LMFDB - Embedded newform 24.3.h.c.5.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [24,3,Mod(5,24)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(24, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("24.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 24 = 2^{3} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	24.h (of order $2$, degree $1$, 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:	$0.653952634465$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 6x^{2} + 16 $ x^4 + 6*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.4
Root			$0.707107 + 1.87083i$ of defining polynomial
Character	$\chi$	$=$	24.5
Dual form			24.3.h.c.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.87083i) q^{2} +(1.41421 - 2.64575i) q^{3} +(-3.00000 + 2.64575i) q^{4} -5.65685 q^{5} +(5.94975 + 0.774923i) q^{6} +4.00000 q^{7} +(-7.07107 - 3.74166i) q^{8} +(-5.00000 - 7.48331i) q^{9} +O(q^{10})$	\(q+(0.707107 + 1.87083i) q^{2} +(1.41421 - 2.64575i) q^{3} +(-3.00000 + 2.64575i) q^{4} -5.65685 q^{5} +(5.94975 + 0.774923i) q^{6} +4.00000 q^{7} +(-7.07107 - 3.74166i) q^{8} +(-5.00000 - 7.48331i) q^{9} +(-4.00000 - 10.5830i) q^{10} +8.48528 q^{11} +(2.75736 + 11.6789i) q^{12} +10.5830i q^{13} +(2.82843 + 7.48331i) q^{14} +(-8.00000 + 14.9666i) q^{15} +(2.00000 - 15.8745i) q^{16} +14.9666i q^{17} +(10.4645 - 14.6456i) q^{18} +5.29150i q^{19} +(16.9706 - 14.9666i) q^{20} +(5.65685 - 10.5830i) q^{21} +(6.00000 + 15.8745i) q^{22} -29.9333i q^{23} +(-19.8995 + 13.4168i) q^{24} +7.00000 q^{25} +(-19.7990 + 7.48331i) q^{26} +(-26.8701 + 2.64575i) q^{27} +(-12.0000 + 10.5830i) q^{28} +16.9706 q^{29} +(-33.6569 - 4.38362i) q^{30} -4.00000 q^{31} +(31.1127 - 7.48331i) q^{32} +(12.0000 - 22.4499i) q^{33} +(-28.0000 + 10.5830i) q^{34} -22.6274 q^{35} +(34.7990 + 9.22119i) q^{36} -52.9150i q^{37} +(-9.89949 + 3.74166i) q^{38} +(28.0000 + 14.9666i) q^{39} +(40.0000 + 21.1660i) q^{40} +29.9333i q^{41} +(23.7990 + 3.09969i) q^{42} -5.29150i q^{43} +(-25.4558 + 22.4499i) q^{44} +(28.2843 + 42.3320i) q^{45} +(56.0000 - 21.1660i) q^{46} +(-39.1716 - 27.7414i) q^{48} -33.0000 q^{49} +(4.94975 + 13.0958i) q^{50} +(39.5980 + 21.1660i) q^{51} +(-28.0000 - 31.7490i) q^{52} -50.9117 q^{53} +(-23.9497 - 48.3984i) q^{54} -48.0000 q^{55} +(-28.2843 - 14.9666i) q^{56} +(14.0000 + 7.48331i) q^{57} +(12.0000 + 31.7490i) q^{58} +48.0833 q^{59} +(-15.5980 - 66.0659i) q^{60} +95.2470i q^{61} +(-2.82843 - 7.48331i) q^{62} +(-20.0000 - 29.9333i) q^{63} +(36.0000 + 52.9150i) q^{64} -59.8665i q^{65} +(50.4853 + 6.57544i) q^{66} -47.6235i q^{67} +(-39.5980 - 44.8999i) q^{68} +(-79.1960 - 42.3320i) q^{69} +(-16.0000 - 42.3320i) q^{70} +89.7998i q^{71} +(7.35534 + 71.6233i) q^{72} -6.00000 q^{73} +(98.9949 - 37.4166i) q^{74} +(9.89949 - 18.5203i) q^{75} +(-14.0000 - 15.8745i) q^{76} +33.9411 q^{77} +(-8.20101 + 62.9662i) q^{78} +124.000 q^{79} +(-11.3137 + 89.7998i) q^{80} +(-31.0000 + 74.8331i) q^{81} +(-56.0000 + 21.1660i) q^{82} -2.82843 q^{83} +(11.0294 + 46.7156i) q^{84} -84.6640i q^{85} +(9.89949 - 3.74166i) q^{86} +(24.0000 - 44.8999i) q^{87} +(-60.0000 - 31.7490i) q^{88} -104.766i q^{89} +(-59.1960 + 82.8483i) q^{90} +42.3320i q^{91} +(79.1960 + 