
$209$	1.16548	+	3.58698i	0.0806180	+	0.248117i
$210$	−2.78894	+	0.592807i	−0.192455	+	0.0409076i
$211$	0.878895	+	1.52229i	0.0605056	+	0.104799i	0.894692	−	0.446685i	$-0.147395\pi$
$211$	0.878895	+	1.52229i	0.0605056	+	0.104799i	−0.834186	+	0.551483i	$0.814062\pi$
$212$	−4.16136	+	7.20768i	−0.285803	+	0.495026i
$213$	4.47081	−	13.7597i	0.306335	−	0.942802i
$214$	0.529262	−	5.03559i	0.0361796	−	0.344226i
$215$	−5.16285	+	3.75103i	−0.352103	+	0.255818i
$216$	−1.00000			−0.0680414
$217$	−7.59055	−	13.9428i	−0.515280	−	0.946498i
$218$	−3.34725			−0.226704
$219$	3.66117	−	2.66000i	0.247399	−	0.179746i
$220$	−0.422347	+	4.01836i	−0.0284746	+	0.270918i
$221$	13.7600	−	42.3490i	0.925599	−	2.84870i
$222$	1.17451	−	2.03431i	0.0788278	−	0.136534i
$223$	−1.78441	−	3.09070i	−0.119493	−	0.206968i	0.800074	−	0.599902i	$-0.204794\pi$
$223$	−1.78441	−	3.09070i	−0.119493	−	0.206968i	−0.919567	+	0.392933i	$0.871460\pi$
$224$	2.78894	−	0.592807i	0.186344	−	0.0396086i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	13.0486	+	2.77356i	0.867978	+	0.184494i
$227$	2.06009	+	19.6005i	0.136733	+	1.30093i	0.820676	+	0.571394i	$0.193597\pi$
$227$	2.06009	+	19.6005i	0.136733	+	1.30093i	−0.683943	+	0.729536i	$0.739736\pi$
$228$	−0.624595	−	0.693683i	−0.0413648	−	0.0459403i
$229$	−22.5656	−	10.0469i	−1.49118	−	0.663915i	−0.510560	−	0.859842i	$-0.670562\pi$
$229$	−22.5656	−	10.0469i	−1.49118	−	0.663915i	−0.980618	+	0.195927i	$0.937228\pi$
$230$	−1.91173	+	0.851155i	−0.126055	+	0.0561235i
$231$	−7.70869	+	8.56137i	−0.507195	+	0.563297i
$232$	−7.71862	−	5.60791i	−0.506752	−	0.368177i
$233$	23.2117	+	16.8643i	1.52065	+	1.10482i	0.961164	+	0.275976i	$0.0890011\pi$
$233$	23.2117	+	16.8643i	1.52065	+	1.10482i	0.559485	+	0.828840i	$0.310999\pi$
$234$	3.93108	−	4.36590i	0.256982	−	0.285408i
$235$	7.74101	−	3.44652i	0.504968	−	0.224826i
$236$	−10.2570	−	4.56673i	−0.667676	−	0.297269i
$237$	0.739059	+	0.820808i	0.0480070	+	0.0533172i
$238$	−2.25894	−	21.4924i	−0.146426	−	1.39315i
$239$	4.71679	+	1.00258i	0.305104	+	0.0648518i	0.357919	−	0.933752i	$-0.383486\pi$
$239$	4.71679	+	1.00258i	0.305104	+	0.0648518i	−0.0528158	+	0.998604i	$0.516820\pi$
$240$	−0.309017	−	0.951057i	−0.0199470	−	0.0613904i
$241$	2.91135	−	0.618826i	0.187536	−	0.0398621i	−0.113186	−	0.993574i	$-0.536106\pi$
$241$	2.91135	−	0.618826i	0.187536	−	0.0398621i	0.300722	+	0.953712i	$0.402772\pi$
$242$	2.66282	+	4.61213i	0.171172	+	0.296479i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	0.680331	−	2.09384i	0.0435537	−	0.134045i
$245$	0.118076	−	1.12342i	0.00754358	−	0.0717724i
$246$	−2.77037	+	2.01279i	−0.176633	+	0.128331i
$247$	5.48388			0.348931
$248$	4.58501	−	3.15875i	0.291148	−	0.200581i
$249$	−6.59544			−0.417969
$250$	−0.809017	+	0.587785i	−0.0511667	+	0.0371748i
$251$	−0.440751	+	4.19347i	−0.0278200	+	0.264689i	0.971767	+	0.235943i	$0.0758180\pi$
$251$	−0.440751	+	4.19347i	−0.0278200	+	0.264689i	−0.999587	+	0.0287458i	$0.990849\pi$
$252$	0.881083	−	2.71170i	0.0555030	−	0.170821i
$253$	−4.22766	+	7.32253i	−0.265791	+	0.460363i
$254$	−4.51622	−	7.82233i	−0.283373	−	0.490817i
$255$	−7.41379	+	1.57585i	−0.464270	+	0.0986836i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−2.39866	−	0.509850i	−0.149624	−	0.0318036i	0.132491	−	0.991184i	$-0.457703\pi$
$257$	−2.39866	−	0.509850i	−0.149624	−	0.0318036i	−0.282115	+	0.959381i	$0.591036\pi$
$258$	−0.667062	−	6.34667i	−0.0415295	−	0.395127i
$259$	4.48158	+	4.97730i	0.278472	+	0.309274i
$260$	5.36699	+	2.38954i	0.332846	+	0.148193i
$261$	−8.71590	+	3.88057i	−0.539501	+	0.240201i
$262$	6.19245	−	6.87742i	0.382571	−	0.424888i
$263$	−11.9732	−	8.69905i	−0.738300	−	0.536407i	0.153878	−	0.988090i	$-0.450824\pi$
$263$	−11.9732	−	8.69905i	−0.738300	−	0.536407i	−0.892178	+	0.451683i	$0.850824\pi$
$264$	−3.26883	−	2.37495i	−0.201183	−	0.146168i
$265$	−5.56898	+	6.18498i	−0.342100	+	0.379941i
$266$	2.43138	−	1.08252i	0.149077	−	0.0663735i
$267$	−6.84425	−	3.04726i	−0.418861	−	0.186489i
$268$	−5.18068	−	5.75373i	−0.316461	−	0.351465i
$269$	−1.71861	−	16.3515i	−0.104785	−	0.996967i	−0.912967	−	0.408034i	$-0.866215\pi$
$269$	−1.71861	−	16.3515i	−0.104785	−	0.996967i	0.808181	−	0.588934i	$-0.200452\pi$
$270$	−0.978148	−	0.207912i	−0.0595282	−	0.0126531i
$271$	−0.0893121	−	0.274874i	−0.00542533	−	0.0166974i	0.948307	−	0.317354i	$-0.102794\pi$
$271$	−0.0893121	−	0.274874i	−0.00542533	−	0.0166974i	−0.953733	+	0.300656i	$0.902794\pi$
$272$	7.41379	−	1.57585i	0.449527	−	0.0955500i
$273$	8.37539	+	14.5066i	0.506902	+	0.877980i
$274$	−6.45065	+	11.1729i	−0.389698	+	0.674977i
$275$	−1.24858	+	3.84274i	−0.0752924	+	0.231726i
$276$	0.218741	−	2.08118i	0.0131667	−	0.125272i
$277$	−17.8732	+	12.9856i	−1.07389	+	0.780230i	−0.976608	−	0.215027i	$-0.931016\pi$
$277$	−17.8732	+	12.9856i	−1.07389	+	0.780230i	−0.0972860	+	0.995256i	$0.531016\pi$
$278$	−18.3208			−1.09881
$279$	−0.443057	−	5.55011i	−0.0265252	−	0.332276i
$280$	2.85125			0.170395
$281$	5.87724	−	4.27007i	0.350607	−	0.254731i	−0.398517	−	0.917161i	$-0.630475\pi$
$281$	5.87724	−	4.27007i	0.350607	−	0.254731i	0.749124	+	0.662430i	$0.230475\pi$
$282$	−0.885731	+	8.42717i	−0.0527445	+	0.501831i
$283$	−3.39623	+	10.4525i	−0.201885	+	0.621337i	0.797942	+	0.602734i	$0.205922\pi$
$283$	−3.39623	+	10.4525i	−0.201885	+	0.621337i	−0.999827	+	0.0186034i	$0.994078\pi$
$284$	−7.23393	+	12.5295i	−0.429255	+	0.743491i
$285$	−0.466721	−	0.808385i	−0.0276462	−	0.0478846i
$286$	23.2188	−	4.93531i	1.37296	−	0.291831i
$287$	−3.01716	−	9.28585i	−0.178097	−	0.548126i
$288$	0.978148	+	0.207912i	0.0576379	+	0.0122513i
$289$	−4.22793	−	40.2261i	−0.248702	−	2.36624i
$290$	−6.38400	−	7.09015i	−0.374882	−	0.416348i
$291$	−4.38078	−	1.95045i	−0.256806	−	0.114337i
$292$	−4.13421	+	1.84067i	−0.241937	+	0.107717i
$293$	10.8210	−	12.0180i	0.632171	−	0.702097i	−0.338918	−	0.940816i	$-0.610061\pi$
$293$	10.8210	−	12.0180i	0.632171	−	0.702097i	0.971089	+	0.238719i	$0.0767275\pi$
$294$	0.913869	+	0.663964i	0.0532979	+	0.0387232i
$295$	−9.08342	−	6.59949i	−0.528857	−	0.384237i
$296$	−1.57180	+	1.74566i	−0.0913589	+	0.101464i
$297$	−3.69118	+	1.64342i	−0.214184	+	0.0953608i
$298$	12.3618	+	5.50384i	0.716101	+	0.318829i
$299$	8.22634	+	9.13628i	0.475742	+	0.528365i
$300$	−0.104528	−	0.994522i	−0.00603495	−	0.0574187i
$301$	17.7980	+	3.78308i	1.02586	+	0.218053i
$302$	1.96900	+	6.05995i	0.113303	+	0.348711i
$303$	−10.0940	+	2.14555i	−0.579887	+	0.123259i
$304$	0.466721	+	0.808385i	0.0267683	+	0.0463641i
$305$	1.10080	−	1.90664i	0.0630315	−	0.109174i
$306$	2.34217	−	7.20846i	0.133893	−	0.412080i
$307$	2.10705	−	20.0472i	0.120255	−	1.14415i	−0.753384	−	0.657581i	$-0.771580\pi$
$307$	2.10705	−	20.0472i	0.120255	−	1.14415i	0.873640	−	0.486574i	$-0.161753\pi$
$308$	9.32025	−	6.77155i	0.531070	−	0.385845i
$309$	17.6287			1.00286
$310$	5.14155	−	2.13645i	0.292021	−	0.121342i
$311$	−28.5830			−1.62079			−0.810397	−	0.585881i	$-0.800749\pi$
$311$	−28.5830			−1.62079			−0.810397	+	0.585881i	$0.800749\pi$
$312$	−4.75289	+	3.45318i	−0.269080	+	0.195498i
$313$	−0.302109	+	2.87438i	−0.0170762	+	0.162469i	−0.999737	−	0.0229445i	$-0.992696\pi$
