LMFDB - Embedded newform 156.2.w.c.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,2,Mod(7,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 11]))

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

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

chi := DirichletCharacter("156.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	156.w (of order $12$, degree $4$, 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:	$1.24566627153$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	156.19
Dual form			156.2.w.c.115.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.737204 + 1.20687i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.913059 - 1.77942i) q^{4} +(0.218120 - 0.218120i) q^{5} +(1.24187 - 0.676576i) q^{6} +(3.40856 + 0.913320i) q^{7} +(2.82063 + 0.209852i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.737204 + 1.20687i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.913059 - 1.77942i) q^{4} +(0.218120 - 0.218120i) q^{5} +(1.24187 - 0.676576i) q^{6} +(3.40856 + 0.913320i) q^{7} +(2.82063 + 0.209852i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.102443 + 0.424042i) q^{10} +(1.20821 + 4.50910i) q^{11} +(-0.0989759 + 1.99755i) q^{12} +(2.32949 - 2.75199i) q^{13} +(-3.61506 + 3.44037i) q^{14} +(-0.297958 + 0.0798376i) q^{15} +(-2.33265 + 3.24942i) q^{16} +(0.140292 - 0.0809975i) q^{17} +(-1.41378 - 0.0350040i) q^{18} +(1.50718 - 5.62489i) q^{19} +(-0.587284 - 0.188970i) q^{20} +(-2.49524 - 2.49524i) q^{21} +(-6.33259 - 1.86598i) q^{22} +(-1.41113 + 2.44415i) q^{23} +(-2.33781 - 1.59205i) q^{24} +4.90485i q^{25} +(1.60398 + 4.84017i) q^{26} -1.00000i q^{27} +(-1.48704 - 6.89916i) q^{28} +(3.09015 - 5.35230i) q^{29} +(0.123303 - 0.418452i) q^{30} +(2.13065 + 2.13065i) q^{31} +(-2.20199 - 5.21069i) q^{32} +(1.20821 - 4.50910i) q^{33} +(-0.00567047 + 0.229025i) q^{34} +(0.942690 - 0.544262i) q^{35} +(1.08449 - 1.68044i) q^{36} +(-7.31471 + 1.95997i) q^{37} +(5.67739 + 5.96566i) q^{38} +(-3.39340 + 1.21855i) q^{39} +(0.661010 - 0.569464i) q^{40} +(-0.682962 - 2.54885i) q^{41} +(4.85092 - 1.17192i) q^{42} +(-3.71119 - 6.42797i) q^{43} +(6.92040 - 6.26698i) q^{44} +(0.297958 + 0.0798376i) q^{45} +(-1.90948 - 3.50489i) q^{46} +(-1.46864 + 1.46864i) q^{47} +(3.64484 - 1.64776i) q^{48} +(4.72194 + 2.72621i) q^{49} +(-5.91950 - 3.61588i) q^{50} -0.161995 q^{51} +(-7.02391 - 1.63241i) q^{52} -12.7170 q^{53} +(1.20687 + 0.737204i) q^{54} +(1.24706 + 0.719991i) q^{55} +(9.42262 + 3.29143i) q^{56} +(-4.11770 + 4.11770i) q^{57} +(4.18145 + 7.67515i) q^{58} +(-4.88673 - 1.30940i) q^{59} +(0.414117 + 0.457295i) q^{60} +(5.88222 + 10.1883i) q^{61} +(-4.14214 + 1.00069i) q^{62} +(0.913320 + 3.40856i) q^{63} +(7.91192 + 1.18383i) q^{64} +(-0.0921557 - 1.10838i) q^{65} +(4.55119 + 4.78228i) q^{66} +(-2.11072 + 0.565565i) q^{67} +(-0.272223 - 0.175682i) q^{68} +(2.44415 - 1.41113i) q^{69} +(-0.0381027 + 1.53893i) q^{70} +(1.15253 - 4.30129i) q^{71} +(1.22858 + 2.54766i) q^{72} +(2.37148 + 2.37148i) q^{73} +(3.02701 - 10.2728i) q^{74} +(2.45242 - 4.24772i) q^{75} +(-11.3852 + 2.45395i) q^{76} +16.4730i q^{77} +(1.03100 - 4.99370i) q^{78} +9.72631i q^{79} +(0.199968 + 1.21756i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.57961 + 1.05478i) q^{82} +(-10.1767 - 10.1767i) q^{83} +(-2.16177 + 6.71837i) q^{84} +(0.0129333 - 0.0482677i) q^{85} +(10.4936 + 0.259813i) q^{86} +(-5.35230 + 3.09015i) q^{87} +(2.46167 + 12.9721i) q^{88} +(5.60967 - 1.50311i) q^{89} +(-0.316009 + 0.300739i) q^{90} +(10.4537 - 7.25275i) q^{91} +(5.63762 + 0.279336i) q^{92} +(-0.779873 - 2.91053i) q^{93} +(-0.689768 - 2.85515i) q^{94} +(-0.898155 - 1.55565i) q^{95} +(-0.698365 + 5.61358i) q^{96} +(-11.3928 - 3.05270i) q^{97} +(-6.77121 + 3.68898i) q^{98} +(-3.30089 + 3.30089i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9} + 12 q^{10} + 4 q^{11} - 4 q^{12} - 22 q^{14} - 4 q^{15} + 12 q^{16} - 2 q^{18} - 22 q^{19} - 4 q^{20} + 10 q^{21} - 34 q^{22} + 2 q^{24} - 4 q^{26} - 14 q^{28} + 8 q^{29} - 16 q^{30} - 2 q^{31} - 34 q^{32} + 4 q^{33} + 20 q^{34} + 24 q^{35} - 4 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} + 28 q^{40} - 36 q^{41} + 6 q^{42} + 10 q^{43} + 20 q^{44} + 4 q^{45} - 2 q^{46} + 20 q^{47} + 32 q^{48} - 54 q^{49} - 24 q^{50} + 36 q^{51} + 4 q^{52} - 36 q^{53} - 4 q^{54} - 24 q^{55} + 70 q^{56} - 32 q^{57} + 48 q^{58} - 36 q^{59} - 28 q^{60} - 2 q^{61} + 64 q^{62} + 8 q^{63} - 8 q^{64} + 16 q^{65} + 20 q^{66} - 16 q^{67} - 10 q^{68} + 12 q^{69} + 36 q^{71} - 2 q^{72} - 40 q^{73} - 30 q^{74} - 8 q^{75} + 58 q^{76} + 24 q^{78} - 48 q^{80} - 12 q^{81} - 30 q^{82} - 24 q^{83} - 26 q^{84} + 18 q^{85} + 30 q^{86} + 6 q^{87} - 78 q^{88} + 66 q^{89} + 12 q^{90} + 42 q^{91} + 36 q^{92} - 10 q^{93} + 6 q^{94} - 28 q^{95} + 8 q^{96} + 4 q^{97} + 44 q^{98} - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9 + 12 * q^10 + 4 * q^11 - 4 * q^12 - 22 * q^14 - 4 * q^15 + 12 * q^16 - 2 * q^18 - 22 * q^19 - 4 * q^20 + 10 * q^21 - 34 * q^22 + 2 * q^24 - 4 * q^26 - 14 * q^28 + 8 * q^29 - 16 * q^30 - 2 * q^31 - 34 * q^32 + 4 * q^33 + 20 * q^34 + 24 * q^35 - 4 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 + 28 * q^40 - 36 * q^41 + 6 * q^42 + 10 * q^43 + 20 * q^44 + 4 * q^45 - 2 * q^46 + 20 * q^47 + 32 * q^48 - 54 * q^49 - 24 * q^50 + 36 * q^51 + 4 * q^52 - 36 * q^53 - 4 * q^54 - 24 * q^55 + 70 * q^56 - 32 * q^57 + 48 * q^58 - 36 * q^59 - 28 * q^60 - 2 * q^61 + 64 * q^62 + 8 * q^63 - 8 * q^64 + 16 * q^65 + 20 * q^66 - 16 * q^67 - 10 * q^68 + 12 * q^69 + 36 * q^71 - 2 * q^72 - 40 * q^73 - 30 * q^74 - 8 * q^75 + 58 * q^76 + 24 * q^78 - 48 * q^80 - 12 * q^81 - 30 * q^82 - 24 * q^83 - 26 * q^84 + 18 * q^85 + 30 * q^86 + 6 * q^87 - 78 * q^88 + 66 * q^89 + 12 * q^90 + 42 * q^91 + 36 * q^92 - 10 * q^93 + 6 * q^94 - 28 * q^95 + 8 * q^96 + 4 * q^97 + 44 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.737204	+	1.20687i	−0.521282	+	0.853384i
$2$	−0.737204	+	1.20687i	−0.521282	+	0.853384i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.913059	−	1.77942i	−0.456530	−	0.889708i
$5$	0.218120	−	0.218120i	0.0975464	−	0.0975464i	−0.656650	−	0.754196i	$-0.728027\pi$
$5$	0.218120	−	0.218120i	0.0975464	−	0.0975464i	0.754196	+	0.656650i	$0.228027\pi$
$6$	1.24187	−	0.676576i	0.506992	−	0.276211i
$7$	3.40856	+	0.913320i	1.28831	+	0.345203i	0.837020	−	0.547173i	$-0.184296\pi$
$7$	3.40856	+	0.913320i	1.28831	+	0.345203i	0.451294	+	0.892375i	$0.350963\pi$
$8$	2.82063	+	0.209852i	0.997244	+	0.0741940i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.102443	+	0.424042i	0.0323953	+	0.134094i
$11$	1.20821	+	4.50910i	0.364289	+	1.35955i	0.868382	+	0.495896i	$0.165160\pi$
$11$	1.20821	+	4.50910i	0.364289	+	1.35955i	−0.504093	+	0.863649i	$0.668173\pi$
$12$	−0.0989759	+	1.99755i	−0.0285719	+	0.576643i
$13$	2.32949	−	2.75199i	0.646085	−	0.763265i
$13$	2.32949	−	2.75199i	0.646085	−	0.763265i
$14$	−3.61506	+	3.44037i	−0.966166	+	0.919479i
$15$	−0.297958	+	0.0798376i	−0.0769324	+	0.0206140i
$16$	−2.33265	+	3.24942i	−0.583162	+	0.812356i
$17$	0.140292	−	0.0809975i	0.0340257	−	0.0196448i	−0.482891	−	0.875681i	$-0.660413\pi$
$17$	0.140292	−	0.0809975i	0.0340257	−	0.0196448i	0.516916	+	0.856036i	$0.327080\pi$
$18$	−1.41378	−	0.0350040i	−0.333231	−	0.00825052i
$19$	1.50718	−	5.62489i	0.345772	−	1.29044i	−0.545936	−	0.837827i	$-0.683826\pi$
$19$	1.50718	−	5.62489i	0.345772	−	1.29044i	0.891708	−	0.452611i	$-0.149507\pi$
$20$	−0.587284	−	0.188970i	−0.131321	−	0.0422550i
$21$	−2.49524	−	2.49524i	−0.544506	−	0.544506i
$22$	−6.33259	−	1.86598i	−1.35011	−	0.397828i
$23$	−1.41113	+	2.44415i	−0.294242	+	0.509641i	−0.974808	−	0.223045i	$-0.928400\pi$
$23$	−1.41113	+	2.44415i	−0.294242	+	0.509641i	0.680567	+	0.732686i	$0.261734\pi$
$24$	−2.33781	−	1.59205i	−0.477204	−	0.324976i
$25$			4.90485i			0.980969i
$26$	1.60398	+	4.84017i	0.314566	+	0.949236i
$27$		−	1.00000i		−	0.192450i
$28$	−1.48704	−	6.89916i	−0.281024	−	1.30382i
$29$	3.09015	−	5.35230i	0.573827	−	0.993897i	−0.422341	−	0.906437i	$-0.638792\pi$
$29$	3.09015	−	5.35230i	0.573827	−	0.993897i	0.996168	−	0.0874604i	$-0.0278751\pi$
$30$	0.123303	−	0.418452i	0.0225119	−	0.0763986i
$31$	2.13065	+	2.13065i	0.382677	+	0.382677i	0.872066	−	0.489389i	$-0.162780\pi$
$31$	2.13065	+	2.13065i	0.382677	+	0.382677i	−0.489389	+	0.872066i	$0.662780\pi$
$32$	−2.20199	−	5.21069i	−0.389260	−	0.921128i
$33$	1.20821	−	4.50910i	0.210322	−	0.784934i
$34$	−0.00567047	+	0.229025i	−0.000972477	+	0.0392775i
$35$	0.942690	−	0.544262i	0.159344	−	0.0919971i
$36$	1.08449	−	1.68044i	0.180748	−	0.280073i
$37$	−7.31471	+	1.95997i	−1.20253	+	0.322217i	−0.803827	−	0.594863i	$-0.797206\pi$
$37$	−7.31471	+	1.95997i	−1.20253	+	0.322217i	−0.398704	+	0.917080i	$0.630540\pi$
$38$	5.67739	+	5.96566i	0.920995	+	0.967759i
$39$	−3.39340	+	1.21855i	−0.543378	+	0.195124i
$40$	0.661010	−	0.569464i	0.104515	−	0.0900402i
$41$	−0.682962	−	2.54885i	−0.106661	−	0.398063i	0.891868	−	0.452297i	$-0.149395\pi$
$41$	−0.682962	−	2.54885i	−0.106661	−	0.398063i	−0.998528	+	0.0542334i	$0.982729\pi$
$42$	4.85092	−	1.17192i	0.748514	−	0.180831i
$43$	−3.71119	−	6.42797i	−0.565951	−	0.980256i	−0.996960	−	0.0779088i	$-0.975176\pi$
$43$	−3.71119	−	6.42797i	−0.565951	−	0.980256i	0.431009	−	0.902348i	$-0.358158\pi$
$44$	6.92040	−	6.26698i	1.04329	−	0.944783i
$45$	0.297958	+	0.0798376i	0.0444169	+	0.0119015i
$46$	−1.90948	−	3.50489i	−0.281537	−	0.516768i
$47$	−1.46864	+	1.46864i	−0.214224	+	0.214224i	−0.806059	−	0.591835i	$-0.798404\pi$
$47$	−1.46864	+	1.46864i	−0.214224	+	0.214224i	0.591835	+	0.806059i	$0.298404\pi$
$48$	3.64484	−	1.64776i	0.526088	−	0.237834i
$49$	4.72194	+	2.72621i	0.674562	+	0.389459i
$50$	−5.91950	−	3.61588i	−0.837144	−	0.511362i
$51$	−0.161995			−0.0226838
$52$	−7.02391	−	1.63241i	−0.974040	−	0.226374i