89.7998i) q^{92} +(-5.65685 + 10.5830i) q^{93} -29.9333i q^{95} +(24.2010 - 92.8995i) q^{96} +118.000 q^{97} +(-23.3345 - 61.7373i) q^{98} +(-42.4264 - 63.4980i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 12 q^{4} + 4 q^{6} + 16 q^{7} - 20 q^{9}+O(q^{10}) $ 4 * q - 12 * q^4 + 4 * q^6 + 16 * q^7 - 20 * q^9	$ 4 q - 12 q^{4} + 4 q^{6} + 16 q^{7} - 20 q^{9} - 16 q^{10} + 28 q^{12} - 32 q^{15} + 8 q^{16} + 56 q^{18} + 24 q^{22} - 40 q^{24} + 28 q^{25} - 48 q^{28} - 112 q^{30} - 16 q^{31} + 48 q^{33} - 112 q^{34} + 60 q^{36} + 112 q^{39} + 160 q^{40} + 16 q^{42} + 224 q^{46} - 168 q^{48} - 132 q^{49} - 112 q^{52} - 76 q^{54} - 192 q^{55} + 56 q^{57} + 48 q^{58} + 96 q^{60} - 80 q^{63} + 144 q^{64} + 168 q^{66} - 64 q^{70} - 112 q^{72} - 24 q^{73} - 56 q^{76} - 112 q^{78} + 496 q^{79} - 124 q^{81} - 224 q^{82} + 112 q^{84} + 96 q^{87} - 240 q^{88} + 80 q^{90} + 176 q^{96} + 472 q^{97}+O(q^{100}) $ 4 * q - 12 * q^4 + 4 * q^6 + 16 * q^7 - 20 * q^9 - 16 * q^10 + 28 * q^12 - 32 * q^15 + 8 * q^16 + 56 * q^18 + 24 * q^22 - 40 * q^24 + 28 * q^25 - 48 * q^28 - 112 * q^30 - 16 * q^31 + 48 * q^33 - 112 * q^34 + 60 * q^36 + 112 * q^39 + 160 * q^40 + 16 * q^42 + 224 * q^46 - 168 * q^48 - 132 * q^49 - 112 * q^52 - 76 * q^54 - 192 * q^55 + 56 * q^57 + 48 * q^58 + 96 * q^60 - 80 * q^63 + 144 * q^64 + 168 * q^66 - 64 * q^70 - 112 * q^72 - 24 * q^73 - 56 * q^76 - 112 * q^78 + 496 * q^79 - 124 * q^81 - 224 * q^82 + 112 * q^84 + 96 * q^87 - 240 * q^88 + 80 * q^90 + 176 * q^96 + 472 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/24\mathbb{Z}\right)^\times$.

$n$	$7$	$13$	$17$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	0.707107	+	1.87083i	0.353553	+	0.935414i
$2$	0.707107	+	1.87083i	0.353553	+	0.935414i
$3$	1.41421	−	2.64575i	0.471405	−	0.881917i
$3$	1.41421	−	2.64575i	0.471405	−	0.881917i
$4$	−3.00000	+	2.64575i	−0.750000	+	0.661438i
$5$	−5.65685			−1.13137			−0.565685	−	0.824621i	$-0.691388\pi$
$5$	−5.65685			−1.13137			−0.565685	+	0.824621i	$0.691388\pi$
$6$	5.94975	+	0.774923i	0.991625	+	0.129154i
$7$	4.00000			0.571429			0.285714	−	0.958315i	$-0.407769\pi$
$7$	4.00000			0.571429			0.285714	+	0.958315i	$0.407769\pi$
$8$	−7.07107	−	3.74166i	−0.883883	−	0.467707i
$9$	−5.00000	−	7.48331i	−0.555556	−	0.831479i
$10$	−4.00000	−	10.5830i	−0.400000	−	1.05830i
$11$	8.48528			0.771389			0.385695	−	0.922627i	$-0.373962\pi$
$11$	8.48528			0.771389			0.385695	+	0.922627i	$0.373962\pi$
$12$	2.75736	+	11.6789i	0.229780	+	0.973243i
$13$			10.5830i			0.814077i	0.913411	+	0.407039i	$0.133439\pi$
$13$			10.5830i			0.814077i	−0.913411	+	0.407039i	$0.866561\pi$
$14$	2.82843	+	7.48331i	0.202031	+	0.534522i
$15$	−8.00000	+	14.9666i	−0.533333	+	0.997775i
$16$	2.00000	−	15.8745i	0.125000	−	0.992157i
$17$			14.9666i			0.880390i	0.897902	+	0.440195i	$0.145091\pi$
$17$			14.9666i			0.880390i	−0.897902	+	0.440195i	$0.854909\pi$
$18$	10.4645	−	14.6456i	0.581359	−	0.813647i
$19$			5.29150i			0.278500i	0.990257	+	0.139250i	$0.0444692\pi$
$19$			5.29150i			0.278500i	−0.990257	+	0.139250i	$0.955531\pi$
$20$	16.9706	−	14.9666i	0.848528	−	0.748331i
$21$	5.65685	−	10.5830i	0.269374	−	0.503953i
$22$	6.00000	+	15.8745i	0.272727	+	0.721569i