$313$	−0.302109	+	2.87438i	−0.0170762	+	0.162469i	0.982661	+	0.185414i	$0.0593626\pi$
$314$	−6.75870	+	20.8011i	−0.381415	+	1.17388i
$315$	1.42562	−	2.46925i	0.0803248	−	0.139127i
$316$	−0.552253	−	0.956531i	−0.0310667	−	0.0538091i
$317$	−17.9256	+	3.81021i	−1.00680	+	0.214002i	−0.681665	−	0.731664i	$-0.738744\pi$
$317$	−17.9256	+	3.81021i	−1.00680	+	0.214002i	−0.325137	+	0.945667i	$0.605411\pi$
$318$	−2.57186	−	7.91537i	−0.144223	−	0.443872i
$319$	−37.7070	−	8.01486i	−2.11118	−	0.448746i
$320$	0.104528	+	0.994522i	0.00584332	+	0.0555955i
$321$	3.38803	+	3.76279i	0.189101	+	0.210018i
$322$	5.45080	+	2.42685i	0.303761	+	0.135243i
$323$	6.46329	−	2.87764i	0.359627	−	0.160116i
$324$	0.669131	−	0.743145i	0.0371739	−	0.0412858i
$325$	4.75289	+	3.45318i	0.263643	+	0.191548i
$326$	−8.53636	−	6.20203i	−0.472785	−	0.343499i
$327$	2.23975	−	2.48749i	0.123858	−	0.137558i
$328$	3.12832	−	1.39282i	0.172732	−	0.0769054i
$329$	−22.0715	−	9.82687i	−1.21684	−	0.541773i
$330$	−2.70362	−	3.00268i	−0.148829	−	0.165292i
$331$	−2.56554	−	24.4095i	−0.141015	−	1.34167i	−0.804712	−	0.593665i	$-0.797681\pi$
$331$	−2.56554	−	24.4095i	−0.141015	−	1.34167i	0.663698	−	0.748001i	$-0.268986\pi$
$332$	6.45132	+	1.37127i	0.354062	+	0.0752582i
$333$	0.725885	+	2.23405i	0.0397783	+	0.122425i
$334$	−12.2465	+	2.60308i	−0.670101	+	0.142434i
$335$	−3.87121	−	6.70512i	−0.211507	−	0.366340i
$336$	−1.42562	+	2.46925i	−0.0777741	+	0.134709i
$337$	−10.0908	+	31.0562i	−0.549680	+	1.69174i	0.159916	+	0.987131i	$0.448878\pi$
$337$	−10.0908	+	31.0562i	−0.549680	+	1.69174i	−0.709596	+	0.704609i	$0.751122\pi$
$338$	2.24887	−	21.3966i	0.122323	−	1.16382i
$339$	−10.7924	+	7.84111i	−0.586160	+	0.425870i
$340$	7.57942			0.411052
$341$	11.7329	−	19.1946i	0.635374	−	1.03945i
$342$	0.933443			0.0504748
$343$	13.5413	−	9.83832i	0.731160	−	0.531219i
$344$	−0.667062	+	6.34667i	−0.0359656	+	0.342190i
$345$	0.646663	−	1.99022i	0.0348151	−	0.107150i
$346$	5.14779	−	8.91624i	0.276747	−	0.479340i
$347$	−1.62834	−	2.82037i	−0.0874140	−	0.151405i	0.819003	−	0.573789i	$-0.194527\pi$
$347$	−1.62834	−	2.82037i	−0.0874140	−	0.151405i	−0.906417	+	0.422383i	$0.861194\pi$
$348$	9.33225	−	1.98363i	0.500261	−	0.106334i
$349$	8.25075	+	25.3932i	0.441652	+	1.35927i	0.886114	+	0.463468i	$0.153395\pi$
$349$	8.25075	+	25.3932i	0.441652	+	1.35927i	−0.444461	+	0.895798i	$0.646605\pi$
$350$	2.78894	+	0.592807i	0.149075	+	0.0316869i
$351$	0.614094	+	5.84272i	0.0327779	+	0.311861i
$352$	2.70362	+	3.00268i	0.144104	+	0.160043i
$353$	−11.6307	−	5.17834i	−0.619042	−	0.275615i	0.0731589	−	0.997320i	$-0.476692\pi$
$353$	−11.6307	−	5.17834i	−0.619042	−	0.275615i	−0.692201	+	0.721705i	$0.743359\pi$
$354$	10.2570	−	4.56673i	0.545155	−	0.242719i
$355$	−9.68088	+	10.7517i	−0.513808	+	0.570642i
$356$	6.06112	+	4.40366i	0.321239	+	0.233394i
$357$	17.4835	+	12.7025i	0.925325	+	0.672288i
$358$	7.13563	−	7.92492i	0.377130	−	0.418845i
$359$	−9.68448	+	4.31181i	−0.511127	+	0.227568i	−0.646060	−	0.763286i	$-0.723585\pi$
$359$	−9.68448	+	4.31181i	−0.511127	+	0.227568i	0.134933	+	0.990855i	$0.456918\pi$
$360$	0.913545	+	0.406737i	0.0481481	+	0.0214369i
$361$	−12.1305	−	13.4722i	−0.638445	−	0.709065i
$362$	1.32102	+	12.5687i	0.0694313	+	0.660595i
$363$	−5.20925	−	1.10726i	−0.273415	−	0.0581161i
$364$	−5.17628	−	15.9309i	−0.271311	−	0.835008i
$365$	−4.42657	+	0.940896i	−0.231697	+	0.0492487i
$366$	1.10080	+	1.90664i	0.0575396	+	0.0996616i
$367$	−12.5773	+	21.7846i	−0.656532	+	1.13715i	0.324976	+	0.945722i	$0.394644\pi$
$367$	−12.5773	+	21.7846i	−0.656532	+	1.13715i	−0.981507	+	0.191424i	$0.938690\pi$
$368$	−0.646663	+	1.99022i	−0.0337096	+	0.103748i
$369$	0.357944	−	3.40561i	0.0186338	−	0.177289i
$370$	−1.90039	+	1.38072i	−0.0987967	+	0.0717800i
$371$	23.7301			1.23201
$372$	−0.720557	+	5.52094i	−0.0373591	+	0.286247i
$373$	14.2977			0.740308			0.370154	−	0.928970i	$-0.379305\pi$
$373$	14.2977			0.740308			0.370154	+	0.928970i	$0.379305\pi$
$374$	24.7759	−	18.0007i	1.28113	−	0.930795i
$375$	0.104528	−	0.994522i	0.00539783	−	0.0513569i
$376$	2.61848	−	8.05886i	0.135038	−	0.415604i
$377$	−28.0255	+	48.5415i	−1.44338	+	2.50001i
$378$	1.42562	+	2.46925i	0.0733261	+	0.127005i
$379$	8.41765	−	1.78923i	0.432386	−	0.0919064i	0.0134231	−	0.999910i	$-0.495727\pi$
$379$	8.41765	−	1.78923i	0.432386	−	0.0919064i	0.418963	+	0.908004i	$0.362394\pi$
$380$	0.288450	+	0.887757i	0.0147972	+	0.0455410i
$381$	8.83507	+	1.87795i	0.452634	+	0.0962104i
$382$	2.17966	+	20.7381i	0.111521	+	1.06105i
$383$	14.2026	+	15.7736i	0.725721	+	0.805995i	0.987246	−	0.159202i	$-0.0508921\pi$
$383$	14.2026	+	15.7736i	0.725721	+	0.805995i	−0.261525	+	0.965197i	$0.584225\pi$
$384$	−0.913545	−	0.406737i	−0.0466192	−	0.0207562i
$385$	10.5245	−	4.68579i	0.536376	−	0.238810i
$386$	11.3520	−	12.6076i	0.577800	−	0.641712i
$387$	5.16285	+	3.75103i	0.262442	+	0.190676i
$388$	3.87953	+	2.81864i	0.196953	+	0.143095i
$389$	−16.3945	+	18.2080i	−0.831236	+	0.923181i	−0.998025	−	0.0628114i	$-0.979993\pi$
$389$	−16.3945	+	18.2080i	−0.831236	+	0.923181i	0.166789	+	0.985993i	$0.446660\pi$
$390$	−5.36699	+	2.38954i	−0.271768	+	0.120999i
$391$	14.4898	+	6.45126i	0.732779	+	0.326254i
$392$	−0.755852	−	0.839459i	−0.0381763	−	0.0423991i
$393$	0.967356	+	9.20378i	0.0487967	+	0.464269i
$394$	3.61600	+	0.768605i	0.182172	+	0.0387218i
$395$	−0.341311	−	1.05045i	−0.0171732	−	0.0528538i
$396$	3.95220	−	0.840067i	0.198606	−	0.0422150i
$397$	−5.80843	−	10.0605i	−0.291517	−	0.504922i	0.682652	−	0.730744i	$-0.260827\pi$
$397$	−5.80843	−	10.0605i	−0.291517	−	0.504922i	−0.974169	+	0.225822i	$0.927493\pi$
$398$	3.50536	−	6.07145i	0.175708	−	0.304335i
$399$	−0.822441	+	2.53121i	−0.0411735	+	0.126719i
$400$	−0.104528	+	0.994522i	−0.00522642	+	0.0497261i
$401$	24.8102	−	18.0257i	1.23896	−	0.900160i	0.241435	−	0.970417i	$-0.422382\pi$
$401$	24.8102	−	18.0257i	1.23896	−	0.900160i	0.997529	+	0.0702571i	$0.0223820\pi$
$402$	7.74241			0.386156
$403$	−21.2713	−	24.8491i	−1.05960	−	1.23782i
$404$	10.3195			0.513416
$405$	0.809017	−	0.587785i	0.0402004	−	0.0292073i
$406$	−2.84349	+	27.0540i	−0.141120	+	1.34267i
$407$	−2.93294	+	9.02666i	−0.145380	+	0.447435i
$408$	−3.78971	+	6.56397i	−0.187619	+	0.324965i
$409$	−11.4981	−	19.9152i	−0.568543	−	0.984745i	−0.996710	−	0.0810454i	$-0.974174\pi$
$409$	−11.4981	−	19.9152i	−0.568543	−	0.984745i	0.428168	−	0.903699i	$-0.359159\pi$
$410$	3.34954	−	0.711967i	0.165422	−	0.0351615i
$411$	−3.98672	−	12.2699i	−0.196651	−	0.605228i
$412$	−17.2434	−	3.66521i	−0.849523	−	0.180572i
$413$	3.34627	+	31.8376i	0.164659	+	1.56663i
$414$	1.40025	+	1.55514i	0.0688186	+	0.0764308i
$415$	6.02524	+	2.68261i	0.295767	+	0.131684i
$416$	5.36699	−	2.38954i	0.263138	−	0.117157i
$417$	12.2590	−	13.6150i	0.600325	−	0.666729i
$418$	3.05127	+	2.21688i	0.149242	+	0.108431i
$419$	−21.8570	−	15.8800i	−1.06778	−	0.775789i	−0.0922701	−	0.995734i	$-0.529412\pi$
$419$	−21.8570	−	15.8800i	−1.06778	−	0.775789i	−0.975512	+	0.219945i	$0.929412\pi$
$420$	−1.90786	+	2.11889i	−0.0930938	+	0.103391i
$421$	−6.68953	+	2.97837i	−0.326028	+	0.145157i	−0.563223	−	0.826305i	$-0.690439\pi$
$421$	−6.68953	+	2.97837i	−0.326028	+	0.145157i	0.237195	+	0.971462i	$0.423772\pi$
