LMFDB - Embedded newform 930.2.bs.a.107.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(107,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 15, 44]))

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

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

chi := DirichletCharacter("930.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bs (of order $60$, degree $16$, 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:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			107.6
Character	$\chi$	$=$	930.107
Dual form			930.2.bs.a.113.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 - 0.891007i) q^{2} +(-1.52373 - 0.823562i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-1.29986 - 1.81944i) q^{5} +(-0.0420417 + 1.73154i) q^{6} +(2.38916 - 1.93471i) q^{7} +(0.987688 + 0.156434i) q^{8} +(1.64349 + 2.50977i) q^{9} +O(q^{10})$	\(q+(-0.453990 - 0.891007i) q^{2} +(-1.52373 - 0.823562i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-1.29986 - 1.81944i) q^{5} +(-0.0420417 + 1.73154i) q^{6} +(2.38916 - 1.93471i) q^{7} +(0.987688 + 0.156434i) q^{8} +(1.64349 + 2.50977i) q^{9} +(-1.03101 + 1.98419i) q^{10} +(-1.87232 - 4.20530i) q^{11} +(1.56190 - 0.748643i) q^{12} +(1.22280 - 0.794095i) q^{13} +(-2.80849 - 1.25042i) q^{14} +(0.482203 + 3.84285i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(1.12968 - 0.433645i) q^{17} +(1.49009 - 2.60377i) q^{18} +(-1.31548 - 6.18886i) q^{19} +(2.23600 + 0.0178354i) q^{20} +(-5.23379 + 0.980340i) q^{21} +(-2.89693 + 3.57741i) q^{22} +(4.55368 + 0.721232i) q^{23} +(-1.37613 - 1.05179i) q^{24} +(-1.62074 + 4.73003i) q^{25} +(-1.26268 - 0.729011i) q^{26} +(-0.437279 - 5.17772i) q^{27} +(0.160895 + 3.07007i) q^{28} +(2.25233 - 6.93197i) q^{29} +(3.20509 - 2.17426i) q^{30} +(4.53521 - 3.22983i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.610421 + 7.94970i) q^{33} +(-0.899247 - 0.809686i) q^{34} +(-6.62566 - 1.83211i) q^{35} +(-2.99646 - 0.145594i) q^{36} +(-0.0863607 + 0.322303i) q^{37} +(-4.91710 + 3.98179i) q^{38} +(-2.51720 + 0.202933i) q^{39} +(-0.999230 - 2.00038i) q^{40} +(-4.15468 + 3.74089i) q^{41} +(3.24958 + 4.21827i) q^{42} +(-6.14390 + 9.46078i) q^{43} +(4.50268 + 0.957074i) q^{44} +(2.43008 - 6.25258i) q^{45} +(-1.42470 - 4.38479i) q^{46} +(-3.43220 - 1.74879i) q^{47} +(-0.312397 + 1.70365i) q^{48} +(0.509631 - 2.39763i) q^{49} +(4.95029 - 0.703295i) q^{50} +(-2.07847 - 0.269609i) q^{51} +(-0.0763069 + 1.45602i) q^{52} +(-1.89825 + 2.34415i) q^{53} +(-4.41486 + 2.74025i) q^{54} +(-5.21755 + 8.87286i) q^{55} +(2.66240 - 1.53714i) q^{56} +(-3.09248 + 10.5135i) q^{57} +(-7.19897 + 1.14021i) q^{58} +(-7.11008 + 7.89654i) q^{59} +(-3.39236 - 1.86866i) q^{60} -4.75538 q^{61} +(-4.93675 - 2.57459i) q^{62} +(8.78223 + 2.81658i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-3.03428 - 1.19260i) q^{65} +(7.36036 - 3.06520i) q^{66} +(-2.61979 + 0.701970i) q^{67} +(-0.313186 + 1.16882i) q^{68} +(-6.34459 - 4.84920i) q^{69} +(1.37557 + 6.73526i) q^{70} +(11.3814 - 1.19624i) q^{71} +(1.23064 + 2.73597i) q^{72} +(-4.79094 + 12.4808i) q^{73} +(0.326381 - 0.0693743i) q^{74} +(6.36505 - 5.87249i) q^{75} +(5.78012 + 2.57347i) q^{76} +(-12.6093 - 6.42475i) q^{77} +(1.32360 + 2.15071i) q^{78} +(3.22004 - 7.23234i) q^{79} +(-1.32872 + 1.79848i) q^{80} +(-3.59788 + 8.24956i) q^{81} +(5.21934 + 2.00352i) q^{82} +(-0.108638 + 2.07295i) q^{83} +(2.28323 - 4.81045i) q^{84} +(-2.25742 - 1.49172i) q^{85} +(11.2189 + 1.17915i) q^{86} +(-9.14086 + 8.70750i) q^{87} +(-1.19141 - 4.44642i) q^{88} +(-5.40139 - 3.92434i) q^{89} +(-6.67432 + 0.673393i) q^{90} +(1.38513 - 4.26298i) q^{91} +(-3.26007 + 3.26007i) q^{92} +(-9.57040 + 1.18636i) q^{93} +3.85204i q^{94} +(-9.55034 + 10.4381i) q^{95} +(1.65978 - 0.495091i) q^{96} +(-2.54744 - 16.0839i) q^{97} +(-2.36767 + 0.634415i) q^{98} +(7.47719 - 11.6104i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 8 q^{3} + 24 q^{7}+O(q^{10}) $ 1024 * q - 8 * q^3 + 24 * q^7	$ 1024 q - 8 q^{3} + 24 q^{7} + 8 q^{10} + 8 q^{12} - 8 q^{15} + 256 q^{16} + 44 q^{22} + 16 q^{25} - 20 q^{27} + 4 q^{28} + 48 q^{30} - 32 q^{31} - 52 q^{33} + 112 q^{37} + 12 q^{42} + 40 q^{45} + 24 q^{46} - 12 q^{48} + 16 q^{51} - 20 q^{55} - 40 q^{57} - 56 q^{58} - 12 q^{60} + 32 q^{61} + 224 q^{63} - 32 q^{66} + 24 q^{67} - 24 q^{70} - 88 q^{73} + 224 q^{75} - 96 q^{76} - 32 q^{78} + 48 q^{81} - 24 q^{85} + 20 q^{87} - 36 q^{88} + 8 q^{90} - 80 q^{91} - 252 q^{93} - 32 q^{97}+O(q^{100}) $ 1024 * q - 8 * q^3 + 24 * q^7 + 8 * q^10 + 8 * q^12 - 8 * q^15 + 256 * q^16 + 44 * q^22 + 16 * q^25 - 20 * q^27 + 4 * q^28 + 48 * q^30 - 32 * q^31 - 52 * q^33 + 112 * q^37 + 12 * q^42 + 40 * q^45 + 24 * q^46 - 12 * q^48 + 16 * q^51 - 20 * q^55 - 40 * q^57 - 56 * q^58 - 12 * q^60 + 32 * q^61 + 224 * q^63 - 32 * q^66 + 24 * q^67 - 24 * q^70 - 88 * q^73 + 224 * q^75 - 96 * q^76 - 32 * q^78 + 48 * q^81 - 24 * q^85 + 20 * q^87 - 36 * q^88 + 8 * q^90 - 80 * q^91 - 252 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{11}{15}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$3$	−1.52373	−	0.823562i	−0.879724	−	0.475484i
$3$	−1.52373	−	0.823562i	−0.879724	−	0.475484i
$4$	−0.587785	+	0.809017i	−0.293893	+	0.404508i
$5$	−1.29986	−	1.81944i	−0.581314	−	0.813680i
$5$	−1.29986	−	1.81944i	−0.581314	−	0.813680i
$6$	−0.0420417	+	1.73154i	−0.0171635	+	0.706898i
$7$	2.38916	−	1.93471i	0.903019	−	0.731250i	−0.0607038	−	0.998156i	$-0.519335\pi$
$7$	2.38916	−	1.93471i	0.903019	−	0.731250i	0.963723	+	0.266906i	$0.0860012\pi$
$8$	0.987688	+	0.156434i	0.349201	+	0.0553079i
$9$	1.64349	+	2.50977i	0.547830	+	0.836590i
$10$	−1.03101	+	1.98419i	−0.326035	+	0.627456i
$11$	−1.87232	−	4.20530i	−0.564525	−	1.26794i	−0.940020	−	0.341120i	$-0.889194\pi$
$11$	−1.87232	−	4.20530i	−0.564525	−	1.26794i	0.375495	−	0.926825i	$-0.377473\pi$
$12$	1.56190	−	0.748643i	0.450882	−	0.216115i
$13$	1.22280	−	0.794095i	0.339144	−	0.220242i	−0.363818	−	0.931470i	$-0.618527\pi$
$13$	1.22280	−	0.794095i	0.339144	−	0.220242i	0.702962	+	0.711228i	$0.251860\pi$
$14$	−2.80849	−	1.25042i	−0.750601	−	0.334189i
$15$	0.482203	+	3.84285i	0.124504	+	0.992219i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	1.12968	−	0.433645i	0.273989	−	0.105174i	−0.217494	−	0.976062i	$-0.569788\pi$
$17$	1.12968	−	0.433645i	0.273989	−	0.105174i	0.491483	+	0.870887i	$0.336455\pi$
$18$	1.49009	−	2.60377i	0.351218	−	0.613715i
$19$	−1.31548	−	6.18886i	−0.301793	−	1.41982i	−0.823799	−	0.566881i	$-0.808150\pi$
$19$	−1.31548	−	6.18886i	−0.301793	−	1.41982i	0.522007	−	0.852941i	$-0.325184\pi$
$20$	2.23600	+	0.0178354i	0.499984	+	0.00398812i
$21$	−5.23379	+	0.980340i	−1.14211	+	0.213928i
$22$	−2.89693	+	3.57741i	−0.617628	+	0.762707i
$23$	4.55368	+	0.721232i	0.949508	+	0.150387i	0.611931	−	0.790911i	$-0.290393\pi$
$23$	4.55368	+	0.721232i	0.949508	+	0.150387i	0.337576	+	0.941298i	$0.390393\pi$
$24$	−1.37613	−	1.05179i	−0.280902	−	0.214695i
$25$	−1.62074	+	4.73003i	−0.324149	+	0.946006i
$26$	−1.26268	−	0.729011i	−0.247633	−	0.142971i
$27$	−0.437279	−	5.17772i	−0.0841544	−	0.996453i
$28$	0.160895	+	3.07007i	0.0304064	+	0.580188i
$29$	2.25233	−	6.93197i	0.418248	−	1.28724i	−0.491065	−	0.871123i	$-0.663392\pi$
$29$	2.25233	−	6.93197i	0.418248	−	1.28724i	0.909313	−	0.416112i	$-0.136608\pi$
$30$	3.20509	−	2.17426i	0.585166	−	0.396964i
$31$	4.53521	−	3.22983i	0.814549	−	0.580095i
$31$	4.53521	−	3.22983i	0.814549	−	0.580095i
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−0.610421	+	7.94970i	−0.106261	+	1.38386i
$34$	−0.899247	−	0.809686i	−0.154220	−	0.138860i
$35$	−6.62566	−	1.83211i	−1.11994	−	0.309682i
$36$	−2.99646	−	0.145594i	−0.499411	−	0.0242657i
$37$	−0.0863607	+	0.322303i	−0.0141976	+	0.0529862i	−0.972661	−	0.232229i	$-0.925398\pi$
$37$	−0.0863607	+	0.322303i	−0.0141976	+	0.0529862i	0.958464	+	0.285215i	$0.0920649\pi$
$38$	−4.91710	+	3.98179i	−0.797659	+	0.645932i
$39$	−2.51720	+	0.202933i	−0.403075	+	0.0324953i
$40$	−0.999230	−	2.00038i	−0.157992	−	0.316289i
$41$	−4.15468	+	3.74089i	−0.648852	+	0.584229i	−0.926427	−	0.376475i	$-0.877136\pi$
$41$	−4.15468	+	3.74089i	−0.648852	+	0.584229i	0.277575	+	0.960704i	$0.410469\pi$
$42$	3.24958	+	4.21827i	0.501421	+	0.650893i
$43$	−6.14390	+	9.46078i	−0.936936	+	1.44276i	−0.0407036	+	0.999171i	$0.512960\pi$
$43$	−6.14390	+	9.46078i	−0.936936	+	1.44276i	−0.896233	+	0.443584i	$0.853707\pi$
$44$	4.50268	+	0.957074i	0.678804	+	0.144284i
$45$	2.43008	−	6.25258i	0.362255	−	0.932079i
$46$	−1.42470	−	4.38479i	−0.210061	−	0.646502i
$47$	−3.43220	−	1.74879i	−0.500637	−	0.255087i	0.185388	−	0.982665i	$-0.440646\pi$
$47$	−3.43220	−	1.74879i	−0.500637	−	0.255087i	−0.686025	+	0.727578i	$0.740646\pi$
$48$	−0.312397	+	1.70365i	−0.0450906	+	0.245900i
$49$	0.509631	−	2.39763i	0.0728045	−	0.342518i
$50$	4.95029	−	0.703295i	0.700077	−	0.0994609i
$51$	−2.07847	−	0.269609i	−0.291043	−	0.0377528i
$52$	−0.0763069	+	1.45602i	−0.0105819	+	0.201914i
$53$	−1.89825	+	2.34415i	−0.260745	+	0.321994i	−0.890659	−	0.454671i	$-0.849757\pi$
$53$	−1.89825	+	2.34415i	−0.260745	+	0.321994i	0.629914	+	0.776665i	$0.283090\pi$
$54$	−4.41486	+	2.74025i	−0.600787	+	0.372901i
$55$	−5.21755	+	8.87286i	−0.703534	+	1.19642i
$56$	2.66240	−	1.53714i	0.355779	−	0.205409i
$57$	−3.09248	+	10.5135i	−0.409609	+	1.39255i
$58$	−7.19897	+	1.14021i	−0.945271	+	0.149716i
$59$	−7.11008	+	7.89654i	−0.925653	+	1.02804i	0.0738729	+	0.997268i	$0.476464\pi$
$59$	−7.11008	+	7.89654i	−0.925653	+	1.02804i	−0.999526	+	0.0307746i	$0.990203\pi$
$60$	−3.39236	−	1.86866i	−0.437952	−	0.241243i
$61$	−4.75538			−0.608864			−0.304432	−	0.952534i	$-0.598467\pi$
$61$	−4.75538			−0.608864			−0.304432	+	0.952534i	$0.598467\pi$
$62$	−4.93675	−	2.57459i	−0.626968	−	0.326973i