$53$	−12.7170			−1.74681			−0.873407	−	0.486990i	$-0.838095\pi$
$53$	−12.7170			−1.74681			−0.873407	+	0.486990i	$0.838095\pi$
$54$	1.20687	+	0.737204i	0.164234	+	0.100321i
$55$	1.24706	+	0.719991i	0.168154	+	0.0970836i
$56$	9.42262	+	3.29143i	1.25915	+	0.439836i
$57$	−4.11770	+	4.11770i	−0.545403	+	0.545403i
$58$	4.18145	+	7.67515i	0.549051	+	1.00780i
$59$	−4.88673	−	1.30940i	−0.636198	−	0.170469i	−0.0737173	−	0.997279i	$-0.523486\pi$
$59$	−4.88673	−	1.30940i	−0.636198	−	0.170469i	−0.562481	+	0.826810i	$0.690153\pi$
$60$	0.414117	+	0.457295i	0.0534623	+	0.0590365i
$61$	5.88222	+	10.1883i	0.753141	+	1.30448i	0.946293	+	0.323310i	$0.104796\pi$
$61$	5.88222	+	10.1883i	0.753141	+	1.30448i	−0.193152	+	0.981169i	$0.561871\pi$
$62$	−4.14214	+	1.00069i	−0.526053	+	0.127088i
$63$	0.913320	+	3.40856i	0.115068	+	0.429438i
$64$	7.91192	+	1.18383i	0.988991	+	0.147979i
$65$	−0.0921557	−	1.10838i	−0.0114305	−	0.137477i
$66$	4.55119	+	4.78228i	0.560213	+	0.588658i
$67$	−2.11072	+	0.565565i	−0.257865	+	0.0690948i	−0.385436	−	0.922735i	$-0.625949\pi$
$67$	−2.11072	+	0.565565i	−0.257865	+	0.0690948i	0.127570	+	0.991830i	$0.459282\pi$
$68$	−0.272223	−	0.175682i	−0.0330119	−	0.0213046i
$69$	2.44415	−	1.41113i	0.294242	−	0.169880i
$70$	−0.0381027	+	1.53893i	−0.00455414	+	0.183938i
$71$	1.15253	−	4.30129i	0.136780	−	0.510469i	−0.863205	−	0.504854i	$-0.831546\pi$
$71$	1.15253	−	4.30129i	0.136780	−	0.510469i	0.999984	−	0.00561434i	$-0.00178711\pi$
$72$	1.22858	+	2.54766i	0.144789	+	0.300245i
$73$	2.37148	+	2.37148i	0.277561	+	0.277561i	0.832134	−	0.554574i	$-0.187119\pi$
$73$	2.37148	+	2.37148i	0.277561	+	0.277561i	−0.554574	+	0.832134i	$0.687119\pi$
$74$	3.02701	−	10.2728i	0.351883	−	1.19419i
$75$	2.45242	−	4.24772i	0.283181	−	0.490485i
$76$	−11.3852	+	2.45395i	−1.30597	+	0.281487i
$77$			16.4730i			1.87727i
$78$	1.03100	−	4.99370i	0.116738	−	0.565425i
$79$			9.72631i			1.09429i	0.837036	+	0.547147i	$0.184286\pi$
$79$			9.72631i			1.09429i	−0.837036	+	0.547147i	$0.815714\pi$
$80$	0.199968	+	1.21756i	0.0223571	+	0.136128i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	3.57961	+	1.05478i	0.395301	+	0.116481i
$83$	−10.1767	−	10.1767i	−1.11704	−	1.11704i	−0.992174	−	0.124862i	$-0.960151\pi$
$83$	−10.1767	−	10.1767i	−1.11704	−	1.11704i	−0.124862	−	0.992174i	$-0.539849\pi$
$84$	−2.16177	+	6.71837i	−0.235868	+	0.733034i
$85$	0.0129333	−	0.0482677i	0.00140281	−	0.00523536i
$86$	10.4936	+	0.259813i	1.13156	+	0.0280163i
$87$	−5.35230	+	3.09015i	−0.573827	+	0.331299i
$88$	2.46167	+	12.9721i	0.262415	+	1.38283i
$89$	5.60967	−	1.50311i	0.594624	−	0.159329i	0.0510584	−	0.998696i	$-0.483741\pi$
$89$	5.60967	−	1.50311i	0.594624	−	0.159329i	0.543566	+	0.839367i	$0.317074\pi$
$90$	−0.316009	+	0.300739i	−0.0333103	+	0.0317007i
$91$	10.4537	−	7.25275i	1.09584	−	0.760295i
$92$	5.63762	+	0.279336i	0.587762	+	0.0291228i
$93$	−0.779873	−	2.91053i	−0.0808691	−	0.301807i
$94$	−0.689768	−	2.85515i	−0.0711441	−	0.294486i
$95$	−0.898155	−	1.55565i	−0.0921487	−	0.159606i
$96$	−0.698365	+	5.61358i	−0.0712766	+	0.572934i
$97$	−11.3928	−	3.05270i	−1.15677	−	0.309955i	−0.371093	−	0.928596i	$-0.621017\pi$
$97$	−11.3928	−	3.05270i	−1.15677	−	0.309955i	−0.785674	+	0.618641i	$0.787683\pi$
$98$	−6.77121	+	3.68898i	−0.683995	+	0.372643i
$99$	−3.30089	+	3.30089i	−0.331752	+	0.331752i
$100$	8.72777	−	4.47842i	0.872777	−	0.447842i
$101$	8.63855	+	4.98747i	0.859568	+	0.496272i	0.863868	−	0.503719i	$-0.168035\pi$
$101$	8.63855	+	4.98747i	0.859568	+	0.496272i	−0.00429955	+	0.999991i	$0.501369\pi$
$102$	0.119423	−	0.195506i	0.0118247	−	0.0193580i
$103$	−3.21343			−0.316628			−0.158314	−	0.987389i	$-0.550606\pi$
$103$	−3.21343			−0.316628			−0.158314	+	0.987389i	$0.550606\pi$
$104$	7.14815	−	7.27351i	0.700934	−	0.713226i
$105$	−1.08852			−0.106229
$106$	9.37503	−	15.3477i	0.910584	−	1.49070i
$107$	4.82266	+	2.78437i	0.466224	+	0.269175i	0.714658	−	0.699474i	$-0.246582\pi$
$107$	4.82266	+	2.78437i	0.466224	+	0.269175i	−0.248433	+	0.968649i	$0.579916\pi$
$108$	−1.77942	+	0.913059i	−0.171224	+	0.0878592i
$109$	8.65596	−	8.65596i	0.829091	−	0.829091i	−0.158300	−	0.987391i	$-0.550601\pi$
$109$	8.65596	−	8.65596i	0.829091	−	0.829091i	0.987391	+	0.158300i	$0.0506014\pi$
$110$	−1.78827	+	0.974258i	−0.170505	+	0.0928918i
$111$	7.31471	+	1.95997i	0.694282	+	0.186032i
$112$	−10.9187	+	8.94540i	−1.03172	+	0.845261i
$113$	−2.44457	−	4.23412i	−0.229966	−	0.398313i	0.727832	−	0.685756i	$-0.240528\pi$
$113$	−2.44457	−	4.23412i	−0.229966	−	0.398313i	−0.957798	+	0.287443i	$0.907195\pi$
$114$	−1.93393	−	8.00511i	−0.181129	−	0.749748i
$115$	0.225323	+	0.840917i	0.0210115	+	0.0784159i
$116$	−12.3455	−	0.611701i	−1.14625	−	0.0567950i
$117$	3.54804	+	0.641404i	0.328017	+	0.0592978i
$118$	5.18279	−	4.93234i	0.477114	−	0.454059i
$119$	0.552169	−	0.147953i	0.0506173	−	0.0135629i
$120$	−0.857184	+	0.162665i	−0.0782498	+	0.0148492i
$121$	−9.34594	+	5.39588i	−0.849631	+	0.490535i
$122$	−16.6323	−	0.411802i	−1.50582	−	0.0372828i
$123$	−0.682962	+	2.54885i	−0.0615806	+	0.229822i
$124$	1.84591	−	5.73673i	0.165767	−	0.515174i
$125$	2.16045	+	2.16045i	0.193236	+	0.193236i
$126$	−4.78698	−	1.41055i	−0.426458	−	0.125662i
$127$	−0.229476	+	0.397465i	−0.0203627	+	0.0352693i	−0.876027	−	0.482262i	$-0.839815\pi$
$127$	−0.229476	+	0.397465i	−0.0203627	+	0.0352693i	0.855664	+	0.517531i	$0.173149\pi$
$128$	−7.26143	+	8.67592i	−0.641826	+	0.766850i
$129$			7.42238i			0.653504i
$130$	1.40560	+	0.705879i	0.123279	+	0.0619097i
$131$		−	18.1232i		−	1.58343i	−0.610887	−	0.791717i	$-0.709187\pi$
$131$		−	18.1232i		−	1.58343i	0.610887	−	0.791717i	$-0.290813\pi$
$132$	−9.12674	+	1.96717i	−0.794380	+	0.171220i
$133$	10.2746	−	17.7962i	0.890925	−	1.54313i
$134$	0.873468	−	2.96429i	0.0754562	−	0.256076i
$135$	−0.218120	−	0.218120i	−0.0187728	−	0.0187728i
$136$	0.412709	−	0.199023i	0.0353895	−	0.0170661i
$137$	6.00990	−	22.4292i	0.513460	−	1.91626i	0.134257	−	0.990947i	$-0.457135\pi$
$137$	6.00990	−	22.4292i	0.513460	−	1.91626i	0.379203	−	0.925313i	$-0.376198\pi$
$138$	−0.0987905	+	3.99006i	−0.00840961	+	0.339657i
$139$	−13.3213	+	7.69106i	−1.12990	+	0.652347i	−0.943909	−	0.330205i	$-0.892882\pi$
$139$	−13.3213	+	7.69106i	−1.12990	+	0.652347i	−0.185989	+	0.982552i	$0.559549\pi$
$140$	−1.82920	−	1.18049i	−0.154596	−	0.0997699i
$141$	2.00621	−	0.537561i	0.168953	−	0.0452708i
$142$	4.34143	+	4.56187i	0.364325	+	0.382824i
$143$	15.2235	+	7.17893i	1.27306	+	0.600333i
$144$	−3.98041	−	0.395418i	−0.331701	−	0.0329515i
$145$	−0.493421	−	1.84147i	−0.0409764	−	0.152926i
$146$	−4.61033	+	1.11380i	−0.381553	+	0.0921784i
$147$	−2.72621	−	4.72194i	−0.224854	−	0.389459i
$148$	10.1664	+	11.2263i	0.835670	+	0.922800i
$149$	−11.7351	−	3.14440i	−0.961374	−	0.257599i	−0.256192	−	0.966626i	$-0.582468\pi$
$149$	−11.7351	−	3.14440i	−0.961374	−	0.257599i	−0.705182	+	0.709026i	$0.749135\pi$
$150$	3.31850	+	6.09119i	0.270954	+	0.497344i
$151$	−0.481425	+	0.481425i	−0.0391778	+	0.0391778i	−0.726424	−	0.687247i	$-0.758819\pi$
$151$	−0.481425	+	0.481425i	−0.0391778	+	0.0391778i	0.687247	+	0.726424i	$0.258819\pi$
$152$	5.43161	−	15.5494i	0.440561	−	1.26123i
$153$	0.140292	+	0.0809975i	0.0113419	+	0.00654826i
$154$	−19.8807	−	12.1440i	−1.60204	−	0.978590i
$155$	0.929477			0.0746574
$156$	5.26668	+	4.92566i	0.421672	+	0.394368i
$157$	−17.7157			−1.41387			−0.706935	−	0.707279i	$-0.749923\pi$
$157$	−17.7157			−1.41387			−0.706935	+	0.707279i	$0.749923\pi$
$158$	−11.7384	−	7.17028i	−0.933854	−	0.570437i
$159$	11.0132	+	6.35850i	0.873407	+	0.504262i
$160$	−1.61685	−	0.656258i	−0.127824	−	0.0518817i
$161$	−7.04222	+	7.04222i	−0.555005	+	0.555005i
$162$	−0.676576	−	1.24187i	−0.0531568	−	0.0975707i
$163$	15.3019	+	4.10013i	1.19854	+	0.321147i	0.802255	−	0.596982i	$-0.203634\pi$
$163$	15.3019	+	4.10013i	1.19854	+	0.321147i	0.396282	+	0.918129i	$0.370300\pi$
$164$	−3.91188	+	3.54252i	−0.305466	+	0.276625i
$165$	−0.719991	−	1.24706i	−0.0560513	−	0.0970836i
$166$	19.7842	−	4.77961i	1.53555	−	0.370970i
$167$	5.53362	+	20.6517i	0.428204	+	1.59808i	0.756825	+	0.653618i	$0.226750\pi$
$167$	5.53362	+	20.6517i	0.428204	+	1.59808i	−0.328621	+	0.944462i	$0.606584\pi$
$168$	−6.51451	−	7.56178i	−0.502606	−	0.583404i
$169$	−2.14692	−	12.8215i	−0.165148	−	0.986269i
$170$	0.0487182	+	0.0511919i	0.00373652	+	0.00392624i
$171$	5.62489	−	1.50718i	0.430146	−	0.115257i
$172$	−8.04950	+	12.4729i	−0.613769	+	0.951047i
$173$	−1.69391	+	0.977978i	−0.128785	+	0.0743543i	−0.563009	−	0.826451i	$-0.690356\pi$
$173$	−1.69391	+	0.977978i	−0.128785	+	0.0743543i	0.434223	+	0.900805i	$0.357023\pi$
$174$	0.216335	−	8.73759i	0.0164003	−	0.662395i
$175$	−4.47970	+	16.7185i	−0.338633	+	1.26380i
$176$	−17.4703	−	6.59215i	−1.31687	−	0.496902i
$177$	3.57733	+	3.57733i	0.268889	+	0.268889i
$178$	−2.32142	+	7.87823i	−0.173998	+	0.590498i
$179$	−4.50231	+	7.79823i	−0.336518	+	0.582867i	−0.983775	−	0.179405i	$-0.942583\pi$
$179$	−4.50231	+	7.79823i	−0.336518	+	0.582867i	0.647257	+	0.762272i	$0.275916\pi$
$180$	−0.129989	−	0.603088i	−0.00968880	−	0.0449515i
$181$		−	9.89145i		−	0.735226i	−0.929979	−	0.367613i	$-0.880175\pi$
$181$		−	9.89145i		−	0.735226i	0.929979	−	0.367613i	$-0.119825\pi$
$182$	1.04663	+	17.9629i	0.0775810	+	1.33150i
$183$		−	11.7644i		−	0.869653i
$184$	−4.49320	+	6.59793i	−0.331243	+	0.486406i
$185$	−1.16798	+	2.02300i	−0.0858714	+	0.148734i
$186$	4.08755	+	1.20445i	0.299713	+	0.0883145i
$187$	0.534728	+	0.534728i	0.0391032	+	0.0391032i
$188$	3.95429	+	1.27237i	0.288396	+	0.0927972i
$189$	0.913320	−	3.40856i	0.0664343	−	0.247936i
$190$	2.53959	+	0.0628780i	0.184241	+	0.00456165i
$191$	−10.9363	+	6.31405i	−0.791320	+	0.456869i	−0.840427	−	0.541925i	$-0.817696\pi$
$191$	−10.9363	+	6.31405i	−0.791320	+	0.456869i	0.0491073	+	0.998794i	$0.484362\pi$