$422$	1.60582	+	0.714957i	0.0781701	+	0.0348036i
$423$	−5.66994	−	6.29710i	−0.275682	−	0.306176i
$424$	0.869961	+	8.27712i	0.0422490	+	0.401973i
$425$	7.41379	+	1.57585i	0.359622	+	0.0764400i
$426$	−4.47081	−	13.7597i	−0.216612	−	0.666662i
$427$	−6.14012	+	1.30512i	−0.297141	+	0.0631593i
$428$	−2.53167	−	4.38497i	−0.122373	−	0.211956i
$429$	−11.8688	+	20.5573i	−0.573029	+	0.992516i
$430$	−1.97203	+	6.06929i	−0.0950999	+	0.292687i
$431$	−1.92190	+	18.2857i	−0.0925748	+	0.880791i	0.845411	+	0.534117i	$0.179356\pi$
$431$	−1.92190	+	18.2857i	−0.0925748	+	0.880791i	−0.937986	+	0.346674i	$0.887311\pi$
$432$	−0.809017	+	0.587785i	−0.0389238	+	0.0282798i
$433$	−9.54497			−0.458702			−0.229351	−	0.973344i	$-0.573660\pi$
$433$	−9.54497			−0.458702			−0.229351	+	0.973344i	$0.573660\pi$
$434$	−14.3362	−	6.81834i	−0.688162	−	0.327291i
$435$	9.54074			0.457444
$436$	−2.70798	+	1.96746i	−0.129689	+	0.0942244i
$437$	−0.204182	+	1.94266i	−0.00976735	+	0.0929301i
$438$	1.39844	−	4.30397i	0.0668202	−	0.205652i
$439$	−7.75682	+	13.4352i	−0.370213	+	0.641228i	−0.989598	−	0.143860i	$-0.954049\pi$
$439$	−7.75682	+	13.4352i	−0.370213	+	0.641228i	0.619385	+	0.785087i	$0.287382\pi$
$440$	2.02025	+	3.49917i	0.0963116	+	0.166817i
$441$	−1.10492	+	0.234858i	−0.0526152	+	0.0111837i
$442$	−13.7600	−	42.3490i	−0.654497	−	2.01434i
$443$	−4.24630	−	0.902580i	−0.201748	−	0.0428829i	0.105929	−	0.994374i	$-0.466218\pi$
$443$	−4.24630	−	0.902580i	−0.201748	−	0.0428829i	−0.307677	+	0.951491i	$0.599552\pi$
$444$	−0.245539	−	2.33615i	−0.0116528	−	0.110869i
$445$	5.01310	+	5.56761i	0.237644	+	0.263930i
$446$	−3.26029	−	1.45157i	−0.154379	−	0.0687340i
$447$	−12.3618	+	5.50384i	−0.584694	+	0.260322i
$448$	1.90786	−	2.11889i	0.0901377	−	0.100108i
$449$	−26.8948	−	19.5402i	−1.26925	−	0.922161i	−0.270073	−	0.962840i	$-0.587048\pi$
$449$	−26.8948	−	19.5402i	−1.26925	−	0.922161i	−0.999172	+	0.0406792i	$0.987048\pi$
$450$	0.809017	+	0.587785i	0.0381374	+	0.0277085i
$451$	9.25820	−	10.2823i	0.435952	−	0.484173i
$452$	12.1868	−	5.42590i	0.573218	−	0.255213i
$453$	−5.82094	−	2.59165i	−0.273492	−	0.121766i
$454$	13.1875	+	14.6462i	0.618921	+	0.687382i
$455$	−1.75093	−	16.6590i	−0.0820850	−	0.780987i
$456$	−0.913045	−	0.194074i	−0.0427572	−	0.00908833i
$457$	6.18857	+	19.0465i	0.289489	+	0.890956i	0.985017	+	0.172457i	$0.0551706\pi$
$457$	6.18857	+	19.0465i	0.289489	+	0.890956i	−0.695528	+	0.718499i	$0.744829\pi$
$458$	−24.1614	+	5.13566i	−1.12899	+	0.239973i
$459$	3.78971	+	6.56397i	0.176889	+	0.306380i
$460$	−1.04632	+	1.81228i	−0.0487850	+	0.0844981i
$461$	−13.1824	+	40.5711i	−0.613964	+	1.88959i	−0.198010	+	0.980200i	$0.563448\pi$
$461$	−13.1824	+	40.5711i	−0.613964	+	1.88959i	−0.415953	+	0.909386i	$0.636552\pi$
$462$	−1.20422	+	11.4573i	−0.0560252	+	0.533044i
$463$	7.35852	−	5.34628i	0.341979	−	0.248462i	−0.403517	−	0.914972i	$-0.632212\pi$
$463$	7.35852	−	5.34628i	0.341979	−	0.248462i	0.745496	+	0.666510i	$0.232212\pi$
$464$	−9.54074			−0.442918
$465$	−1.85268	+	5.25048i	−0.0859159	+	0.243485i
$466$	28.6912			1.32910
$467$	−8.39027	+	6.09589i	−0.388255	+	0.282084i	−0.764740	−	0.644339i	$-0.777133\pi$
$467$	−8.39027	+	6.09589i	−0.388255	+	0.282084i	0.376485	+	0.926423i	$0.377133\pi$
$468$	0.614094	−	5.84272i	0.0283865	−	0.270080i
$469$	−6.82171	+	20.9951i	−0.314997	+	0.969462i
$470$	4.23679	−	7.33834i	0.195429	−	0.338493i
$471$	−10.9358	−	18.9414i	−0.503895	−	0.872772i
$472$	−10.9824	+	2.33438i	−0.505505	+	0.107448i
$473$	7.96800	+	24.5230i	0.366369	+	1.12757i
$474$	1.08037	+	0.229640i	0.0496231	+	0.0105477i
$475$	0.0975713	+	0.928329i	0.00447688	+	0.0425947i
$476$	−14.4604	−	16.0600i	−0.662794	−	0.736107i
$477$	7.60318	+	3.38515i	0.348126	+	0.154996i
$478$	4.40527	−	1.96135i	0.201492	−	0.0897101i
$479$	20.8805	−	23.1901i	0.954055	−	1.05958i	−0.0441102	−	0.999027i	$-0.514045\pi$
$479$	20.8805	−	23.1901i	0.954055	−	1.05958i	0.998165	−	0.0605582i	$-0.0192881\pi$
$480$	−0.809017	−	0.587785i	−0.0369264	−	0.0268286i
$481$	11.1646	+	8.11157i	0.509063	+	0.369856i
$482$	1.99159	−	2.21189i	0.0907145	−	0.100749i
$483$	−5.45080	+	2.42685i	−0.248020	+	0.110426i
$484$	4.86521	+	2.16613i	0.221146	+	0.0984605i
$485$	3.20872	+	3.56365i	0.145701	+	0.161817i
$486$	0.104528	+	0.994522i	0.00474151	+	0.0451124i
$487$	−15.6346	−	3.32324i	−0.708472	−	0.150590i	−0.160438	−	0.987046i	$-0.551291\pi$
$487$	−15.6346	−	3.32324i	−0.708472	−	0.150590i	−0.548035	+	0.836456i	$0.684624\pi$
$488$	−0.680331	−	2.09384i	−0.0307971	−	0.0947838i
$489$	10.3209	−	2.19379i	0.466729	−	0.0992064i
$490$	−0.564802	−	0.978265i	−0.0255151	−	0.0441935i
$491$	−16.0014	+	27.7152i	−0.722131	+	1.25077i	0.238013	+	0.971262i	$0.423504\pi$
$491$	−16.0014	+	27.7152i	−0.722131	+	1.25077i	−0.960144	+	0.279505i	$0.909830\pi$
$492$	−1.05819	+	3.25677i	−0.0477068	+	0.146827i
$493$	−7.55880	+	71.9172i	−0.340431	+	3.23899i
$494$	4.43655	−	3.22334i	0.199610	−	0.145025i
$495$	4.04050			0.181607
$496$	1.85268	−	5.25048i	0.0831878	−	0.235754i
$497$	41.2514			1.85038
$498$	−5.33583	+	3.87670i	−0.239104	+	0.173719i
$499$	−1.03429	+	9.84066i	−0.0463014	+	0.440528i	0.946673	+	0.322197i	$0.104421\pi$
$499$	−1.03429	+	9.84066i	−0.0463014	+	0.440528i	−0.992974	+	0.118332i	$0.962245\pi$
$500$	−0.309017	+	0.951057i	−0.0138197	+	0.0425325i
$501$	6.26007	−	10.8428i	0.279679	−	0.484418i
$502$	2.10828	+	3.65165i	0.0940972	+	0.162981i
$503$	−30.4686	+	6.47631i	−1.35853	+	0.288764i	−0.828868	−	0.559445i	$-0.811014\pi$
$503$	−30.4686	+	6.47631i	−1.35853	+	0.288764i	−0.529662	+	0.848209i	$0.677681\pi$
$504$	−0.881083	−	2.71170i	−0.0392466	−	0.120789i
$505$	10.0940	+	2.14555i	0.449179	+	0.0954759i
$506$	0.883822	+	8.40901i	0.0392907	+	0.373826i
$507$	14.3960	+	15.9884i	0.639348	+	0.710068i
$508$	−8.25155	−	3.67383i	−0.366103	−	0.163000i
$509$	4.02410	−	1.79164i	0.178365	−	0.0794132i	−0.315611	−	0.948889i	$-0.602210\pi$
$509$	4.02410	−	1.79164i	0.178365	−	0.0794132i	0.493976	+	0.869475i	$0.335543\pi$
$510$	−5.07162	+	5.63261i	−0.224575	+	0.249416i
$511$	10.4389	+	7.58431i	0.461790	+	0.335510i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−0.624595	+	0.693683i	−0.0275765	+	0.0306269i
$514$	−2.24023	+	0.997417i	−0.0988125	+	0.0439942i
$515$	−16.1046	−	7.17022i	−0.709653	−	0.315958i
$516$	−4.27015	−	4.74248i	−0.187983	−	0.208776i
$517$	−3.57880	−	34.0500i	−0.157395	−	1.49752i
$518$	6.55126	+	1.39251i	0.287846	+	0.0611835i
$519$	3.18151	+	9.79168i	0.139653	+	0.429807i
$520$	5.74652	−	1.22146i	0.252002	−	0.0535646i
$521$	−11.5062	−	19.9294i	−0.504097	−	0.873122i	−0.999989	−	0.00473786i	$-0.998492\pi$
$521$	−11.5062	−	19.9294i	−0.504097	−	0.873122i	0.495891	−	0.868385i	$-0.334841\pi$
$522$	−4.77037	+	8.26253i	−0.208793	+	0.361641i
$523$	−3.81273	+	11.7344i	−0.166719	+	0.513108i	−0.999159	−	0.0410073i	$-0.986943\pi$
$523$	−3.81273	+	11.7344i	−0.166719	+	0.513108i	0.832440	+	0.554115i	$0.186943\pi$
$524$	0.967356	−	9.20378i	0.0422591	−	0.402069i
$525$	−2.30671	+	1.67592i	−0.100673	+	0.0731432i
$526$	−14.7997			−0.645298
$527$	−38.1098	−	18.1251i	−1.66009	−	0.789541i
$528$	−4.04050			−0.175840