$63$	8.78223	+	2.81658i	1.10646	+	0.354855i
$64$	0.951057	+	0.309017i	0.118882	+	0.0386271i
$65$	−3.03428	−	1.19260i	−0.376356	−	0.147924i
$66$	7.36036	−	3.06520i	0.905997	−	0.377300i
$67$	−2.61979	+	0.701970i	−0.320058	+	0.0857592i	−0.415271	−	0.909698i	$-0.636313\pi$
$67$	−2.61979	+	0.701970i	−0.320058	+	0.0857592i	0.0952134	+	0.995457i	$0.469647\pi$
$68$	−0.313186	+	1.16882i	−0.0379793	+	0.141741i
$69$	−6.34459	−	4.84920i	−0.763798	−	0.583775i
$70$	1.37557	+	6.73526i	0.164412	+	0.805018i
$71$	11.3814	−	1.19624i	1.35073	−	0.141967i	0.598634	−	0.801023i	$-0.295710\pi$
$71$	11.3814	−	1.19624i	1.35073	−	0.141967i	0.752095	+	0.659055i	$0.229044\pi$
$72$	1.23064	+	2.73597i	0.145032	+	0.322437i
$73$	−4.79094	+	12.4808i	−0.560738	+	1.46077i	0.301103	+	0.953592i	$0.402645\pi$
$73$	−4.79094	+	12.4808i	−0.560738	+	1.46077i	−0.861840	+	0.507180i	$0.830688\pi$
$74$	0.326381	−	0.0693743i	0.0379410	−	0.00806460i
$75$	6.36505	−	5.87249i	0.734972	−	0.678097i
$76$	5.78012	+	2.57347i	0.663025	+	0.295198i
$77$	−12.6093	−	6.42475i	−1.43696	−	0.732169i
$78$	1.32360	+	2.15071i	0.149868	+	0.243520i
$79$	3.22004	−	7.23234i	0.362283	−	0.813701i	−0.636806	−	0.771024i	$-0.719745\pi$
$79$	3.22004	−	7.23234i	0.362283	−	0.813701i	0.999089	−	0.0426770i	$-0.0135887\pi$
$80$	−1.32872	+	1.79848i	−0.148555	+	0.201076i
$81$	−3.59788	+	8.24956i	−0.399765	+	0.916618i
$82$	5.21934	+	2.00352i	0.576380	+	0.221251i
$83$	−0.108638	+	2.07295i	−0.0119246	+	0.227535i	0.986166	+	0.165763i	$0.0530086\pi$
$83$	−0.108638	+	2.07295i	−0.0119246	+	0.227535i	−0.998090	+	0.0617724i	$0.980325\pi$
$84$	2.28323	−	4.81045i	0.249121	−	0.524863i
$85$	−2.25742	−	1.49172i	−0.244852	−	0.161800i
$86$	11.2189	+	1.17915i	1.20976	+	0.127151i
$87$	−9.14086	+	8.70750i	−0.980003	+	0.933542i
$88$	−1.19141	−	4.44642i	−0.127005	−	0.473990i
$89$	−5.40139	−	3.92434i	−0.572547	−	0.415979i	0.263483	−	0.964664i	$-0.415129\pi$
$89$	−5.40139	−	3.92434i	−0.572547	−	0.415979i	−0.836029	+	0.548685i	$0.815129\pi$
$90$	−6.67432	+	0.673393i	−0.703535	+	0.0709819i
$91$	1.38513	−	4.26298i	0.145201	−	0.446882i
$92$	−3.26007	+	3.26007i	−0.339886	+	0.339886i
$93$	−9.57040	+	1.18636i	−0.992404	+	0.123019i
$94$			3.85204i			0.397308i
$95$	−9.55034	+	10.4381i	−0.979845	+	1.07092i
$96$	1.65978	−	0.495091i	0.169401	−	0.0505301i
$97$	−2.54744	−	16.0839i	−0.258653	−	1.63307i	−0.685022	−	0.728522i	$-0.740208\pi$
$97$	−2.54744	−	16.0839i	−0.258653	−	1.63307i	0.426369	−	0.904549i	$-0.359792\pi$
$98$	−2.36767	+	0.634415i	−0.239171	+	0.0640856i
$99$	7.47719	−	11.6104i	0.751485	−	1.16689i
$100$	−2.87403	−	4.09145i	−0.287403	−	0.409145i
$101$	−2.99974	−	4.12879i	−0.298486	−	0.410830i	0.633262	−	0.773938i	$-0.281716\pi$
$101$	−2.99974	−	4.12879i	−0.298486	−	0.410830i	−0.931747	+	0.363108i	$0.881716\pi$
$102$	0.703380	+	1.97433i	0.0696450	+	0.195487i
$103$	−0.649370	−	0.0340320i	−0.0639843	−	0.00335328i	0.0203169	−	0.999794i	$-0.493532\pi$
$103$	−0.649370	−	0.0340320i	−0.0639843	−	0.00335328i	−0.0843012	+	0.996440i	$0.526866\pi$
$104$	1.33197	−	0.593031i	0.130610	−	0.0581514i
$105$	8.58684	+	8.24827i	0.837990	+	0.804949i
$106$	2.95044	+	0.627136i	0.286572	+	0.0609128i
$107$	9.82290	−	3.77066i	0.949615	−	0.364523i	0.166249	−	0.986084i	$-0.446834\pi$
$107$	9.82290	−	3.77066i	0.949615	−	0.364523i	0.783366	+	0.621561i	$0.213501\pi$
$108$	4.44589	+	2.68962i	0.427806	+	0.258809i
$109$	−5.50217	+	1.78776i	−0.527012	+	0.171237i	−0.560425	−	0.828205i	$-0.689362\pi$
$109$	−5.50217	+	1.78776i	−0.527012	+	0.171237i	0.0334132	+	0.999442i	$0.489362\pi$
$110$	10.2745	+	0.620677i	0.979634	+	0.0591793i
$111$	0.397026	−	0.419978i	0.0376841	−	0.0398625i
$112$	−2.57831	−	1.67437i	−0.243627	−	0.158213i
$113$	13.5595	+	5.20502i	1.27557	+	0.489647i	0.899491	−	0.436939i	$-0.143937\pi$
$113$	13.5595	+	5.20502i	1.27557	+	0.489647i	0.376083	+	0.926586i	$0.377271\pi$
$114$	10.7716	−	2.01762i	1.00885	−	0.188968i
$115$	−4.60689	−	9.22266i	−0.429595	−	0.860017i
$116$	4.28419	+	5.89669i	0.397778	+	0.547494i
$117$	4.00265	+	1.76386i	0.370046	+	0.163069i
$118$	10.2638	+	2.75017i	0.944857	+	0.253174i
$119$	1.86002	−	3.22166i	0.170508	−	0.295329i
$120$	−0.124888	+	3.87097i	−0.0114007	+	0.353370i
$121$	−6.81850	+	7.57271i	−0.619864	+	0.688428i
$122$	2.15890	+	4.23707i	0.195457	+	0.383606i
$123$	9.41145	−	2.27846i	0.848602	−	0.205442i
$124$	−0.0527410	+	5.56751i	−0.00473628	+	0.499978i
$125$	10.7128	−	3.19951i	0.958178	−	0.286173i
$126$	−1.47746	−	9.10373i	−0.131623	−	0.811024i
$127$	18.6122	−	0.975425i	1.65157	−	0.0865550i	0.796354	−	0.604830i	$-0.206759\pi$
$127$	18.6122	−	0.975425i	1.65157	−	0.0865550i	0.855214	+	0.518275i	$0.173426\pi$
$128$	−0.156434	−	0.987688i	−0.0138270	−	0.0873001i
$129$	17.1532	−	9.35576i	1.51025	−	0.823729i
$130$	0.314915	+	3.24499i	0.0276198	+	0.284604i
$131$	−3.64267	−	0.382860i	−0.318261	−	0.0334506i	−0.0559490	−	0.998434i	$-0.517818\pi$
$131$	−3.64267	−	0.382860i	−0.318261	−	0.0334506i	−0.262312	+	0.964983i	$0.584485\pi$
$132$	−6.07264	−	5.16655i	−0.528556	−	0.449691i
$133$	−15.1165	−	12.2411i	−1.31077	−	1.06144i
$134$	1.81482	+	2.01556i	0.156776	+	0.174118i
$135$	−8.85217	+	7.52590i	−0.761873	+	0.647726i
$136$	1.18361	−	0.251585i	0.101494	−	0.0215732i
$137$	7.36758	−	4.78456i	0.629454	−	0.408773i	−0.190107	−	0.981763i	$-0.560884\pi$
$137$	7.36758	−	4.78456i	0.629454	−	0.408773i	0.819562	+	0.572991i	$0.194217\pi$
$138$	−1.44029	+	7.85456i	−0.122605	+	0.668624i
$139$	7.45869	−	2.42348i	0.632638	−	0.205557i	0.0248947	−	0.999690i	$-0.492075\pi$
$139$	7.45869	−	2.42348i	0.632638	−	0.205557i	0.607743	+	0.794134i	$0.292075\pi$
$140$	5.37667	−	4.28339i	0.454411	−	0.362012i
$141$	3.78949	+	5.49131i	0.319133	+	0.462452i
$142$	−6.23292	−	9.59786i	−0.523055	−	0.805434i
$143$	−5.62888	−	3.65543i	−0.470710	−	0.305683i
$144$	1.87907	−	2.33861i	0.156589	−	0.194884i
$145$	−15.5400	+	4.91258i	−1.29053	+	0.407967i
$146$	13.2955	−	1.39742i	1.10035	−	0.115651i
$147$	−2.75113	+	3.23362i	−0.226910	+	0.266704i
$148$	−0.209987	−	0.259312i	−0.0172608	−	0.0213153i
$149$	−0.442916	−	0.767153i	−0.0362851	−	0.0628476i	0.847313	−	0.531095i	$-0.178219\pi$
$149$	−0.442916	−	0.767153i	−0.0362851	−	0.0628476i	−0.883598	+	0.468247i	$0.844886\pi$
$150$	−8.12210	−	3.00524i	−0.663167	−	0.245377i
$151$	−16.4912	−	11.9816i	−1.34204	−	0.975048i	−0.999366	−	0.0355932i	$-0.988668\pi$
$151$	−16.4912	−	11.9816i	−1.34204	−	0.975048i	−0.342672	−	0.939455i	$-0.611332\pi$
$152$	−0.331136	−	6.31846i	−0.0268587	−	0.512494i
$153$	2.94497	+	2.12256i	0.238087	+	0.171598i
$154$			14.1517i			1.14038i
$155$	−11.7716	−	4.05324i	−0.945520	−	0.325564i
$156$	1.31540	−	2.15574i	0.105316	−	0.172597i
$157$	−8.69209	+	4.42884i	−0.693704	+	0.353460i	−0.765031	−	0.643993i	$-0.777277\pi$
$157$	−8.69209	+	4.42884i	−0.693704	+	0.353460i	0.0713271	+	0.997453i	$0.477277\pi$
$158$	−7.90593	+	0.414332i	−0.628962	+	0.0329625i
$159$	4.82298	−	2.00851i	0.382487	−	0.159285i
$160$	2.20568	+	0.367403i	0.174374	+	0.0290457i
$161$	12.2749	−	7.08689i	0.967394	−	0.558525i
$162$	8.98382	−	0.539486i	0.705835	−	0.0423860i
$163$	−0.624948	+	3.94577i	−0.0489497	+	0.309056i	0.951050	+	0.309036i	$0.100006\pi$
$163$	−0.624948	+	3.94577i	−0.0489497	+	0.309056i	−1.00000		2.02460e-5i	$0.999994\pi$
$164$	−0.584384	−	5.56004i	−0.0456327	−	0.434166i
$165$	15.2575	−	9.22284i	1.18779	−	0.717997i
$166$	1.89633	−	0.844300i	0.147184	−	0.0655304i
$167$	−9.26561	+	14.2678i	−0.716995	+	1.10408i	0.272868	+	0.962051i	$0.412028\pi$
$167$	−9.26561	+	14.2678i	−0.716995	+	1.10408i	−0.989863	+	0.142024i	$0.954639\pi$
$168$	−5.32271	+	0.149526i	−0.410656	+	0.0115362i
$169$	−4.42293	+	9.93405i	−0.340225	+	0.764158i
$170$	−0.304284	+	2.68860i	−0.0233375	+	0.206206i
$171$	13.3706	−	13.4729i	1.02248	−	1.03030i
$172$	−4.04264	−	10.5314i	−0.308248	−	0.803014i
$173$	5.61512	+	8.64653i	0.426910	+	0.657384i	0.985031	−	0.172376i	$-0.0551443\pi$
$173$	5.61512	+	8.64653i	0.426910	+	0.657384i	−0.558121	+	0.829759i	$0.688478\pi$
$174$	11.9083	+	4.19144i	0.902766	+	0.317752i
$175$	5.27900	+	14.4365i	0.399055	+	1.09130i
$176$	−3.42090	+	3.08019i	−0.257860	+	0.232178i
$177$	17.3371	−	6.17658i	1.30314	−	0.464261i
$178$	−1.04443	+	6.59429i	−0.0782836	+	0.494263i
$179$	0.865259	−	8.23239i	0.0646725	−	0.615318i	−0.913401	−	0.407060i	$-0.866554\pi$
$179$	0.865259	−	8.23239i	0.0646725	−	0.615318i	0.978074	−	0.208258i	$-0.0667793\pi$
$180$	3.63008	+	5.64115i	0.270570	+	0.420466i
$181$	−3.67433	+	6.36413i	−0.273111	+	0.473042i	−0.969657	−	0.244470i	$-0.921386\pi$
$181$	−3.67433	+	6.36413i	−0.273111	+	0.473042i	0.696546	+	0.717512i	$0.254719\pi$
$182$	−4.42718	+	0.701196i	−0.328164	+	0.0519761i
$183$	7.24590	+	3.91635i	0.535632	+	0.289505i
$184$	4.38479	+	1.42470i	0.323251	+	0.105031i
$185$	0.698668	−	0.261819i	0.0513671	−	0.0192493i
$186$	5.40192	+	7.98870i	0.396088	+	0.585760i
$187$	−3.93874	−	3.93874i	−0.288029	−	0.288029i
$188$	3.43220	−	1.74879i	0.250319	−	0.127544i
$189$	−11.0621	−	11.5244i	−0.804649	−	0.838278i
$190$	13.6362	+	3.77063i	0.989272	+	0.273550i
$191$	9.28607	+	5.36132i	0.671917	+	0.387931i	0.796803	−	0.604240i	$-0.206523\pi$
$191$	9.28607	+	5.36132i	0.671917	+	0.387931i	−0.124886	+	0.992171i	$0.539856\pi$
$192$	−1.19466	−	1.25411i	−0.0862169	−	0.0905077i
$193$	−11.6779	−	14.4210i	−0.840596	−	1.03805i	−0.998717	−	0.0506300i	$-0.983877\pi$
$193$	−11.6779	−	14.4210i	−0.840596	−	1.03805i	0.158121	−	0.987420i	$-0.449456\pi$
$194$	−13.1743	+	9.57172i	−0.945862	+	0.687209i
$195$	3.64122	+	4.31612i	0.260754	+	0.309084i
$196$	1.64017	+	1.82159i	0.117155	+	0.130114i
$197$	4.16725	−	10.8561i	0.296905	−	0.773463i	−0.701260	−	0.712906i	$-0.747379\pi$
$197$	4.16725	−	10.8561i	0.296905	−	0.773463i	0.998165	−	0.0605574i	$-0.0192878\pi$
$198$	−13.7396	−	1.39119i	−0.976428	−	0.0988674i