$23$		−	29.9333i		−	1.30145i	−0.759315	−	0.650723i	$-0.774466\pi$
$23$		−	29.9333i		−	1.30145i	0.759315	−	0.650723i	$-0.225534\pi$
$24$	−19.8995	+	13.4168i	−0.829146	+	0.559033i
$25$	7.00000			0.280000
$26$	−19.7990	+	7.48331i	−0.761500	+	0.287820i
$27$	−26.8701	+	2.64575i	−0.995187	+	0.0979908i
$28$	−12.0000	+	10.5830i	−0.428571	+	0.377964i
$29$	16.9706			0.585192			0.292596	−	0.956236i	$-0.405481\pi$
$29$	16.9706			0.585192			0.292596	+	0.956236i	$0.405481\pi$
$30$	−33.6569	−	4.38362i	−1.12190	−	0.146121i
$31$	−4.00000			−0.129032			−0.0645161	−	0.997917i	$-0.520550\pi$
$31$	−4.00000			−0.129032			−0.0645161	+	0.997917i	$0.520550\pi$
$32$	31.1127	−	7.48331i	0.972272	−	0.233854i
$33$	12.0000	−	22.4499i	0.363636	−	0.680301i
$34$	−28.0000	+	10.5830i	−0.823529	+	0.311265i
$35$	−22.6274			−0.646498
$36$	34.7990	+	9.22119i	0.966639	+	0.256144i
$37$		−	52.9150i		−	1.43014i	−0.699055	−	0.715068i	$-0.746396\pi$
$37$		−	52.9150i		−	1.43014i	0.699055	−	0.715068i	$-0.253604\pi$
$38$	−9.89949	+	3.74166i	−0.260513	+	0.0984647i
$39$	28.0000	+	14.9666i	0.717949	+	0.383760i
$40$	40.0000	+	21.1660i	1.00000	+	0.529150i
$41$			29.9333i			0.730079i	0.930992	+	0.365040i	$0.118945\pi$
$41$			29.9333i			0.730079i	−0.930992	+	0.365040i	$0.881055\pi$
$42$	23.7990	+	3.09969i	0.566643	+	0.0738022i
$43$		−	5.29150i		−	0.123058i	−0.998105	−	0.0615291i	$-0.980402\pi$
$43$		−	5.29150i		−	0.123058i	0.998105	−	0.0615291i	$-0.0195977\pi$
$44$	−25.4558	+	22.4499i	−0.578542	+	0.510226i
$45$	28.2843	+	42.3320i	0.628539	+	0.940712i
$46$	56.0000	−	21.1660i	1.21739	−	0.460131i
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	−39.1716	−	27.7414i	−0.816074	−	0.577947i
$49$	−33.0000			−0.673469
$50$	4.94975	+	13.0958i	0.0989949	+	0.261916i
$51$	39.5980	+	21.1660i	0.776431	+	0.415020i
$52$	−28.0000	−	31.7490i	−0.538462	−	0.610558i
$53$	−50.9117			−0.960598			−0.480299	−	0.877105i	$-0.659472\pi$
$53$	−50.9117			−0.960598			−0.480299	+	0.877105i	$0.659472\pi$
$54$	−23.9497	−	48.3984i	−0.443514	−	0.896268i
$55$	−48.0000			−0.872727
$56$	−28.2843	−	14.9666i	−0.505076	−	0.267261i
$57$	14.0000	+	7.48331i	0.245614	+	0.131286i
$58$	12.0000	+	31.7490i	0.206897	+	0.547397i
$59$	48.0833			0.814971			0.407485	−	0.913212i	$-0.366406\pi$
$59$	48.0833			0.814971			0.407485	+	0.913212i	$0.366406\pi$
$60$	−15.5980	−	66.0659i	−0.259966	−	1.10110i
$61$			95.2470i			1.56143i	0.624889	+	0.780714i	$0.285144\pi$
$61$			95.2470i			1.56143i	−0.624889	+	0.780714i	$0.714856\pi$
$62$	−2.82843	−	7.48331i	−0.0456198	−	0.120699i
$63$	−20.0000	−	29.9333i	−0.317460	−	0.475131i
$64$	36.0000	+	52.9150i	0.562500	+	0.826797i
$65$		−	59.8665i		−	0.921023i
$66$	50.4853	+	6.57544i	0.764929	+	0.0996278i
$67$		−	47.6235i		−	0.710799i	−0.934715	−	0.355399i	$-0.884345\pi$
$67$		−	47.6235i		−	0.710799i	0.934715	−	0.355399i	$-0.115655\pi$
$68$	−39.5980	−	44.8999i	−0.582323	−	0.660292i
$69$	−79.1960	−	42.3320i	−1.14777	−	0.613508i
$70$	−16.0000	−	42.3320i	−0.228571	−	0.604743i
$71$			89.7998i			1.26479i	0.774648	+	0.632393i	$0.217927\pi$
$71$			89.7998i			1.26479i	−0.774648	+	0.632393i	$0.782073\pi$
$72$	7.35534	+	71.6233i	0.102157	+	0.994768i
$73$	−6.00000			−0.0821918			−0.0410959	−	0.999155i	$-0.513085\pi$