$529$	15.0646	−	10.9451i	0.654982	−	0.475872i
$530$	−0.869961	+	8.27712i	−0.0377887	+	0.359535i
$531$	−3.46956	+	10.6782i	−0.150566	+	0.463395i
$532$	1.33074	−	2.30490i	0.0576948	−	0.0999303i
$533$	−10.0589	−	17.4226i	−0.435700	−	0.754655i
$534$	−7.32824	+	1.55767i	−0.317124	+	0.0674068i
$535$	−1.56466	−	4.81551i	−0.0676459	−	0.208193i
$536$	−7.57322	−	1.60974i	−0.327113	−	0.0695301i
$537$	1.11470	+	10.6056i	0.0481026	+	0.457666i
$538$	−11.0015	−	12.2184i	−0.474310	−	0.526775i
$539$	−4.16957	−	1.85641i	−0.179596	−	0.0799613i
$540$	−0.913545	+	0.406737i	−0.0393127	+	0.0175032i
$541$	−17.2913	+	19.2039i	−0.743411	+	0.825642i	−0.989640	−	0.143570i	$-0.954142\pi$
$541$	−17.2913	+	19.2039i	−0.743411	+	0.825642i	0.246229	+	0.969212i	$0.420808\pi$
$542$	−0.233822	−	0.169882i	−0.0100435	−	0.00729705i
$543$	−10.2243	−	7.42837i	−0.438766	−	0.318782i
$544$	5.07162	−	5.63261i	0.217444	−	0.241496i
$545$	−3.05786	+	1.36145i	−0.130984	+	0.0583180i
$546$	15.3026	+	6.81316i	0.654891	+	0.291576i
$547$	−4.70102	−	5.22101i	−0.201001	−	0.223234i	0.634214	−	0.773157i	$-0.281324\pi$
$547$	−4.70102	−	5.22101i	−0.201001	−	0.223234i	−0.835215	+	0.549923i	$0.814657\pi$
$548$	1.34855	+	12.8306i	0.0576074	+	0.548097i
$549$	−2.15349	−	0.457738i	−0.0919086	−	0.0195358i
$550$	1.24858	+	3.84274i	0.0532398	+	0.163855i
$551$	−8.71112	+	1.85161i	−0.371106	+	0.0788811i
$552$	−1.04632	−	1.81228i	−0.0445344	−	0.0771359i
$553$	−1.57461	+	2.72730i	−0.0669592	+	0.115977i
$554$	−6.82694	+	21.0112i	−0.290049	+	0.892679i
$555$	0.245539	−	2.33615i	0.0104225	−	0.0991639i
$556$	−14.8218	+	10.7687i	−0.628585	+	0.456694i
$557$	25.6834			1.08824			0.544120	−	0.839008i	$-0.316864\pi$
$557$	25.6834			1.08824			0.544120	+	0.839008i	$0.316864\pi$
$558$	−3.62071	−	4.22971i	−0.153277	−	0.179058i
$559$	37.4915			1.58572
$560$	2.30671	−	1.67592i	0.0974761	−	0.0708206i
$561$	−3.20115	+	30.4569i	−0.135153	+	1.28589i
$562$	2.24491	−	6.90911i	0.0946957	−	0.291443i
$563$	4.41097	−	7.64003i	0.185900	−	0.321989i	−0.757979	−	0.652279i	$-0.773813\pi$
$563$	4.41097	−	7.64003i	0.185900	−	0.321989i	0.943880	+	0.330290i	$0.107146\pi$
$564$	4.23679	+	7.33834i	0.178401	+	0.309000i
$565$	13.0486	−	2.77356i	0.548958	−	0.116685i
$566$	3.39623	+	10.4525i	0.142754	+	0.439352i
$567$	−2.78894	−	0.592807i	−0.117124	−	0.0248956i
$568$	1.51230	+	14.3886i	0.0634548	+	0.603732i
$569$	12.1011	+	13.4396i	0.507304	+	0.563419i	0.941332	−	0.337481i	$-0.109575\pi$
$569$	12.1011	+	13.4396i	0.507304	+	0.563419i	−0.434028	+	0.900899i	$0.642908\pi$
$570$	−0.852742	−	0.379665i	−0.0357174	−	0.0159024i
$571$	11.9694	−	5.32913i	0.500905	−	0.223017i	−0.140700	−	0.990052i	$-0.544935\pi$
$571$	11.9694	−	5.32913i	0.500905	−	0.223017i	0.641605	+	0.767035i	$0.278269\pi$
$572$	15.8835	−	17.6404i	0.664123	−	0.737583i
$573$	−16.8699	−	12.2567i	−0.704750	−	0.512031i
$574$	−7.89902	−	5.73897i	−0.329699	−	0.239540i
$575$	−1.40025	+	1.55514i	−0.0583946	+	0.0648537i
$576$	0.913545	−	0.406737i	0.0380644	−	0.0169474i
$577$	−15.6228	−	6.95570i	−0.650384	−	0.289570i	0.0549029	−	0.998492i	$-0.482515\pi$
$577$	−15.6228	−	6.95570i	−0.650384	−	0.289570i	−0.705287	+	0.708922i	$0.749182\pi$
$578$	−27.0648	−	30.0585i	−1.12575	−	1.25027i
$579$	1.77335	+	16.8723i	0.0736979	+	0.701189i
$580$	−9.33225	−	1.98363i	−0.387501	−	0.0823658i
$581$	−5.81114	−	17.8848i	−0.241087	−	0.741988i
$582$	−4.69057	+	0.997012i	−0.194430	+	0.0413275i
$583$	16.8140	+	29.1226i	0.696363	+	1.20614i
$584$	−2.26273	+	3.91916i	−0.0936324	+	0.162176i
$585$	1.81544	−	5.58736i	0.0750594	−	0.231009i
$586$	1.69041	−	16.0832i	0.0698302	−	0.664390i
$587$	37.8805	−	27.5218i	1.56350	−	1.13595i	0.630426	−	0.776249i	$-0.282880\pi$
$587$	37.8805	−	27.5218i	1.56350	−	1.13595i	0.933069	−	0.359697i	$-0.117120\pi$
$588$	1.12960			0.0465841
$589$	0.672598	−	5.15348i	0.0277139	−	0.212346i
$590$	−11.2277			−0.462238
$591$	−2.99076	+	2.17292i	−0.123024	+	0.0893818i
$592$	−0.245539	+	2.33615i	−0.0100916	+	0.0960150i
$593$	12.4481	−	38.3114i	0.511183	−	1.57326i	−0.278939	−	0.960309i	$-0.589983\pi$
$593$	12.4481	−	38.3114i	0.511183	−	1.57326i	0.790122	−	0.612950i	$-0.210017\pi$
$594$	−2.02025	+	3.49917i	−0.0828918	+	0.143573i
$595$	−10.8054	−	18.7155i	−0.442978	−	0.767261i
$596$	13.2360	−	2.81340i	0.542167	−	0.115241i
$597$	2.16643	+	6.66758i	0.0886660	+	0.272886i
$598$	12.0254	+	2.55608i	0.491756	+	0.104526i
$599$	−3.68229	−	35.0346i	−0.150454	−	1.43148i	−0.765729	−	0.643164i	$-0.777621\pi$
$599$	−3.68229	−	35.0346i	−0.150454	−	1.43148i	0.615274	−	0.788313i	$-0.289045\pi$
$600$	−0.669131	−	0.743145i	−0.0273171	−	0.0303388i
$601$	6.62538	+	2.94981i	0.270255	+	0.120325i	0.537390	−	0.843334i	$-0.319410\pi$
$601$	6.62538	+	2.94981i	0.270255	+	0.120325i	−0.267135	+	0.963659i	$0.586077\pi$
$602$	16.6225	−	7.40082i	0.677483	−	0.301635i
$603$	−5.18068	+	5.75373i	−0.210974	+	0.234310i
$604$	5.15490	+	3.74526i	0.209750	+	0.152392i
$605$	4.30853	+	3.13033i	0.175167	+	0.127266i
$606$	−6.90512	+	7.66891i	−0.280501	+	0.311528i
$607$	−34.9434	+	15.5578i	−1.41831	+	0.631471i	−0.965563	−	0.260169i	$-0.916222\pi$
$607$	−34.9434	+	15.5578i	−1.41831	+	0.631471i	−0.452745	+	0.891640i	$0.649555\pi$
$608$	0.852742	+	0.379665i	0.0345833	+	0.0153975i
$609$	−18.2024	−	20.2158i	−0.737597	−	0.819184i
$610$	−0.230129	−	2.18954i	−0.00931767	−	0.0886517i
$611$	−48.6936	−	10.3502i	−1.96993	−	0.418722i
$612$	−2.34217	−	7.20846i	−0.0946766	−	0.291385i
$613$	−18.4779	+	3.92761i	−0.746317	+	0.158635i	−0.565346	−	0.824854i	$-0.691257\pi$
$613$	−18.4779	+	3.92761i	−0.746317	+	0.158635i	−0.180971	+	0.983488i	$0.557924\pi$
$614$	−10.0788	−	17.4570i	−0.406748	−	0.704508i
$615$	−1.71219	+	2.96559i	−0.0690420	+	0.119584i
$616$	3.56002	−	10.9566i	0.143437	−	0.441454i
$617$	2.71192	−	25.8022i	0.109178	−	1.03876i	−0.793538	−	0.608521i	$-0.791763\pi$
$617$	2.71192	−	25.8022i	0.109178	−	1.03876i	0.902716	−	0.430237i	$-0.141570\pi$
$618$	14.2619	−	10.3619i	0.573697	−	0.416815i
$619$	−10.0753			−0.404962			−0.202481	−	0.979286i	$-0.564901\pi$
$619$	−10.0753			−0.404962			−0.202481	+	0.979286i	$0.564901\pi$
$620$	2.90383	−	4.75055i	0.116621	−	0.190787i
$621$	−2.09264			−0.0839749
$622$	−23.1241	+	16.8007i	−0.927194	+	0.673646i
$623$	2.23288	−	21.2444i	0.0894583	−	0.851139i
$624$	−1.81544	+	5.58736i	−0.0726759	+	0.223673i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	1.44510	+	2.50299i	0.0577580	+	0.100040i
$627$	−3.68916	+	0.784154i	−0.147331	+	0.0313161i
$628$	6.75870	+	20.8011i	0.269701	+	0.830056i
$629$	17.4151	+	3.70170i	0.694386	+	0.147596i
$630$	−0.298036	−	2.83563i	−0.0118741	−	0.112974i
$631$	28.7120	+	31.8879i	1.14301	+	1.26944i	0.958022	+	0.286696i	$0.0925570\pi$
$631$	28.7120	+	31.8879i	1.14301	+	1.26944i	0.184985	+	0.982741i	$0.440776\pi$
$632$	−1.00902	−	0.449243i	−0.0401365	−	0.0178699i
$633$	−1.60582	+	0.714957i	−0.0638256	+	0.0284170i
$634$	−12.2625	+	13.6189i	−0.487008	+	0.540877i
$635$	−7.30740	−	5.30914i	−0.289985	−	0.210687i
$636$	−6.73322	−	4.89197i	−0.266990	−	0.193979i
$637$	−4.44056	+	4.93174i	−0.175941	+	0.195403i
$638$	−35.2166	+	15.6794i	−1.39424	+	0.620755i
$639$	13.2170	+	5.88461i	0.522858	+	0.232791i
$640$	0.669131	+	0.743145i	0.0264497	+	0.0293754i