$199$	4.47249	−	21.0414i	0.317046	−	1.49159i	−0.474379	−	0.880320i	$-0.657328\pi$
$199$	4.47249	−	21.0414i	0.317046	−	1.49159i	0.791426	−	0.611265i	$-0.209339\pi$
$200$	−2.34073	+	4.41826i	−0.165515	+	0.312418i
$201$	4.56996	+	1.08795i	0.322340	+	0.0767379i
$202$	−2.31693	+	4.54722i	−0.163018	+	0.319941i
$203$	−8.03014	−	20.9192i	−0.563605	−	1.46824i
$204$	1.43981	−	1.52304i	0.100807	−	0.106634i
$205$	12.2068	+	2.69658i	0.852561	+	0.188337i
$206$	0.264485	+	0.594043i	0.0184275	+	0.0413889i
$207$	5.67380	+	12.6140i	0.394356	+	0.876735i
$208$	−1.13310	−	0.917562i	−0.0785660	−	0.0636215i
$209$	−23.5630	+	17.1195i	−1.62989	+	1.18418i
$210$	3.45092	−	11.3956i	0.238136	−	0.786369i
$211$	10.0965	+	17.4876i	0.695069	+	1.20389i	0.970157	+	0.242476i	$0.0779595\pi$
$211$	10.0965	+	17.4876i	0.695069	+	1.20389i	−0.275088	+	0.961419i	$0.588707\pi$
$212$	−0.780690	−	2.91358i	−0.0536180	−	0.200105i
$213$	−18.3274	−	7.55059i	−1.25577	−	0.517358i
$214$	−7.81918	−	7.04042i	−0.534508	−	0.481273i
$215$	25.1995	−	1.11918i	1.71859	−	0.0763275i
$216$	0.378078	−	5.18238i	0.0257250	−	0.352616i
$217$	4.58659	−	16.4909i	0.311358	−	1.11948i
$218$	4.09084	+	4.09084i	0.277067	+	0.277067i
$219$	17.5788	−	15.0718i	1.18787	−	1.01845i
$220$	−4.11149	−	9.43642i	−0.277197	−	0.636203i
$221$	1.03702	−	1.42734i	0.0697577	−	0.0960132i
$222$	−0.554449	−	0.163087i	−0.0372122	−	0.0109457i
$223$	−9.44471	−	2.53070i	−0.632464	−	0.169468i	−0.0716766	−	0.997428i	$-0.522835\pi$
$223$	−9.44471	−	2.53070i	−0.632464	−	0.169468i	−0.560788	+	0.827960i	$0.689502\pi$
$224$	−0.321350	+	3.05744i	−0.0214711	+	0.204284i
$225$	−14.5350	+	3.70606i	−0.968997	+	0.247071i
$226$	−1.51820	−	14.4447i	−0.100989	−	0.960845i
$227$	21.5000	+	1.12677i	1.42701	+	0.0747862i	0.750120	−	0.661302i	$-0.229996\pi$
$227$	21.5000	+	1.12677i	1.42701	+	0.0747862i	0.676886	+	0.736088i	$0.263329\pi$
$228$	−6.68791	−	8.68156i	−0.442917	−	0.574950i
$229$	−3.22926	−	15.1925i	−0.213395	−	1.00395i	−0.946219	−	0.323527i	$-0.895131\pi$
$229$	−3.22926	−	15.1925i	−0.213395	−	1.00395i	0.732824	−	0.680418i	$-0.238202\pi$
$230$	−6.12596	+	8.29177i	−0.403934	+	0.546743i
$231$	13.9219	+	20.1741i	0.915996	+	1.32736i
$232$	3.30900	−	6.49429i	0.217247	−	0.426371i
$233$	−13.2766	+	26.0568i	−0.869779	+	1.70704i	−0.179159	+	0.983820i	$0.557338\pi$
$233$	−13.2766	+	26.0568i	−0.869779	+	1.70704i	−0.690620	+	0.723218i	$0.742662\pi$
$234$	−0.245559	−	4.36717i	−0.0160527	−	0.285491i
$235$	1.27954	+	8.51786i	0.0834678	+	0.555644i
$236$	−2.20924	−	10.3936i	−0.143809	−	0.676569i
$237$	−10.8627	+	8.36820i	−0.705611	+	0.543573i
$238$	−3.71495	−	0.194692i	−0.240805	−	0.0126200i
$239$	−0.240306	−	2.28636i	−0.0155441	−	0.147892i	0.983997	−	0.178185i	$-0.0570226\pi$
$239$	−0.240306	−	2.28636i	−0.0155441	−	0.147892i	−0.999541	+	0.0302931i	$0.990356\pi$
$240$	3.50576	−	1.64611i	0.226296	−	0.106256i
$241$	1.94670	−	18.5216i	0.125398	−	1.19308i	−0.733047	−	0.680178i	$-0.761903\pi$
$241$	1.94670	−	18.5216i	0.125398	−	1.19308i	0.858445	−	0.512905i	$-0.171431\pi$
$242$	9.84287	+	2.63739i	0.632724	+	0.169538i
$243$	12.2762	−	9.60700i	0.787520	−	0.616289i
$244$	2.79514	−	3.84718i	0.178941	−	0.246291i
$245$	−5.02479	+	2.18933i	−0.321022	+	0.139871i
$246$	−6.30283	−	7.35127i	−0.401854	−	0.468700i
$247$	−6.52312	−	6.52312i	−0.415056	−	0.415056i
$248$	4.98464	−	2.48061i	0.316525	−	0.157519i
$249$	1.87274	−	3.06913i	0.118680	−	0.194498i
$250$	−7.71427	−	8.09259i	−0.487894	−	0.511820i
$251$	−15.9509	−	14.3623i	−1.00681	−	0.906539i	−0.0111846	−	0.999937i	$-0.503560\pi$
$251$	−15.9509	−	14.3623i	−1.00681	−	0.906539i	−0.995629	+	0.0933986i	$0.970227\pi$
$252$	−7.44073	+	5.44943i	−0.468722	+	0.343282i
$253$	−5.49294	−	20.4999i	−0.345338	−	1.28882i
$254$	−9.31888	−	16.1408i	−0.584719	−	1.01276i
$255$	2.21117	+	4.13210i	0.138469	+	0.258762i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−0.370734	−	0.300215i	−0.0231258	−	0.0187269i	0.617688	−	0.786423i	$-0.288070\pi$
$257$	−0.370734	−	0.300215i	−0.0231258	−	0.0187269i	−0.640814	+	0.767696i	$0.721403\pi$
$258$	−16.1234	−	11.0362i	−1.00380	−	0.687082i
$259$	0.417231	+	0.937116i	0.0259255	+	0.0582296i
$260$	2.74834	−	1.75379i	0.170445	−	0.108765i
$261$	21.0993	−	5.73979i	1.30602	−	0.355284i
$262$	1.31261	+	3.41946i	0.0810931	+	0.211255i
$263$	8.34152	−	16.3711i	0.514360	−	1.00949i	−0.477072	−	0.878864i	$-0.658302\pi$
$263$	8.34152	−	16.3711i	0.514360	−	1.00949i	0.991432	−	0.130624i	$-0.0416981\pi$
$264$	−1.84651	+	7.75633i	−0.113645	+	0.477369i
$265$	6.73250	+	0.406707i	0.413574	+	0.0249838i
$266$	−4.04416	+	19.0263i	−0.247964	+	1.16658i
$267$	4.99831	+	10.4280i	0.305892	+	0.638184i
$268$	0.971966	−	2.53206i	0.0593723	−	0.154670i
$269$	−0.178493	−	0.198236i	−0.0108829	−	0.0120867i	0.737679	−	0.675152i	$-0.235922\pi$
$269$	−0.178493	−	0.198236i	−0.0108829	−	0.0120867i	−0.748562	+	0.663065i	$0.769255\pi$
$270$	10.7244	+	4.47065i	0.652668	+	0.272075i
$271$	15.6478	−	11.3688i	0.950539	−	0.690607i	−0.000395423	−	1.00000i	$-0.500126\pi$
$271$	15.6478	−	11.3688i	0.950539	−	0.690607i	0.950934	+	0.309393i	$0.100126\pi$
$272$	−0.761513	−	0.940390i	−0.0461735	−	0.0570195i
$273$	−5.62139	+	5.35488i	−0.340222	+	0.324092i
$274$	−7.60788	−	4.39241i	−0.459609	−	0.265355i
$275$	22.9257	−	2.04041i	1.38247	−	0.123042i
$276$	7.65234	−	2.28259i	0.460617	−	0.137396i
$277$	12.0126	−	6.12074i	0.721769	−	0.367760i	−0.0542006	−	0.998530i	$-0.517261\pi$
$277$	12.0126	−	6.12074i	0.721769	−	0.367760i	0.775969	+	0.630770i	$0.217261\pi$
$278$	−5.54551	−	5.54551i	−0.332598	−	0.332598i
$279$	15.5597	+	6.07414i	0.931536	+	0.363649i
$280$	−6.25748	−	2.84603i	−0.373956	−	0.170083i
$281$	−12.9239	−	4.19924i	−0.770977	−	0.250506i	−0.102994	−	0.994682i	$-0.532842\pi$
$281$	−12.9239	−	4.19924i	−0.770977	−	0.250506i	−0.667983	+	0.744176i	$0.732842\pi$
$282$	3.17240	−	5.86946i	0.188914	−	0.349521i
$283$	5.47932	−	0.867839i	0.325712	−	0.0515877i	0.00856264	−	0.999963i	$-0.497274\pi$
$283$	5.47932	−	0.867839i	0.325712	−	0.0515877i	0.317149	+	0.948376i	$0.397274\pi$
$284$	−5.72207	+	9.91091i	−0.339542	+	0.588104i
$285$	23.1485	−	8.03949i	1.37120	−	0.476218i
$286$	−0.701560	+	6.67490i	−0.0414841	+	0.394695i
$287$	−2.68868	+	16.9757i	−0.158708	+	1.00204i
$288$	−2.93680	−	0.612552i	−0.173052	−	0.0360950i
$289$	−11.5453	+	10.3955i	−0.679137	+	0.611497i
$290$	11.4322	+	11.6160i	0.671320	+	0.682116i
$291$	−9.36449	+	26.6054i	−0.548956	+	1.55964i
$292$	−7.28116	−	11.2120i	−0.426098	−	0.656133i
$293$	9.70891	+	25.2926i	0.567200	+	1.47761i	0.854338	+	0.519718i	$0.173963\pi$
$293$	9.70891	+	25.2926i	0.567200	+	1.47761i	−0.287137	+	0.957889i	$0.592704\pi$
$294$	4.13016	+	0.983248i	0.240876	+	0.0573442i
$295$	23.6094	+	2.67201i	1.37459	+	0.155570i
$296$	−0.135717	+	0.304825i	−0.00788837	+	0.0177176i
$297$	−20.9551	+	11.5332i	−1.21594	+	0.669226i
$298$	−0.482459	+	0.742921i	−0.0279481	+	0.0430363i
$299$	6.14096	−	2.73413i	0.355141	−	0.158119i
$300$	1.00966	+	8.60120i	0.0582930	+	0.496590i
$301$	3.62504	+	34.4900i	0.208944	+	1.98797i
$302$	−3.18881	+	20.1333i	−0.183495	+	1.15854i
$303$	1.17047	+	8.76163i	0.0672419	+	0.503342i
$304$	−5.47945	+	3.16356i	−0.314268	+	0.181443i
$305$	6.18131	+	8.65214i	0.353941	+	0.495420i
$306$	0.554221	−	3.58761i	0.0316827	−	0.205090i
$307$	14.1444	−	0.741277i	0.807264	−	0.0423069i	0.355761	−	0.934577i	$-0.384222\pi$
$307$	14.1444	−	0.741277i	0.807264	−	0.0423069i	0.451502	+	0.892270i	$0.350888\pi$
$308$	12.6093	−	6.42475i	0.718481	−	0.366084i
$309$	0.961435	+	0.586652i	0.0546941	+	0.0333735i
$310$	1.73274	+	12.3287i	0.0984132	+	0.700225i
$311$		−	30.3142i		−	1.71896i	−0.511169	−	0.859480i	$-0.670787\pi$
$311$		−	30.3142i		−	1.71896i	0.511169	−	0.859480i	$-0.329213\pi$
$312$	−2.51795	−	0.193342i	−0.142551	−	0.0109459i
$313$	0.157968	+	3.01420i	0.00892885	+	0.170373i	0.999454	+	0.0330411i	$0.0105192\pi$
$313$	0.157968	+	3.01420i	0.00892885	+	0.170373i	−0.990525	+	0.137332i	$0.956147\pi$
$314$	7.89225	+	5.73406i	0.445386	+	0.323592i
$315$	−6.29104	−	19.6399i	−0.354460	−	1.10658i
$316$	3.95839	+	6.85613i	0.222677	+	0.385687i
$317$	12.1296	+	14.9788i	0.681268	+	0.841296i	0.994095	−	0.108514i	$-0.0346093\pi$
$317$	12.1296	+	14.9788i	0.681268	+	0.841296i	−0.312827	+	0.949810i	$0.601276\pi$
$318$	−3.97918	−	3.38546i	−0.223142	−	0.189847i
$319$	−33.3681	+	3.50713i	−1.86825	+	0.196361i
$320$	−0.673999	−	2.13207i	−0.0376777	−	0.119186i
$321$	−18.0728	−	2.34432i	−1.00872	−	0.130847i
$322$	−11.8871	−	7.71960i	−0.662444	−	0.430196i
$323$	−4.16985	−	6.42101i	−0.232017	−	0.357275i
$324$	−4.55925	−	7.75972i	−0.253292	−	0.431095i
$325$	1.77425	+	7.07090i	0.0984176	+	0.392223i
$326$	3.79943	−	1.23451i	0.210431	−	0.0683731i
$327$	9.85613	+	1.80732i	0.545045	+	0.0999448i
$328$	−4.68873	+	3.04490i	−0.258892	+	0.168126i
$329$	−11.5835	+	2.46214i	−0.638618	+	0.135742i
$330$	−15.1444	−	9.40743i	−0.833670	−	0.517862i
$331$	21.8886	+	24.3097i	1.20310	+	1.33618i	0.927003	+	0.375054i	$0.122376\pi$
$331$	21.8886	+	24.3097i	1.20310	+	1.33618i	0.276101	+	0.961129i	$0.410957\pi$
$332$	−1.61319	−	1.30634i	−0.0885354	−	0.0716946i
$333$	−0.950838	+	0.312956i	−0.0521056	+	0.0171499i
$334$	16.9192	+	1.77828i	0.925777	+	0.0973031i
$335$	4.68254	+	3.85409i	0.255835	+	0.210571i
$336$	2.54969	+	4.67468i	0.139097	+	0.255025i
$337$	−1.18274	−	7.46756i	−0.0644282	−	0.406784i	−0.998734	−	0.0503102i	$-0.983979\pi$
$337$	−1.18274	−	7.46756i	−0.0644282	−	0.406784i	0.934305	−	0.356474i	$-0.116021\pi$
$338$	10.8593	−	0.569110i	0.590666	−	0.0309555i
$339$	−16.3744	−	19.0982i	−0.889335	−	1.03727i
$340$	2.53371	−	0.949481i	0.137409	−	0.0514928i
$341$	−22.0738	−	13.0246i	−1.19536	−	0.705324i
$342$	−18.0746	−	5.79676i	−0.977361	−	0.313453i
$343$	6.34874	+	12.4601i	0.342800	+	0.672783i