$192$	−6.26001	−	4.98119i	−0.451777	−	0.359486i
$193$	13.0641	−	3.50052i	0.940376	−	0.251973i	0.244102	−	0.969749i	$-0.421507\pi$
$193$	13.0641	−	3.50052i	0.940376	−	0.251973i	0.696274	+	0.717777i	$0.254840\pi$
$194$	12.0830	−	11.4992i	0.867512	−	0.825592i
$195$	−0.474378	+	1.00596i	−0.0339709	+	0.0720382i
$196$	0.539658	−	10.8915i	0.0385470	−	0.777963i
$197$	3.26670	+	12.1915i	0.232743	+	0.868609i	0.979153	+	0.203123i	$0.0651091\pi$
$197$	3.26670	+	12.1915i	0.232743	+	0.868609i	−0.746410	+	0.665486i	$0.768224\pi$
$198$	−1.55031	−	6.41717i	−0.110176	−	0.456048i
$199$	−3.95616	−	6.85228i	−0.280445	−	0.485745i	0.691049	−	0.722808i	$-0.257149\pi$
$199$	−3.95616	−	6.85228i	−0.280445	−	0.485745i	−0.971494	+	0.237063i	$0.923815\pi$
$200$	−1.02929	+	13.8348i	−0.0727820	+	0.978266i
$201$	2.11072	+	0.565565i	0.148879	+	0.0398919i
$202$	−12.3876	+	6.74880i	−0.871588	+	0.474844i
$203$	15.4213	−	15.4213i	1.08237	−	1.08237i
$204$	0.147911	+	0.288256i	0.0103558	+	0.0201820i
$205$	−0.704924	−	0.406988i	−0.0492340	−	0.0284253i
$206$	2.36895	−	3.87818i	0.165053	−	0.270206i
$207$	−2.82227			−0.196161
$208$	3.50851	+	13.9889i	0.243271	+	0.969958i
$209$	27.1842			1.88037
$210$	0.802465	−	1.31370i	0.0553753	−	0.0906542i
$211$	−10.7380	−	6.19959i	−0.739234	−	0.426797i	0.0825565	−	0.996586i	$-0.473692\pi$
$211$	−10.7380	−	6.19959i	−0.739234	−	0.426797i	−0.821791	+	0.569789i	$0.807025\pi$
$212$	11.6114	+	22.6288i	0.797473	+	1.55416i
$213$	−3.14876	+	3.14876i	−0.215749	+	0.215749i
$214$	−6.91565	+	3.76767i	−0.472744	+	0.257553i
$215$	−2.21156	−	0.592585i	−0.150827	−	0.0404140i
$216$	0.209852	−	2.82063i	0.0142786	−	0.191920i
$217$	5.31649	+	9.20842i	0.360907	+	0.625108i
$218$	4.06539	+	16.8278i	0.275343	+	1.13972i
$219$	−0.868021	−	3.23950i	−0.0586555	−	0.218905i
$220$	0.142524	−	2.87644i	0.00960893	−	0.193929i
$221$	0.103904	−	0.574765i	0.00698935	−	0.0386629i
$222$	−7.75786	+	7.38299i	−0.520674	+	0.495514i
$223$	−1.84423	+	0.494160i	−0.123499	+	0.0330914i	−0.320039	−	0.947404i	$-0.603696\pi$
$223$	−1.84423	+	0.494160i	−0.123499	+	0.0330914i	0.196540	+	0.980496i	$0.437029\pi$
$224$	−2.74658	−	19.7720i	−0.183514	−	1.32108i
$225$	−4.24772	+	2.45242i	−0.283181	+	0.163495i
$226$	6.91217	+	0.171139i	0.459791	+	0.0113840i
$227$	5.70740	−	21.3003i	0.378813	−	1.41375i	−0.468879	−	0.883262i	$-0.655342\pi$
$227$	5.70740	−	21.3003i	0.378813	−	1.41375i	0.847692	−	0.530488i	$-0.177991\pi$
$228$	11.0868	+	3.56740i	0.734242	+	0.236257i
$229$	11.0263	+	11.0263i	0.728640	+	0.728640i	0.970349	−	0.241709i	$-0.0777078\pi$
$229$	11.0263	+	11.0263i	0.728640	+	0.728640i	−0.241709	+	0.970349i	$0.577708\pi$
$230$	−1.18098	−	0.347993i	−0.0778718	−	0.0229459i
$231$	8.23651	−	14.2660i	0.541922	−	0.938637i
$232$	9.83937	−	14.4484i	0.645987	−	0.948584i
$233$			1.44748i			0.0948275i	0.998875	+	0.0474138i	$0.0150979\pi$
$233$			1.44748i			0.0948275i	−0.998875	+	0.0474138i	$0.984902\pi$
$234$	−3.38972	+	3.80917i	−0.221593	+	0.249013i
$235$			0.640682i			0.0417935i
$236$	2.13191	+	9.89108i	0.138776	+	0.643855i
$237$	4.86315	−	8.42323i	0.315896	−	0.547147i
$238$	−0.228502	+	0.775467i	−0.0148116	+	0.0502661i
$239$	9.99869	+	9.99869i	0.646761	+	0.646761i	0.952209	−	0.305448i	$-0.0988061\pi$
$239$	9.99869	+	9.99869i	0.646761	+	0.646761i	−0.305448	+	0.952209i	$0.598806\pi$
$240$	0.435604	−	1.15442i	0.0281181	−	0.0745178i
$241$	−1.16746	+	4.35700i	−0.0752024	+	0.280659i	−0.993279	−	0.115743i	$-0.963075\pi$
$241$	−1.16746	+	4.35700i	−0.0752024	+	0.280659i	0.918077	+	0.396403i	$0.129742\pi$
$242$	0.377754	−	15.2572i	0.0242830	−	0.980769i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	12.7584	−	19.7695i	0.816775	−	1.26561i
$245$	1.62459	−	0.435308i	0.103791	−	0.0278108i
$246$	−2.57264	−	2.70327i	−0.164026	−	0.172354i
$247$	−11.9687	−	17.2509i	−0.761548	−	1.09765i
$248$	5.56266	+	6.45691i	0.353230	+	0.410014i
$249$	3.72493	+	13.9016i	0.236058	+	0.880979i
$250$	−4.20007	+	1.01468i	−0.265636	+	0.0641742i
$251$	15.1940	+	26.3168i	0.959038	+	1.66110i	0.724846	+	0.688911i	$0.241911\pi$
$251$	15.1940	+	26.3168i	0.959038	+	1.66110i	0.234192	+	0.972190i	$0.424756\pi$
$252$	5.23133	−	4.73739i	0.329543	−	0.298428i
$253$	−12.7259	−	3.40989i	−0.800069	−	0.214378i
$254$	−0.310517	−	0.569961i	−0.0194835	−	0.0357625i
$255$	−0.0353344	+	0.0353344i	−0.00221273	+	0.00221273i
$256$	−5.11752	−	15.1595i	−0.319845	−	0.947470i
$257$	−4.32247	−	2.49558i	−0.269628	−	0.155670i	0.359091	−	0.933303i	$-0.383087\pi$
$257$	−4.32247	−	2.49558i	−0.269628	−	0.155670i	−0.628719	+	0.777633i	$0.716420\pi$
$258$	−8.95783	−	5.47181i	−0.557690	−	0.340660i
$259$	−26.7227			−1.66047
$260$	−1.88812	+	1.17600i	−0.117096	+	0.0729321i
$261$	6.18031			0.382551
$262$	21.8724	+	13.3605i	1.35128	+	0.825417i
$263$	−6.54817	−	3.78059i	−0.403778	−	0.233121i	0.284335	−	0.958725i	$-0.408227\pi$
$263$	−6.54817	−	3.78059i	−0.403778	−	0.233121i	−0.688113	+	0.725604i	$0.741561\pi$
$264$	4.35416	−	12.4650i	0.267980	−	0.767166i
$265$	−2.77384	+	2.77384i	−0.170395	+	0.170395i
$266$	13.9032	+	25.5196i	0.852457	+	1.56471i
$267$	−5.60967	−	1.50311i	−0.343306	−	0.0919887i
$268$	2.93359	+	3.23945i	0.179197	+	0.197881i
$269$	13.8459	+	23.9817i	0.844197	+	1.46219i	0.886317	+	0.463080i	$0.153256\pi$
$269$	13.8459	+	23.9817i	0.844197	+	1.46219i	−0.0421193	+	0.999113i	$0.513411\pi$
$270$	0.424042	−	0.102443i	0.0258064	−	0.00623449i
$271$	−2.78060	−	10.3773i	−0.168909	−	0.630378i	−0.997509	−	0.0705370i	$-0.977529\pi$
$271$	−2.78060	−	10.3773i	−0.168909	−	0.630378i	0.828600	−	0.559841i	$-0.189138\pi$
$272$	−0.0640558	+	0.644806i	−0.00388395	+	0.0390971i
$273$	−12.6795	+	1.05424i	−0.767399	+	0.0638053i
$274$	22.6386	+	23.7881i	1.36765	+	1.43709i
$275$	−22.1164	+	5.92608i	−1.33367	+	0.357356i
$276$	−4.74265	−	3.06072i	−0.285474	−	0.184234i
$277$	−14.8531	+	8.57542i	−0.892435	+	0.515247i	−0.874738	−	0.484596i	$-0.838967\pi$
$277$	−14.8531	+	8.57542i	−0.892435	+	0.515247i	−0.0176965	+	0.999843i	$0.505633\pi$
$278$	0.538435	−	21.7469i	0.0322932	−	1.30429i
$279$	−0.779873	+	2.91053i	−0.0466898	+	0.174249i
$280$	2.77319	−	1.33734i	0.165730	−	0.0799212i
$281$	−20.7005	−	20.7005i	−1.23489	−	1.23489i	−0.962063	−	0.272828i	$-0.912041\pi$
$281$	−20.7005	−	20.7005i	−1.23489	−	1.23489i	−0.272828	−	0.962063i	$-0.587959\pi$
$282$	−0.830218	+	2.81752i	−0.0494388	+	0.167781i
$283$	−8.70056	+	15.0698i	−0.517194	+	0.895807i	0.482606	+	0.875838i	$0.339690\pi$
$283$	−8.70056	+	15.0698i	−0.517194	+	0.895807i	−0.999801	+	0.0199696i	$0.993643\pi$
$284$	−8.70610	+	1.87650i	−0.516612	+	0.111350i
$285$			1.79631i			0.106404i
$286$	−19.8869	+	13.0804i	−1.17594	+	0.773463i
$287$		−	9.31166i		−	0.549650i
$288$	3.41159	−	4.51232i	0.201030	−	0.265891i
$289$	−8.48688	+	14.6997i	−0.499228	+	0.864689i
$290$	2.58616	+	0.762047i	0.151865	+	0.0447490i
$291$	8.34013	+	8.34013i	0.488907	+	0.488907i
$292$	2.05455	−	6.38515i	0.120233	−	0.373663i
$293$	−0.661736	+	2.46963i	−0.0386591	+	0.144278i	−0.982558	−	0.185957i	$-0.940461\pi$
$293$	−0.661736	+	2.46963i	−0.0386591	+	0.144278i	0.943899	+	0.330235i	$0.107128\pi$
$294$	7.70853	+	0.190856i	0.449570	+	0.0111310i
$295$	−1.35150	+	0.780289i	−0.0786874	+	0.0454302i
$296$	−21.0434	+	3.99335i	−1.22312	+	0.232109i
$297$	4.50910	−	1.20821i	0.261645	−	0.0701074i
$298$	12.4460	−	11.8446i	0.720979	−	0.686140i
$299$	3.43907	+	9.57707i	0.198887	+	0.553856i
$300$	−9.79767	−	0.485461i	−0.565669	−	0.0280281i
$301$	−6.77901	−	25.2996i	−0.390736	−	1.45825i
$302$	−0.226107	−	0.935924i	−0.0130110	−	0.0538564i
$303$	−4.98747	−	8.63855i	−0.286523	−	0.496272i
$304$	14.7619	+	18.0184i	0.846654	+	1.03342i
$305$	3.50531	+	0.939245i	0.200713	+	0.0537810i
$306$	−0.201177	+	0.109602i	−0.0115005	+	0.00626552i
$307$	7.90899	−	7.90899i	0.451390	−	0.451390i	−0.444426	−	0.895816i	$-0.646592\pi$
$307$	7.90899	−	7.90899i	0.451390	−	0.451390i	0.895816	+	0.444426i	$0.146592\pi$
$308$	29.3124	−	15.0408i	1.67023	−	0.857031i
$309$	2.78291	+	1.60671i	0.158314	+	0.0914028i
$310$	−0.685215	+	1.12176i	−0.0389176	+	0.0637115i
$311$	−6.80463			−0.385855			−0.192927	−	0.981213i	$-0.561798\pi$
$311$	−6.80463			−0.385855			−0.192927	+	0.981213i	$0.561798\pi$
$312$	−9.82724	+	2.72497i	−0.556358	+	0.154271i
$313$	−19.0315			−1.07572			−0.537861	−	0.843033i	$-0.680768\pi$
$313$	−19.0315			−1.07572			−0.537861	+	0.843033i	$0.680768\pi$
$314$	13.0601	−	21.3805i	0.737025	−	1.20657i
$315$	0.942690	+	0.544262i	0.0531145	+	0.0306657i
$316$	17.3071	−	8.88069i	0.973603	−	0.499578i
$317$	−15.7399	+	15.7399i	−0.884040	+	0.884040i	−0.993942	−	0.109902i	$-0.964946\pi$
$317$	−15.7399	+	15.7399i	−0.884040	+	0.884040i	0.109902	+	0.993942i	$0.464946\pi$
$318$	−15.7929	+	8.60402i	−0.885621	+	0.482489i
$319$	27.8676	+	7.46711i	1.56029	+	0.418078i
$320$	1.98397	−	1.46753i	0.110907	−	0.0820376i
$321$	−2.78437	−	4.82266i	−0.155408	−	0.269175i
$322$	−3.30747	−	13.6906i	−0.184318	−	0.762947i
$323$	−0.244156	−	0.911203i	−0.0135852	−	0.0507007i
$324$	1.99755	+	0.0989759i	0.110975	+	0.00549866i
$325$	13.4981	+	11.4258i	0.748740	+	0.633790i
$326$	−16.2289	+	15.4447i	−0.898838	+	0.855404i
$327$	−11.8243	+	3.16830i	−0.653883	+	0.175207i
$328$	−1.39150	−	7.33268i	−0.0768329	−	0.404880i
$329$	−6.34730	+	3.66462i	−0.349938	+	0.202037i
$330$	2.03582	+	0.0504051i	0.112068	+	0.00277471i
$331$	1.98032	−	7.39065i	0.108848	−	0.406227i	−0.889905	−	0.456146i	$-0.849230\pi$
$331$	1.98032	−	7.39065i	0.108848	−	0.406227i	0.998753	+	0.0499189i	$0.0158963\pi$
$332$	−8.81665	+	27.4005i	−0.483876	+	1.50380i
$333$	−5.35474	−	5.35474i	−0.293438	−	0.293438i
$334$	−29.0033	−	8.54621i	−1.58699	−	0.467628i
$335$	−0.337029	+	0.583752i	−0.0184139	+	0.0318938i
$336$	13.9286	−	2.28758i	0.759867	−	0.124798i
$337$		−	14.5349i		−	0.791766i	−0.918301	−	0.395883i	$-0.870439\pi$
$337$		−	14.5349i		−	0.791766i	0.918301	−	0.395883i	$-0.129561\pi$