$641$	−3.05982	−	29.1123i	−0.120856	−	1.14987i	−0.871924	−	0.489641i	$-0.837128\pi$
$641$	−3.05982	−	29.1123i	−0.120856	−	1.14987i	0.751068	−	0.660224i	$-0.229539\pi$
$642$	4.95268	+	1.05273i	0.195467	+	0.0415478i
$643$	−1.51991	−	4.67780i	−0.0599394	−	0.184474i	0.916603	−	0.399798i	$-0.130920\pi$
$643$	−1.51991	−	4.67780i	−0.0599394	−	0.184474i	−0.976543	+	0.215323i	$0.930920\pi$
$644$	5.83626	−	1.24053i	0.229981	−	0.0488839i
$645$	−3.19082	−	5.52666i	−0.125638	−	0.217612i
$646$	3.53748	−	6.12709i	0.139180	−	0.241067i
$647$	11.2091	−	34.4980i	0.440674	−	1.35626i	−0.446485	−	0.894791i	$-0.647324\pi$
$647$	11.2091	−	34.4980i	0.440674	−	1.35626i	0.887159	−	0.461464i	$-0.152676\pi$
$648$	0.104528	−	0.994522i	0.00410627	−	0.0390685i
$649$	−36.7016	+	26.6652i	−1.44066	+	1.04670i
$650$	5.87490			0.230433
$651$	14.6598	−	6.09155i	0.574564	−	0.238746i
$652$	−10.5515			−0.413230
$653$	25.2178	−	18.3218i	0.986849	−	0.716988i	0.0276200	−	0.999618i	$-0.491207\pi$
$653$	25.2178	−	18.3218i	0.986849	−	0.716988i	0.959229	+	0.282631i	$0.0912071\pi$
$654$	0.349883	−	3.32891i	0.0136815	−	0.130171i
$655$	2.85979	−	8.80153i	0.111741	−	0.343904i
$656$	1.71219	−	2.96559i	0.0668496	−	0.115787i
$657$	2.26273	+	3.91916i	0.0882775	+	0.152901i
$658$	−23.6323	+	5.02321i	−0.921284	+	0.195825i
$659$	−4.24659	−	13.0697i	−0.165424	−	0.509122i	0.833644	−	0.552303i	$-0.186251\pi$
$659$	−4.24659	−	13.0697i	−0.165424	−	0.509122i	−0.999067	+	0.0431811i	$0.986251\pi$
$660$	−3.95220	−	0.840067i	−0.153839	−	0.0326996i
$661$	3.97008	+	37.7728i	0.154418	+	1.46919i	0.747614	+	0.664134i	$0.231199\pi$
$661$	3.97008	+	37.7728i	0.154418	+	1.46919i	−0.593196	+	0.805058i	$0.702134\pi$
$662$	−16.4231	−	18.2397i	−0.638302	−	0.708906i
$663$	40.6787	+	18.1113i	1.57983	+	0.703385i
$664$	6.02524	−	2.68261i	0.233825	−	0.104105i
$665$	1.78087	−	1.97786i	0.0690593	−	0.0766982i
$666$	1.90039	+	1.38072i	0.0736387	+	0.0535017i
$667$	−16.1523	−	11.7354i	−0.625421	−	0.454395i
$668$	−8.37760	+	9.30427i	−0.324139	+	0.359993i
$669$	3.26029	−	1.45157i	0.126050	−	0.0561211i
$670$	−7.07304	−	3.14912i	−0.273256	−	0.121661i
$671$	−5.95228	−	6.61068i	−0.229785	−	0.255202i
$672$	0.298036	+	2.83563i	0.0114970	+	0.109387i
$673$	−5.83332	−	1.23991i	−0.224858	−	0.0477950i	0.0941048	−	0.995562i	$-0.470001\pi$
$673$	−5.83332	−	1.23991i	−0.224858	−	0.0477950i	−0.318963	+	0.947767i	$0.603334\pi$
$674$	10.0908	+	31.0562i	0.388682	+	1.19624i
$675$	−0.978148	+	0.207912i	−0.0376489	+	0.00800252i
$676$	−10.7572	−	18.6321i	−0.413739	−	0.716618i
$677$	11.6649	−	20.2043i	0.448320	−	0.776513i	−0.549957	−	0.835193i	$-0.685356\pi$
$677$	11.6649	−	20.2043i	0.448320	−	0.776513i	0.998277	+	0.0586802i	$0.0186892\pi$
$678$	−4.12231	+	12.6872i	−0.158317	+	0.487248i
$679$	1.42919	−	13.5979i	0.0548474	−	0.521838i
$680$	6.13188	−	4.45507i	0.235147	−	0.170844i
$681$	−19.7085			−0.755230
$682$	−1.79017	−	22.4252i	−0.0685493	−	0.858706i
$683$	32.2078			1.23240			0.616199	−	0.787591i	$-0.288672\pi$
$683$	32.2078			1.23240			0.616199	+	0.787591i	$0.288672\pi$
$684$	0.755171	−	0.548664i	0.0288747	−	0.0209787i
$685$	−1.34855	+	12.8306i	−0.0515256	+	0.490233i
$686$	5.17231	−	15.9187i	0.197480	−	0.607780i
$687$	12.3506	−	21.3918i	0.471204	−	0.816149i
$688$	3.19082	+	5.52666i	0.121649	+	0.210702i
$689$	47.8267	−	10.1659i	1.82205	−	0.387289i
$690$	−0.646663	−	1.99022i	−0.0246180	−	0.0757665i
$691$	−2.83867	−	0.603378i	−0.107988	−	0.0229536i	0.153601	−	0.988133i	$-0.450913\pi$
$691$	−2.83867	−	0.603378i	−0.107988	−	0.0229536i	−0.261589	+	0.965179i	$0.584246\pi$
$692$	−1.07618	−	10.2392i	−0.0409103	−	0.389235i
$693$	−7.70869	−	8.56137i	−0.292829	−	0.325219i
$694$	−2.97513	−	1.32461i	−0.112934	−	0.0502816i
$695$	−16.7369	+	7.45173i	−0.634865	+	0.282660i
$696$	6.38400	−	7.09015i	0.241985	−	0.268752i
$697$	−20.9978	−	15.2558i	−0.795350	−	0.577855i
$698$	21.6007	+	15.6939i	0.817600	+	0.594021i
$699$	−19.1982	+	21.3218i	−0.726142	+	0.806463i
$700$	2.60474	−	1.15971i	0.0984500	−	0.0438328i
$701$	−17.5144	−	7.79792i	−0.661510	−	0.294523i	0.0483871	−	0.998829i	$-0.484592\pi$
$701$	−17.5144	−	7.79792i	−0.661510	−	0.294523i	−0.709897	+	0.704305i	$0.751259\pi$
$702$	3.93108	+	4.36590i	0.148369	+	0.164780i
$703$	0.229196	+	2.18066i	0.00864431	+	0.0822451i
$704$	3.95220	+	0.840067i	0.148954	+	0.0316612i
$705$	2.61848	+	8.05886i	0.0986178	+	0.303514i
$706$	−12.4532	+	2.64701i	−0.468683	+	0.0996216i
$707$	−14.7118	−	25.4815i	−0.553293	−	0.958332i
$708$	5.61386	−	9.72350i	0.210982	−	0.365431i
$709$	−3.18333	+	9.79727i	−0.119552	+	0.367944i	−0.992869	−	0.119208i	$-0.961964\pi$
$709$	−3.18333	+	9.79727i	−0.119552	+	0.367944i	0.873317	+	0.487152i	$0.161964\pi$
$710$	−1.51230	+	14.3886i	−0.0567557	+	0.539994i
$711$	−0.893565	+	0.649213i	−0.0335113	+	0.0243474i
$712$	7.49196			0.280773
$713$	9.59479	−	6.61015i	0.359328	−	0.247552i
$714$	21.6108			0.808764
$715$	19.2041	−	13.9526i	0.718191	−	0.521796i
$716$	1.11470	−	10.6056i	0.0416581	−	0.396350i
$717$	−1.49013	+	4.58615i	−0.0556499	+	0.171273i
$718$	−5.30049	+	9.18072i	−0.197813	+	0.342621i
$719$	23.7821	+	41.1919i	0.886924	+	1.53620i	0.843493	+	0.537141i	$0.180496\pi$
$719$	23.7821	+	41.1919i	0.886924	+	1.53620i	0.0434314	+	0.999056i	$0.486171\pi$
$720$	0.978148	−	0.207912i	0.0364534	−	0.00774841i
$721$	15.5323	+	47.8036i	0.578454	+	1.78030i
$722$	−17.7325	−	3.76917i	−0.659936	−	0.140274i
$723$	0.311117	+	2.96008i	0.0115706	+	0.110087i
$724$	8.45641	+	9.39179i	0.314280	+	0.349043i
$725$	−8.71590	−	3.88057i	−0.323700	−	0.144121i
$726$	−4.86521	+	2.16613i	−0.180565	+	0.0803926i
$727$	−11.0252	+	12.2447i	−0.408900	+	0.454130i	−0.912056	−	0.410066i	$-0.865506\pi$
$727$	−11.0252	+	12.2447i	−0.408900	+	0.454130i	0.503156	+	0.864196i	$0.332172\pi$
$728$	−13.5517	−	9.84586i	−0.502258	−	0.364912i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−3.02812	+	3.36307i	−0.112076	+	0.124473i
$731$	44.1874	−	19.6735i	1.63433	−	0.727650i
$732$	2.01126	+	0.895470i	0.0743382	+	0.0330975i
$733$	−25.0488	−	27.8196i	−0.925200	−	1.02754i	−0.999541	−	0.0303059i	$-0.990352\pi$
$733$	−25.0488	−	27.8196i	−0.925200	−	1.02754i	0.0743406	−	0.997233i	$-0.476315\pi$
$734$	2.62938	+	25.0169i	0.0970522	+	0.923390i
$735$	1.10492	+	0.234858i	0.0407556	+	0.00866286i
$736$	0.646663	+	1.99022i	0.0238363	+	0.0733606i
$737$	−30.5996	+	6.50414i	−1.12715	+	0.239583i
$738$	−1.71219	−	2.96559i	−0.0630264	−	0.109165i
$739$	5.53414	−	9.58542i	0.203577	−	0.352605i	−0.746102	−	0.665832i	$-0.768077\pi$
$739$	5.53414	−	9.58542i	0.203577	−	0.352605i	0.949678	+	0.313227i	$0.101410\pi$
$740$	−0.725885	+	2.23405i	−0.0266841	+	0.0821252i
$741$	−0.573222	+	5.45384i	−0.0210578	+	0.200352i
$742$	19.1981	−	13.9482i	0.704783	−	0.512055i
$743$	−27.4676			−1.00769			−0.503845	−	0.863794i	$-0.668082\pi$
$743$	−27.4676			−1.00769			−0.503845	+	0.863794i	$0.668082\pi$
$744$	2.66219	+	4.89007i	0.0976005	+	0.179279i
$745$	13.5317			0.495763
$746$	11.5671	−	8.40399i	0.423501	−	0.307692i
$747$	0.689412	−	6.55931i	0.0252243	−	0.239993i
$748$	9.46354	−	29.1258i	0.346021	−	1.06494i
$749$	−7.21840	+	12.5026i	−0.263755	+	0.456836i