$344$	−7.54825	+	8.38318i	−0.406975	+	0.451991i
$345$	−0.575789	+	17.8469i	−0.0309994	+	0.960844i
$346$	5.15490	−	8.92855i	0.277129	−	0.480002i
$347$	−21.8247	−	5.84790i	−1.17161	−	0.313932i	−0.380016	−	0.924980i	$-0.624082\pi$
$347$	−21.8247	−	5.84790i	−1.17161	−	0.313932i	−0.791594	+	0.611048i	$0.790748\pi$
$348$	−1.67165	−	12.5132i	−0.0896101	−	0.670780i
$349$	13.9502	+	19.2009i	0.746740	+	1.02780i	0.998202	+	0.0599320i	$0.0190884\pi$
$349$	13.9502	+	19.2009i	0.746740	+	1.02780i	−0.251463	+	0.967867i	$0.580912\pi$
$350$	10.4664	−	11.2576i	0.559452	−	0.601746i
$351$	−4.64631	−	5.98407i	−0.248002	−	0.319406i
$352$	4.29752	+	1.64966i	0.229059	+	0.0879274i
$353$	3.13354	+	2.03495i	0.166782	+	0.108309i	0.625331	−	0.780360i	$-0.284964\pi$
$353$	3.13354	+	2.03495i	0.166782	+	0.108309i	−0.458549	+	0.888669i	$0.651631\pi$
$354$	−13.3743	−	12.6434i	−0.710834	−	0.671988i
$355$	−16.9707	−	19.1529i	−0.900713	−	1.01653i
$356$	6.34972	−	2.06315i	0.336534	−	0.109347i
$357$	−5.48741	+	3.37708i	−0.290424	+	0.178734i
$358$	−7.72793	+	2.96647i	−0.408434	+	0.156783i
$359$	−2.45547	−	0.521926i	−0.129595	−	0.0275462i	0.142658	−	0.989772i	$-0.454435\pi$
$359$	−2.45547	−	0.521926i	−0.129595	−	0.0275462i	−0.272252	+	0.962226i	$0.587769\pi$
$360$	3.37828	−	5.79545i	0.178051	−	0.305447i
$361$	−19.2142	+	8.55470i	−1.01127	+	0.450248i
$362$	7.33860	+	0.384600i	0.385708	+	0.0202141i
$363$	16.6261	−	5.92329i	0.872646	−	0.310892i
$364$	2.63467	+	3.62631i	0.138094	+	0.190070i
$365$	28.9357	−	7.50645i	1.51456	−	0.392906i
$366$	0.199924	−	8.23413i	0.0104502	−	0.430405i
$367$	−7.23298	+	1.93807i	−0.377558	+	0.101166i	−0.442607	−	0.896716i	$-0.645946\pi$
$367$	−7.23298	+	1.93807i	−0.377558	+	0.101166i	0.0650488	+	0.997882i	$0.479280\pi$
$368$	−0.721232	−	4.55368i	−0.0375968	−	0.237377i
$369$	−16.2169	−	4.27917i	−0.844220	−	0.222765i
$370$	−0.550471	−	0.503654i	−0.0286176	−	0.0261837i
$371$			9.27312i			0.481436i
$372$	4.66556	−	8.43994i	0.241898	−	0.437590i
$373$	−18.8351	+	18.8351i	−0.975246	+	0.975246i	−0.999701	−	0.0244553i	$-0.992215\pi$
$373$	−18.8351	+	18.8351i	−0.975246	+	0.975246i	0.0244553	+	0.999701i	$0.492215\pi$
$374$	−1.72129	+	5.29759i	−0.0890058	+	0.273932i
$375$	−18.9583	−	3.94744i	−0.979003	−	0.203845i
$376$	−3.11637	−	2.26417i	−0.160714	−	0.116766i
$377$	−2.75049	−	10.2650i	−0.141658	−	0.528673i
$378$	−5.24624	+	15.0884i	−0.269837	+	0.776062i
$379$	28.1130	+	2.95479i	1.44407	+	0.151778i	0.793916	−	0.608028i	$-0.208039\pi$
$379$	28.1130	+	2.95479i	1.44407	+	0.151778i	0.650151	+	0.759805i	$0.274706\pi$
$380$	−2.83104	−	13.8617i	−0.145229	−	0.711092i
$381$	−29.1633	−	13.8420i	−1.49408	−	0.709150i
$382$	0.561179	−	10.7079i	0.0287124	−	0.547866i
$383$	14.9597	+	5.74250i	0.764406	+	0.293428i	0.709163	−	0.705045i	$-0.249073\pi$
$383$	14.9597	+	5.74250i	0.764406	+	0.293428i	0.0552436	+	0.998473i	$0.482406\pi$
$384$	−0.575060	+	1.63380i	−0.0293459	+	0.0833746i
$385$	4.70080	+	31.2931i	0.239575	+	1.59485i
$386$	−7.54758	+	16.9521i	−0.384162	+	0.862841i
$387$	−33.8418	+	0.128920i	−1.72028	+	0.00655339i
$388$	14.5095	+	7.39295i	0.736608	+	0.375320i
$389$	−12.8295	−	5.71205i	−0.650480	−	0.289612i	0.0548468	−	0.998495i	$-0.482533\pi$
$389$	−12.8295	−	5.71205i	−0.650480	−	0.289612i	−0.705327	+	0.708883i	$0.749200\pi$
$390$	2.19261	−	5.20383i	0.111027	−	0.263506i
$391$	5.45698	−	1.15992i	0.275971	−	0.0586595i
$392$	0.878428	−	2.28838i	0.0443673	−	0.115581i
$393$	5.23512	+	3.58334i	0.264077	+	0.180756i
$394$	−11.5647	+	1.21550i	−0.582622	+	0.0612361i
$395$	−17.3444	+	3.54232i	−0.872692	+	0.178233i
$396$	4.99807	+	12.8736i	0.251163	+	0.646924i
$397$	1.49436	−	5.57703i	0.0749999	−	0.279903i	−0.918233	−	0.396040i	$-0.870384\pi$
$397$	1.49436	−	5.57703i	0.0749999	−	0.279903i	0.993233	+	0.116136i	$0.0370509\pi$
$398$	−20.7785	+	5.56758i	−1.04153	+	0.279078i
$399$	12.9521	+	31.1016i	0.648418	+	1.55703i
$400$	4.99936	+	0.0797599i	0.249968	+	0.00398799i
$401$	−33.8581	−	11.0012i	−1.69079	−	0.549372i	−0.703838	−	0.710361i	$-0.748532\pi$
$401$	−33.8581	−	11.0012i	−1.69079	−	0.549372i	−0.986956	+	0.160988i	$0.948532\pi$
$402$	−1.10535	−	4.56578i	−0.0551298	−	0.227720i
$403$	2.98086	−	7.55083i	0.148487	−	0.376134i
$404$	5.10347			0.253907
$405$	19.6863	−	4.17711i	0.978222	−	0.207562i
$406$	−14.9936	+	16.6520i	−0.744118	+	0.826427i
$407$	1.51707	−	0.240281i	0.0751985	−	0.0119103i
$408$	−2.01070	−	0.591433i	−0.0995445	−	0.0292803i
$409$	5.96632	−	3.44466i	0.295015	−	0.170327i	−0.345186	−	0.938534i	$-0.612184\pi$
$409$	5.96632	−	3.44466i	0.295015	−	0.170327i	0.640202	+	0.768207i	$0.278851\pi$
$410$	−3.13911	−	12.1006i	−0.155030	−	0.597605i
$411$	−15.1666	+	1.22271i	−0.748111	+	0.0603116i
$412$	0.409222	−	0.505348i	0.0201609	−	0.0248967i
$413$	−1.70965	+	32.6220i	−0.0841263	+	1.60523i
$414$	8.66332	−	10.7820i	0.425779	−	0.529908i
$415$	3.91282	−	2.49687i	0.192073	−	0.122567i
$416$	−0.303140	+	1.42616i	−0.0148626	+	0.0699232i
$417$	−13.3609	−	2.44998i	−0.654286	−	0.119976i
$418$	25.9510	+	13.2227i	1.26930	+	0.646743i
$419$	−1.31441	−	4.04534i	−0.0642132	−	0.197628i	0.913803	−	0.406158i	$-0.133132\pi$
$419$	−1.31441	−	4.04534i	−0.0642132	−	0.197628i	−0.978016	+	0.208531i	$0.933132\pi$
$420$	−11.7202	+	2.09869i	−0.571888	+	0.102406i
$421$	−2.99211	−	0.635993i	−0.145827	−	0.0309964i	0.134420	−	0.990924i	$-0.457083\pi$
$421$	−2.99211	−	0.635993i	−0.145827	−	0.0309964i	−0.280247	+	0.959928i	$0.590416\pi$
$422$	10.9979	−	16.9352i	0.535367	−	0.824393i
$423$	−1.25172	−	11.4881i	−0.0608606	−	0.558572i
$424$	−2.24159	+	2.01834i	−0.108861	+	0.0980191i
$425$	0.220225	+	6.04627i	0.0106825	+	0.293287i
$426$	1.59284	+	19.7577i	0.0771733	+	0.957265i
$427$	−11.3614	+	9.20026i	−0.549815	+	0.445232i
$428$	−2.72323	+	10.1632i	−0.131632	+	0.491258i
$429$	5.56639	+	10.2056i	0.268748	+	0.492732i
$430$	−12.4375	−	21.9449i	−0.599792	−	1.05828i
$431$	−3.69749	−	3.32924i	−0.178102	−	0.160364i	0.575258	−	0.817972i	$-0.304902\pi$
$431$	−3.69749	−	3.32924i	−0.178102	−	0.160364i	−0.753360	+	0.657608i	$0.771568\pi$
$432$	−4.78918	+	2.01588i	−0.230419	+	0.0969891i
$433$	3.36017	−	3.36017i	0.161479	−	0.161479i	−0.621742	−	0.783222i	$-0.713575\pi$
$433$	3.36017	−	3.36017i	0.161479	−	0.161479i	0.783222	+	0.621742i	$0.213575\pi$
$434$	−16.7758	+	3.40004i	−0.805263	+	0.163207i
$435$	27.7246	+	5.31276i	1.32929	+	0.254728i
$436$	1.78776	−	5.50217i	0.0856183	−	0.263506i
$437$	−1.52668	−	29.1309i	−0.0730312	−	1.39352i
$438$	−21.4097	−	8.82043i	−1.02299	−	0.421456i
$439$	2.68991	+	1.55302i	0.128382	+	0.0741216i	0.562816	−	0.826582i	$-0.309718\pi$
$439$	2.68991	+	1.55302i	0.128382	+	0.0741216i	−0.434433	+	0.900704i	$0.643051\pi$
$440$	−6.54133	+	7.94741i	−0.311846	+	0.378878i
$441$	6.85506	−	2.66142i	0.326432	−	0.126734i
$442$	−1.74257	−	0.275995i	−0.0828854	−	0.0131278i
$443$	−0.590151	+	0.728776i	−0.0280389	+	0.0346252i	−0.790973	−	0.611852i	$-0.790425\pi$
$443$	−0.590151	+	0.728776i	−0.0280389	+	0.0346252i	0.762934	+	0.646477i	$0.223758\pi$
$444$	0.106403	+	0.568058i	0.00504966	+	0.0269588i
$445$	−0.119078	+	14.9286i	−0.00564484	+	0.707684i
$446$	2.03294	+	9.56421i	0.0962623	+	0.452878i
$447$	0.0430848	+	1.53370i	0.00203784	+	0.0725416i
$448$	2.87009	−	1.10172i	0.135599	−	0.0520515i
$449$	0.349337	+	1.07515i	0.0164862	+	0.0507394i	0.958961	−	0.283537i	$-0.0915080\pi$
$449$	0.349337	+	1.07515i	0.0164862	+	0.0507394i	−0.942475	+	0.334277i	$0.891508\pi$
$450$	9.90086	+	11.2682i	0.466731	+	0.531189i
$451$	23.5104	+	10.4675i	1.10706	+	0.492896i
$452$	−12.1811	+	7.91047i	−0.572948	+	0.372077i
$453$	15.2606	+	31.8383i	0.717004	+	1.49589i
$454$	−8.75684	−	19.6682i	−0.410979	−	0.923074i
$455$	−9.55672	+	3.02111i	−0.448026	+	0.141632i
$456$	−4.69908	+	9.90032i	−0.220055	+	0.463625i
$457$	32.3706	+	5.12700i	1.51423	+	0.239831i	0.857575	−	0.514359i	$-0.171970\pi$
$457$	32.3706	+	5.12700i	1.51423	+	0.239831i	0.656657	+	0.754190i	$0.271970\pi$
$458$	−12.0705	+	9.77452i	−0.564018	+	0.456733i
$459$	−2.73928	−	5.65957i	−0.127859	−	0.264166i
$460$	10.1691	+	1.69389i	0.474139	+	0.0789780i
$461$	17.4160	−	23.9711i	0.811144	−	1.11644i	−0.180002	−	0.983666i	$-0.557610\pi$
$461$	17.4160	−	23.9711i	0.811144	−	1.11644i	0.991146	−	0.132778i	$-0.0423896\pi$
$462$	11.6548	−	21.5634i	0.542232	−	1.00322i
$463$	−0.979150	−	1.92169i	−0.0455050	−	0.0893085i	0.867134	−	0.498074i	$-0.165959\pi$
$463$	−0.979150	−	1.92169i	−0.0455050	−	0.0893085i	−0.912639	+	0.408766i	$0.865959\pi$
$464$	−7.28871			−0.338370
$465$	14.5987	+	15.8707i	0.676996	+	0.735986i
$466$	29.2442			1.35471
$467$	−17.7196	−	34.7766i	−0.819964	−	1.60927i	−0.792677	−	0.609642i	$-0.791313\pi$
$467$	−17.7196	−	34.7766i	−0.819964	−	1.60927i	−0.0272873	−	0.999628i	$-0.508687\pi$
$468$	−3.77969	+	2.20145i	−0.174716	+	0.101762i
$469$	−4.90099	+	6.74564i	−0.226307	+	0.311485i
$470$	7.00857	−	5.00710i	0.323281	−	0.230961i
$471$	16.8918	+	0.410132i	0.778333	+	0.0188979i
$472$	−8.25783	+	6.68706i	−0.380098	+	0.307797i
$473$	51.2887	+	8.12334i	2.35826	+	0.373511i
$474$	12.3877	+	5.87970i	0.568986	+	0.270063i
$475$	31.4056	+	3.80829i	1.44099	+	0.174736i
$476$	1.51308	+	3.39843i	0.0693519	+	0.155767i
$477$	−9.00303	−	0.911595i	−0.412221	−	0.0417391i
$478$	−1.92806	+	1.25210i	−0.0881875	+	0.0572696i
$479$	−12.7274	−	5.66659i	−0.581529	−	0.258913i	0.0948205	−	0.995494i	$-0.469772\pi$
$479$	−12.7274	−	5.66659i	−0.581529	−	0.258913i	−0.676349	+	0.736581i	$0.736439\pi$
$480$	−3.05827	−	2.37634i	−0.139590	−	0.108464i
$481$	0.150337	+	0.462690i	0.00685478	+	0.0210969i
$482$	−17.3867	+	6.67412i	−0.791941	+	0.303998i
$483$	−24.5400	+	0.689380i	−1.11661	+	0.0313679i
$484$	−2.11864	−	9.96741i	−0.0963018	−	0.453064i
$485$	−25.9524	+	25.5417i	−1.17844	+	1.15979i
$486$	−14.1332	−	6.57670i	−0.641094	−	0.298325i