$338$	17.0566	+	6.86101i	0.927755	+	0.373190i
$339$			4.88914i			0.265542i
$340$	−0.0976972	+	0.0210575i	−0.00529837	+	0.00114201i
$341$	−7.03305	+	12.1816i	−0.380861	+	0.659671i
$342$	−2.32772	+	7.89960i	−0.125869	+	0.427161i
$343$	−3.86157	−	3.86157i	−0.208505	−	0.208505i
$344$	−9.11898	−	18.9097i	−0.491662	−	1.01954i
$345$	0.225323	−	0.840917i	0.0121310	−	0.0452734i
$346$	0.0684662	−	2.76529i	0.00368077	−	0.148663i
$347$	10.1714	−	5.87244i	0.546027	−	0.315249i	−0.201491	−	0.979490i	$-0.564579\pi$
$347$	10.1714	−	5.87244i	0.546027	−	0.315249i	0.747518	+	0.664241i	$0.231245\pi$
$348$	10.3856	+	6.70248i	0.556729	+	0.359291i
$349$	26.5017	−	7.10112i	1.41860	−	0.380114i	0.533616	−	0.845727i	$-0.320833\pi$
$349$	26.5017	−	7.10112i	1.41860	−	0.380114i	0.884989	+	0.465613i	$0.154166\pi$
$350$	−16.8745	−	17.7313i	−0.901981	−	0.947779i
$351$	−2.75199	−	2.32949i	−0.146890	−	0.124339i
$352$	20.8350	−	16.2246i	1.11051	−	0.864774i
$353$	−0.425990	−	1.58981i	−0.0226731	−	0.0846173i	0.953662	−	0.300879i	$-0.0972801\pi$
$353$	−0.425990	−	1.58981i	−0.0226731	−	0.0846173i	−0.976335	+	0.216262i	$0.930613\pi$
$354$	−6.95460	+	1.68014i	−0.369633	+	0.0892986i
$355$	−0.686808	−	1.18959i	−0.0364520	−	0.0631367i
$356$	−7.79662	−	8.60952i	−0.413220	−	0.456304i
$357$	−0.552169	−	0.147953i	−0.0292239	−	0.00783052i
$358$	−6.09231	−	11.1826i	−0.321988	−	0.591018i
$359$	−6.26184	+	6.26184i	−0.330487	+	0.330487i	−0.852771	−	0.522284i	$-0.825080\pi$
$359$	−6.26184	+	6.26184i	−0.330487	+	0.330487i	0.522284	+	0.852771i	$0.325080\pi$
$360$	0.823675	+	0.287720i	0.0434115	+	0.0151642i
$361$	−12.9133	−	7.45548i	−0.679646	−	0.392394i
$362$	11.9377	+	7.29202i	0.627430	+	0.383260i
$363$	10.7918			0.566421
$364$	−22.4505	−	11.9792i	−1.17672	−	0.627882i
$365$	1.03454			0.0541501
$366$	14.1981	+	8.67280i	0.742148	+	0.453335i
$367$	10.6837	+	6.16822i	0.557683	+	0.321979i	0.752215	−	0.658918i	$-0.228985\pi$
$367$	10.6837	+	6.16822i	0.557683	+	0.321979i	−0.194532	+	0.980896i	$0.562319\pi$
$368$	−4.65042	−	10.2867i	−0.242420	−	0.536232i
$369$	1.86589	−	1.86589i	0.0971342	−	0.0971342i
$370$	−1.58045	−	2.90096i	−0.0821637	−	0.150814i
$371$	−43.3466	−	11.6147i	−2.25045	−	0.603005i
$372$	−4.46697	+	4.04520i	−0.231601	+	0.209734i
$373$	−1.05480	−	1.82697i	−0.0546157	−	0.0945972i	0.837425	−	0.546552i	$-0.184060\pi$
$373$	−1.05480	−	1.82697i	−0.0546157	−	0.0945972i	−0.892041	+	0.451955i	$0.850727\pi$
$374$	−1.03955	+	0.251142i	−0.0537538	+	0.0129862i
$375$	−0.790779	−	2.95123i	−0.0408357	−	0.152401i
$376$	−4.45070	+	3.83431i	−0.229527	+	0.197739i
$377$	−7.53100	−	20.9722i	−0.387866	−	1.08012i
$378$	3.44037	+	3.61506i	0.176954	+	0.185939i
$379$	11.0281	−	2.95498i	0.566478	−	0.151787i	0.0357972	−	0.999359i	$-0.488603\pi$
$379$	11.0281	−	2.95498i	0.566478	−	0.151787i	0.530681	+	0.847572i	$0.321936\pi$
$380$	−1.94808	+	3.01859i	−0.0999344	+	0.154850i
$381$	0.397465	−	0.229476i	0.0203627	−	0.0117564i
$382$	0.442034	−	17.8534i	0.0226164	−	0.913457i
$383$	4.45345	−	16.6205i	0.227561	−	0.849268i	−0.753802	−	0.657102i	$-0.771782\pi$
$383$	4.45345	−	16.6205i	0.227561	−	0.849268i	0.981362	−	0.192166i	$-0.0615513\pi$
$384$	10.6265	−	3.88285i	0.542284	−	0.198146i
$385$	3.59310	+	3.59310i	0.183121	+	0.183121i
$386$	−5.40626	+	18.3473i	−0.275172	+	0.933851i
$387$	3.71119	−	6.42797i	0.188650	−	0.326752i
$388$	4.97030	+	23.0599i	0.252329	+	1.17069i
$389$		−	26.0133i		−	1.31893i	−0.751737	−	0.659463i	$-0.770784\pi$
$389$		−	26.0133i		−	1.31893i	0.751737	−	0.659463i	$-0.229216\pi$
$390$	−0.864345	−	1.31411i	−0.0437678	−	0.0665425i
$391$			0.457193i			0.0231212i
$392$	12.7467	+	8.68055i	0.643808	+	0.438434i
$393$	−9.06162	+	15.6952i	−0.457098	+	0.791717i
$394$	−17.1218	−	5.04515i	−0.862582	−	0.254171i
$395$	2.12151	+	2.12151i	0.106745	+	0.106745i
$396$	8.88757	+	2.85975i	0.446617	+	0.143708i
$397$	−3.38475	+	12.6321i	−0.169876	+	0.633986i	0.827492	+	0.561478i	$0.189767\pi$
$397$	−3.38475	+	12.6321i	−0.169876	+	0.633986i	−0.997368	+	0.0725080i	$0.976900\pi$
$398$	11.1863	+	0.276963i	0.560718	+	0.0138829i
$399$	−17.7962	+	10.2746i	−0.890925	+	0.514376i
$400$	−15.9379	−	11.4413i	−0.796897	−	0.572064i
$401$	23.8669	−	6.39511i	1.19185	−	0.319356i	0.392236	−	0.919865i	$-0.371702\pi$
$401$	23.8669	−	6.39511i	1.19185	−	0.319356i	0.799618	+	0.600508i	$0.205035\pi$
$402$	−2.23859	+	2.13042i	−0.111651	+	0.106256i
$403$	10.8269	−	0.900200i	0.539325	−	0.0448421i
$404$	0.987278	−	19.9254i	0.0491189	−	0.991328i
$405$	0.0798376	+	0.297958i	0.00396716	+	0.0148056i
$406$	7.24283	+	29.9802i	0.359456	+	1.48789i
$407$	−17.6754	−	30.6147i	−0.876138	−	1.51752i
$408$	−0.456928	−	0.0339950i	−0.0226213	−	0.00168300i
$409$	32.8566	+	8.80391i	1.62466	+	0.435325i	0.952365	−	0.304962i	$-0.0986437\pi$
$409$	32.8566	+	8.80391i	1.62466	+	0.435325i	0.672291	+	0.740287i	$0.265310\pi$
$410$	1.01085	−	0.550716i	0.0499225	−	0.0271979i
$411$	−16.4193	+	16.4193i	−0.809907	+	0.809907i
$412$	2.93405	+	5.71803i	0.144550	+	0.281707i
$413$	−15.4608	−	8.92630i	−0.760776	−	0.439234i
$414$	2.08059	−	3.40610i	0.102255	−	0.167401i
$415$	−4.43948			−0.217926
$416$	−19.4693	−	6.07840i	−0.954560	−	0.298018i
$417$	15.3821			0.753265
$418$	−20.0403	+	32.8077i	−0.980203	+	1.60468i
$419$	22.7432	+	13.1308i	1.11108	+	0.641481i	0.939108	−	0.343622i	$-0.111654\pi$
$419$	22.7432	+	13.1308i	1.11108	+	0.641481i	0.171969	+	0.985102i	$0.444987\pi$
$420$	0.993887	+	1.93694i	0.0484967	+	0.0945129i
$421$	5.77997	−	5.77997i	0.281699	−	0.281699i	−0.552088	−	0.833786i	$-0.686169\pi$
$421$	5.77997	−	5.77997i	0.281699	−	0.281699i	0.833786	+	0.552088i	$0.186169\pi$
$422$	15.3982	−	8.38898i	0.749572	−	0.408369i
$423$	−2.00621	−	0.537561i	−0.0975450	−	0.0261371i
$424$	−35.8700	−	2.66869i	−1.74200	−	0.129603i
$425$	0.397280	+	0.688110i	0.0192709	+	0.0333782i
$426$	−1.47886	−	6.12142i	−0.0716508	−	0.296584i
$427$	10.7447	+	40.0998i	0.519973	+	1.94056i
$428$	0.551170	−	11.1238i	0.0266418	−	0.537690i
$429$	−9.59449	−	13.8289i	−0.463227	−	0.667666i
$430$	2.34554	−	2.23220i	0.113112	−	0.107646i
$431$	15.7057	−	4.20834i	0.756518	−	0.202708i	0.140111	−	0.990136i	$-0.455254\pi$
$431$	15.7057	−	4.20834i	0.756518	−	0.202708i	0.616407	+	0.787427i	$0.288587\pi$
$432$	3.24942	+	2.33265i	0.156338	+	0.112229i
$433$	18.0856	−	10.4417i	0.869137	−	0.501797i	0.00207588	−	0.999998i	$-0.499339\pi$
$433$	18.0856	−	10.4417i	0.869137	−	0.501797i	0.867061	+	0.498201i	$0.166006\pi$
$434$	−15.0327	−	0.372196i	−0.721592	−	0.0178660i
$435$	−0.493421	+	1.84147i	−0.0236577	+	0.0882918i
$436$	−23.3060	−	7.49915i	−1.11615	−	0.359144i
$437$	11.6213	+	11.6213i	0.555920	+	0.555920i
$438$	4.54956	+	1.34059i	0.217386	+	0.0640557i
$439$	4.36021	−	7.55210i	0.208101	−	0.360442i	−0.743015	−	0.669275i	$-0.766605\pi$
$439$	4.36021	−	7.55210i	0.208101	−	0.360442i	0.951116	+	0.308833i	$0.0999383\pi$
$440$	3.36641	+	2.29253i	0.160487	+	0.109292i
$441$			5.45242i			0.259639i
$442$	0.617066	+	0.549118i	0.0293509	+	0.0261189i
$443$			5.30045i			0.251832i	0.992041	+	0.125916i	$0.0401870\pi$
$443$			5.30045i			0.251832i	−0.992041	+	0.125916i	$0.959813\pi$
$444$	−3.19116	−	14.8055i	−0.151446	−	0.702637i
$445$	0.895725	−	1.55144i	0.0424615	−	0.0735454i
$446$	0.763189	−	2.59004i	0.0361381	−	0.122642i
$447$	8.59067	+	8.59067i	0.406325	+	0.406325i
$448$	25.8870	+	11.2613i	1.22305	+	0.532046i
$449$	−4.66510	+	17.4104i	−0.220160	+	0.821647i	0.764127	+	0.645066i	$0.223170\pi$
$449$	−4.66510	+	17.4104i	−0.220160	+	0.821647i	−0.984286	+	0.176580i	$0.943496\pi$
$450$	0.171689	−	6.93438i	0.00809350	−	0.326890i
$451$	10.6679	−	6.15909i	0.502330	−	0.290020i
$452$	−5.30223	+	8.21592i	−0.249396	+	0.386444i
$453$	0.657638	−	0.176214i	0.0308985	−	0.00827924i
$454$	21.4991	+	22.5908i	1.00900	+	1.06024i
$455$	0.698184	−	3.86213i	0.0327314	−	0.181059i
$456$	−12.4786	+	10.7504i	−0.584366	+	0.503434i
$457$	8.96232	+	33.4478i	0.419240	+	1.56462i	0.776189	+	0.630500i	$0.217150\pi$
$457$	8.96232	+	33.4478i	0.419240	+	1.56462i	−0.356950	+	0.934124i	$0.616183\pi$
$458$	−21.4360	+	5.17866i	−1.00164	+	0.241983i
$459$	−0.0809975	−	0.140292i	−0.00378064	−	0.00654826i
$460$	1.29061	−	1.16875i	0.0601749	−	0.0544932i
$461$	12.3707	+	3.31471i	0.576160	+	0.154382i	0.535120	−	0.844776i	$-0.320266\pi$
$461$	12.3707	+	3.31471i	0.576160	+	0.154382i	0.0410399	+	0.999158i	$0.486933\pi$
$462$	11.1452	+	20.4574i	0.518524	+	0.951763i
$463$	16.3874	−	16.3874i	0.761585	−	0.761585i	−0.215023	−	0.976609i	$-0.568983\pi$
$463$	16.3874	−	16.3874i	0.761585	−	0.761585i	0.976609	+	0.215023i	$0.0689828\pi$
$464$	10.1837	+	22.5262i	0.472765	+	1.04575i
$465$	−0.804951	−	0.464739i	−0.0373287	−	0.0215517i
$466$	−1.74692	−	1.06709i	−0.0809243	−	0.0494319i
$467$	21.5139			0.995545			0.497773	−	0.867308i	$-0.334151\pi$
$467$	21.5139			0.995545			0.497773	+	0.867308i	$0.334151\pi$
$468$	−2.09825	−	6.89908i	−0.0969915	−	0.318910i
$469$	−7.71104			−0.356063
$470$	−0.773219	−	0.472314i	−0.0356659	−	0.0217862i
$471$	15.3423	+	8.85787i	0.706935	+	0.408149i
$472$	−13.5089	−	4.71881i	−0.621797	−	0.217201i
$473$	24.5005	−	24.5005i	1.12653	−	1.12653i
$474$	6.58058	+	12.0788i	0.302256	+	0.554799i
$475$	27.5892	+	7.39251i	1.26588	+	0.339192i
$476$	−0.767434	−	0.847449i	−0.0351753	−	0.0388428i
$477$	−6.35850	−	11.0132i	−0.291136	−	0.504262i
$478$	−19.4382	+	4.69602i	−0.889081	+	0.214791i
$479$	−1.20951	−	4.51397i	−0.0552641	−	0.206249i	0.932773	−	0.360464i	$-0.117382\pi$
$479$	−1.20951	−	4.51397i	−0.0552641	−	0.206249i	−0.988037	+	0.154215i	$0.950715\pi$
$480$	1.07211	+	1.37676i	0.0489348	+	0.0628404i
$481$	−11.6457	+	24.6958i	−0.531000	+	1.12603i
$482$	−4.39767	−	4.62097i	−0.200309	−	0.210479i
$483$	9.61986	−	2.57763i	0.437719	−	0.117286i
$484$	18.1349	+	11.7036i	0.824314	+	0.531980i
$485$	−3.15086	+	1.81915i	−0.143073	+	0.0826034i
$486$	−0.0350040	+	1.41378i	−0.00158781	+	0.0641304i