$73$	−6.00000			−0.0821918			−0.0410959	+	0.999155i	$0.513085\pi$
$74$	98.9949	−	37.4166i	1.33777	−	0.505629i
$75$	9.89949	−	18.5203i	0.131993	−	0.246937i
$76$	−14.0000	−	15.8745i	−0.184211	−	0.208875i
$77$	33.9411			0.440794
$78$	−8.20101	+	62.9662i	−0.105141	+	0.807259i
$79$	124.000			1.56962			0.784810	−	0.619736i	$-0.212760\pi$
$79$	124.000			1.56962			0.784810	+	0.619736i	$0.212760\pi$
$80$	−11.3137	+	89.7998i	−0.141421	+	1.12250i
$81$	−31.0000	+	74.8331i	−0.382716	+	0.923866i
$82$	−56.0000	+	21.1660i	−0.682927	+	0.258122i
$83$	−2.82843			−0.0340774			−0.0170387	−	0.999855i	$-0.505424\pi$
$83$	−2.82843			−0.0340774			−0.0170387	+	0.999855i	$0.505424\pi$
$84$	11.0294	+	46.7156i	0.131303	+	0.556139i
$85$		−	84.6640i		−	0.996048i
$86$	9.89949	−	3.74166i	0.115110	−	0.0435076i
$87$	24.0000	−	44.8999i	0.275862	−	0.516091i
$88$	−60.0000	−	31.7490i	−0.681818	−	0.360784i
$89$		−	104.766i		−	1.17715i	−0.808442	−	0.588575i	$-0.799689\pi$
$89$		−	104.766i		−	1.17715i	0.808442	−	0.588575i	$-0.200311\pi$
$90$	−59.1960	+	82.8483i	−0.657733	+	0.920537i
$91$			42.3320i			0.465187i
$92$	79.1960	+	89.7998i	0.860826	+	0.976085i
$93$	−5.65685	+	10.5830i	−0.0608264	+	0.113796i
$94$		0			0
$95$		−	29.9333i		−	0.315087i
$96$	24.2010	−	92.8995i	0.252094	−	0.967703i
$97$	118.000			1.21649			0.608247	−	0.793747i	$-0.291873\pi$
$97$	118.000			1.21649			0.608247	+	0.793747i	$0.291873\pi$
$98$	−23.3345	−	61.7373i	−0.238107	−	0.629973i
$99$	−42.4264	−	63.4980i	−0.428550	−	0.641394i
$100$	−21.0000	+	18.5203i	−0.210000	+	0.185203i
$101$	62.2254			0.616093			0.308047	−	0.951371i	$-0.400325\pi$
$101$	62.2254			0.616093			0.308047	+	0.951371i	$0.400325\pi$
$102$	−11.5980	+	89.0477i	−0.113706	+	0.873016i
$103$	−108.000			−1.04854			−0.524272	−	0.851551i	$-0.675662\pi$
$103$	−108.000			−1.04854			−0.524272	+	0.851551i	$0.675662\pi$
$104$	39.5980	−	74.8331i	0.380750	−	0.719549i
$105$	−32.0000	+	59.8665i	−0.304762	+	0.570157i
$106$	−36.0000	−	95.2470i	−0.339623	−	0.898557i
$107$	−144.250			−1.34813			−0.674064	−	0.738673i	$-0.735453\pi$
$107$	−144.250			−1.34813			−0.674064	+	0.738673i	$0.735453\pi$
$108$	73.6102	−	79.0287i	0.681576	−	0.731748i
$109$			52.9150i			0.485459i	0.970094	+	0.242729i	$0.0780427\pi$
$109$			52.9150i			0.485459i	−0.970094	+	0.242729i	$0.921957\pi$
$110$	−33.9411	−	89.7998i	−0.308556	−	0.816362i
$111$	−140.000	−	74.8331i	−1.26126	−	0.674173i
$112$	8.00000	−	63.4980i	0.0714286	−	0.566947i
$113$			89.7998i			0.794688i	0.917670	+	0.397344i	$0.130068\pi$
$113$			89.7998i			0.794688i	−0.917670	+	0.397344i	$0.869932\pi$
$114$	−4.10051	+	31.4831i	−0.0359693	+	0.276168i
$115$			169.328i			1.47242i
$116$	−50.9117	+	44.8999i	−0.438894	+	0.387068i
$117$	79.1960	−	52.9150i	0.676889	−	0.452265i
$118$	34.0000	+	89.9555i	0.288136	+	0.762335i
$119$			59.8665i			0.503080i
$120$	112.569	−	75.8968i	0.938071	−	0.632473i
$121$	−49.0000			−0.404959
$122$	−178.191	+	67.3498i	−1.46058	+	0.552048i
$123$	79.1960	+	42.3320i	0.643870	+	0.344163i
$124$	12.0000	−	10.5830i	0.0967742	−	0.0853468i
$125$	101.823			0.814587
$126$	41.8579	−	58.5826i	0.332205	−	0.464941i
$127$	76.0000			0.598425			0.299213	−	0.954186i	$-0.403276\pi$
$127$	76.0000			0.598425			0.299213	+	0.954186i	$0.403276\pi$