$487$	−10.4765	+	12.9374i	−0.474735	+	0.586249i	−0.957113	−	0.289714i	$-0.906440\pi$
$487$	−10.4765	+	12.9374i	−0.474735	+	0.586249i	0.482378	+	0.875963i	$0.339773\pi$
$488$	−4.69683	−	0.743905i	−0.212616	−	0.0336750i
$489$	4.20184	−	5.49759i	0.190014	−	0.248610i
$490$	4.23191	+	3.48319i	0.191178	+	0.157354i
$491$	−12.3263	−	7.11662i	−0.556280	−	0.321169i	0.195371	−	0.980729i	$-0.437409\pi$
$491$	−12.3263	−	7.11662i	−0.556280	−	0.321169i	−0.751651	+	0.659561i	$0.770742\pi$
$492$	−3.68860	+	8.95327i	−0.166295	+	0.403644i
$493$	−0.461590	−	8.80766i	−0.0207890	−	0.396677i
$494$	−2.85071	+	8.77358i	−0.128259	+	0.394742i
$495$	−30.8438	+	1.48761i	−1.38633	+	0.0668631i
$496$	−4.47321	−	3.31517i	−0.200853	−	0.148856i
$497$	24.8778	−	24.8778i	1.11592	−	1.11592i
$498$	−3.58482	−	0.275262i	−0.160640	−	0.0123348i
$499$	14.3607	+	12.9304i	0.642871	+	0.578844i	0.924736	−	0.380610i	$-0.124286\pi$
$499$	14.3607	+	12.9304i	0.642871	+	0.578844i	−0.281864	+	0.959454i	$0.590953\pi$
$500$	−3.70834	+	10.5474i	−0.165842	+	0.471695i
$501$	25.8687	−	14.1094i	1.15573	−	0.630362i
$502$	−5.55531	+	20.7327i	−0.247946	+	0.925346i
$503$	25.2066	−	20.4119i	1.12391	−	0.910121i	0.127253	−	0.991870i	$-0.459384\pi$
$503$	25.2066	−	20.4119i	1.12391	−	0.910121i	0.996653	+	0.0817493i	$0.0260507\pi$
$504$	8.23350	+	4.15575i	0.366749	+	0.185112i
$505$	−3.61286	+	10.8247i	−0.160770	+	0.481693i
$506$	−15.7718	+	14.2010i	−0.701144	+	0.631313i
$507$	14.9206	−	11.4942i	0.662649	−	0.510477i
$508$	−10.1509	+	15.6309i	−0.450371	+	0.693511i
$509$	37.1904	+	7.90505i	1.64843	+	0.350385i	0.936176	−	0.351532i	$-0.114339\pi$
$509$	37.1904	+	7.90505i	1.64843	+	0.350385i	0.712258	+	0.701918i	$0.247673\pi$
$510$	2.67788	−	3.84610i	0.118578	−	0.170308i
$511$	12.7004	+	39.0878i	0.561833	+	1.72914i
$512$	0.891007	+	0.453990i	0.0393773	+	0.0200637i
$513$	−31.4690	+	9.51747i	−1.38939	+	0.420206i
$514$	−0.0991834	+	0.466621i	−0.00437479	+	0.0205818i
$515$	0.782168	+	1.22573i	0.0344665	+	0.0540120i
$516$	−2.51341	+	19.3764i	−0.110647	+	0.852998i
$517$	−0.928021	+	17.7077i	−0.0408143	+	0.778783i
$518$	0.645558	−	0.797197i	0.0283642	−	0.0350268i
$519$	−1.43496	−	17.7994i	−0.0629877	−	0.781305i
$520$	−2.81035	−	1.65259i	−0.123242	−	0.0724707i
$521$	−11.8996	+	6.87025i	−0.521332	+	0.300991i	−0.737479	−	0.675370i	$-0.763984\pi$
$521$	−11.8996	+	6.87025i	−0.521332	+	0.300991i	0.216148	+	0.976361i	$0.430651\pi$
$522$	−14.6931	−	16.1938i	−0.643099	−	0.708785i
$523$	30.5254	−	4.83475i	1.33478	−	0.211409i	0.552074	−	0.833795i	$-0.313837\pi$
$523$	30.5254	−	4.83475i	1.33478	−	0.211409i	0.782710	+	0.622386i	$0.213837\pi$
$524$	2.45085	−	2.72194i	0.107066	−	0.118909i
$525$	3.84559	−	26.3448i	0.167835	−	1.14978i
$526$	−18.3738			−0.801134
$527$	3.72276	−	5.61537i	0.162166	−	0.244609i
$528$	7.74924	−	1.87605i	0.337242	−	0.0816444i
$529$	−1.65848	−	0.538872i	−0.0721078	−	0.0234292i
$530$	−2.69411	−	6.18335i	−0.117025	−	0.268587i
$531$	−31.5038	−	4.86677i	−1.36715	−	0.211200i
$532$	18.7886	−	5.03438i	0.814588	−	0.218268i
$533$	−2.10972	+	7.87357i	−0.0913819	+	0.341042i
$534$	7.02224	−	9.18775i	0.303882	−	0.397593i
$535$	−19.6289	−	12.9709i	−0.848629	−	0.560780i
$536$	−2.69734	+	0.283502i	−0.116508	+	0.0122454i
$537$	−8.09830	+	11.8313i	−0.349468	+	0.510559i
$538$	−0.0955959	+	0.249036i	−0.00412143	+	0.0107367i
$539$	−11.0369	+	2.34597i	−0.475394	+	0.101048i
$540$	−0.885408	−	11.5852i	−0.0381019	−	0.498546i
$541$	5.77332	+	2.57045i	0.248214	+	0.110512i	0.527073	−	0.849820i	$-0.323289\pi$
$541$	5.77332	+	2.57045i	0.248214	+	0.110512i	−0.278859	+	0.960332i	$0.589956\pi$
$542$	−17.2337	−	8.78099i	−0.740249	−	0.377176i
$543$	10.8399	−	6.67116i	0.465187	−	0.286287i
$544$	−0.492174	+	1.10544i	−0.0211018	+	0.0473954i
$545$	10.4048	+	7.68704i	0.445691	+	0.329277i
$546$	7.32329	+	2.57763i	0.313408	+	0.110312i
$547$	−33.9691	−	13.0395i	−1.45241	−	0.557529i	−0.501000	−	0.865447i	$-0.667034\pi$
$547$	−33.9691	−	13.0395i	−1.45241	−	0.557529i	−0.951413	+	0.307918i	$0.900368\pi$
$548$	−0.459762	+	8.77279i	−0.0196401	+	0.374755i
$549$	−7.81541	−	11.9349i	−0.333554	−	0.509369i
$550$	−12.2261	−	19.5006i	−0.521322	−	0.831510i
$551$	−45.8639	−	4.82050i	−1.95387	−	0.205360i
$552$	−5.50789	−	5.78201i	−0.234431	−	0.246099i
$553$	−6.29924	−	23.5091i	−0.267871	−	0.999707i
$554$	−10.9072	−	7.92457i	−0.463404	−	0.336683i
$555$	−1.28020	−	0.176456i	−0.0543416	−	0.00749014i
$556$	−2.42348	+	7.45869i	−0.102778	+	0.316319i
$557$	9.27885	−	9.27885i	0.393158	−	0.393158i	−0.482654	−	0.875811i	$-0.660327\pi$
$557$	9.27885	−	9.27885i	0.393158	−	0.393158i	0.875811	+	0.482654i	$0.160327\pi$
$558$	−1.65187	−	16.6214i	−0.0699291	−	0.703640i
$559$			16.4475i			0.695654i
$560$	0.305006	+	6.86753i	0.0128888	+	0.290206i
$561$	2.75776	+	9.24535i	0.116433	+	0.390339i
$562$	2.12579	+	13.4217i	0.0896711	+	0.566161i
$563$	−41.4531	+	11.1073i	−1.74704	+	0.468118i	−0.983990	−	0.178222i	$-0.942965\pi$
$563$	−41.4531	+	11.1073i	−1.74704	+	0.468118i	−0.763049	+	0.646340i	$0.776299\pi$
$564$	−6.66997	−	0.161947i	−0.280856	−	0.00681918i
$565$	−8.15523	−	31.4366i	−0.343093	−	1.32255i
$566$	−3.26081	−	4.48812i	−0.137062	−	0.188650i
$567$	7.36455	+	26.6704i	0.309282	+	1.12005i
$568$	11.4285	+	0.598940i	0.479527	+	0.0251310i
$569$	−26.6458	+	11.8635i	−1.11705	+	0.497343i	−0.880391	−	0.474249i	$-0.842720\pi$
$569$	−26.6458	+	11.8635i	−1.11705	+	0.497343i	−0.236660	+	0.971592i	$0.576053\pi$
$570$	−17.6725	−	16.9756i	−0.740218	−	0.711031i
$571$	−31.9523	−	6.79166i	−1.33716	−	0.284222i	−0.516818	−	0.856095i	$-0.672884\pi$
$571$	−31.9523	−	6.79166i	−1.33716	−	0.284222i	−0.820342	+	0.571873i	$0.806217\pi$
$572$	6.26588	−	2.40525i	0.261990	−	0.100568i
$573$	−9.73406	−	15.8168i	−0.406646	−	0.660758i
$574$	16.3461	−	5.31116i	0.682272	−	0.221684i
$575$	−10.7918	+	20.3701i	−0.450049	+	0.849492i
$576$	0.787491	+	2.89480i	0.0328121	+	0.120617i
$577$	−1.52371	−	0.989508i	−0.0634328	−	0.0411937i	0.512533	−	0.858668i	$-0.328707\pi$
$577$	−1.52371	−	0.989508i	−0.0634328	−	0.0411937i	−0.575966	+	0.817474i	$0.695374\pi$
$578$	14.5039	+	5.56752i	0.603282	+	0.231578i
$579$	5.91735	+	31.5913i	0.245917	+	1.31289i
$580$	5.15985	−	15.4597i	0.214251	−	0.641929i
$581$	3.75099	+	5.16279i	0.155617	+	0.214189i
$582$	27.9570	−	3.73480i	1.15886	−	0.154812i
$583$	13.4120	+	3.59373i	0.555467	+	0.148837i
$584$	−6.68439	+	11.5777i	−0.276602	+	0.479089i
$585$	−1.99364	−	9.57536i	−0.0824269	−	0.395893i
$586$	18.1281	−	20.1333i	0.748865	−	0.831698i
$587$	17.0049	+	33.3739i	0.701866	+	1.37749i	0.916197	+	0.400728i	$0.131243\pi$
$587$	17.0049	+	33.3739i	0.701866	+	1.37749i	−0.214331	+	0.976761i	$0.568757\pi$
$588$	−0.998974	−	4.12639i	−0.0411970	−	0.170169i
$589$	−25.9550	−	23.8190i	−1.06946	−	0.981446i
$590$	−8.33766	−	22.2492i	−0.343256	−	0.915985i
$591$	−15.2904	+	13.1097i	−0.628963	+	0.539261i
$592$	0.333215	−	0.0174631i	0.0136950	−	0.000717727i
$593$	−6.90379	−	43.5888i	−0.283505	−	1.78998i	−0.559511	−	0.828823i	$-0.689011\pi$
$593$	−6.90379	−	43.5888i	−0.283505	−	1.78998i	0.276006	−	0.961156i	$-0.410989\pi$
$594$	19.7896	+	13.4352i	0.811977	+	0.551252i
$595$	−8.27939	+	0.803485i	−0.339422	+	0.0329397i
$596$	0.880979	+	0.0925947i	0.0360863	+	0.00379282i
$597$	−24.1438	+	28.3780i	−0.988138	+	1.16143i
$598$	−5.22407	−	4.23037i	−0.213628	−	0.172993i
$599$	22.0765	+	24.5185i	0.902022	+	1.00180i	0.999978	+	0.00660606i	$0.00210279\pi$
$599$	22.0765	+	24.5185i	0.902022	+	1.00180i	−0.0979563	+	0.995191i	$0.531231\pi$
$600$	7.20534	−	4.80448i	0.294157	−	0.196142i
$601$	9.14572	−	1.94398i	0.373062	−	0.0792967i	−0.0175654	−	0.999846i	$-0.505592\pi$
$601$	9.14572	−	1.94398i	0.373062	−	0.0792967i	0.390627	+	0.920549i	$0.372258\pi$
$602$	29.0851	−	18.8881i	1.18542	−	0.769820i
$603$	−6.06737	−	5.42138i	−0.247083	−	0.220776i
$604$	19.3866	−	6.29910i	0.788831	−	0.256307i
$605$	22.6412	+	2.56243i	0.920495	+	0.104178i
$606$	7.27528	−	5.02059i	0.295538	−	0.203948i
$607$	7.27056	+	11.1957i	0.295103	+	0.454419i	0.954858	−	0.297062i	$-0.0960067\pi$
$607$	7.27056	+	11.1957i	0.295103	+	0.454419i	−0.659755	+	0.751481i	$0.729340\pi$
$608$	5.30638	+	3.44600i	0.215202	+	0.139754i
$609$	−4.99255	+	38.4885i	−0.202308	+	1.55963i
$610$	4.90285	−	9.43557i	0.198511	−	0.382035i
$611$	−5.58559	+	0.587070i	−0.225969	+	0.0237503i
$612$	−3.44820	+	1.13493i	−0.139385	+	0.0458767i
$613$	14.0477	+	17.3475i	0.567383	+	0.700660i	0.977395	−	0.211420i	$-0.0678089\pi$
$613$	14.0477	+	17.3475i	0.567383	+	0.700660i	−0.410012	+	0.912080i	$0.634476\pi$
$614$	−7.08191	−	12.2662i	−0.285803	−	0.495025i
$615$	−16.3791	−	14.1619i	−0.660468	−	0.571064i
$616$	−11.4490	−	8.31818i	−0.461293	−	0.335149i
$617$	0.634562	+	12.1082i	0.0255465	+	0.487457i	0.981204	+	0.192975i	$0.0618136\pi$
$617$	0.634562	+	12.1082i	0.0255465	+	0.487457i	−0.955657	+	0.294482i	$0.904853\pi$
$618$	0.0862285	−	1.12298i	0.00346862	−	0.0451728i
$619$		−	10.8690i		−	0.436861i	−0.975853	−	0.218430i	$-0.929906\pi$
$619$		−	10.8690i		−	0.436861i	0.975853	−	0.218430i	$-0.0700937\pi$
$620$	10.1983	−	7.14101i	0.409575	−	0.286790i
$621$	1.74311	−	23.8931i	0.0699485	−	0.958795i
$622$	−27.0101	+	13.7624i	−1.08301	+	0.551820i
$623$	−20.4973	+	1.07422i	−0.821206	+	0.0430376i
$624$	0.970858	+	2.33129i	0.0388654	+	0.0933263i
$625$	−19.7464	−	15.3323i	−0.789855	−	0.613294i
$626$	2.61396	−	1.50917i	0.104475	−	0.0603185i
$627$	50.0026	−	6.67988i	1.99691	−	0.266769i
$628$	1.52607	−	9.63526i	0.0608970	−	0.384489i
$629$	0.0422046	+	0.401550i	0.00168281	+	0.0160109i
$630$	−14.6432	+	14.5217i	−0.583400	+	0.578558i
$631$	6.19614	−	2.75870i	0.246665	−	0.109822i	−0.279681	−	0.960093i	$-0.590229\pi$
$631$	6.19614	−	2.75870i	0.246665	−	0.109822i	0.526345	+	0.850271i	$0.323562\pi$
$632$	4.31179	−	6.63957i	0.171514	−	0.264108i