$487$	−4.72308	+	17.6268i	−0.214023	+	0.798746i	0.772485	+	0.635033i	$0.219014\pi$
$487$	−4.72308	+	17.6268i	−0.214023	+	0.798746i	−0.986508	+	0.163713i	$0.947653\pi$
$488$	14.4535	+	29.9719i	0.654281	+	1.35676i
$489$	−11.2018	−	11.2018i	−0.506561	−	0.506561i
$490$	−0.672297	+	2.28158i	−0.0303713	+	0.103071i
$491$	−17.0275	+	29.4926i	−0.768442	+	1.33098i	0.169965	+	0.985450i	$0.445634\pi$
$491$	−17.0275	+	29.4926i	−0.768442	+	1.33098i	−0.938407	+	0.345531i	$0.887699\pi$
$492$	5.15905	−	1.11198i	0.232588	−	0.0501317i
$493$		−	1.00118i		−	0.0450908i
$494$	29.6429	−	1.72717i	1.33370	−	0.0777089i
$495$			1.43998i			0.0647224i
$496$	−11.8935	+	1.95334i	−0.534032	+	0.0877074i
$497$	7.85690	−	13.6086i	0.352430	−	0.610427i
$498$	−19.5234	−	5.75284i	−0.874866	−	0.257791i
$499$	−25.4009	−	25.4009i	−1.13710	−	1.13710i	−0.988967	−	0.148135i	$-0.952673\pi$
$499$	−25.4009	−	25.4009i	−1.13710	−	1.13710i	−0.148135	−	0.988967i	$-0.547327\pi$
$500$	1.87172	−	5.81695i	0.0837059	−	0.260142i
$501$	5.53362	−	20.6517i	0.247224	−	0.922652i
$502$	−42.9620	−	1.06370i	−1.91749	−	0.0474753i
$503$	6.98372	−	4.03205i	0.311389	−	0.179780i	−0.336159	−	0.941805i	$-0.609128\pi$
$503$	6.98372	−	4.03205i	0.311389	−	0.179780i	0.647548	+	0.762025i	$0.275795\pi$
$504$	1.86085	+	9.80595i	0.0828887	+	0.436792i
$505$	2.97211	−	0.796375i	0.132257	−	0.0354382i
$506$	13.4969	−	12.8447i	0.600009	−	0.571015i
$507$	−4.55146	+	12.1772i	−0.202137	+	0.540809i
$508$	0.916781	+	0.0454253i	0.0406756	+	0.00201542i
$509$	2.06870	+	7.72048i	0.0916934	+	0.342204i	0.996497	−	0.0836239i	$-0.0266494\pi$
$509$	2.06870	+	7.72048i	0.0916934	+	0.342204i	−0.904804	+	0.425828i	$0.859983\pi$
$510$	−0.0165953	−	0.0686926i	−0.000734851	−	0.00304176i
$511$	5.91740	+	10.2492i	0.261771	+	0.453400i
$512$	22.0682	+	4.99949i	0.975286	+	0.220948i
$513$	−5.62489	−	1.50718i	−0.248345	−	0.0665438i
$514$	6.19837	−	3.37689i	0.273398	−	0.148948i
$515$	−0.700914	+	0.700914i	−0.0308860	+	0.0308860i
$516$	13.2075	−	6.77707i	0.581428	−	0.298344i
$517$	−8.39669	−	4.84783i	−0.369286	−	0.213207i
$518$	19.7001	−	32.2508i	0.865572	−	1.41702i
$519$	1.95596			0.0858569
$520$	−0.0273423	−	3.14566i	−0.00119904	−	0.137946i
$521$	−6.25785			−0.274161			−0.137081	−	0.990560i	$-0.543772\pi$
$521$	−6.25785			−0.274161			−0.137081	+	0.990560i	$0.543772\pi$
$522$	−4.55615	+	7.45881i	−0.199417	+	0.326463i
$523$	−8.82704	−	5.09629i	−0.385979	−	0.222845i	0.294437	−	0.955671i	$-0.404868\pi$
$523$	−8.82704	−	5.09629i	−0.385979	−	0.222845i	−0.680417	+	0.732825i	$0.738201\pi$
$524$	−32.2488	+	16.5476i	−1.40880	+	0.722885i
$525$	12.2388	−	12.2388i	0.534143	−	0.534143i
$526$	9.39001	−	5.11571i	0.409424	−	0.223056i
$527$	0.471490	+	0.126335i	0.0205384	+	0.00550326i
$528$	11.8337	+	14.4441i	0.514994	+	0.628600i
$529$	7.51741	+	13.0205i	0.326844	+	0.566110i
$530$	−1.30277	−	5.39254i	−0.0565887	−	0.234237i
$531$	−1.30940	−	4.88673i	−0.0568229	−	0.212066i
$532$	−41.0482	−	2.03388i	−1.77967	−	0.0881801i
$533$	−8.60537	−	4.05802i	−0.372740	−	0.175772i
$534$	5.94953	−	5.66203i	0.257461	−	0.245020i
$535$	1.65925	−	0.444594i	0.0717355	−	0.0192215i
$536$	−6.07224	+	1.15231i	−0.262281	+	0.0497723i
$537$	7.79823	−	4.50231i	0.336518	−	0.194289i
$538$	−39.1500	−	0.969321i	−1.68788	−	0.0417904i
$539$	−6.58767	+	24.5855i	−0.283751	+	1.05897i
$540$	−0.188970	+	0.587284i	−0.00813198	+	0.0252727i
$541$	−9.92025	−	9.92025i	−0.426505	−	0.426505i	0.460931	−	0.887436i	$-0.347515\pi$
$541$	−9.92025	−	9.92025i	−0.426505	−	0.426505i	−0.887436	+	0.460931i	$0.847515\pi$
$542$	14.5739	+	4.29440i	0.626004	+	0.184460i
$543$	−4.94573	+	8.56625i	−0.212241	+	0.367613i
$544$	−0.730973	−	0.552661i	−0.0313402	−	0.0236951i
$545$		−	3.77608i		−	0.161750i
$546$	8.07507	−	16.0797i	0.345581	−	0.688147i
$547$			24.6614i			1.05444i	0.849727	+	0.527222i	$0.176767\pi$
$547$			24.6614i			1.05444i	−0.849727	+	0.527222i	$0.823233\pi$
$548$	−45.3984	+	9.78512i	−1.93932	+	0.417999i
$549$	−5.88222	+	10.1883i	−0.251047	+	0.434826i
$550$	9.15235	−	31.0604i	0.390257	−	1.32442i
$551$	−25.4487	−	25.4487i	−1.08415	−	1.08415i
$552$	7.19019	−	3.46738i	0.306035	−	0.147581i
$553$	−8.88323	+	33.1527i	−0.377754	+	1.40980i
$554$	0.600348	−	24.2475i	0.0255063	−	1.03018i
$555$	2.02300	−	1.16798i	0.0858714	−	0.0495779i
$556$	25.8487	+	16.6818i	1.09623	+	0.707464i
$557$	−27.4046	+	7.34303i	−1.16117	+	0.311134i	−0.787432	−	0.616401i	$-0.788590\pi$
$557$	−27.4046	+	7.34303i	−1.16117	+	0.311134i	−0.373736	+	0.927535i	$0.621923\pi$
$558$	−2.93769	−	3.08686i	−0.124362	−	0.130677i
$559$	−26.3349	−	4.76074i	−1.11385	−	0.201358i
$560$	−0.430422	+	4.33277i	−0.0181887	+	0.183093i
$561$	−0.195724	−	0.730452i	−0.00826347	−	0.0308397i
$562$	40.2434	−	9.72228i	1.69756	−	0.410110i
$563$	7.94273	+	13.7572i	0.334746	+	0.579797i	0.983436	−	0.181255i	$-0.0580161\pi$
$563$	7.94273	+	13.7572i	0.334746	+	0.579797i	−0.648690	+	0.761053i	$0.724683\pi$
$564$	−2.78833	−	3.07905i	−0.117410	−	0.129651i
$565$	−1.45676	−	0.390337i	−0.0612863	−	0.0164216i
$566$	−11.7732	−	21.6100i	−0.494863	−	0.908334i
$567$	−2.49524	+	2.49524i	−0.104790	+	0.104790i
$568$	4.15349	−	11.8905i	0.174276	−	0.498913i
$569$	5.59285	+	3.22903i	0.234464	+	0.135368i	0.612630	−	0.790370i	$-0.290112\pi$
$569$	5.59285	+	3.22903i	0.234464	+	0.135368i	−0.378166	+	0.925738i	$0.623445\pi$
$570$	−2.16791	−	1.32425i	−0.0908037	−	0.0554666i
$571$	30.0075			1.25578			0.627888	−	0.778304i	$-0.283920\pi$
$571$	30.0075			1.25578			0.627888	+	0.778304i	$0.283920\pi$
$572$	−1.12567	−	33.6438i	−0.0470665	−	1.40672i
$573$	12.6281			0.527546
$574$	11.2379	+	6.86460i	0.469063	+	0.286523i
$575$	−11.9882	−	6.92139i	−0.499943	−	0.288642i
$576$	2.93073	+	7.44384i	0.122114	+	0.310160i
$577$	10.5831	−	10.5831i	0.440581	−	0.440581i	−0.451627	−	0.892207i	$-0.649156\pi$
$577$	10.5831	−	10.5831i	0.440581	−	0.440581i	0.892207	+	0.451627i	$0.149156\pi$
$578$	−11.4840	−	21.0792i	−0.477673	−	0.876780i
$579$	−13.0641	−	3.50052i	−0.542926	−	0.145477i
$580$	−2.82622	+	2.55937i	−0.117352	+	0.106272i
$581$	−25.3933	−	43.9824i	−1.05349	−	1.82470i
$582$	−16.2138	+	3.91705i	−0.672084	+	0.162367i
$583$	−15.3648	−	57.3423i	−0.636345	−	2.37487i
$584$	6.19141	+	7.18673i	0.256202	+	0.297389i
$585$	0.913803	−	0.633997i	0.0377811	−	0.0262125i
$586$	−2.49269	−	2.61925i	−0.102972	−	0.108200i
$587$	7.35983	−	1.97206i	0.303773	−	0.0813957i	−0.103713	−	0.994607i	$-0.533072\pi$
$587$	7.35983	−	1.97206i	0.303773	−	0.0813957i	0.407486	+	0.913212i	$0.366406\pi$
$588$	−5.91310	+	9.16247i	−0.243852	+	0.377854i
$589$	15.1960	−	8.77340i	0.626139	−	0.361502i
$590$	0.0546265	−	2.20632i	0.00224894	−	0.0908326i
$591$	3.26670	−	12.1915i	0.134374	−	0.501492i
$592$	10.6939	−	28.3405i	0.439515	−	1.16479i
$593$	−13.2291	−	13.2291i	−0.543253	−	0.543253i	0.381228	−	0.924481i	$-0.375501\pi$
$593$	−13.2291	−	13.2291i	−0.543253	−	0.543253i	−0.924481	+	0.381228i	$0.875501\pi$
$594$	−1.86598	+	6.33259i	−0.0765621	+	0.259829i
$595$	0.0881677	−	0.152711i	0.00361452	−	0.00626054i
$596$	5.11961	+	23.7526i	0.209707	+	0.972944i
$597$			7.91233i			0.323830i
$598$	−14.0936	−	2.90976i	−0.576328	−	0.118989i
$599$		−	1.47553i		−	0.0602886i	−0.999546	−	0.0301443i	$-0.990403\pi$
$599$		−	1.47553i		−	0.0602886i	0.999546	−	0.0301443i	$-0.00959668\pi$
$600$	7.80878	−	11.4666i	0.318792	−	0.468122i
$601$	4.60479	−	7.97573i	0.187833	−	0.325337i	−0.756694	−	0.653769i	$-0.773187\pi$
$601$	4.60479	−	7.97573i	0.187833	−	0.325337i	0.944528	+	0.328432i	$0.106520\pi$
$602$	35.5308	+	10.4696i	1.44813	+	0.426710i
$603$	−1.54515	−	1.54515i	−0.0629235	−	0.0629235i
$604$	1.29622	+	0.417086i	0.0527426	+	0.0169710i
$605$	−0.861588	+	3.21549i	−0.0350285	+	0.130728i
$606$	14.1024	+	0.349163i	0.572870	+	0.0141838i
$607$	22.2789	−	12.8627i	0.904273	−	0.522083i	0.0256893	−	0.999670i	$-0.491822\pi$
$607$	22.2789	−	12.8627i	0.904273	−	0.522083i	0.878584	+	0.477587i	$0.158489\pi$
$608$	−32.6283	+	4.53248i	−1.32325	+	0.183816i
$609$	−21.0659	+	5.64460i	−0.853635	+	0.228731i
$610$	−3.71767	+	3.53803i	−0.150524	+	0.143251i
$611$	0.620501	+	7.46289i	0.0251028	+	0.301916i
$612$	0.0160336	−	0.323593i	0.000648119	−	0.0130805i
$613$	5.87075	+	21.9099i	0.237117	+	0.884934i	0.977183	+	0.212399i	$0.0681277\pi$
$613$	5.87075	+	21.9099i	0.237117	+	0.884934i	−0.740066	+	0.672535i	$0.765206\pi$
$614$	3.71456	+	15.3756i	0.149907	+	0.620510i
$615$	0.406988	+	0.704924i	0.0164113	+	0.0284253i
$616$	−3.45690	+	46.4643i	−0.139282	+	1.87210i
$617$	20.2985	+	5.43897i	0.817188	+	0.218965i	0.643117	−	0.765768i	$-0.277641\pi$
$617$	20.2985	+	5.43897i	0.817188	+	0.218965i	0.174071	+	0.984733i	$0.444308\pi$
$618$	−3.99067	+	2.17413i	−0.160528	+	0.0874562i
$619$	−3.49742	+	3.49742i	−0.140573	+	0.140573i	−0.773891	−	0.633318i	$-0.781692\pi$
$619$	−3.49742	+	3.49742i	−0.140573	+	0.140573i	0.633318	+	0.773891i	$0.281692\pi$
$620$	−0.848668	−	1.65393i	−0.0340833	−	0.0664233i
$621$	2.44415	+	1.41113i	0.0980805	+	0.0566268i
$622$	5.01640	−	8.21228i	0.201139	−	0.329283i
$623$	20.4937			0.821063
$624$	3.95601	−	13.8690i	0.158367	−	0.555206i
$625$	−23.5818			−0.943270
$626$	14.0301	−	22.9685i	0.560755	−	0.918005i
$627$	−23.5422	−	13.5921i	−0.940185	−	0.542816i
$628$	16.1755	+	31.5237i	0.645473	+	1.25793i
$629$	−0.867441	+	0.867441i	−0.0345871	+	0.0345871i
$630$	−1.35181	+	0.736469i	−0.0538573	+	0.0293416i
$631$	11.1743	+	2.99416i	0.444843	+	0.119195i	0.474286	−	0.880371i	$-0.342706\pi$
$631$	11.1743	+	2.99416i	0.444843	+	0.119195i	−0.0294422	+	0.999566i	$0.509373\pi$
$632$	−2.04109	+	27.4343i	−0.0811901	+	1.09128i
$633$	6.19959	+	10.7380i	0.246411	+	0.426797i
$634$	−7.39244	−	30.5995i	−0.293591	−	1.21526i
$635$	0.0366417	+	0.136749i	0.00145408	+	0.00542671i
$636$	1.25868	−	25.4028i	0.0499098	−	1.00729i
$637$	18.5022	−	6.64404i	0.733085	−	0.263247i