$128$	−73.5391	+	104.766i	−0.574524	+	0.818488i
$129$	−14.0000	−	7.48331i	−0.108527	−	0.0580102i
$130$	112.000	−	42.3320i	0.861538	−	0.325631i
$131$	14.1421			0.107955			0.0539776	−	0.998542i	$-0.482810\pi$
$131$	14.1421			0.107955			0.0539776	+	0.998542i	$0.482810\pi$
$132$	23.3970	+	99.0988i	0.177250	+	0.750749i
$133$			21.1660i			0.159143i
$134$	89.0955	−	33.6749i	0.664891	−	0.251305i
$135$	152.000	−	14.9666i	1.12593	−	0.110864i
$136$	56.0000	−	105.830i	0.411765	−	0.778162i
$137$		0			0		1.00000			$0$
$137$		0			0		−1.00000			$\pi$
$138$	23.1960	−	178.095i	0.168087	−	1.29055i
$139$		−	121.705i		−	0.875572i	−0.899079	−	0.437786i	$-0.855763\pi$
$139$		−	121.705i		−	0.875572i	0.899079	−	0.437786i	$-0.144237\pi$
$140$	67.8823	−	59.8665i	0.484873	−	0.427618i
$141$		0			0
$142$	−168.000	+	63.4980i	−1.18310	+	0.447169i
$143$			89.7998i			0.627970i
$144$	−128.794	+	64.4059i	−0.894402	+	0.447263i
$145$	−96.0000			−0.662069
$146$	−4.24264	−	11.2250i	−0.0290592	−	0.0768834i
$147$	−46.6690	+	87.3098i	−0.317477	+	0.593944i
$148$	140.000	+	158.745i	0.945946	+	1.07260i
$149$	−186.676			−1.25286			−0.626430	−	0.779478i	$-0.715485\pi$
$149$	−186.676			−1.25286			−0.626430	+	0.779478i	$0.715485\pi$
$150$	41.6482	+	5.42446i	0.277655	+	0.0361631i
$151$	−60.0000			−0.397351			−0.198675	−	0.980065i	$-0.563664\pi$
$151$	−60.0000			−0.397351			−0.198675	+	0.980065i	$0.563664\pi$
$152$	19.7990	−	37.4166i	0.130257	−	0.246162i
$153$	112.000	−	74.8331i	0.732026	−	0.489106i
$154$	24.0000	+	63.4980i	0.155844	+	0.412325i
$155$	22.6274			0.145983
$156$	−123.598	+	29.1811i	−0.792295	+	0.187059i
$157$		−	116.413i		−	0.741484i	−0.928736	−	0.370742i	$-0.879103\pi$
$157$		−	116.413i		−	0.741484i	0.928736	−	0.370742i	$-0.120897\pi$
$158$	87.6812	+	231.983i	0.554945	+	1.46825i
$159$	−72.0000	+	134.700i	−0.452830	+	0.847168i
$160$	−176.000	+	42.3320i	−1.10000	+	0.264575i
$161$		−	119.733i		−	0.743683i
$162$	−161.920	−	5.08066i	−0.999508	−	0.0313621i
$163$		−	291.033i		−	1.78548i	−0.450576	−	0.892738i	$-0.648781\pi$
$163$		−	291.033i		−	1.78548i	0.450576	−	0.892738i	$-0.351219\pi$
$164$	−79.1960	−	89.7998i	−0.482902	−	0.547560i
$165$	−67.8823	+	126.996i	−0.411408	+	0.769673i
$166$	−2.00000	−	5.29150i	−0.0120482	−	0.0318765i
$167$		−	329.266i		−	1.97165i	−0.167772	−	0.985826i	$-0.553657\pi$
$167$		−	329.266i		−	1.97165i	0.167772	−	0.985826i	$-0.446343\pi$
$168$	−79.5980	+	53.6671i	−0.473797	+	0.319447i
$169$	57.0000			0.337278
$170$	158.392	−	59.8665i	0.931717	−	0.352156i
$171$	39.5980	−	26.4575i	0.231567	−	0.154722i
$172$	14.0000	+	15.8745i	0.0813953	+	0.0922937i
$173$	−186.676			−1.07905			−0.539527	−	0.841969i	$-0.681397\pi$
$173$	−186.676			−1.07905			−0.539527	+	0.841969i	$0.681397\pi$
$174$	100.971	+	13.1509i	0.580291	+	0.0755797i
$175$	28.0000			0.160000
$176$	16.9706	−	134.700i	0.0964237	−	0.765339i
$177$	68.0000	−	127.216i	0.384181	−	0.718736i
$178$	196.000	−	74.0810i	1.10112	−	0.416186i
$179$	319.612			1.78554			0.892772	−	0.450509i	$-0.148758\pi$
$179$	319.612			1.78554			0.892772	+	0.450509i	$0.148758\pi$
$180$	−196.853	−	52.1629i	−1.09363	−	0.289794i
$181$			116.413i			0.643166i	0.946881	+	0.321583i	$0.104215\pi$
$181$			116.413i			0.643166i	−0.946881	+	0.321583i	$0.895785\pi$