$633$	−0.982137	−	34.9614i	−0.0390364	−	1.38959i
$634$	7.83951	−	17.6078i	0.311347	−	0.699296i
$635$	−25.9680	−	32.5960i	−1.03051	−	1.29353i
$636$	−1.20995	+	5.08244i	−0.0479777	+	0.201532i
$637$	−1.28077	−	3.33651i	−0.0507458	−	0.132197i
$638$	18.2737	+	28.1390i	0.723461	+	1.11403i
$639$	21.7076	+	26.5988i	0.858738	+	1.05223i
$640$	−1.59370	+	1.56848i	−0.0629965	+	0.0619995i
$641$	23.6684	−	21.3111i	0.934846	−	0.841739i	−0.0527739	−	0.998606i	$-0.516806\pi$
$641$	23.6684	−	21.3111i	0.934846	−	0.841739i	0.987620	+	0.156868i	$0.0501396\pi$
$642$	6.11607	+	17.1673i	0.241382	+	0.677538i
$643$	7.50640	−	47.3935i	0.296023	−	1.86902i	−0.171708	−	0.985148i	$-0.554929\pi$
$643$	7.50640	−	47.3935i	0.296023	−	1.86902i	0.467732	−	0.883870i	$-0.345071\pi$
$644$	−1.48156	+	14.0961i	−0.0583818	+	0.555466i
$645$	−39.3189	−	19.0481i	−1.54818	−	0.750017i
$646$	−3.82809	+	6.63044i	−0.150614	+	0.260871i
$647$	−8.89351	+	1.40859i	−0.349640	+	0.0553775i	−0.328784	−	0.944405i	$-0.606639\pi$
$647$	−8.89351	+	1.40859i	−0.349640	+	0.0553775i	−0.0208554	+	0.999783i	$0.506639\pi$
$648$	−4.84410	+	7.58516i	−0.190294	+	0.297973i
$649$	46.5196	+	15.1151i	1.82606	+	0.593321i
$650$	5.49473	−	4.79099i	0.215521	−	0.187918i
$651$	−20.5700	+	21.3503i	−0.806202	+	0.836785i
$652$	−2.82486	−	2.82486i	−0.110630	−	0.110630i
$653$	−14.8976	+	7.59071i	−0.582989	+	0.297048i	−0.720503	−	0.693452i	$-0.756089\pi$
$653$	−14.8976	+	7.59071i	−0.582989	+	0.297048i	0.137514	+	0.990500i	$0.456089\pi$
$654$	−2.86426	−	9.60238i	−0.112001	−	0.375483i
$655$	4.03836	+	7.12529i	0.157792	+	0.278408i
$656$	4.84166	+	2.79534i	0.189035	+	0.109139i
$657$	−39.1979	+	8.48797i	−1.52926	+	0.331147i
$658$	7.45257	+	9.20316i	0.290532	+	0.358777i
$659$	7.08827	−	5.14993i	0.276120	−	0.200613i	−0.441103	−	0.897456i	$-0.645413\pi$
$659$	7.08827	−	5.14993i	0.276120	−	0.200613i	0.717223	+	0.696844i	$0.245413\pi$
$660$	−1.50669	+	17.7646i	−0.0586477	+	0.691486i
$661$	−3.01965	−	3.35366i	−0.117451	−	0.130442i	0.681552	−	0.731770i	$-0.261305\pi$
$661$	−3.01965	−	3.35366i	−0.117451	−	0.130442i	−0.799003	+	0.601328i	$0.794639\pi$
$662$	11.7229	−	30.5392i	0.455624	−	1.18694i
$663$	−2.75564	+	1.32082i	−0.107020	+	0.0512965i
$664$	−0.431581	+	2.03043i	−0.0167486	+	0.0787959i
$665$	−2.62270	+	43.4154i	−0.101704	+	1.68358i
$666$	0.710517	+	0.705124i	0.0275320	+	0.0273230i
$667$	15.2560	−	29.9415i	0.590714	−	1.15934i
$668$	−6.09670	−	15.8824i	−0.235888	−	0.614510i
$669$	12.3070	+	11.6344i	0.475815	+	0.449812i
$670$	1.30819	−	5.92189i	0.0505398	−	0.228783i
$671$	8.90358	+	19.9978i	0.343719	+	0.772005i
$672$	3.00764	−	4.39405i	0.116022	−	0.169504i
$673$	21.0219	+	17.0232i	0.810333	+	0.656195i	0.942192	−	0.335073i	$-0.108761\pi$
$673$	21.0219	+	17.0232i	0.810333	+	0.656195i	−0.131859	+	0.991269i	$0.542094\pi$
$674$	−6.11669	+	4.44403i	−0.235606	+	0.171178i
$675$	25.1995	+	6.32342i	0.969929	+	0.243388i
$676$	−5.43709	−	9.41731i	−0.209119	−	0.362204i
$677$	−0.774285	−	2.88967i	−0.0297582	−	0.111059i	0.949449	−	0.313921i	$-0.101643\pi$
$677$	−0.774285	−	2.88967i	−0.0297582	−	0.111059i	−0.979207	+	0.202861i	$0.934976\pi$
$678$	−9.58277	+	23.2601i	−0.368024	+	0.893298i
$679$	−37.2038	−	33.4985i	−1.42775	−	1.28555i
$680$	−1.99627	−	1.82649i	−0.0765535	−	0.0700428i
$681$	−31.8322	−	19.4235i	−1.21981	−	0.744309i
$682$	−1.58375	+	25.5809i	−0.0606451	+	0.979545i
$683$	−30.8750	−	30.8750i	−1.18140	−	1.18140i	−0.979382	−	0.202019i	$-0.935250\pi$
$683$	−30.8750	−	30.8750i	−1.18140	−	1.18140i	−0.202019	−	0.979382i	$-0.564750\pi$
$684$	3.04074	+	18.7362i	0.116266	+	0.716398i
$685$	−18.2820	−	7.18564i	−0.698520	−	0.274549i
$686$	8.21977	−	11.3135i	0.313832	−	0.431953i
$687$	−7.59143	+	25.8086i	−0.289631	+	0.984661i
$688$	10.8963	+	2.91966i	0.415418	+	0.111311i
$689$	−0.459707	+	4.37382i	−0.0175134	+	0.166629i
$690$	16.1631	−	7.58928i	0.615318	−	0.288919i
$691$	2.81973	+	26.8280i	0.107268	+	1.02058i	0.907259	+	0.420573i	$0.138171\pi$
$691$	2.81973	+	26.8280i	0.107268	+	1.02058i	−0.799991	+	0.600012i	$0.795163\pi$
$692$	−10.2957	−	0.539574i	−0.391383	−	0.0205115i
$693$	−4.59859	−	42.2054i	−0.174686	−	1.60325i
$694$	4.69768	+	22.1008i	0.178321	+	0.838936i
$695$	−14.1046	−	10.4205i	−0.535018	−	0.395272i
$696$	−10.3905	+	7.17035i	−0.393850	+	0.271791i
$697$	−3.07126	+	6.02768i	−0.116332	+	0.228315i
$698$	10.7748	−	21.1468i	0.407833	−	0.800417i
$699$	41.6893	−	28.7694i	1.57684	−	1.08816i
$700$	−14.7823	−	4.21475i	−0.558717	−	0.159303i
$701$	6.20693	+	29.2013i	0.234432	+	1.10292i	0.925093	+	0.379739i	$0.123986\pi$
$701$	6.20693	+	29.2013i	0.234432	+	1.10292i	−0.690661	+	0.723179i	$0.742680\pi$
$702$	−3.22247	+	6.85660i	−0.121624	+	0.258786i
$703$	2.10829	+	0.110491i	0.0795158	+	0.00416725i
$704$	−0.481173	−	4.57805i	−0.0181349	−	0.172542i
$705$	5.06532	−	14.0327i	0.190771	−	0.528501i
$706$	0.390552	−	3.71585i	0.0146986	−	0.139848i
$707$	−15.1549	−	4.06074i	−0.569958	−	0.152720i
$708$	−5.19354	+	17.6565i	−0.195185	+	0.663573i
$709$	19.7983	−	27.2500i	0.743541	−	1.02340i	−0.254866	−	0.966976i	$-0.582031\pi$
$709$	19.7983	−	27.2500i	0.743541	−	1.02340i	0.998407	−	0.0564199i	$-0.0179686\pi$
$710$	−9.36085	+	23.8163i	−0.351306	+	0.893809i
$711$	23.4436	−	3.80471i	0.879204	−	0.142688i
$712$	−4.72099	−	4.72099i	−0.176927	−	0.176927i
$713$	22.9814	−	11.4367i	0.860659	−	0.428307i
$714$	5.50023	+	3.35615i	0.205841	+	0.125601i
$715$	0.665878	+	14.9930i	0.0249024	+	0.560705i
$716$	6.15156	+	5.53889i	0.229894	+	0.206998i
$717$	−1.51680	+	3.68169i	−0.0566458	+	0.137495i
$718$	0.649719	+	2.42479i	0.0242473	+	0.0904922i
$719$	−13.0842	−	22.6624i	−0.487957	−	0.845166i	0.511947	−	0.859017i	$-0.328924\pi$
$719$	−13.0842	−	22.6624i	−0.487957	−	0.845166i	−0.999904	+	0.0138510i	$0.995591\pi$
$720$	−6.69749	−	0.378991i	−0.249601	−	0.0141242i
$721$	−1.61729	+	1.17503i	−0.0602311	+	0.0437605i
$722$	16.3454	+	13.2362i	0.608311	+	0.492600i
$723$	−18.2200	+	26.6187i	−0.677608	+	0.989959i
$724$	−2.98897	−	6.71334i	−0.111084	−	0.249499i
$725$	29.1380	+	21.8886i	1.08216	+	0.812921i
$726$	−12.8258	−	12.1249i	−0.476010	−	0.449997i
$727$	3.50715	+	9.13644i	0.130073	+	0.338852i	0.983115	−	0.182991i	$-0.0585780\pi$
$727$	3.50715	+	9.13644i	0.130073	+	0.338852i	−0.853042	+	0.521843i	$0.825245\pi$
$728$	2.03495	−	3.99382i	0.0754203	−	0.148021i
$729$	−26.6176	+	4.52822i	−0.985836	+	0.167712i
$730$	−19.8248	−	22.3740i	−0.733750	−	0.828101i
$731$	−2.83805	+	13.3520i	−0.104969	+	0.493841i
$732$	−7.42743	+	3.56008i	−0.274526	+	0.131584i
$733$	12.7881	−	33.3140i	0.472338	−	1.23048i	−0.466007	−	0.884781i	$-0.654308\pi$
$733$	12.7881	−	33.3140i	0.472338	−	1.23048i	0.938345	−	0.345701i	$-0.112359\pi$
$734$	5.01054	+	5.56476i	0.184942	+	0.205399i
$735$	9.45946	+	0.802294i	0.348917	+	0.0295930i
$736$	−3.72993	+	2.70995i	−0.137487	+	0.0998901i
$737$	7.85706	+	9.70267i	0.289419	+	0.357402i
$738$	3.54957	+	16.3921i	0.130661	+	0.603401i
$739$	42.3128	+	24.4293i	1.55650	+	0.898647i	0.997587	+	0.0694229i	$0.0221158\pi$
$739$	42.3128	+	24.4293i	1.55650	+	0.898647i	0.558916	+	0.829224i	$0.311218\pi$
$740$	−0.198851	+	0.719127i	−0.00730990	+	0.0264356i
$741$	4.56726	+	15.3117i	0.167782	+	0.562488i
$742$	8.26241	−	4.20991i	0.303323	−	0.154551i
$743$	−18.9078	−	18.9078i	−0.693659	−	0.693659i	0.269376	−	0.963035i	$-0.413183\pi$
$743$	−18.9078	−	18.9078i	−0.693659	−	0.693659i	−0.963035	+	0.269376i	$0.913183\pi$
$744$	−9.63816	−	0.325391i	−0.353352	−	0.0119294i
$745$	−0.820064	+	1.80305i	−0.0300448	+	0.0660586i
$746$	25.3332	+	8.23125i	0.927514	+	0.301367i
$747$	−5.38116	+	3.13421i	−0.196886	+	0.114675i
$748$	5.50164	−	0.871373i	0.201160	−	0.0318606i
$749$	16.1734	−	28.0131i	0.590963	−	1.02358i
$750$	5.08970	+	18.6841i	0.185850	+	0.682246i
$751$	−2.78701	+	26.5166i	−0.101700	+	0.967606i	0.818062	+	0.575129i	$0.195048\pi$
$751$	−2.78701	+	26.5166i	−0.101700	+	0.967606i	−0.919762	+	0.392477i	$0.871618\pi$
$752$	−0.602592	+	3.80462i	−0.0219743	+	0.138740i
$753$	12.4766	+	35.0208i	0.454674	+	1.27623i
$754$	−7.89747	+	7.11091i	−0.287609	+	0.258964i
$755$	−0.363563	+	45.5792i	−0.0132314	+	1.65880i
$756$	15.8256	−	2.17555i	0.575571	−	0.0791239i
$757$	−3.21002	−	4.94300i	−0.116670	−	0.179656i	0.775511	−	0.631334i	$-0.217492\pi$
$757$	−3.21002	−	4.94300i	−0.116670	−	0.179656i	−0.892181	+	0.451678i	$0.850826\pi$
$758$	−10.1303	−	26.3903i	−0.367948	−	0.958539i
$759$	−8.51324	+	35.7601i	−0.309011	+	1.29801i
$760$	−11.0656	+	8.81557i	−0.401393	+	0.319774i
$761$	15.3256	−	34.4219i	0.555554	−	1.24779i	−0.389545	−	0.921008i	$-0.627368\pi$
$761$	15.3256	−	34.4219i	0.555554	−	1.24779i	0.945098	−	0.326786i	$-0.105966\pi$
$762$	0.906498	+	32.2688i	0.0328390	+	1.16898i
$763$	−9.68678	+	14.9163i	−0.350685	+	0.540007i
$764$	−9.79561	+	4.36129i	−0.354393	+	0.157786i
$765$	0.0338234	−	8.11723i	0.00122289	−	0.293479i
$766$	−1.67497	−	15.9363i	−0.0605190	−	0.575800i
$767$	−2.42359	+	15.3020i	−0.0875109	+	0.552522i
$768$	1.71680	−	0.229348i	0.0619497	−	0.00827590i
$769$	10.3116	−	5.95342i	0.371847	−	0.214686i	−0.302418	−	0.953175i	$-0.597794\pi$
$769$	10.3116	−	5.95342i	0.371847	−	0.214686i	0.674265	+	0.738489i	$0.264461\pi$
$770$	25.7483	−	18.3952i	0.927903	−	0.662918i
$771$	0.317652	+	0.762768i	0.0114400	+	0.0274704i
$772$	18.5310	−	0.971168i	0.666945	−	0.0349531i
$773$	22.8476	−	11.6414i	0.821769	−	0.418712i	0.00804803	−	0.999968i	$-0.497438\pi$
$773$	22.8476	−	11.6414i	0.821769	−	0.418712i	0.813721	+	0.581255i	$0.197438\pi$
$774$	15.4787	+	30.0947i	0.556371	+	1.08173i
$775$	7.92679	+	26.6864i	0.284739	+	0.958605i
$776$		−	16.2844i		−	0.584575i
$777$	0.136027	−	1.77153i	0.00487995	−	0.0635531i
$778$	0.734985	+	14.0244i	0.0263505	+	0.502797i
$779$	28.6173	+	20.7917i	1.02532	+	0.744938i
$780$	−5.63207	+	0.408862i	−0.201660	+	0.0146396i