$638$	−29.5559	+	28.1277i	−1.17013	+	1.11359i
$639$	4.30129	−	1.15253i	0.170156	−	0.0455932i
$640$	0.308528	+	3.47626i	0.0121956	+	0.137411i
$641$	6.62028	−	3.82222i	0.261485	−	0.150969i	−0.363527	−	0.931584i	$-0.618427\pi$
$641$	6.62028	−	3.82222i	0.261485	−	0.150969i	0.625012	+	0.780615i	$0.285094\pi$
$642$	7.87296	+	0.194928i	0.310721	+	0.00769318i
$643$	0.271786	−	1.01432i	0.0107182	−	0.0400008i	−0.960360	−	0.278764i	$-0.910075\pi$
$643$	0.271786	−	1.01432i	0.0107182	−	0.0400008i	0.971078	+	0.238763i	$0.0767420\pi$
$644$	18.9610	+	6.10108i	0.747169	+	0.240416i
$645$	1.61897	+	1.61897i	0.0637470	+	0.0637470i
$646$	1.27969	+	0.377079i	0.0503489	+	0.0148360i
$647$	17.1391	−	29.6858i	0.673809	−	1.16707i	−0.303007	−	0.952988i	$-0.597990\pi$
$647$	17.1391	−	29.6858i	0.673809	−	1.16707i	0.976816	−	0.214083i	$-0.0686762\pi$
$648$	−1.59205	+	2.33781i	−0.0625418	+	0.0918379i
$649$		−	23.6168i		−	0.927040i
$650$	−23.7403	+	7.86727i	−0.931171	+	0.308580i
$651$		−	10.6330i		−	0.416739i
$652$	−6.67570	−	30.9721i	−0.261440	−	1.21296i
$653$	−17.8505	+	30.9180i	−0.698545	+	1.20992i	0.270426	+	0.962741i	$0.412835\pi$
$653$	−17.8505	+	30.9180i	−0.698545	+	1.20992i	−0.968971	+	0.247174i	$0.920498\pi$
$654$	4.89318	−	16.6060i	0.191338	−	0.649346i
$655$	−3.95305	−	3.95305i	−0.154458	−	0.154458i
$656$	9.87540	+	3.72633i	0.385570	+	0.145489i
$657$	−0.868021	+	3.23950i	−0.0338647	+	0.126385i
$658$	0.256552	−	10.3619i	0.0100014	−	0.403950i
$659$	−7.36267	+	4.25084i	−0.286809	+	0.165589i	−0.636502	−	0.771275i	$-0.719619\pi$
$659$	−7.36267	+	4.25084i	−0.286809	+	0.165589i	0.349693	+	0.936864i	$0.386286\pi$
$660$	−1.56165	+	2.41981i	−0.0607870	+	0.0941908i
$661$	3.90098	−	1.04526i	0.151730	−	0.0406560i	−0.182154	−	0.983270i	$-0.558307\pi$
$661$	3.90098	−	1.04526i	0.151730	−	0.0406560i	0.333885	+	0.942614i	$0.391640\pi$
$662$	7.45963	+	7.83840i	0.289927	+	0.304648i
$663$	−0.377366	+	0.445809i	−0.0146557	+	0.0173138i
$664$	−26.5691	−	30.8403i	−1.03108	−	1.19684i
$665$	−1.64061	−	6.12283i	−0.0636200	−	0.237433i
$666$	10.4100	−	2.51492i	0.403379	−	0.0974513i
$667$	8.72123	+	15.1056i	0.337688	+	0.584892i
$668$	31.6955	−	28.7029i	1.22634	−	1.11055i
$669$	1.84423	+	0.494160i	0.0713021	+	0.0191053i
$670$	−0.456052	−	0.837094i	−0.0176188	−	0.0323398i
$671$	−38.8331	+	38.8331i	−1.49914	+	1.49914i
$672$	−7.50741	+	18.4964i	−0.289605	+	0.713514i
$673$	−32.4615	−	18.7416i	−1.25130	−	0.722437i	−0.279930	−	0.960020i	$-0.590311\pi$
$673$	−32.4615	−	18.7416i	−1.25130	−	0.722437i	−0.971367	+	0.237583i	$0.923645\pi$
$674$	17.5417	+	10.7152i	0.675681	+	0.412734i
$675$	4.90485			0.188788
$676$	−20.8545	+	15.5271i	−0.802096	+	0.597194i
$677$	23.3255			0.896472			0.448236	−	0.893915i	$-0.352052\pi$
$677$	23.3255			0.896472			0.448236	+	0.893915i	$0.352052\pi$
$678$	−5.90055	−	3.60430i	−0.226609	−	0.138422i
$679$	−36.0450	−	20.8106i	−1.38328	−	0.798638i
$680$	0.0466091	−	0.133431i	0.00178738	−	0.00511685i
$681$	−15.5929	+	15.5929i	−0.597521	+	0.597521i
$682$	−9.51679	−	17.4683i	−0.364417	−	0.668896i
$683$	−26.3528	−	7.06122i	−1.00836	−	0.270190i	−0.283418	−	0.958996i	$-0.591468\pi$
$683$	−26.3528	−	7.06122i	−1.00836	−	0.270190i	−0.724945	+	0.688806i	$0.758135\pi$
$684$	−7.81776	−	8.63287i	−0.298920	−	0.330086i
$685$	−3.58139	−	6.20316i	−0.136838	−	0.237010i
$686$	7.50718	−	1.81364i	0.286625	−	0.0692451i
$687$	−4.03592	−	15.0622i	−0.153980	−	0.574660i
$688$	29.5441	+	2.93495i	1.12636	+	0.111894i
$689$	−29.6242	+	34.9971i	−1.12859	+	1.33328i
$690$	0.848766	+	0.891862i	0.0323120	+	0.0339526i
$691$	−25.2872	+	6.77570i	−0.961972	+	0.257760i	−0.705435	−	0.708775i	$-0.749248\pi$
$691$	−25.2872	+	6.77570i	−0.961972	+	0.257760i	−0.256537	+	0.966534i	$0.582582\pi$
$692$	3.28687	+	2.12122i	0.124948	+	0.0806365i
$693$	−14.2660	+	8.23651i	−0.541922	+	0.312879i
$694$	−0.411117	+	16.6047i	−0.0156058	+	0.630305i
$695$	−1.22807	+	4.58322i	−0.0465834	+	0.173852i
$696$	−15.7453	+	7.59299i	−0.596826	+	0.287812i
$697$	−0.302264	−	0.302264i	−0.0114491	−	0.0114491i
$698$	−10.9671	+	37.2191i	−0.415110	+	1.40876i
$699$	0.723740	−	1.25355i	0.0273743	−	0.0474138i
$700$	33.8393	−	7.29369i	1.27901	−	0.275676i
$701$			45.2731i			1.70994i	0.518675	+	0.854972i	$0.326426\pi$
$701$			45.2731i			1.70994i	−0.518675	+	0.854972i	$0.673574\pi$
$702$	4.84017	−	1.60398i	0.182680	−	0.0605383i
$703$			44.0985i			1.66321i
$704$	4.22125	+	37.1060i	0.159094	+	1.39848i
$705$	0.320341	−	0.554847i	0.0120647	−	0.0208968i
$706$	2.23274	+	0.657906i	0.0840302	+	0.0247606i
$707$	24.8898	+	24.8898i	0.936079	+	0.936079i
$708$	3.09925	−	9.63189i	0.116477	−	0.361988i
$709$	−4.60235	+	17.1762i	−0.172845	+	0.645066i	0.824064	+	0.566497i	$0.191702\pi$
$709$	−4.60235	+	17.1762i	−0.172845	+	0.645066i	−0.996909	+	0.0785692i	$0.974965\pi$
$710$	1.94199	+	0.0480820i	0.0728817	+	0.00180449i
$711$	−8.42323	+	4.86315i	−0.315896	+	0.182382i
$712$	16.1382	−	3.06251i	0.604806	−	0.114772i
$713$	−8.21428	+	2.20101i	−0.307627	+	0.0824284i
$714$	0.585622	−	0.557323i	0.0219163	−	0.0208573i
$715$	4.88643	−	1.75469i	0.182742	−	0.0656217i
$716$	17.9872	+	0.891240i	0.672212	+	0.0333072i
$717$	−3.65977	−	13.6585i	−0.136677	−	0.510085i
$718$	−2.94096	−	12.1735i	−0.109755	−	0.454310i
$719$	−0.606805	−	1.05102i	−0.0226300	−	0.0391963i	0.854489	−	0.519470i	$-0.173871\pi$
$719$	−0.606805	−	1.05102i	−0.0226300	−	0.0391963i	−0.877119	+	0.480274i	$0.840537\pi$
$720$	−0.954457	+	0.781959i	−0.0355705	+	0.0291419i
$721$	−10.9532	−	2.93489i	−0.407917	−	0.109301i
$722$	18.5175	−	10.0884i	0.689150	−	0.375451i
$723$	3.18955	−	3.18955i	0.118621	−	0.118621i
$724$	−17.6010	+	9.03148i	−0.654136	+	0.335652i
$725$	26.2522	+	15.1567i	0.974983	+	0.562907i
$726$	−7.95573	+	13.0242i	−0.295265	+	0.483374i
$727$	−16.8399			−0.624557			−0.312278	−	0.949991i	$-0.601092\pi$
$727$	−16.8399			−0.624557			−0.312278	+	0.949991i	$0.601092\pi$
$728$	31.0079	−	18.2636i	1.14923	−	0.676895i
$729$	−1.00000			−0.0370370
$730$	−0.762664	+	1.24855i	−0.0282275	+	0.0462108i
$731$	−1.04130	−	0.601194i	−0.0385138	−	0.0222360i
$732$	−20.9338	+	10.7416i	−0.773737	+	0.397022i
$733$	−11.9466	+	11.9466i	−0.441259	+	0.441259i	−0.892435	−	0.451176i	$-0.851005\pi$
$733$	−11.9466	+	11.9466i	−0.441259	+	0.441259i	0.451176	+	0.892435i	$0.351005\pi$
$734$	−15.3203	+	8.34654i	−0.565482	+	0.308076i
$735$	−1.62459	−	0.435308i	−0.0599240	−	0.0160566i
$736$	15.8430	+	1.97097i	0.583981	+	0.0726510i
$737$	−5.10038	−	8.83412i	−0.187875	−	0.325409i
$738$	0.876338	+	3.62742i	0.0322585	+	0.133527i
$739$	1.78818	+	6.67357i	0.0657792	+	0.245491i	0.990985	−	0.133975i	$-0.0427742\pi$
$739$	1.78818	+	6.67357i	0.0657792	+	0.245491i	−0.925206	+	0.379466i	$0.876108\pi$
$740$	4.66619	+	0.231203i	0.171532	+	0.00849920i
$741$	1.73973	+	20.9241i	0.0639105	+	0.768664i
$742$	45.9727	−	43.7513i	1.68771	−	1.60616i
$743$	17.0725	−	4.57456i	0.626329	−	0.167824i	0.0683259	−	0.997663i	$-0.478234\pi$
$743$	17.0725	−	4.57456i	0.626329	−	0.167824i	0.558004	+	0.829839i	$0.311568\pi$
$744$	−1.58895	−	8.37318i	−0.0582539	−	0.306976i
$745$	−3.24551	+	1.87380i	−0.118906	+	0.0686507i
$746$	2.98252	+	0.0738447i	0.109198	+	0.00270365i
$747$	3.72493	−	13.9016i	0.136288	−	0.508633i
$748$	0.463265	−	1.43974i	0.0169387	−	0.0526421i
$749$	13.8953	+	13.8953i	0.507724	+	0.507724i
$750$	4.14471	+	1.22129i	0.151343	+	0.0445953i
$751$	22.5112	−	38.9905i	0.821444	−	1.42278i	−0.0831626	−	0.996536i	$-0.526502\pi$
$751$	22.5112	−	38.9905i	0.821444	−	1.42278i	0.904607	−	0.426247i	$-0.140165\pi$
$752$	−1.34642	−	8.19808i	−0.0490989	−	0.298953i
$753$		−	30.3880i		−	1.10740i
$754$	30.8626	+	6.37189i	1.12395	+	0.232051i
$755$			0.210017i			0.00764330i
$756$	−6.89916	+	1.48704i	−0.250920	+	0.0540830i
$757$	2.41527	−	4.18338i	0.0877846	−	0.152047i	−0.818790	−	0.574093i	$-0.805355\pi$
$757$	2.41527	−	4.18338i	0.0877846	−	0.152047i	0.906574	+	0.422046i	$0.138688\pi$
$758$	−4.56373	+	15.4879i	−0.165762	+	0.562547i
$759$	9.31599	+	9.31599i	0.338149	+	0.338149i
$760$	−2.20691	−	4.57639i	−0.0800529	−	0.166003i
$761$	0.885243	−	3.30377i	0.0320900	−	0.119762i	−0.948023	−	0.318202i	$-0.896921\pi$
$761$	0.885243	−	3.30377i	0.0320900	−	0.119762i	0.980113	+	0.198440i	$0.0635876\pi$
$762$	−0.0160652	+	0.648859i	−0.000581980	+	0.0235057i
$763$	37.4100	−	21.5987i	1.35433	−	0.781925i
$764$	21.2208	+	13.6951i	0.767741	+	0.495470i
$765$	0.0482677	−	0.0129333i	0.00174512	−	0.000467604i
$766$	16.7757	+	17.6274i	0.606129	+	0.636905i
$767$	−14.9870	+	10.3980i	−0.541151	+	0.375451i
$768$	−3.14785	+	15.6873i	−0.113588	+	0.566066i
$769$	−6.28045	−	23.4390i	−0.226479	−	0.845231i	−0.981807	−	0.189884i	$-0.939189\pi$
$769$	−6.28045	−	23.4390i	−0.226479	−	0.845231i	0.755328	−	0.655347i	$-0.227478\pi$
$770$	−6.98524	+	1.68755i	−0.251731	+	0.0608150i
$771$	2.49558	+	4.32247i	0.0898760	+	0.155670i
$772$	−18.1572	−	20.0503i	−0.653492	−	0.721627i
$773$	18.2992	+	4.90326i	0.658178	+	0.176358i	0.572423	−	0.819958i	$-0.306003\pi$
$773$	18.2992	+	4.90326i	0.658178	+	0.176358i	0.0857542	+	0.996316i	$0.472670\pi$
$774$	5.02180	+	9.21764i	0.180505	+	0.331321i
$775$	−10.4505	+	10.4505i	−0.375394	+	0.375394i
$776$	−31.4944	−	11.0013i	−1.13058	−	0.394925i
$777$	23.1425	+	13.3614i	0.830234	+	0.479336i
$778$	31.3946	+	19.1771i	1.12555	+	0.687533i
$779$	−15.3663			−0.550556
$780$	2.22316	−	0.0743832i	0.0796017	−	0.00266335i
$781$	20.7874			0.743832
$782$	−0.551771	−	0.337045i	−0.0197313	−	0.0120527i
$783$	−5.35230	−	3.09015i	−0.191276	−	0.110433i
$784$	−19.8732	+	8.98429i	−0.709758	+	0.320868i
$785$	−3.86416	+	3.86416i	−0.137918	+	0.137918i
$786$	−12.2617	−	22.5067i	−0.437362	−	0.802789i
$787$	−38.8099	−	10.3991i	−1.38342	−	0.370688i	−0.511061	−	0.859545i	$-0.670747\pi$
$787$	−38.8099	−	10.3991i	−1.38342	−	0.370688i	−0.872364	+	0.488857i	$0.837414\pi$
$788$	18.7111	−	16.9444i	0.666554	−	0.603619i