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	8.45929	−	1.79808i	0.308684	−	0.0656128i	−0.0509652	−	0.998700i	$-0.516230\pi$
$751$	8.45929	−	1.79808i	0.308684	−	0.0656128i	0.359649	+	0.933088i	$0.382896\pi$
$752$	−2.61848	−	8.05886i	−0.0954863	−	0.293876i
$753$	−4.12442	−	0.876673i	−0.150302	−	0.0319477i
$754$	5.85892	+	55.7439i	0.213369	+	2.03007i
$755$	4.26357	+	4.73518i	0.155167	+	0.172331i
$756$	2.60474	+	1.15971i	0.0947336	+	0.0421781i
$757$	−5.25371	+	2.33910i	−0.190949	+	0.0850161i	−0.499984	−	0.866035i	$-0.666661\pi$
$757$	−5.25371	+	2.33910i	−0.190949	+	0.0850161i	0.309035	+	0.951051i	$0.399994\pi$
$758$	5.75834	−	6.39529i	0.209152	−	0.232287i
$759$	−6.84050	−	4.96992i	−0.248295	−	0.180397i
$760$	0.755171	+	0.548664i	0.0273929	+	0.0199021i
$761$	0.210245	−	0.233500i	0.00762136	−	0.00846438i	−0.739322	−	0.673352i	$-0.764854\pi$
$761$	0.210245	−	0.233500i	0.00762136	−	0.00846438i	0.746943	+	0.664888i	$0.231521\pi$
$762$	8.25155	−	3.67383i	0.298922	−	0.133089i
$763$	8.71872	+	3.88182i	0.315639	+	0.140531i
$764$	13.9529	+	15.4963i	0.504800	+	0.560637i
$765$	−0.792265	−	7.53790i	−0.0286444	−	0.272533i
$766$	20.7617	+	4.41303i	0.750150	+	0.159449i
$767$	20.3833	+	62.7334i	0.735999	+	2.26517i
$768$	−0.978148	+	0.207912i	−0.0352959	+	0.00750237i
$769$	−19.6927	−	34.1087i	−0.710136	−	1.22999i	−0.964806	−	0.262964i	$-0.915300\pi$
$769$	−19.6927	−	34.1087i	−0.710136	−	1.22999i	0.254669	−	0.967028i	$-0.418033\pi$
$770$	5.76023	−	9.97701i	0.207584	−	0.359546i
$771$	0.757785	−	2.33222i	0.0272909	−	0.0839929i
$772$	1.77335	−	16.8723i	0.0638243	−	0.607247i
$773$	3.58809	−	2.60690i	0.129054	−	0.0937636i	−0.521385	−	0.853321i	$-0.674585\pi$
$773$	3.58809	−	2.60690i	0.129054	−	0.0937636i	0.650440	+	0.759558i	$0.274585\pi$
$774$	6.38163			0.229383
$775$	3.82807	−	4.04300i	0.137508	−	0.145229i
$776$	4.79536			0.172143
$777$	−5.41849	+	3.93676i	−0.194387	+	0.141231i
$778$	−2.56108	+	24.3670i	−0.0918191	+	0.873600i
$779$	0.987758	−	3.04001i	0.0353901	−	0.108920i
$780$	−2.93745	+	5.08781i	−0.105178	+	0.182173i
$781$	29.2287	+	50.6255i	1.04588	+	1.81152i
$782$	15.5144	−	3.29769i	0.554795	−	0.117925i
$783$	−2.94825	−	9.07379i	−0.105362	−	0.324271i
$784$	−1.10492	−	0.234858i	−0.0394614	−	0.00838778i
$785$	2.28621	+	21.7518i	0.0815982	+	0.776355i
$786$	6.19245	+	6.87742i	0.220877	+	0.245309i
$787$	30.7643	+	13.6972i	1.09663	+	0.488251i	0.873642	−	0.486570i	$-0.161752\pi$
$787$	30.7643	+	13.6972i	1.09663	+	0.488251i	0.222988	+	0.974821i	$0.428419\pi$
$788$	3.37718	−	1.50362i	0.120307	−	0.0535642i
$789$	9.90294	−	10.9983i	0.352554	−	0.391551i
$790$	−0.893565	−	0.649213i	−0.0317916	−	0.0230979i
$791$	−30.7717	−	22.3569i	−1.09411	−	0.794921i
$792$	2.70362	−	3.00268i	0.0960690	−	0.106695i
$793$	−11.8159	+	5.26080i	−0.419596	+	0.186816i
$794$	−10.6125	−	4.72500i	−0.376625	−	0.167684i
$795$	−5.56898	−	6.18498i	−0.197512	−	0.219359i
$796$	−0.732819	−	6.97231i	−0.0259741	−	0.247127i
$797$	22.1684	+	4.71203i	0.785243	+	0.166909i	0.583049	−	0.812437i	$-0.301859\pi$
$797$	22.1684	+	4.71203i	0.785243	+	0.166909i	0.202194	+	0.979345i	$0.435193\pi$
$798$	0.822441	+	2.53121i	0.0291141	+	0.0896040i
$799$	−62.8215	+	13.3531i	−2.22246	+	0.472399i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	3.74598	−	6.48823i	0.132358	−	0.229250i
$802$	9.47667	−	29.1662i	0.334633	−	1.02989i
$803$	−1.91132	+	18.1849i	−0.0674488	+	0.641733i
$804$	6.26374	−	4.55088i	0.220905	−	0.160497i
$805$	5.96664			0.210297
$806$	−31.8148	−	7.60039i	−1.12063	−	0.267712i
$807$	16.4415			0.578770
$808$	8.34868	−	6.06567i	0.293706	−	0.213390i
$809$	1.32850	−	12.6398i	0.0467076	−	0.444393i	−0.946029	−	0.324083i	$-0.894944\pi$
$809$	1.32850	−	12.6398i	0.0467076	−	0.444393i	0.992736	−	0.120310i	$-0.0383890\pi$
$810$	0.309017	−	0.951057i	0.0108578	−	0.0334167i
$811$	19.5582	−	33.8757i	0.686780	−	1.18954i	−0.286093	−	0.958202i	$-0.592357\pi$
$811$	19.5582	−	33.8757i	0.686780	−	1.18954i	0.972874	−	0.231337i	$-0.0743099\pi$
$812$	13.6015	+	23.5585i	0.477319	+	0.826741i
$813$	0.282704	−	0.0600907i	0.00991487	−	0.00210747i
$814$	2.93294	+	9.02666i	0.102799	+	0.316384i
$815$	−10.3209	−	2.19379i	−0.361527	−	0.0768449i
$816$	0.792265	+	7.53790i	0.0277348	+	0.263879i
$817$	3.98594	+	4.42683i	0.139450	+	0.154875i
$818$	−21.0080	−	9.35337i	−0.734528	−	0.327033i
$819$	−15.3026	+	6.81316i	−0.534716	+	0.238071i
$820$	2.29135	−	2.54480i	0.0800174	−	0.0888684i
$821$	29.0330	+	21.0937i	1.01326	+	0.736176i	0.964890	−	0.262654i	$-0.0845977\pi$
$821$	29.0330	+	21.0937i	1.01326	+	0.736176i	0.0483689	+	0.998830i	$0.484598\pi$
$822$	−10.4374	−	7.58320i	−0.364045	−	0.264494i
$823$	12.9669	−	14.4012i	0.451998	−	0.501994i	−0.473476	−	0.880807i	$-0.657001\pi$
$823$	12.9669	−	14.4012i	0.451998	−	0.501994i	0.925473	+	0.378813i	$0.123668\pi$
$824$	−16.1046	+	7.17022i	−0.561030	+	0.249787i
$825$	−3.69118	−	1.64342i	−0.128510	−	0.0572165i
$826$	21.4209	+	23.7903i	0.745328	+	0.827771i
$827$	−0.602655	−	5.73387i	−0.0209564	−	0.199386i	0.979034	−	0.203695i	$-0.0652951\pi$
$827$	−0.602655	−	5.73387i	−0.0209564	−	0.199386i	−0.999991	+	0.00430877i	$0.998628\pi$
$828$	2.04691	+	0.435085i	0.0711352	+	0.0151203i
$829$	−12.6379	−	38.8956i	−0.438934	−	1.35090i	−0.889001	−	0.457905i	$-0.848600\pi$
$829$	−12.6379	−	38.8956i	−0.438934	−	1.35090i	0.450067	−	0.892995i	$-0.351400\pi$
$830$	6.45132	−	1.37127i	0.223928	−	0.0475975i
$831$	−11.0462	−	19.1326i	−0.383189	−	0.663703i
$832$	2.93745	−	5.08781i	0.101838	−	0.176388i
$833$	−2.64572	+	8.14270i	−0.0916689	+	0.282128i
$834$	1.91504	−	18.2204i	0.0663125	−	0.630921i
$835$	−10.1290	+	7.35915i	−0.350528	+	0.254674i
$836$	3.77157			0.130443
$837$	5.56602	+	0.139514i	0.192390	+	0.00482231i
$838$	−27.0167			−0.933276
$839$	−12.3127	+	8.94569i	−0.425081	+	0.308840i	−0.779679	−	0.626179i	$-0.784618\pi$
$839$	−12.3127	+	8.94569i	−0.425081	+	0.308840i	0.354598	+	0.935019i	$0.384618\pi$
$840$	−0.298036	+	2.83563i	−0.0102832	+	0.0978384i
$841$	19.1670	−	58.9900i	0.660932	−	2.03414i
$842$	−3.66130	+	6.34156i	−0.126177	+	0.218544i
$843$	3.63233	+	6.29139i	0.125104	+	0.216687i
$844$	1.71938	−	0.365465i	0.0591834	−	0.0125798i
$845$	−6.64833	−	20.4615i	−0.228710	−	0.703896i
$846$	−8.28842	−	1.76176i	−0.284962	−	0.0605705i
$847$	−1.58723	−	15.1015i	−0.0545379	−	0.518894i
$848$	5.56898	+	6.18498i	0.191240	+	0.212393i
$849$	−10.0403	−	4.47021i	−0.344581	−	0.153417i
$850$	6.92415	−	3.08283i	0.237496	−	0.105740i
$851$	−3.28921	+	3.65304i	−0.112753	+	0.125225i
$852$	−11.7047	−	8.50399i	−0.400998	−	0.291342i
$853$	−32.4671	−	23.5887i	−1.11165	−	0.807662i	−0.128728	−	0.991680i	$-0.541089\pi$
$853$	−32.4671	−	23.5887i	−1.11165	−	0.807662i	−0.982923	+	0.184018i	$0.941089\pi$
$854$	−4.20033	+	4.66494i	−0.143732	+	0.159631i
$855$	0.852742	−	0.379665i	0.0291632	−	0.0129843i
$856$	−4.62558	−	2.05944i	−0.158099	−	0.0703903i
$857$	−24.9350	−	27.6931i	−0.851763	−	0.945978i	0.147308	−	0.989091i	$-0.452939\pi$
$857$	−24.9350	−	27.6931i	−0.851763	−	0.945978i	−0.999070	+	0.0431125i	$0.986273\pi$
$858$	2.48125	+	23.6075i	0.0847084	+	0.805946i
$859$	17.9256	+	3.81020i	0.611613	+	0.130002i	0.503296	−	0.864114i	$-0.332120\pi$