$781$	−26.3402	−	45.6226i	−0.942527	−	1.63250i
$782$	−3.51091	−	4.33561i	−0.125550	−	0.155041i
$783$	−36.8767	−	8.63075i	−1.31787	−	0.308438i
$784$	−2.43776	+	0.256219i	−0.0870630	+	0.00915069i
$785$	19.3565	+	10.0579i	0.690863	+	0.358982i
$786$	0.816082	−	6.29133i	0.0291087	−	0.224404i
$787$	−18.4064	−	11.9533i	−0.656118	−	0.426088i	0.173183	−	0.984890i	$-0.444595\pi$
$787$	−18.4064	−	11.9533i	−0.656118	−	0.426088i	−0.829302	+	0.558801i	$0.811261\pi$
$788$	6.33329	+	9.75242i	0.225614	+	0.347415i
$789$	−26.1929	+	18.0754i	−0.932490	+	0.643501i
$790$	11.0304	+	13.8458i	0.392445	+	0.492612i
$791$	42.4662	−	13.7981i	1.50992	−	0.490604i
$792$	9.20140	−	10.2978i	0.326958	−	0.365917i
$793$	−5.81487	+	3.77622i	−0.206492	+	0.134098i
$794$	−5.64760	+	1.20043i	−0.200426	+	0.0426018i
$795$	−9.92355	−	6.16435i	−0.351952	−	0.218627i
$796$	14.3940	+	15.9861i	0.510182	+	0.566614i
$797$	−5.09693	−	4.12741i	−0.180542	−	0.146200i	0.534789	−	0.844986i	$-0.320391\pi$
$797$	−5.09693	−	4.12741i	−0.180542	−	0.146200i	−0.715332	+	0.698785i	$0.753724\pi$
$798$	21.8315	−	25.6603i	0.772828	−	0.908363i
$799$	−4.63565	−	0.487227i	−0.163998	−	0.0172368i
$800$	−2.19860	−	4.49068i	−0.0777321	−	0.158769i
$801$	0.972057	−	20.0059i	0.0343459	−	0.706873i
$802$	5.56915	+	35.1622i	0.196654	+	1.24162i
$803$	61.4558	−	3.22076i	2.16873	−	0.113658i
$804$	−3.56632	+	3.05769i	−0.125774	+	0.107836i
$805$	−28.8498	−	13.1215i	−1.01682	−	0.462471i
$806$	−8.08112	+	0.772039i	−0.284645	+	0.0271939i
$807$	0.108714	+	0.449058i	0.00382693	+	0.0158076i
$808$	−2.31693	−	4.54722i	−0.0815091	−	0.159971i
$809$	30.3025	−	33.6544i	1.06538	−	1.18323i	0.0829585	−	0.996553i	$-0.473563\pi$
$809$	30.3025	−	33.6544i	1.06538	−	1.18323i	0.982422	−	0.186672i	$-0.0597702\pi$
$810$	−12.6592	−	15.6443i	−0.444800	−	0.549684i
$811$	22.3514	−	38.7138i	0.784865	−	1.35943i	−0.144215	−	0.989546i	$-0.546066\pi$
$811$	22.3514	−	38.7138i	0.784865	−	1.35943i	0.929080	−	0.369879i	$-0.120601\pi$
$812$	21.6440	+	5.79949i	0.759556	+	0.203522i
$813$	−33.2060	+	4.43601i	−1.16458	+	0.155578i
$814$	−0.902828	−	1.24264i	−0.0316441	−	0.0435544i
$815$	7.99145	−	3.99188i	0.279928	−	0.139829i
$816$	0.385868	+	2.06005i	0.0135081	+	0.0721162i
$817$	66.6337	+	25.5783i	2.33122	+	0.894871i
$818$	−5.77786	−	3.75219i	−0.202018	−	0.131192i
$819$	12.9755	−	3.52982i	0.453402	−	0.123342i
$820$	−9.35657	+	8.29051i	−0.326745	+	0.289517i
$821$	−23.0498	+	7.48933i	−0.804444	+	0.261380i	−0.682243	−	0.731126i	$-0.738995\pi$
$821$	−23.0498	+	7.48933i	−0.804444	+	0.261380i	−0.122201	+	0.992505i	$0.538995\pi$
$822$	7.97491	+	12.9584i	0.278157	+	0.451976i
$823$	19.9577	−	7.66105i	0.695682	−	0.267047i	0.0152768	−	0.999883i	$-0.495137\pi$
$823$	19.9577	−	7.66105i	0.695682	−	0.267047i	0.680405	+	0.732836i	$0.261804\pi$
$824$	−0.636051	−	0.135197i	−0.0221579	−	0.00470981i
$825$	−36.6130	−	15.7717i	−1.27470	−	0.549101i
$826$	29.8426	−	13.2868i	1.03836	−	0.462307i
$827$	−20.9271	−	1.09674i	−0.727707	−	0.0381375i	−0.315115	−	0.949053i	$-0.602043\pi$
$827$	−20.9271	−	1.09674i	−0.727707	−	0.0381375i	−0.412592	+	0.910916i	$0.635376\pi$
$828$	−13.5399	−	2.82413i	−0.470545	−	0.0981455i
$829$	−11.3161	−	15.5753i	−0.393024	−	0.540951i	0.565952	−	0.824438i	$-0.308509\pi$
$829$	−11.3161	−	15.5753i	−0.393024	−	0.540951i	−0.958976	+	0.283487i	$0.908509\pi$
$830$	−4.00111	−	2.35279i	−0.138881	−	0.0816666i
$831$	−23.3448	−	0.566810i	−0.809821	−	0.0196624i
$832$	1.40834	−	0.377364i	0.0488254	−	0.0130827i
$833$	−0.463997	−	2.92956i	−0.0160765	−	0.101503i
$834$	3.88277	+	13.0169i	0.134449	+	0.450739i
$835$	38.0034	−	1.68783i	1.31516	−	0.0584099i
$836$		−	29.1255i		−	1.00733i
$837$	−18.7063	−	22.0697i	−0.646585	−	0.762842i
$838$	−3.00769	+	3.00769i	−0.103899	+	0.103899i
$839$	−14.9206	+	45.9208i	−0.515116	+	1.58536i	0.267956	+	0.963431i	$0.413652\pi$
$839$	−14.9206	+	45.9208i	−0.515116	+	1.58536i	−0.783072	+	0.621932i	$0.786348\pi$
$840$	7.19081	+	9.49000i	0.248107	+	0.327436i
$841$	−19.5177	−	14.1805i	−0.673026	−	0.488982i
$842$	0.791717	+	2.95473i	0.0272844	+	0.101827i
$843$	16.2342	+	17.0422i	0.559136	+	0.586963i
$844$	−20.0823	−	2.11073i	−0.691261	−	0.0726545i
$845$	23.8236	−	4.86559i	0.819557	−	0.167381i
$846$	−9.66774	+	6.33079i	−0.332384	+	0.217657i
$847$	−1.63954	+	31.2842i	−0.0563352	+	1.07494i
$848$	2.81601	+	1.08097i	0.0967022	+	0.0371205i
$849$	−9.06371	−	3.19021i	−0.311066	−	0.109488i
$850$	5.28729	−	2.94117i	0.181352	−	0.100881i
$851$	−0.625714	+	1.40538i	−0.0214492	+	0.0481757i
$852$	16.8811	−	10.3890i	0.578338	−	0.355923i
$853$	13.0368	+	6.64260i	0.446373	+	0.227438i	0.662703	−	0.748882i	$-0.269409\pi$
$853$	13.0368	+	6.64260i	0.446373	+	0.227438i	−0.216331	+	0.976320i	$0.569409\pi$
$854$	13.3554	+	5.94623i	0.457014	+	0.203476i
$855$	−41.8931	−	6.81427i	−1.43271	−	0.233043i
$856$	10.2918	−	2.18759i	0.351767	−	0.0747704i
$857$	10.3015	−	26.8363i	0.351892	−	0.916710i	−0.637370	−	0.770558i	$-0.719978\pi$
$857$	10.3015	−	26.8363i	0.351892	−	0.916710i	0.989262	−	0.146152i	$-0.0466890\pi$
$858$	6.56618	−	9.59295i	0.224166	−	0.327498i
$859$	−19.0014	+	1.99712i	−0.648318	+	0.0681410i	−0.422979	−	0.906139i	$-0.639016\pi$
$859$	−19.0014	+	1.99712i	−0.648318	+	0.0681410i	−0.225339	+	0.974280i	$0.572349\pi$
$860$	−13.9065	+	21.0447i	−0.474207	+	0.717618i
$861$	18.0773	−	23.6520i	0.616074	−	0.806058i
$862$	−1.28775	+	4.80593i	−0.0438608	+	0.163691i
$863$	−20.6793	+	5.54099i	−0.703930	+	0.188618i	−0.592990	−	0.805210i	$-0.702053\pi$
$863$	−20.6793	+	5.54099i	−0.703930	+	0.188618i	−0.110940	+	0.993827i	$0.535386\pi$
$864$	3.97040	+	3.35200i	0.135076	+	0.114037i
$865$	8.43301	−	21.4556i	0.286731	−	0.729514i
$866$	−4.51942	−	1.46845i	−0.153576	−	0.0498999i
$867$	26.1532	−	6.33155i	0.888210	−	0.215031i
$868$	10.6455	+	13.4037i	0.361332	+	0.454953i
$869$	−36.4431			−1.23625
$870$	−7.85300	−	27.1147i	−0.266242	−	0.919276i
$871$	−2.64604	+	2.93873i	−0.0896577	+	0.0995750i
$872$	−5.71409	+	0.905023i	−0.193504	+	0.0306480i
$873$	36.1802	−	32.8272i	1.22451	−	1.11103i
$874$	−25.2627	+	14.5854i	−0.854523	+	0.493359i
$875$	19.4044	−	28.3702i	0.655989	−	0.959087i
$876$	1.86072	+	23.0805i	0.0628679	+	0.779819i
$877$	10.3130	−	12.7355i	0.348246	−	0.430048i	−0.572684	−	0.819776i	$-0.694098\pi$
$877$	10.3130	−	12.7355i	0.348246	−	0.430048i	0.920930	+	0.389728i	$0.127431\pi$
$878$	0.162558	−	3.10178i	0.00548605	−	0.104680i
$879$	6.03628	−	46.5349i	0.203599	−	1.56958i
$880$	10.0509	+	2.22032i	0.338816	+	0.0748470i
$881$	5.57502	−	26.2284i	0.187827	−	0.883658i	−0.778760	−	0.627321i	$-0.784151\pi$
$881$	5.57502	−	26.2284i	0.187827	−	0.883658i	0.966588	−	0.256336i	$-0.0825155\pi$
$882$	−5.48347	−	4.89965i	−0.184638	−	0.164980i
$883$	−1.13620	−	0.578924i	−0.0382362	−	0.0194823i	0.434768	−	0.900543i	$-0.356830\pi$
$883$	−1.13620	−	0.578924i	−0.0382362	−	0.0194823i	−0.473004	+	0.881060i	$0.656830\pi$
$884$	0.545195	+	1.67794i	0.0183369	+	0.0564351i
$885$	−33.7737	−	23.5152i	−1.13529	−	0.790455i
$886$	0.917267	+	0.194971i	0.0308162	+	0.00655018i
$887$	−14.0019	+	21.5610i	−0.470137	+	0.723948i	−0.991602	−	0.129325i	$-0.958719\pi$
$887$	−14.0019	+	21.5610i	−0.470137	+	0.723948i	0.521465	+	0.853273i	$0.325386\pi$
$888$	0.457837	−	0.352699i	0.0153640	−	0.0118358i
$889$	42.5805	−	38.3396i	1.42810	−	1.28587i
$890$	13.3556	−	6.67135i	0.447679	−	0.223624i
$891$	41.4282	−	0.315646i	1.38790	−	0.0105745i
$892$	7.59884	−	6.15342i	0.254428	−	0.206032i
$893$	−6.30803	+	23.5419i	−0.211090	+	0.787800i
$894$	1.34698	−	0.734675i	0.0450497	−	0.0245712i
$895$	−16.1031	+	9.12664i	−0.538266	+	0.305070i
$896$	−2.28463	−	2.05709i	−0.0763243	−	0.0687227i
$897$	−11.6089	−	0.891393i	−0.387609	−	0.0297628i
$898$	0.799369	−	0.799369i	0.0266753	−	0.0266753i
$899$	−12.1743	−	38.7127i	−0.406036	−	1.29114i
$900$	5.54517	−	13.9374i	0.184839	−	0.464580i
$901$	−1.12790	+	3.47132i	−0.0375758	+	0.115646i
$902$	−1.34688	−	25.7001i	−0.0448464	−	0.855719i
$903$	22.8811	−	55.5388i	0.761435	−	1.84822i
$904$	12.5784	+	7.26212i	0.418350	+	0.241535i
$905$	16.3553	−	1.58722i	0.543668	−	0.0527610i
$906$	21.4399	−	28.0515i	0.712294	−	0.931950i
$907$	24.5198	+	3.88355i	0.814165	+	0.128951i	0.549612	−	0.835420i	$-0.314776\pi$
$907$	24.5198	+	3.88355i	0.814165	+	0.128951i	0.264553	+	0.964371i	$0.414776\pi$
$908$	−13.5490	+	16.7316i	−0.449638	+	0.555257i
$909$	5.43227	−	14.3143i	0.180177	−	0.474775i
$910$	7.03048	+	7.14354i	0.233058	+	0.236806i
$911$	−4.57994	−	21.5469i	−0.151740	−	0.713881i	−0.986566	−	0.163366i	$-0.947765\pi$
$911$	−4.57994	−	21.5469i	−0.151740	−	0.713881i	0.834825	−	0.550515i	$-0.185569\pi$
$912$	10.9546	−	0.307737i	0.362743	−	0.0101902i
$913$	8.92075	−	3.42436i	0.295234	−	0.113330i
$914$	−10.1277	−	31.1700i	−0.334996	−	1.03101i
$915$	−2.29306	−	18.2742i	−0.0758061	−	0.604126i
$916$	14.1891	+	6.31738i	0.468820	+	0.208732i
$917$	−9.44365	+	6.13278i	−0.311857	+	0.202522i
$918$	−3.79910	+	5.01011i	−0.125389	+	0.165358i
$919$	4.71971	+	10.6006i	0.155689	+	0.349683i	0.974503	−	0.224376i	$-0.0720345\pi$
$919$	4.71971	+	10.6006i	0.155689	+	0.349683i	−0.818814	+	0.574059i	$0.805368\pi$
$920$	−3.10743	−	9.82979i	−0.102449	−	0.324079i
$921$	−22.1627	−	10.5193i	−0.730286	−	0.346623i
$922$	−29.2651	−	4.63513i	−0.963794	−	0.152650i
$923$	12.9673	−	10.5007i	0.426824	−	0.345635i
$924$	−24.5043	−	0.594964i	−0.806132	−	0.0195729i
$925$	−1.38453	−	0.930859i	−0.0455231	−	0.0306065i
$926$	−1.26771	+	1.74486i	−0.0416596	+	0.0573396i
$927$	−0.981820	−	1.68570i	−0.0322472	−	0.0553656i
$928$	3.30900	+	6.49429i	0.108623	+	0.213185i
$929$	1.20444			0.0395163			0.0197581	−	0.999805i	$-0.493710\pi$
$929$	1.20444			0.0395163			0.0197581	+	0.999805i	$0.493710\pi$
$930$	7.51325	−	20.2126i	0.246369	−	0.662799i
$931$	−15.5090			−0.508287
$932$	−13.2766	−	26.0568i	−0.434890	−	0.853519i