$182$	−79.1960	+	29.9333i	−0.435143	+	0.164468i
$183$	252.000	+	134.700i	1.37705	+	0.736064i
$184$	−112.000	+	211.660i	−0.608696	+	1.15033i
$185$			299.333i			1.61801i
$186$	−23.7990	−	3.09969i	−0.127952	−	0.0166650i
$187$			126.996i			0.679123i
$188$		0			0
$189$	−107.480	+	10.5830i	−0.568678	+	0.0559947i
$190$	56.0000	−	21.1660i	0.294737	−	0.111400i
$191$			59.8665i			0.313437i	0.987643	+	0.156719i	$0.0500916\pi$
$191$			59.8665i			0.313437i	−0.987643	+	0.156719i	$0.949908\pi$
$192$	190.912	−	20.4139i	0.994332	−	0.106322i
$193$	−102.000			−0.528497			−0.264249	−	0.964455i	$-0.585124\pi$
$193$	−102.000			−0.528497			−0.264249	+	0.964455i	$0.585124\pi$
$194$	83.4386	+	220.758i	0.430096	+	1.13793i
$195$	−158.392	−	84.6640i	−0.812266	−	0.434175i
$196$	99.0000	−	87.3098i	0.505102	−	0.445458i
$197$	243.245			1.23474			0.617372	−	0.786671i	$-0.288197\pi$
$197$	243.245			1.23474			0.617372	+	0.786671i	$0.288197\pi$
$198$	88.7939	−	124.272i	0.448454	−	0.627639i
$199$	−188.000			−0.944724			−0.472362	−	0.881405i	$-0.656598\pi$
$199$	−188.000			−0.944724			−0.472362	+	0.881405i	$0.656598\pi$
$200$	−49.4975	−	26.1916i	−0.247487	−	0.130958i
$201$	−126.000	−	67.3498i	−0.626866	−	0.335074i
$202$	44.0000	+	116.413i	0.217822	+	0.576302i
$203$	67.8823			0.334395
$204$	−174.794	+	41.2684i	−0.856833	+	0.202296i
$205$		−	169.328i		−	0.825991i
$206$	−76.3675	−	202.049i	−0.370716	−	0.980823i
$207$	−224.000	+	149.666i	−1.08213	+	0.723026i
$208$	168.000	+	21.1660i	0.807692	+	0.101760i
$209$			44.8999i			0.214832i
$210$	−134.627	−	17.5345i	−0.641083	−	0.0834976i
$211$			248.701i			1.17868i	0.807887	+	0.589338i	$0.200611\pi$
$211$			248.701i			1.17868i	−0.807887	+	0.589338i	$0.799389\pi$
$212$	152.735	−	134.700i	0.720448	−	0.635376i
$213$	237.588	+	126.996i	1.11544	+	0.596226i
$214$	−102.000	−	269.867i	−0.476636	−	1.26106i
$215$			29.9333i			0.139224i
$216$	199.899	+	81.8303i	0.925461	+	0.378844i
$217$	−16.0000			−0.0737327
$218$	−98.9949	+	37.4166i	−0.454105	+	0.171636i
$219$	−8.48528	+	15.8745i	−0.0387456	+	0.0724863i
$220$	144.000	−	126.996i	0.654545	−	0.577255i
$221$	−158.392			−0.716706
$222$	41.0051	−	314.831i	0.184707	−	1.41816i
$223$	188.000			0.843049			0.421525	−	0.906817i	$-0.361495\pi$
$223$	188.000			0.843049			0.421525	+	0.906817i	$0.361495\pi$
$224$	124.451	−	29.9333i	0.555584	−	0.133631i
$225$	−35.0000	−	52.3832i	−0.155556	−	0.232814i
$226$	−168.000	+	63.4980i	−0.743363	+	0.280965i
$227$	−387.495			−1.70702			−0.853512	−	0.521073i	$-0.825532\pi$
$227$	−387.495			−1.70702			−0.853512	+	0.521073i	$0.825532\pi$
$228$	−61.7990	+	14.5906i	−0.271048	+	0.0639937i
$229$			243.409i			1.06292i	0.847083	+	0.531461i	$0.178357\pi$
$229$			243.409i			1.06292i	−0.847083	+	0.531461i	$0.821643\pi$
$230$	−316.784	+	119.733i	−1.37732	+	0.520578i
$231$	48.0000	−	89.7998i	0.207792	−	0.388744i
$232$	−120.000	−	63.4980i	−0.517241	−	0.273698i
$233$		−	104.766i		−	0.449641i	−0.974400	−	0.224821i	$-0.927820\pi$
$233$		−	104.766i		−	0.449641i	0.974400	−	0.224821i	$-0.0721796\pi$
$234$	154.995	+	110.745i	0.662372	+	0.473271i
$235$		0			0
$236$	−144.250	+	127.216i	−0.611228	+	0.539052i
$237$	175.362	−	328.073i	0.739926	−	1.38427i