$789$	3.78059	+	6.54817i	0.134593	+	0.233121i
$790$	−4.12436	+	0.996393i	−0.146738	+	0.0354501i
$791$	−4.46535	−	16.6649i	−0.158770	−	0.592537i
$792$	−10.0033	+	8.61790i	−0.355452	+	0.306224i
$793$	41.7407	+	7.54576i	1.48226	+	0.267958i
$794$	−12.7500	−	13.3974i	−0.452480	−	0.475455i
$795$	3.78913	−	1.01529i	0.134387	−	0.0360088i
$796$	−8.58084	+	13.2962i	−0.304140	+	0.471271i
$797$	38.9883	−	22.5099i	1.38104	−	0.797342i	0.388755	−	0.921341i	$-0.372905\pi$
$797$	38.9883	−	22.5099i	1.38104	−	0.797342i	0.992282	+	0.123999i	$0.0395719\pi$
$798$	0.719307	−	29.0522i	0.0254632	−	1.02844i
$799$	−0.0870822	+	0.324995i	−0.00308075	+	0.0114975i
$800$	25.5576	−	10.8004i	0.903598	−	0.381852i
$801$	4.10657	+	4.10657i	0.145098	+	0.145098i
$802$	−9.87671	+	33.5186i	−0.348759	+	1.18358i
$803$	−7.82799	+	13.5585i	−0.276244	+	0.478468i
$804$	−0.920834	−	4.27224i	−0.0324753	−	0.150670i
$805$			3.07210i			0.108277i
$806$	−6.89520	+	13.7302i	−0.242873	+	0.483627i
$807$		−	27.6917i		−	0.974795i
$808$	23.3195	+	15.8806i	0.820379	+	0.558679i
$809$	−2.86504	+	4.96239i	−0.100729	+	0.174468i	−0.911985	−	0.410223i	$-0.865451\pi$
$809$	−2.86504	+	4.96239i	−0.100729	+	0.174468i	0.811256	+	0.584691i	$0.198784\pi$
$810$	−0.418452	−	0.123303i	−0.0147029	−	0.00433241i
$811$	−4.92129	−	4.92129i	−0.172810	−	0.172810i	0.615403	−	0.788213i	$-0.288993\pi$
$811$	−4.92129	−	4.92129i	−0.172810	−	0.172810i	−0.788213	+	0.615403i	$0.788993\pi$
$812$	−41.5216	−	13.3604i	−1.45712	−	0.468858i
$813$	−2.78060	+	10.3773i	−0.0975199	+	0.363949i
$814$	49.9783	+	1.23742i	1.75174	+	0.0433715i
$815$	4.23198	−	2.44333i	0.148240	−	0.0855862i
$816$	0.377877	−	0.526390i	0.0132283	−	0.0184274i
$817$	−41.7501	+	11.1869i	−1.46065	+	0.391380i
$818$	−34.8472	+	33.1633i	−1.21840	+	1.15953i
$819$	11.5079	+	5.42676i	0.402119	+	0.189626i
$820$	−0.0805639	+	1.62596i	−0.00281341	+	0.0567809i
$821$	−6.07914	−	22.6877i	−0.212164	−	0.791805i	−0.987146	−	0.159822i	$-0.948908\pi$
$821$	−6.07914	−	22.6877i	−0.212164	−	0.791805i	0.774982	−	0.631983i	$-0.217759\pi$
$822$	−7.71156	−	31.9204i	−0.268972	−	1.11335i
$823$	5.37431	+	9.30857i	0.187337	+	0.324476i	0.944361	−	0.328910i	$-0.106681\pi$
$823$	5.37431	+	9.30857i	0.187337	+	0.324476i	−0.757025	+	0.653386i	$0.773348\pi$
$824$	−9.06390	−	0.674345i	−0.315756	−	0.0234919i
$825$	22.1164	+	5.92608i	0.769996	+	0.206320i
$826$	22.1706	−	12.0786i	0.771415	−	0.420270i
$827$	25.7134	−	25.7134i	0.894141	−	0.894141i	−0.100769	−	0.994910i	$-0.532130\pi$
$827$	25.7134	−	25.7134i	0.894141	−	0.894141i	0.994910	+	0.100769i	$0.0321302\pi$
$828$	2.57690	+	5.02199i	0.0895533	+	0.174526i
$829$	−18.6087	−	10.7437i	−0.646307	−	0.373145i	0.140733	−	0.990048i	$-0.455054\pi$
$829$	−18.6087	−	10.7437i	−0.646307	−	0.373145i	−0.787040	+	0.616902i	$0.788387\pi$
$830$	3.27281	−	5.35787i	0.113601	−	0.185974i
$831$	17.1508			0.594956
$832$	21.6887	−	19.0158i	0.751919	−	0.659255i
$833$	0.883265			0.0306033
$834$	−11.3398	+	18.5642i	−0.392664	+	0.642825i
$835$	5.71156	+	3.29757i	0.197657	+	0.114117i
$836$	−24.8208	−	48.3720i	−0.858444	−	1.67298i
$837$	2.13065	−	2.13065i	0.0736461	−	0.0736461i
$838$	−32.6135	+	17.7679i	−1.12661	+	0.613783i
$839$	41.0730	+	11.0055i	1.41800	+	0.379951i	0.884772	−	0.466023i	$-0.154314\pi$
$839$	41.0730	+	11.0055i	1.41800	+	0.379951i	0.533224	+	0.845974i	$0.320980\pi$
$840$	−3.07033	−	0.228429i	−0.105936	−	0.00788156i
$841$	−4.59809	−	7.96412i	−0.158555	−	0.274625i
$842$	2.71464	+	11.2367i	0.0935527	+	0.387242i
$843$	7.57693	+	28.2775i	0.260963	+	0.973928i
$844$	−1.22722	+	24.7680i	−0.0422426	+	0.852549i
$845$	−3.26492	−	2.32834i	−0.112317	−	0.0800974i
$846$	2.12775	−	2.02493i	0.0731535	−	0.0696186i
$847$	−36.7843	+	9.85633i	−1.26392	+	0.338668i
$848$	29.6643	−	41.3230i	1.01868	−	1.41904i
$849$	15.0698	−	8.70056i	0.517194	−	0.298602i
$850$	−1.12333	−	0.0278128i	−0.0385300	−	0.000953970i
$851$	5.53156	−	20.6441i	0.189619	−	0.707669i
$852$	8.47796	+	2.72795i	0.290450	+	0.0934581i
$853$	14.2337	+	14.2337i	0.487353	+	0.487353i	0.907470	−	0.420117i	$-0.138011\pi$
$853$	14.2337	+	14.2337i	0.487353	+	0.487353i	−0.420117	+	0.907470i	$0.638011\pi$
$854$	−56.3162	−	16.5943i	−1.92710	−	0.567845i
$855$	0.898155	−	1.55565i	0.0307162	−	0.0532021i
$856$	13.0187	+	8.86572i	0.444968	+	0.303024i
$857$		−	36.4229i		−	1.24418i	−0.782945	−	0.622091i	$-0.786283\pi$
$857$		−	36.4229i		−	1.24418i	0.782945	−	0.622091i	$-0.213717\pi$
$858$	23.7628	−	1.38456i	0.811247	−	0.0472680i
$859$			17.8024i			0.607411i	0.952766	+	0.303706i	$0.0982239\pi$
$859$			17.8024i			0.607411i	−0.952766	+	0.303706i	$0.901776\pi$
$860$	0.964827	+	4.47635i	0.0329003	+	0.152642i
$861$	−4.65583	+	8.06414i	−0.158670	+	0.274825i
$862$	−6.49943	+	22.0571i	−0.221371	+	0.751269i
$863$	40.2696	+	40.2696i	1.37079	+	1.37079i	0.859268	+	0.511525i	$0.170919\pi$
$863$	40.2696	+	40.2696i	1.37079	+	1.37079i	0.511525	+	0.859268i	$0.329081\pi$
$864$	−5.21069	+	2.20199i	−0.177271	+	0.0749132i
$865$	−0.156159	+	0.582793i	−0.00530956	+	0.0198155i
$866$	−0.731003	+	29.5246i	−0.0248405	+	1.00329i
$867$	14.6997	−	8.48688i	0.499228	−	0.288230i
$868$	11.5314	−	17.8681i	0.391400	−	0.606482i
$869$	−43.8569	+	11.7514i	−1.48774	+	0.398640i
$870$	−1.85866	−	1.95303i	−0.0630145	−	0.0662141i
$871$	−3.36047	+	7.12616i	−0.113865	+	0.241461i
$872$	26.2317	−	22.5988i	0.888319	−	0.765292i
$873$	−3.05270	−	11.3928i	−0.103318	−	0.385589i
$874$	−22.5926	+	5.45808i	−0.764205	+	0.184622i
$875$	5.39083	+	9.33720i	0.182243	+	0.315655i
$876$	−4.97187	+	4.50243i	−0.167984	+	0.152123i
$877$	−3.73858	−	1.00175i	−0.126243	−	0.0338267i	0.195144	−	0.980775i	$-0.437482\pi$
$877$	−3.73858	−	1.00175i	−0.126243	−	0.0338267i	−0.321387	+	0.946948i	$0.604149\pi$
$878$	5.90002	+	10.8296i	0.199116	+	0.365482i
$879$	1.80790	−	1.80790i	0.0609789	−	0.0609789i
$880$	−5.24851	+	2.37275i	−0.176927	+	0.0799853i
$881$	31.4715	+	18.1701i	1.06030	+	0.612166i	0.925516	−	0.378709i	$-0.123632\pi$
$881$	31.4715	+	18.1701i	1.06030	+	0.612166i	0.134786	+	0.990875i	$0.456965\pi$
$882$	−6.58035	−	4.01955i	−0.221572	−	0.135345i
$883$	−57.7003			−1.94177			−0.970885	−	0.239548i	$-0.923001\pi$
$883$	−57.7003			−1.94177			−0.970885	+	0.239548i	$0.923001\pi$
$884$	−1.11762	+	0.339905i	−0.0375895	+	0.0114323i
$885$	1.56058			0.0524583
$886$	−6.39694	−	3.90752i	−0.214909	−	0.131276i
$887$	−14.2341	−	8.21804i	−0.477933	−	0.275935i	0.241622	−	0.970371i	$-0.422321\pi$
$887$	−14.2341	−	8.21804i	−0.477933	−	0.275935i	−0.719555	+	0.694436i	$0.755654\pi$
$888$	20.2208	+	7.06336i	0.678566	+	0.237031i
$889$	−1.14520	+	1.14520i	−0.0384087	+	0.0384087i
$890$	1.21205	+	2.22475i	0.0406281	+	0.0745739i
$891$	−4.50910	−	1.20821i	−0.151061	−	0.0404766i
$892$	2.56321	+	2.83046i	0.0858226	+	0.0947707i
$893$	6.04744	+	10.4745i	0.202370	+	0.350515i
$894$	−16.7009	+	4.03472i	−0.558561	+	0.134941i
$895$	0.718907	+	2.68300i	0.0240304	+	0.0896827i
$896$	−32.6749	+	22.9404i	−1.09159	+	0.766384i
$897$	1.81021	−	10.0135i	0.0604412	−	0.334342i
$898$	−17.5729	−	18.4652i	−0.586415	−	0.616191i
$899$	17.9879	−	4.81985i	0.599931	−	0.160751i
$900$	8.24230	+	5.31926i	0.274743	+	0.177309i
$901$	−1.78409	+	1.03005i	−0.0594367	+	0.0343158i
$902$	−0.431185	+	17.4152i	−0.0143569	+	0.579863i
$903$	−6.77901	+	25.2996i	−0.225591	+	0.841919i
$904$	−6.00670	−	12.4559i	−0.199780	−	0.414277i
$905$	−2.15753	−	2.15753i	−0.0717186	−	0.0717186i
$906$	−0.272147	+	0.923588i	−0.00904149	+	0.0306842i
$907$	−24.8940	+	43.1177i	−0.826593	+	1.43170i	0.0741028	+	0.997251i	$0.476391\pi$
$907$	−24.8940	+	43.1177i	−0.826593	+	1.43170i	−0.900696	+	0.434450i	$0.856943\pi$
$908$	−43.1133	+	9.29260i	−1.43077	+	0.308386i
$909$			9.97494i			0.330848i
$910$	4.14637	+	3.68979i	0.137451	+	0.122315i
$911$			13.2157i			0.437857i	0.975741	+	0.218928i	$0.0702561\pi$
$911$			13.2157i			0.437857i	−0.975741	+	0.218928i	$0.929744\pi$
$912$	−3.77502	−	22.9853i	−0.125004	−	0.761120i
$913$	33.5921	−	58.1833i	1.11174	−	1.92559i
$914$	−46.9742	−	13.8416i	−1.55377	−	0.457838i
$915$	−2.56606	−	2.56606i	−0.0848315	−	0.0848315i
$916$	9.55274	−	29.6881i	0.315631	−	0.980923i
$917$	16.5523	−	61.7741i	0.546606	−	2.03996i
$918$	0.229025	+	0.00567047i	0.00755896	+	0.000187153i
$919$	−0.916871	+	0.529356i	−0.0302448	+	0.0174618i	−0.515046	−	0.857162i	$-0.672225\pi$
$919$	−0.916871	+	0.529356i	−0.0302448	+	0.0174618i	0.484801	+	0.874624i	$0.338892\pi$
$920$	0.459085	+	2.41920i	0.0151356	+	0.0797587i
$921$	−10.8039	+	2.89489i	−0.356000	+	0.0953899i
$922$	−13.1201	+	12.4862i	−0.432089	+	0.411210i
$923$	−9.15230	−	13.1916i	−0.301252	−	0.434205i
$924$	−32.9057	−	1.63043i	−1.08252	−	0.0536372i
$925$	−9.61336	−	35.8775i	−0.316085	−	1.17965i
$926$	7.69654	+	31.8582i	0.252924	+	1.04693i
$927$	−1.60671	−	2.78291i	−0.0527714	−	0.0914028i
$928$	−34.6936	−	4.31611i	−1.13887	−	0.141683i
$929$	−48.6155	−	13.0265i	−1.59502	−	0.427385i	−0.651487	−	0.758660i	$-0.725855\pi$
$929$	−48.6155	−	13.0265i	−1.59502	−	0.427385i	−0.943534	+	0.331275i	$0.892521\pi$
$930$	1.15429	−	0.628862i	0.0378507	−	0.0206212i
$931$	22.4515	−	22.4515i	0.735817	−	0.735817i
$932$	2.57567	−	1.32163i	0.0843688	−	0.0432916i
$933$	5.89298	+	3.40231i	0.192927	+	0.111387i
$934$	−15.8602	+	25.9644i	−0.518960	+	0.849583i
$935$	0.233270			0.00762874
$936$	9.87312	+	2.55373i	0.322713	+	0.0834712i
$937$	10.8927			0.355848			0.177924	−	0.984044i	$-0.443062\pi$
$937$	10.8927			0.355848			0.177924	+	0.984044i	$0.443062\pi$
$938$	5.68462	−	9.30621i	0.185609	−	0.303859i
$939$	16.4817	+	9.51574i	0.537861	+	0.310534i
$940$	1.14004	−	0.584981i	0.0371840	−	0.0190800i
$941$	−5.22433	+	5.22433i	−0.170308	+	0.170308i	−0.787115	−	0.616806i	$-0.788426\pi$
$941$	−5.22433	+	5.22433i	−0.170308	+	0.170308i	0.616806	+	0.787115i	$0.288426\pi$
$942$	−22.0007	+	11.9860i	−0.716820	+	0.390526i