$933$	−24.9656	+	46.1906i	−0.817338	+	1.51221i
$934$	−22.9417	+	31.5765i	−0.750675	+	1.03321i
$935$	−2.04651	+	12.2861i	−0.0669281	+	0.401798i
$936$	3.67745	+	2.36829i	0.120201	+	0.0774101i
$937$	13.8018	−	11.1765i	0.450884	−	0.365119i	−0.376817	−	0.926288i	$-0.622981\pi$
$937$	13.8018	−	11.1765i	0.450884	−	0.365119i	0.827701	+	0.561169i	$0.189648\pi$
$938$	8.23541	+	1.30436i	0.268896	+	0.0425889i
$939$	2.24168	−	4.72292i	0.0731546	−	0.154127i
$940$	−7.64319	−	3.97151i	−0.249293	−	0.129536i
$941$	12.7138	+	28.5557i	0.414458	+	0.930889i	0.993312	+	0.115458i	$0.0368335\pi$
$941$	12.7138	+	28.5557i	0.414458	+	0.930889i	−0.578854	+	0.815431i	$0.696500\pi$
$942$	−7.30329	−	15.2369i	−0.237954	−	0.496445i
$943$	−21.6171	+	14.0383i	−0.703950	+	0.457151i
$944$	9.70719	+	4.32192i	0.315942	+	0.140667i
$945$	−6.58887	+	35.1069i	−0.214336	+	1.14203i
$946$	−16.0466	−	49.3865i	−0.521721	−	1.60569i
$947$	52.7219	−	20.2380i	1.71323	−	0.657648i	0.714129	−	0.700014i	$-0.246823\pi$
$947$	52.7219	−	20.2380i	1.71323	−	0.657648i	0.999102	+	0.0423656i	$0.0134894\pi$
$948$	−0.385054	−	13.7069i	−0.0125060	−	0.445178i
$949$	4.05261	+	19.0660i	0.131553	+	0.618909i
$950$	−10.8646	−	29.7115i	−0.352495	−	0.963968i
$951$	−6.14623	−	32.8132i	−0.199305	−	1.06404i
$952$	2.34110	−	2.89102i	0.0758756	−	0.0936985i
$953$	45.3243	+	7.17866i	1.46820	+	0.232540i	0.838756	−	0.544508i	$-0.183284\pi$
$953$	45.3243	+	7.17866i	1.46820	+	0.232540i	0.629442	+	0.777048i	$0.283284\pi$
$954$	3.27506	+	8.43562i	0.106034	+	0.273113i
$955$	−2.31596	−	23.8644i	−0.0749426	−	0.772235i
$956$	1.99095	+	1.14948i	0.0643919	+	0.0371767i
$957$	53.7322	+	22.1368i	1.73692	+	0.715581i
$958$	0.729137	+	13.9128i	0.0235573	+	0.449501i
$959$	8.34562	−	25.6852i	0.269494	−	0.829418i
$960$	−0.728903	+	3.80377i	−0.0235253	+	0.122766i
$961$	10.1363	−	29.2960i	0.326979	−	0.945032i
$962$	0.344008	−	0.344008i	0.0110913	−	0.0110913i
$963$	25.6073	+	18.4562i	0.825184	+	0.594742i
$964$	13.8401	+	12.4617i	0.445759	+	0.401363i
$965$	−11.0586	+	39.9926i	−0.355990	+	1.28741i
$966$	11.7552	+	21.5524i	0.378217	+	0.693436i
$967$	9.97492	−	37.2269i	0.320772	−	1.19714i	−0.597723	−	0.801703i	$-0.703928\pi$
$967$	9.97492	−	37.2269i	0.320772	−	1.19714i	0.918494	−	0.395434i	$-0.129406\pi$
$968$	−7.91919	+	6.41283i	−0.254532	+	0.206116i
$969$	1.06562	+	13.2180i	0.0342325	+	0.424623i
$970$	34.5399	+	11.5281i	1.10901	+	0.370145i
$971$	−18.4119	+	16.5781i	−0.590865	+	0.532017i	−0.909416	−	0.415889i	$-0.863471\pi$
$971$	−18.4119	+	16.5781i	−0.590865	+	0.532017i	0.318551	+	0.947906i	$0.396804\pi$
$972$	0.556446	+	15.5785i	0.0178480	+	0.499681i
$973$	13.1313	−	20.2205i	0.420971	−	0.648238i
$974$	16.2835	+	3.46117i	0.521757	+	0.110903i
$975$	3.11986	−	12.2353i	0.0999155	−	0.391844i
$976$	1.46949	+	4.52263i	0.0470373	+	0.144766i
$977$	27.3088	+	13.9145i	0.873685	+	0.445165i	0.832525	−	0.553988i	$-0.186895\pi$
$977$	27.3088	+	13.9145i	0.873685	+	0.445165i	0.0411601	+	0.999153i	$0.486895\pi$
$978$	−6.80599	−	1.24801i	−0.217631	−	0.0399070i
$979$	−6.38989	+	30.0621i	−0.204222	+	0.960788i
$980$	1.18230	−	5.35200i	0.0377671	−	0.170963i
$981$	−13.5296	−	10.8710i	−0.431968	−	0.347084i
$982$	−0.744910	+	14.2137i	−0.0237710	+	0.453578i
$983$	3.56913	−	4.40751i	0.113838	−	0.140578i	−0.717042	−	0.697030i	$-0.754504\pi$
$983$	3.56913	−	4.40751i	0.113838	−	0.140578i	0.830880	+	0.556452i	$0.187838\pi$
$984$	9.65201	−	0.778131i	0.307695	−	0.0248059i
$985$	−25.1688	+	6.52925i	−0.801946	+	0.208039i
$986$	−7.63812	+	4.40987i	−0.243247	+	0.140439i
$987$	19.6778	+	5.78808i	0.626351	+	0.184237i
$988$	9.11151	−	1.44312i	0.289876	−	0.0459118i
$989$	−34.8008	+	38.6502i	−1.10660	+	1.22900i
$990$	15.3283	+	26.8067i	0.487164	+	0.851972i
$991$	−56.9219			−1.80818			−0.904092	−	0.427337i	$-0.859452\pi$
$991$	−56.9219			−1.80818			−0.904092	+	0.427337i	$0.859452\pi$
$992$	−0.923043	+	5.49072i	−0.0293066	+	0.174330i
$993$	−13.3316	−	55.0680i	−0.423067	−	1.74753i
$994$	−33.4605	−	10.8720i	−1.06130	−	0.344838i
$995$	−44.0972	+	19.2134i	−1.39798	+	0.609105i
$996$	1.38221	+	3.31907i	0.0437971	+	0.105169i
$997$	−30.7323	+	8.23469i	−0.973301	+	0.260795i	−0.710221	−	0.703979i	$-0.751405\pi$
$997$	−30.7323	+	8.23469i	−0.973301	+	0.260795i	−0.263080	+	0.964774i	$0.584738\pi$
$998$	5.00146	−	18.6657i	0.158319	−	0.590853i
$999$	1.70656	+	0.306215i	0.0539931	+	0.00968823i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bs.a.107.6	✓	1024
3.2	odd	2	inner	930.2.bs.a.107.58	yes	1024
5.3	odd	4	inner	930.2.bs.a.293.20	yes	1024
15.8	even	4	inner	930.2.bs.a.293.54	yes	1024
31.20	even	15	inner	930.2.bs.a.857.54	yes	1024
93.20	odd	30	inner	930.2.bs.a.857.20	yes	1024
155.113	odd	60	inner	930.2.bs.a.113.58	yes	1024
465.113	even	60	inner	930.2.bs.a.113.6	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bs.a.107.6	✓	1024	1.1	even	1	trivial
930.2.bs.a.107.58	yes	1024	3.2	odd	2	inner
930.2.bs.a.113.6	yes	1024	465.113	even	60	inner
930.2.bs.a.113.58	yes	1024	155.113	odd	60	inner
930.2.bs.a.293.20	yes	1024	5.3	odd	4	inner
930.2.bs.a.293.54	yes	1024	15.8	even	4	inner
930.2.bs.a.857.20	yes	1024	93.20	odd	30	inner
930.2.bs.a.857.54	yes	1024	31.20	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.bs (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 - 0.891007i) q^{2} +(-1.52373 - 0.823562i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-1.29986 - 1.81944i) q^{5} +(-0.0420417 + 1.73154i) q^{6} +(2.38916 - 1.93471i) q^{7} +(0.987688 + 0.156434i) q^{8} +(1.64349 + 2.50977i) q^{9} +O(q^{10})\)	\(q+(-0.453990 - 0.891007i) q^{2} +(-1.52373 - 0.823562i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-1.29986 - 1.81944i) q^{5} +(-0.0420417 + 1.73154i) q^{6} +(2.38916 - 1.93471i) q^{7} +(0.987688 + 0.156434i) q^{8} +(1.64349 + 2.50977i) q^{9} +(-1.03101 + 1.98419i) q^{10} +(-1.87232 - 4.20530i) q^{11} +(1.56190 - 0.748643i) q^{12} +(1.22280 - 0.794095i) q^{13} +(-2.80849 - 1.25042i) q^{14} +(0.482203 + 3.84285i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(1.12968 - 0.433645i) q^{17} +(1.49009 - 2.60377i) q^{18} +(-1.31548 - 6.18886i) q^{19} +(2.23600 + 0.0178354i) q^{20} +(-5.23379 + 0.980340i) q^{21} +(-2.89693 + 3.57741i) q^{22} +(4.55368 + 0.721232i) q^{23} +(-1.37613 - 1.05179i) q^{24} +(-1.62074 + 4.73003i) q^{25} +(-1.26268 - 0.729011i) q^{26} +(-0.437279 - 5.17772i) q^{27} +(0.160895 + 3.07007i) q^{28} +(2.25233 - 6.93197i) q^{29} +(3.20509 - 2.17426i) q^{30} +(4.53521 - 3.22983i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.610421 + 7.94970i) q^{33} +(-0.899247 - 0.809686i) q^{34} +(-6.62566 - 1.83211i) q^{35} +(-2.99646 - 0.145594i) q^{36} +(-0.0863607 + 0.322303i) q^{37} +(-4.91710 + 3.98179i) q^{38} +(-2.51720 + 0.202933i) q^{39} +(-0.999230 - 2.00038i) q^{40} +(-4.15468 + 3.74089i) q^{41} +(3.24958 + 4.21827i) q^{42} +(-6.14390 + 9.46078i) q^{43} +(4.50268 + 0.957074i) q^{44} +(2.43008 - 6.25258i) q^{45} +(-1.42470 - 4.38479i) q^{46} +(-3.43220 - 1.74879i) q^{47} +(-0.312397 + 1.70365i) q^{48} +(0.509631 - 2.39763i) q^{49} +(4.95029 - 0.703295i) q^{50} +(-2.07847 - 0.269609i) q^{51} +(-0.0763069 + 1.45602i) q^{52} +(-1.89825 + 2.34415i) q^{53} +(-4.41486 + 2.74025i) q^{54} +(-5.21755 + 8.87286i) q^{55} +(2.66240 - 1.53714i) q^{56} +(-3.09248 + 10.5135i) q^{57} +(-7.19897 + 1.14021i) q^{58} +(-7.11008 + 7.89654i) q^{59} +(-3.39236 - 1.86866i) q^{60} -4.75538 q^{61} +(-4.93675 - 2.57459i) q^{62} +(8.78223 + 2.81658i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-3.03428 - 1.19260i) q^{65} +(7.36036 - 3.06520i) q^{66} +(-2.61979 + 0.701970i) q^{67} +(-0.313186 + 1.16882i) q^{68} +(-6.34459 - 4.84920i) q^{69} +(1.37557 + 6.73526i) q^{70} +(11.3814 - 1.19624i) q^{71} +(1.23064 + 2.73597i) q^{72} +(-4.79094 + 12.4808i) q^{73} +(0.326381 - 0.0693743i) q^{74} +(6.36505 - 5.87249i) q^{75} +(5.78012 + 2.57347i) q^{76} +(-12.6093 - 6.42475i) q^{77} +(1.32360 + 2.15071i) q^{78} +(3.22004 - 7.23234i) q^{79} +(-1.32872 + 1.79848i) q^{80} +(-3.59788 + 8.24956i) q^{81} +(5.21934 + 2.00352i) q^{82} +(-0.108638 + 2.07295i) q^{83} +(2.28323 - 4.81045i) q^{84} +(-2.25742 - 1.49172i) q^{85} +(11.2189 + 1.17915i) q^{86} +(-9.14086 + 8.70750i) q^{87} +(-1.19141 - 4.44642i) q^{88} +(-5.40139 - 3.92434i) q^{89} +(-6.67432 + 0.673393i) q^{90} +(1.38513 - 4.26298i) q^{91} +(-3.26007 + 3.26007i) q^{92} +(-9.57040 + 1.18636i) q^{93} +3.85204i q^{94} +(-9.55034 + 10.4381i) q^{95} +(1.65978 - 0.495091i) q^{96} +(-2.54744 - 16.0839i) q^{97} +(-2.36767 + 0.634415i) q^{98} +(7.47719 - 11.6104i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 8 q^{3} + 24 q^{7}+O(q^{10}) \) 1024 * q - 8 * q^3 + 24 * q^7	\( 1024 q - 8 q^{3} + 24 q^{7} + 8 q^{10} + 8 q^{12} - 8 q^{15} + 256 q^{16} + 44 q^{22} + 16 q^{25} - 20 q^{27} + 4 q^{28} + 48 q^{30} - 32 q^{31} - 52 q^{33} + 112 q^{37} + 12 q^{42} + 40 q^{45} + 24 q^{46} - 12 q^{48} + 16 q^{51} - 20 q^{55} - 40 q^{57} - 56 q^{58} - 12 q^{60} + 32 q^{61} + 224 q^{63} - 32 q^{66} + 24 q^{67} - 24 q^{70} - 88 q^{73} + 224 q^{75} - 96 q^{76} - 32 q^{78} + 48 q^{81} - 24 q^{85} + 20 q^{87} - 36 q^{88} + 8 q^{90} - 80 q^{91} - 252 q^{93} - 32 q^{97}+O(q^{100}) \) 1024 * q - 8 * q^3 + 24 * q^7 + 8 * q^10 + 8 * q^12 - 8 * q^15 + 256 * q^16 + 44 * q^22 + 16 * q^25 - 20 * q^27 + 4 * q^28 + 48 * q^30 - 32 * q^31 - 52 * q^33 + 112 * q^37 + 12 * q^42 + 40 * q^45 + 24 * q^46 - 12 * q^48 + 16 * q^51 - 20 * q^55 - 40 * q^57 - 56 * q^58 - 12 * q^60 + 32 * q^61 + 224 * q^63 - 32 * q^66 + 24 * q^67 - 24 * q^70 - 88 * q^73 + 224 * q^75 - 96 * q^76 - 32 * q^78 + 48 * q^81 - 24 * q^85 + 20 * q^87 - 36 * q^88 + 8 * q^90 - 80 * q^91 - 252 * q^93 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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