$238$	−112.000	+	42.3320i	−0.470588	+	0.177866i
$239$		−	359.199i		−	1.50293i	−0.659776	−	0.751463i	$-0.729349\pi$
$239$		−	359.199i		−	1.50293i	0.659776	−	0.751463i	$-0.270651\pi$
$240$	221.588	+	156.929i	0.923283	+	0.653872i
$241$	122.000			0.506224			0.253112	−	0.967437i	$-0.418546\pi$
$241$	122.000			0.506224			0.253112	+	0.967437i	$0.418546\pi$
$242$	−34.6482	−	91.6706i	−0.143175	−	0.378804i
$243$	154.149	+	187.848i	0.634359	+	0.773038i
$244$	−252.000	−	285.741i	−1.03279	−	1.17107i
$245$	186.676			0.761944
$246$	−23.1960	+	178.095i	−0.0942925	+	0.723965i
$247$	−56.0000			−0.226721
$248$	28.2843	+	14.9666i	0.114049	+	0.0603493i
$249$	−4.00000	+	7.48331i	−0.0160643	+	0.0300535i
$250$	72.0000	+	190.494i	0.288000	+	0.761976i
$251$	−161.220			−0.642312			−0.321156	−	0.947026i	$-0.604071\pi$
$251$	−161.220			−0.642312			−0.321156	+	0.947026i	$0.604071\pi$
$252$	139.196	+	36.8848i	0.552365	+	0.146368i
$253$		−	253.992i		−	1.00392i
$254$	53.7401	+	142.183i	0.211575	+	0.559776i
$255$	−224.000	−	119.733i	−0.878431	−	0.469541i
$256$	−248.000	−	63.4980i	−0.968750	−	0.248039i
$257$			448.999i			1.74708i	0.486755	+	0.873539i	$0.338181\pi$
$257$			448.999i			1.74708i	−0.486755	+	0.873539i	$0.661819\pi$
$258$	4.10051	−	31.4831i	0.0158934	−	0.122028i
$259$		−	211.660i		−	0.817220i
$260$	158.392	+	179.600i	0.609200	+	0.690768i
$261$	−84.8528	−	126.996i	−0.325107	−	0.486575i
$262$	10.0000	+	26.4575i	0.0381679	+	0.100983i
$263$			209.533i			0.796703i	0.917233	+	0.398351i	$0.130418\pi$
$263$			209.533i			0.796703i	−0.917233	+	0.398351i	$0.869582\pi$
$264$	−168.853	+	113.845i	−0.639594	+	0.431232i
$265$	288.000			1.08679
$266$	−39.5980	+	14.9666i	−0.148865	+	0.0562655i
$267$	−277.186	−	148.162i	−1.03815	−	0.554914i
$268$	126.000	+	142.871i	0.470149	+	0.533099i
$269$	−50.9117			−0.189263			−0.0946314	−	0.995512i	$-0.530167\pi$
$269$	−50.9117			−0.189263			−0.0946314	+	0.995512i	$0.530167\pi$
$270$	135.480	+	273.783i	0.501779	+	1.01401i
$271$	348.000			1.28413			0.642066	−	0.766649i	$-0.278077\pi$
$271$	348.000			1.28413			0.642066	+	0.766649i	$0.278077\pi$
$272$	237.588	+	29.9333i	0.873485	+	0.110049i
$273$	112.000	+	59.8665i	0.410256	+	0.219291i
$274$		0			0
$275$	59.3970			0.215989
$276$	349.588	−	82.5368i	1.26662	−	0.299046i
$277$			243.409i			0.878733i	0.898308	+	0.439367i	$0.144797\pi$
$277$			243.409i			0.878733i	−0.898308	+	0.439367i	$0.855203\pi$
$278$	227.688	−	86.0581i	0.819023	−	0.309562i
$279$	20.0000	+	29.9333i	0.0716846	+	0.107288i
$280$	160.000	+	84.6640i	0.571429	+	0.302372i
$281$		−	314.299i		−	1.11850i	−0.828998	−	0.559251i	$-0.811089\pi$
$281$		−	314.299i		−	1.11850i	0.828998	−	0.559251i	$-0.188911\pi$
$282$		0			0
$283$			89.9555i			0.317864i	0.987290	+	0.158932i	$0.0508051\pi$
$283$			89.9555i			0.317864i	−0.987290	+	0.158932i	$0.949195\pi$
$284$	−237.588	−	269.399i	−0.836577	−	0.948589i
$285$	−79.1960	−	42.3320i	−0.277881	−	0.148533i
$286$	−168.000	+	63.4980i	−0.587413	+	0.222021i
$287$			119.733i			0.417188i
$288$	−211.563	−	195.410i	−0.734595	−	0.678505i
$289$	65.0000			0.224913
$290$	−67.8823	−	179.600i	−0.234077	−	0.619309i
$291$	166.877	−	312.199i	0.573461	−	1.07285i
$292$	18.0000	−	15.8745i	0.0616438	−	0.0543648i