$859$	17.9256	+	3.81020i	0.611613	+	0.130002i	0.108317	+	0.994116i	$0.465454\pi$
$860$	1.97203	+	6.06929i	0.0672458	+	0.206961i
$861$	9.55036	−	2.02999i	0.325475	−	0.0691819i
$862$	9.19321	+	15.9231i	0.313122	+	0.542343i
$863$	−17.2604	+	29.8958i	−0.587549	+	1.01767i	0.407003	+	0.913427i	$0.366574\pi$
$863$	−17.2604	+	29.8958i	−0.587549	+	1.01767i	−0.994552	+	0.104239i	$0.966759\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$	1.07618	−	10.2392i	0.0365913	−	0.348143i
$866$	−7.72204	+	5.61039i	−0.262406	+	0.190649i
$867$	40.4477			1.37367
$868$	−15.6060	+	2.91048i	−0.529702	+	0.0987881i
$869$	−4.46276			−0.151389
$870$	7.71862	−	5.60791i	0.261686	−	0.190126i
$871$	−4.75457	+	45.2367i	−0.161102	+	1.53279i
$872$	−1.03436	+	3.18342i	−0.0350277	+	0.107804i
$873$	2.39768	−	4.15290i	0.0811492	−	0.140555i
$874$	0.976681	+	1.69166i	0.0330367	+	0.0572213i
$875$	2.78894	−	0.592807i	0.0942834	−	0.0200405i
$876$	−1.39844	−	4.30397i	−0.0472490	−	0.145418i
$877$	29.0999	+	6.18537i	0.982634	+	0.208865i	0.671098	−	0.741369i	$-0.265823\pi$
$877$	29.0999	+	6.18537i	0.982634	+	0.208865i	0.311536	+	0.950234i	$0.399157\pi$
$878$	1.62162	+	15.4287i	0.0547270	+	0.520692i
$879$	10.8210	+	12.0180i	0.364984	+	0.405356i
$880$	3.69118	+	1.64342i	0.124430	+	0.0553996i
$881$	−5.67681	+	2.52748i	−0.191257	+	0.0851530i	−0.500130	−	0.865950i	$-0.666715\pi$
$881$	−5.67681	+	2.52748i	−0.191257	+	0.0851530i	0.308874	+	0.951103i	$0.400048\pi$
$882$	−0.755852	+	0.839459i	−0.0254509	+	0.0282661i
$883$	2.05885	+	1.49584i	0.0692858	+	0.0503391i	0.621889	−	0.783105i	$-0.286365\pi$
$883$	2.05885	+	1.49584i	0.0692858	+	0.0503391i	−0.552603	+	0.833444i	$0.686365\pi$
$884$	−36.0242	−	26.1731i	−1.21162	−	0.880297i
$885$	7.51282	−	8.34383i	0.252541	−	0.280475i
$886$	−3.96586	+	1.76571i	−0.133236	+	0.0593203i
$887$	2.47296	+	1.10103i	0.0830339	+	0.0369691i	0.447833	−	0.894117i	$-0.352196\pi$
$887$	2.47296	+	1.10103i	0.0830339	+	0.0369691i	−0.364799	+	0.931086i	$0.618862\pi$
$888$	−1.57180	−	1.74566i	−0.0527461	−	0.0585805i
$889$	2.69200	+	25.6127i	0.0902867	+	0.859021i
$890$	7.32824	+	1.55767i	0.245643	+	0.0522131i
$891$	−1.24858	−	3.84274i	−0.0418291	−	0.128737i
$892$	−3.49084	+	0.742001i	−0.116882	+	0.0248440i
$893$	−3.95480	−	6.84992i	−0.132342	−	0.229224i
$894$	−6.76585	+	11.7188i	−0.226284	+	0.391935i
$895$	3.29537	−	10.1421i	0.110152	−	0.339013i
$896$	0.298036	−	2.83563i	0.00995670	−	0.0947316i
$897$	−9.94611	+	7.22628i	−0.332091	+	0.241278i
$898$	−33.2438			−1.10936
$899$	42.1796	+	32.2906i	1.40677	+	1.07695i
$900$	1.00000			0.0333333
$901$	51.0339	−	37.0783i	1.70019	−	1.23526i
$902$	1.44627	−	13.7604i	0.0481556	−	0.458170i
$903$	−5.62275	+	17.3050i	−0.187113	+	0.575876i
$904$	6.67004	−	11.5529i	0.221842	−	0.384242i
$905$	6.31895	+	10.9447i	0.210049	+	0.363816i
$906$	−6.23257	+	1.32477i	−0.207063	+	0.0440127i
$907$	−8.93311	−	27.4933i	−0.296619	−	0.912900i	−0.982673	−	0.185349i	$-0.940658\pi$
$907$	−8.93311	−	27.4933i	−0.296619	−	0.912900i	0.686054	−	0.727551i	$-0.259342\pi$
$908$	19.2778	+	4.09762i	0.639755	+	0.135984i
$909$	−1.07869	−	10.2630i	−0.0357777	−	0.340402i
$910$	−11.2085	−	12.4483i	−0.371557	−	0.412656i
$911$	−47.2083	−	21.0185i	−1.56408	−	0.696374i	−0.571801	−	0.820392i	$-0.693755\pi$
$911$	−47.2083	−	21.0185i	−1.56408	−	0.696374i	−0.992280	+	0.124019i	$0.960422\pi$
$912$	−0.852742	+	0.379665i	−0.0282371	+	0.0125720i
$913$	17.8316	−	19.8040i	0.590139	−	0.655416i
$914$	16.2019	+	11.7714i	0.535911	+	0.389362i
$915$	1.78113	+	1.29407i	0.0588823	+	0.0427805i
$916$	−16.5283	+	18.3565i	−0.546110	+	0.606517i
$917$	−24.1055	+	10.7325i	−0.796035	+	0.354417i
$918$	6.92415	+	3.08283i	0.228531	+	0.101749i
$919$	13.9694	+	15.5146i	0.460807	+	0.511778i	0.928103	−	0.372323i	$-0.121438\pi$
$919$	13.9694	+	15.5146i	0.460807	+	0.511778i	−0.467296	+	0.884101i	$0.654772\pi$
$920$	0.218741	+	2.08118i	0.00721167	+	0.0686145i
$921$	19.7171	+	4.19101i	0.649702	+	0.138098i
$922$	13.1824	+	40.5711i	0.434138	+	1.33614i
$923$	83.1398	−	17.6719i	2.73658	−	0.581678i
$924$	5.76023	+	9.97701i	0.189498	+	0.328219i
$925$	−1.17451	+	2.03431i	−0.0386176	+	0.0668876i
$926$	2.81070	−	8.65045i	0.0923654	−	0.284272i
$927$	−1.84270	+	17.5321i	−0.0605221	+	0.575829i
$928$	−7.71862	+	5.60791i	−0.253376	+	0.184089i
$929$	29.6517			0.972839			0.486420	−	0.873725i	$-0.338303\pi$
$929$	29.6517			0.972839			0.486420	+	0.873725i	$0.338303\pi$
$930$	1.58731	+	5.33671i	0.0520499	+	0.174998i
$931$	−1.05442			−0.0345572
$932$	23.2117	−	16.8643i	0.760325	−	0.552408i
$933$	2.98774	−	28.4264i	0.0978142	−	0.930640i
$934$	−3.20480	+	9.86335i	−0.104864	+	0.322739i
$935$	15.3123	−	26.5217i	0.500767	−	0.867353i
$936$	−2.93745	−	5.08781i	−0.0960136	−	0.166300i
$937$	29.8121	−	6.33675i	0.973917	−	0.207013i	0.306643	−	0.951825i	$-0.400794\pi$
$937$	29.8121	−	6.33675i	0.973917	−	0.207013i	0.667274	+	0.744812i	$0.267461\pi$
$938$	6.82171	+	20.9951i	0.222737	+	0.685513i
$939$	−2.82705	−	0.600908i	−0.0922573	−	0.0196099i
$940$	−0.885731	−	8.42717i	−0.0288894	−	0.274864i
$941$	20.7647	+	23.0615i	0.676908	+	0.751783i	0.979523	−	0.201330i	$-0.0645263\pi$
$941$	20.7647	+	23.0615i	0.676908	+	0.751783i	−0.302615	+	0.953113i	$0.597860\pi$
$942$	−19.9807	−	8.89598i	−0.651007	−	0.289847i
$943$	6.54646	−	2.91467i	0.213182	−	0.0949147i
$944$	−7.51282	+	8.34383i	−0.244521	+	0.271568i
$945$	2.30671	+	1.67592i	0.0750372	+	0.0545177i
$946$	20.8605	+	15.1560i	0.678233	+	0.492765i
$947$	13.9305	−	15.4714i	0.452681	−	0.502753i	−0.472998	−	0.881064i	$-0.656828\pi$
$947$	13.9305	−	15.4714i	0.452681	−	0.502753i	0.925679	+	0.378311i	$0.123495\pi$
$948$	1.00902	−	0.449243i	0.0327713	−	0.0145907i
$949$	24.2881	+	10.8138i	0.788425	+	0.351029i
$950$	0.624595	+	0.693683i	0.0202645	+	0.0225060i
$951$	−1.91560	−	18.2257i	−0.0621175	−	0.591008i
$952$	−21.1386	−	4.49314i	−0.685104	−	0.145623i
$953$	0.110991	+	0.341594i	0.00359534	+	0.0110653i	0.952838	−	0.303479i	$-0.0981483\pi$
$953$	0.110991	+	0.341594i	0.00359534	+	0.0110653i	−0.949243	+	0.314544i	$0.898148\pi$
$954$	8.14085	−	1.73039i	0.263570	−	0.0560235i
$955$	10.4262	+	18.0587i	0.337383	+	0.584364i
$956$	2.41108	−	4.17612i	0.0779800	−	0.135065i
$957$	11.9124	−	36.6626i	0.385073	−	1.18513i
$958$	3.26185	−	31.0345i	0.105386	−	1.00268i
$959$	29.7595	−	21.6216i	0.960985	−	0.698197i
$960$	−1.00000			−0.0322749
$961$	−25.9609	+	16.9420i	−0.837449	+	0.546516i
$962$	13.8002			0.444937
$963$	−4.09632	+	2.97615i	−0.132002	+	0.0959051i
$964$	0.311117	−	2.96008i	0.0100204	−	0.0953378i
$965$	5.24255	−	16.1349i	0.168764	−	0.519401i
$966$	−2.98332	+	5.16726i	−0.0959868	+	0.166254i
$967$	11.2265	+	19.4448i	0.361020	+	0.625304i	0.988129	−	0.153627i	$-0.0490954\pi$
$967$	11.2265	+	19.4448i	0.361020	+	0.625304i	−0.627109	+	0.778931i	$0.715762\pi$
$968$	5.20925	−	1.10726i	0.167432	−	0.0355887i
$969$	2.18628	+	6.72868i	0.0702335	+	0.216156i
$970$	4.69057	+	0.997012i	0.150605	+	0.0320121i
$971$	−1.54450	−	14.6949i	−0.0495653	−	0.471582i	−0.990948	−	0.134243i	$-0.957140\pi$
$971$	−1.54450	−	14.6949i	−0.0495653	−	0.471582i	0.941383	−	0.337339i	$-0.109527\pi$
$972$	0.669131	+	0.743145i	0.0214624	+	0.0238364i