$943$	7.19353	+	1.92750i	0.234254	+	0.0627680i
$944$	15.6538	−	12.8247i	0.509488	−	0.417409i
$945$	−0.544262	−	0.942690i	−0.0177048	−	0.0306657i
$946$	11.5070	+	47.6307i	0.374124	+	1.54861i
$947$	−8.46903	−	31.6069i	−0.275207	−	1.02708i	−0.955703	−	0.294333i	$-0.904902\pi$
$947$	−8.46903	−	31.6069i	−0.275207	−	1.02708i	0.680496	−	0.732752i	$-0.261764\pi$
$948$	−19.4288	−	0.962669i	−0.631017	−	0.0312660i
$949$	12.0506	−	1.00195i	0.391180	−	0.0325246i
$950$	−29.2607	+	27.8467i	−0.949342	+	0.903468i
$951$	21.5011	−	5.76120i	0.697220	−	0.186820i
$952$	1.58851	−	0.301448i	0.0514840	−	0.00976998i
$953$	−13.0481	+	7.53332i	−0.422669	+	0.244028i	−0.696219	−	0.717830i	$-0.745136\pi$
$953$	−13.0481	+	7.53332i	−0.422669	+	0.244028i	0.273549	+	0.961858i	$0.411802\pi$
$954$	17.9791	+	0.445146i	0.582093	+	0.0144121i
$955$	−1.00820	+	3.76264i	−0.0326245	+	0.121756i
$956$	8.66244	−	26.9212i	0.280163	−	0.870695i
$957$	−20.4005	−	20.4005i	−0.659455	−	0.659455i
$958$	6.33943	+	1.86800i	0.204818	+	0.0603522i
$959$	40.9702	−	70.9624i	1.32300	−	2.29150i
$960$	−2.45193	+	0.278937i	−0.0791358	+	0.00900265i
$961$		−	21.9206i		−	0.707117i
$962$	−21.2192	−	32.2607i	−0.684135	−	1.04013i
$963$			5.56873i			0.179450i
$964$	8.81888	−	1.90081i	0.284037	−	0.0612210i
$965$	2.08602	−	3.61308i	0.0671512	−	0.116309i
$966$	−3.98094	+	13.5101i	−0.128085	+	0.434682i
$967$	28.6161	+	28.6161i	0.920232	+	0.920232i	0.997046	−	0.0768131i	$-0.0244745\pi$
$967$	28.6161	+	28.6161i	0.920232	+	0.920232i	−0.0768131	+	0.997046i	$0.524474\pi$
$968$	−27.4938	+	13.2585i	−0.883684	+	0.426145i
$969$	−0.244156	+	0.911203i	−0.00784343	+	0.0292721i
$970$	0.127355	−	5.14376i	0.00408912	−	0.165156i
$971$	15.8452	−	9.14823i	0.508497	−	0.293581i	−0.223719	−	0.974654i	$-0.571820\pi$
$971$	15.8452	−	9.14823i	0.508497	−	0.293581i	0.732216	+	0.681073i	$0.238486\pi$
$972$	−1.68044	−	1.08449i	−0.0539002	−	0.0347850i
$973$	−52.4308	+	14.0488i	−1.68086	+	0.450384i
$974$	−17.7913	−	18.6947i	−0.570071	−	0.599016i
$975$	−5.97680	−	16.6441i	−0.191411	−	0.533037i
$976$	−46.8273	−	4.65188i	−1.49890	−	0.148903i
$977$	6.00491	+	22.4106i	0.192114	+	0.716979i	0.992995	+	0.118156i	$0.0376982\pi$
$977$	6.00491	+	22.4106i	0.192114	+	0.716979i	−0.800881	+	0.598823i	$0.795635\pi$
$978$	21.7770	−	5.26106i	0.696353	−	0.168230i
$979$	13.5553	+	23.4785i	0.433230	+	0.750376i
$980$	−2.25794	−	2.49336i	−0.0721274	−	0.0796476i
$981$	11.8243	+	3.16830i	0.377520	+	0.101156i
$982$	−23.0408	−	42.2920i	−0.735263	−	1.34959i
$983$	−9.44152	+	9.44152i	−0.301138	+	0.301138i	−0.841459	−	0.540321i	$-0.818303\pi$
$983$	−9.44152	+	9.44152i	−0.301138	+	0.301138i	0.540321	+	0.841459i	$0.318303\pi$
$984$	−2.46127	+	7.04604i	−0.0784623	+	0.224620i
$985$	3.37175	+	1.94668i	0.107433	+	0.0620264i
$986$	1.20829	+	0.738073i	0.0384798	+	0.0235050i
$987$	7.32923			0.233292
$988$	−19.7684	+	37.0483i	−0.628917	+	1.17866i
$989$	20.9479			0.666106
$990$	−1.73787	−	1.06156i	−0.0552331	−	0.0337386i
$991$	18.9934	+	10.9658i	0.603345	+	0.348342i	0.770356	−	0.637613i	$-0.220078\pi$
$991$	18.9934	+	10.9658i	0.603345	+	0.348342i	−0.167011	+	0.985955i	$0.553412\pi$
$992$	6.41049	−	15.7938i	0.203533	−	0.501455i
$993$	−5.41033	+	5.41033i	−0.171692	+	0.171692i
$994$	10.6316	+	19.5145i	0.337213	+	0.618963i
$995$	−2.35754	−	0.631701i	−0.0747391	−	0.0200263i
$996$	21.3357	−	19.3212i	0.676047	−	0.612215i
$997$	−27.2207	−	47.1476i	−0.862088	−	1.49318i	−0.869910	−	0.493211i	$-0.835823\pi$
$997$	−27.2207	−	47.1476i	−0.862088	−	1.49318i	0.00782136	−	0.999969i	$-0.497510\pi$
$998$	49.3813	−	11.9299i	1.56314	−	0.377634i
$999$	1.95997	+	7.31471i	0.0620107	+	0.231427i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.2.w.c.19.3	✓	24
3.2	odd	2		468.2.cb.h.19.4		24
4.3	odd	2		156.2.w.d.19.5	yes	24
12.11	even	2		468.2.cb.g.19.2		24
13.11	odd	12		156.2.w.d.115.5	yes	24
39.11	even	12		468.2.cb.g.271.2		24
52.11	even	12	inner	156.2.w.c.115.3	yes	24
156.11	odd	12		468.2.cb.h.271.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.w.c.19.3	✓	24	1.1	even	1	trivial
156.2.w.c.115.3	yes	24	52.11	even	12	inner
156.2.w.d.19.5	yes	24	4.3	odd	2
156.2.w.d.115.5	yes	24	13.11	odd	12
468.2.cb.g.19.2		24	12.11	even	2
468.2.cb.g.271.2		24	39.11	even	12
468.2.cb.h.19.4		24	3.2	odd	2
468.2.cb.h.271.4		24	156.11	odd	12

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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	156.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.737204 + 1.20687i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.913059 - 1.77942i) q^{4} +(0.218120 - 0.218120i) q^{5} +(1.24187 - 0.676576i) q^{6} +(3.40856 + 0.913320i) q^{7} +(2.82063 + 0.209852i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.737204 + 1.20687i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.913059 - 1.77942i) q^{4} +(0.218120 - 0.218120i) q^{5} +(1.24187 - 0.676576i) q^{6} +(3.40856 + 0.913320i) q^{7} +(2.82063 + 0.209852i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.102443 + 0.424042i) q^{10} +(1.20821 + 4.50910i) q^{11} +(-0.0989759 + 1.99755i) q^{12} +(2.32949 - 2.75199i) q^{13} +(-3.61506 + 3.44037i) q^{14} +(-0.297958 + 0.0798376i) q^{15} +(-2.33265 + 3.24942i) q^{16} +(0.140292 - 0.0809975i) q^{17} +(-1.41378 - 0.0350040i) q^{18} +(1.50718 - 5.62489i) q^{19} +(-0.587284 - 0.188970i) q^{20} +(-2.49524 - 2.49524i) q^{21} +(-6.33259 - 1.86598i) q^{22} +(-1.41113 + 2.44415i) q^{23} +(-2.33781 - 1.59205i) q^{24} +4.90485i q^{25} +(1.60398 + 4.84017i) q^{26} -1.00000i q^{27} +(-1.48704 - 6.89916i) q^{28} +(3.09015 - 5.35230i) q^{29} +(0.123303 - 0.418452i) q^{30} +(2.13065 + 2.13065i) q^{31} +(-2.20199 - 5.21069i) q^{32} +(1.20821 - 4.50910i) q^{33} +(-0.00567047 + 0.229025i) q^{34} +(0.942690 - 0.544262i) q^{35} +(1.08449 - 1.68044i) q^{36} +(-7.31471 + 1.95997i) q^{37} +(5.67739 + 5.96566i) q^{38} +(-3.39340 + 1.21855i) q^{39} +(0.661010 - 0.569464i) q^{40} +(-0.682962 - 2.54885i) q^{41} +(4.85092 - 1.17192i) q^{42} +(-3.71119 - 6.42797i) q^{43} +(6.92040 - 6.26698i) q^{44} +(0.297958 + 0.0798376i) q^{45} +(-1.90948 - 3.50489i) q^{46} +(-1.46864 + 1.46864i) q^{47} +(3.64484 - 1.64776i) q^{48} +(4.72194 + 2.72621i) q^{49} +(-5.91950 - 3.61588i) q^{50} -0.161995 q^{51} +(-7.02391 - 1.63241i) q^{52} -12.7170 q^{53} +(1.20687 + 0.737204i) q^{54} +(1.24706 + 0.719991i) q^{55} +(9.42262 + 3.29143i) q^{56} +(-4.11770 + 4.11770i) q^{57} +(4.18145 + 7.67515i) q^{58} +(-4.88673 - 1.30940i) q^{59} +(0.414117 + 0.457295i) q^{60} +(5.88222 + 10.1883i) q^{61} +(-4.14214 + 1.00069i) q^{62} +(0.913320 + 3.40856i) q^{63} +(7.91192 + 1.18383i) q^{64} +(-0.0921557 - 1.10838i) q^{65} +(4.55119 + 4.78228i) q^{66} +(-2.11072 + 0.565565i) q^{67} +(-0.272223 - 0.175682i) q^{68} +(2.44415 - 1.41113i) q^{69} +(-0.0381027 + 1.53893i) q^{70} +(1.15253 - 4.30129i) q^{71} +(1.22858 + 2.54766i) q^{72} +(2.37148 + 2.37148i) q^{73} +(3.02701 - 10.2728i) q^{74} +(2.45242 - 4.24772i) q^{75} +(-11.3852 + 2.45395i) q^{76} +16.4730i q^{77} +(1.03100 - 4.99370i) q^{78} +9.72631i q^{79} +(0.199968 + 1.21756i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.57961 + 1.05478i) q^{82} +(-10.1767 - 10.1767i) q^{83} +(-2.16177 + 6.71837i) q^{84} +(0.0129333 - 0.0482677i) q^{85} +(10.4936 + 0.259813i) q^{86} +(-5.35230 + 3.09015i) q^{87} +(2.46167 + 12.9721i) q^{88} +(5.60967 - 1.50311i) q^{89} +(-0.316009 + 0.300739i) q^{90} +(10.4537 - 7.25275i) q^{91} +(5.63762 + 0.279336i) q^{92} +(-0.779873 - 2.91053i) q^{93} +(-0.689768 - 2.85515i) q^{94} +(-0.898155 - 1.55565i) q^{95} +(-0.698365 + 5.61358i) q^{96} +(-11.3928 - 3.05270i) q^{97} +(-6.77121 + 3.68898i) q^{98} +(-3.30089 + 3.30089i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9} + 12 q^{10} + 4 q^{11} - 4 q^{12} - 22 q^{14} - 4 q^{15} + 12 q^{16} - 2 q^{18} - 22 q^{19} - 4 q^{20} + 10 q^{21} - 34 q^{22} + 2 q^{24} - 4 q^{26} - 14 q^{28} + 8 q^{29} - 16 q^{30} - 2 q^{31} - 34 q^{32} + 4 q^{33} + 20 q^{34} + 24 q^{35} - 4 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} + 28 q^{40} - 36 q^{41} + 6 q^{42} + 10 q^{43} + 20 q^{44} + 4 q^{45} - 2 q^{46} + 20 q^{47} + 32 q^{48} - 54 q^{49} - 24 q^{50} + 36 q^{51} + 4 q^{52} - 36 q^{53} - 4 q^{54} - 24 q^{55} + 70 q^{56} - 32 q^{57} + 48 q^{58} - 36 q^{59} - 28 q^{60} - 2 q^{61} + 64 q^{62} + 8 q^{63} - 8 q^{64} + 16 q^{65} + 20 q^{66} - 16 q^{67} - 10 q^{68} + 12 q^{69} + 36 q^{71} - 2 q^{72} - 40 q^{73} - 30 q^{74} - 8 q^{75} + 58 q^{76} + 24 q^{78} - 48 q^{80} - 12 q^{81} - 30 q^{82} - 24 q^{83} - 26 q^{84} + 18 q^{85} + 30 q^{86} + 6 q^{87} - 78 q^{88} + 66 q^{89} + 12 q^{90} + 42 q^{91} + 36 q^{92} - 10 q^{93} + 6 q^{94} - 28 q^{95} + 8 q^{96} + 4 q^{97} + 44 q^{98} - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9 + 12 * q^10 + 4 * q^11 - 4 * q^12 - 22 * q^14 - 4 * q^15 + 12 * q^16 - 2 * q^18 - 22 * q^19 - 4 * q^20 + 10 * q^21 - 34 * q^22 + 2 * q^24 - 4 * q^26 - 14 * q^28 + 8 * q^29 - 16 * q^30 - 2 * q^31 - 34 * q^32 + 4 * q^33 + 20 * q^34 + 24 * q^35 - 4 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 + 28 * q^40 - 36 * q^41 + 6 * q^42 + 10 * q^43 + 20 * q^44 + 4 * q^45 - 2 * q^46 + 20 * q^47 + 32 * q^48 - 54 * q^49 - 24 * q^50 + 36 * q^51 + 4 * q^52 - 36 * q^53 - 4 * q^54 - 24 * q^55 + 70 * q^56 - 32 * q^57 + 48 * q^58 - 36 * q^59 - 28 * q^60 - 2 * q^61 + 64 * q^62 + 8 * q^63 - 8 * q^64 + 16 * q^65 + 20 * q^66 - 16 * q^67 - 10 * q^68 + 12 * q^69 + 36 * q^71 - 2 * q^72 - 40 * q^73 - 30 * q^74 - 8 * q^75 + 58 * q^76 + 24 * q^78 - 48 * q^80 - 12 * q^81 - 30 * q^82 - 24 * q^83 - 26 * q^84 + 18 * q^85 + 30 * q^86 + 6 * q^87 - 78 * q^88 + 66 * q^89 + 12 * q^90 + 42 * q^91 + 36 * q^92 - 10 * q^93 + 6 * q^94 - 28 * q^95 + 8 * q^96 + 4 * q^97 + 44 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

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