$973$	47.7209	+	21.2467i	1.52986	+	0.681138i
$974$	−14.6020	+	6.50124i	−0.467879	+	0.208313i
$975$	−3.93108	+	4.36590i	−0.125895	+	0.139821i
$976$	−1.78113	−	1.29407i	−0.0570125	−	0.0414220i
$977$	34.5463	+	25.0994i	1.10523	+	0.803000i	0.981906	−	0.189366i	$-0.0606434\pi$
$977$	34.5463	+	25.0994i	1.10523	+	0.803000i	0.123328	+	0.992366i	$0.460643\pi$
$978$	7.06035	−	7.84131i	0.225765	−	0.250737i
$979$	27.6542	−	12.3124i	0.883831	−	0.393507i
$980$	−1.03194	−	0.459451i	−0.0329642	−	0.0146766i
$981$	2.23975	+	2.48749i	0.0715096	+	0.0794194i
$982$	3.34519	+	31.8274i	0.106749	+	1.01565i
$983$	28.1630	+	5.98622i	0.898259	+	0.190931i	0.633828	−	0.773474i	$-0.281483\pi$
$983$	28.1630	+	5.98622i	0.898259	+	0.190931i	0.264431	+	0.964405i	$0.414816\pi$
$984$	1.05819	+	3.25677i	0.0337338	+	0.103822i
$985$	3.61600	−	0.768605i	0.115215	−	0.0244898i
$986$	36.1567	+	62.6252i	1.15146	+	1.99439i
$987$	12.0801	−	20.9234i	0.384515	−	0.666000i
$988$	1.69461	−	5.21548i	0.0539128	−	0.165927i
$989$	−1.39592	+	13.2813i	−0.0443878	+	0.422322i
$990$	3.26883	−	2.37495i	0.103890	−	0.0754807i
$991$	−29.5570			−0.938908			−0.469454	−	0.882957i	$-0.655549\pi$
$991$	−29.5570			−0.938908			−0.469454	+	0.882957i	$0.655549\pi$
$992$	−1.58731	−	5.33671i	−0.0503971	−	0.169441i
$993$	24.5439			0.778878
$994$	33.3731	−	24.2470i	1.05853	−	0.769067i
$995$	0.732819	−	6.97231i	0.0232319	−	0.221037i
$996$	−2.03810	+	6.27264i	−0.0645798	+	0.198756i
$997$	25.3455	−	43.8997i	0.802700	−	1.39032i	−0.115133	−	0.993350i	$-0.536729\pi$
$997$	25.3455	−	43.8997i	0.802700	−	1.39032i	0.917833	−	0.396967i	$-0.129937\pi$
$998$	4.94743	+	8.56920i	0.156608	+	0.271253i
$999$	−2.29768	+	0.488388i	−0.0726955	+	0.0154519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.i.121.1	✓	24
31.10	even	15	inner	930.2.bg.i.661.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.i.121.1	✓	24	1.1	even	1	trivial
930.2.bg.i.661.1	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)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.78894 + 0.592807i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(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} +(-2.78894 + 0.592807i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(-0.104528 - 0.994522i) q^{10} +(-2.70362 - 3.00268i) q^{11} +(0.913545 + 0.406737i) q^{12} +(-5.36699 + 2.38954i) q^{13} +(-1.90786 + 2.11889i) q^{14} +(0.809017 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-5.07162 + 5.63261i) q^{17} +(-0.913545 + 0.406737i) q^{18} +(-0.852742 - 0.379665i) q^{19} +(-0.669131 - 0.743145i) q^{20} +(-0.298036 - 2.83563i) q^{21} +(-3.95220 - 0.840067i) q^{22} +(-0.646663 - 1.99022i) q^{23} +(0.978148 - 0.207912i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.93745 + 5.08781i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.298036 + 2.83563i) q^{28} +(7.71862 - 5.60791i) q^{29} +1.00000 q^{30} +(1.58731 + 5.33671i) q^{31} -1.00000 q^{32} +(3.26883 - 2.37495i) q^{33} +(-0.792265 + 7.53790i) q^{34} +(-0.881083 + 2.71170i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-1.17451 - 2.03431i) q^{37} +(-0.913045 + 0.194074i) q^{38} +(-1.81544 - 5.58736i) q^{39} +(-0.978148 - 0.207912i) q^{40} +(0.357944 + 3.40561i) q^{41} +(-1.90786 - 2.11889i) q^{42} +(-5.82991 - 2.59564i) q^{43} +(-3.69118 + 1.64342i) q^{44} +(-0.669131 + 0.743145i) q^{45} +(-1.69298 - 1.23003i) q^{46} +(6.85528 + 4.98065i) q^{47} +(0.669131 - 0.743145i) q^{48} +(1.03194 - 0.459451i) q^{49} +(-0.913545 - 0.406737i) q^{50} +(-5.07162 - 5.63261i) q^{51} +(0.614094 + 5.84272i) q^{52} +(-8.14085 - 1.73039i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-3.95220 + 0.840067i) q^{55} +(1.42562 + 2.46925i) q^{56} +(0.466721 - 0.808385i) q^{57} +(2.94825 - 9.07379i) q^{58} +(1.17362 - 11.1662i) q^{59} +(0.809017 - 0.587785i) q^{60} +2.20160 q^{61} +(4.42100 + 3.38449i) q^{62} +2.85125 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.614094 + 5.84272i) q^{65} +(1.24858 - 3.84274i) q^{66} +(3.87121 - 6.70512i) q^{67} +(3.78971 + 6.56397i) q^{68} +(2.04691 - 0.435085i) q^{69} +(0.881083 + 2.71170i) q^{70} +(-14.1517 - 3.00804i) q^{71} +(0.104528 + 0.994522i) q^{72} +(-3.02812 - 3.36307i) q^{73} +(-2.14593 - 0.955430i) q^{74} +(0.913545 - 0.406737i) q^{75} +(-0.624595 + 0.693683i) q^{76} +(9.32025 + 6.77155i) q^{77} +(-4.75289 - 3.45318i) q^{78} +(0.739059 - 0.820808i) q^{79} +(-0.913545 + 0.406737i) q^{80} +(0.913545 + 0.406737i) q^{81} +(2.29135 + 2.54480i) q^{82} +(0.689412 + 6.55931i) q^{83} +(-2.78894 - 0.592807i) q^{84} +(2.34217 + 7.20846i) q^{85} +(-6.24218 + 1.32682i) q^{86} +(4.77037 + 8.26253i) q^{87} +(-2.02025 + 3.49917i) q^{88} +(-2.31514 + 7.12528i) q^{89} +(-0.104528 + 0.994522i) q^{90} +(13.5517 - 9.84586i) q^{91} -2.09264 q^{92} +(-5.47339 + 1.02077i) q^{93} +8.47359 q^{94} +(-0.755171 + 0.548664i) q^{95} +(0.104528 - 0.994522i) q^{96} +(-1.48185 + 4.56066i) q^{97} +(0.564802 - 0.978265i) q^{98} +(2.02025 + 3.49917i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9} + 3 q^{10} - 13 q^{11} + 3 q^{12} + 11 q^{13} - 8 q^{14} + 6 q^{15} - 6 q^{16} - 29 q^{17} - 3 q^{18} + 9 q^{19} - 3 q^{20} - 2 q^{21} - 17 q^{22} - 5 q^{23} - 3 q^{24} - 12 q^{25} + 9 q^{26} - 6 q^{27} - 2 q^{28} + 13 q^{29} + 24 q^{30} + 57 q^{31} - 24 q^{32} + 16 q^{33} + 29 q^{34} + q^{35} - 12 q^{36} - 24 q^{37} + 6 q^{38} - 17 q^{39} + 3 q^{40} + 32 q^{41} - 8 q^{42} + 49 q^{43} - 8 q^{44} - 3 q^{45} + 28 q^{47} + 3 q^{48} + 12 q^{49} - 3 q^{50} - 29 q^{51} - 19 q^{52} - 36 q^{53} + 6 q^{54} - 17 q^{55} - 3 q^{56} - 6 q^{57} + 2 q^{58} + 6 q^{60} + 33 q^{62} - 6 q^{63} - 6 q^{64} + 19 q^{65} + 4 q^{66} - 5 q^{67} + 11 q^{68} + 10 q^{69} - q^{70} - 11 q^{71} - 3 q^{72} - 13 q^{73} + 9 q^{74} + 3 q^{75} - 6 q^{76} + 4 q^{77} - 8 q^{78} - 68 q^{79} - 3 q^{80} + 3 q^{81} - 2 q^{82} + 10 q^{83} - 7 q^{84} + 2 q^{85} - 34 q^{86} + 11 q^{87} - 12 q^{88} + 55 q^{89} + 3 q^{90} + 38 q^{91} + 10 q^{92} + 19 q^{93} + 42 q^{94} + 18 q^{95} - 3 q^{96} - q^{97} + 63 q^{98} + 12 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9 + 3 * q^10 - 13 * q^11 + 3 * q^12 + 11 * q^13 - 8 * q^14 + 6 * q^15 - 6 * q^16 - 29 * q^17 - 3 * q^18 + 9 * q^19 - 3 * q^20 - 2 * q^21 - 17 * q^22 - 5 * q^23 - 3 * q^24 - 12 * q^25 + 9 * q^26 - 6 * q^27 - 2 * q^28 + 13 * q^29 + 24 * q^30 + 57 * q^31 - 24 * q^32 + 16 * q^33 + 29 * q^34 + q^35 - 12 * q^36 - 24 * q^37 + 6 * q^38 - 17 * q^39 + 3 * q^40 + 32 * q^41 - 8 * q^42 + 49 * q^43 - 8 * q^44 - 3 * q^45 + 28 * q^47 + 3 * q^48 + 12 * q^49 - 3 * q^50 - 29 * q^51 - 19 * q^52 - 36 * q^53 + 6 * q^54 - 17 * q^55 - 3 * q^56 - 6 * q^57 + 2 * q^58 + 6 * q^60 + 33 * q^62 - 6 * q^63 - 6 * q^64 + 19 * q^65 + 4 * q^66 - 5 * q^67 + 11 * q^68 + 10 * q^69 - q^70 - 11 * q^71 - 3 * q^72 - 13 * q^73 + 9 * q^74 + 3 * q^75 - 6 * q^76 + 4 * q^77 - 8 * q^78 - 68 * q^79 - 3 * q^80 + 3 * q^81 - 2 * q^82 + 10 * q^83 - 7 * q^84 + 2 * q^85 - 34 * q^86 + 11 * q^87 - 12 * q^88 + 55 * q^89 + 3 * q^90 + 38 * q^91 + 10 * q^92 + 19 * q^93 + 42 * q^94 + 18 * q^95 - 3 * q^96 - q^97 + 63 * q^98 + 12 * q^99

Introduction

L-functions

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