$293$	16.9706			0.0579200			0.0289600	−	0.999581i	$-0.490780\pi$
$293$	16.9706			0.0579200			0.0289600	+	0.999581i	$0.490780\pi$
$294$	−196.342	−	25.5724i	−0.667829	−	0.0869811i
$295$	−272.000			−0.922034
$296$	−197.990	+	374.166i	−0.668885	+	1.26407i
$297$	−228.000	+	22.4499i	−0.767677	+	0.0755890i
$298$	−132.000	−	349.239i	−0.442953	−	1.17194i
$299$	316.784			1.05948
$300$	19.3015	+	81.7524i	0.0643384	+	0.272508i
$301$		−	21.1660i		−	0.0703190i
$302$	−42.4264	−	112.250i	−0.140485	−	0.371688i
$303$	88.0000	−	164.633i	0.290429	−	0.543343i
$304$	84.0000	+	10.5830i	0.276316	+	0.0348125i
$305$		−	538.799i		−	1.76655i
$306$	219.196	+	156.618i	0.716327	+	0.511823i
$307$			460.361i			1.49955i	0.661695	+	0.749773i	$0.269837\pi$
$307$			460.361i			1.49955i	−0.661695	+	0.749773i	$0.730163\pi$
$308$	−101.823	+	89.7998i	−0.330595	+	0.291558i
$309$	−152.735	+	285.741i	−0.494288	+	0.924729i
$310$	16.0000	+	42.3320i	0.0516129	+	0.136555i
$311$			149.666i			0.481242i	0.970619	+	0.240621i	$0.0773511\pi$
$311$			149.666i			0.481242i	−0.970619	+	0.240621i	$0.922649\pi$
$312$	−141.990	−	210.596i	−0.455096	−	0.674989i
$313$	−562.000			−1.79553			−0.897764	−	0.440478i	$-0.854809\pi$
$313$	−562.000			−1.79553			−0.897764	+	0.440478i	$0.854809\pi$
$314$	217.789	−	82.3165i	0.693595	−	0.262154i
$315$	113.137	+	169.328i	0.359165	+	0.537549i
$316$	−372.000	+	328.073i	−1.17722	+	1.03821i
$317$	−5.65685			−0.0178450			−0.00892248	−	0.999960i	$-0.502840\pi$
$317$	−5.65685			−0.0178450			−0.00892248	+	0.999960i	$0.502840\pi$
$318$	−302.912	−	39.4526i	−0.952552	−	0.124065i
$319$	144.000			0.451411
$320$	−203.647	−	299.333i	−0.636396	−	0.935414i
$321$	−204.000	+	381.649i	−0.635514	+	1.18894i
$322$	224.000	−	84.6640i	0.695652	−	0.262932i
$323$	−79.1960			−0.245189
$324$	−104.990	−	306.518i	−0.324043	−	0.946042i
$325$			74.0810i			0.227942i
$326$	544.472	−	205.791i	1.67016	−	0.631261i
$327$	140.000	+	74.8331i	0.428135	+	0.228848i
$328$	112.000	−	211.660i	0.341463	−	0.645305i
$329$		0			0
$330$	−285.588	−	37.1963i	−0.865418	−	0.112716i
$331$		−	418.029i		−	1.26293i	−0.775406	−	0.631463i	$-0.782455\pi$
$331$		−	418.029i		−	1.26293i	0.775406	−	0.631463i	$-0.217545\pi$
$332$	8.48528	−	7.48331i	0.0255581	−	0.0225401i
$333$	−395.980	+	264.575i	−1.18913	+	0.794520i
$334$	616.000	−	232.826i	1.84431	−	0.697084i
$335$			269.399i			0.804177i
$336$	−156.686	−	110.966i	−0.466328	−	0.330255i
$337$	−50.0000			−0.148368			−0.0741840	−	0.997245i	$-0.523635\pi$
$337$	−50.0000			−0.148368			−0.0741840	+	0.997245i	$0.523635\pi$
$338$	40.3051	+	106.637i	0.119246	+	0.315495i
$339$	237.588	+	126.996i	0.700849	+	0.374620i
$340$	224.000	+	253.992i	0.658824	+	0.747036i
$341$	−33.9411			−0.0995341
$342$	77.4975	+	55.3727i	0.226601	+	0.161909i
$343$	−328.000			−0.956268
$344$	−19.7990	+	37.4166i	−0.0575552	+	0.108769i
$345$	448.000	+	239.466i	1.29855	+	0.694105i
$346$	−132.000	−	349.239i	−0.381503	−	1.00936i
$347$	359.210			1.03519			0.517594	−	0.855626i	$-0.326828\pi$
$347$	359.210			1.03519			0.517594	+	0.855626i	$0.326828\pi$
$348$	46.7939	+	198.198i	0.134465	+	0.569534i
$349$		−	116.413i		−	0.333562i	−0.985994	−	0.166781i	$-0.946663\pi$
$349$		−	116.413i		−	0.333562i	0.985994	−	0.166781i	$-0.0533373\pi$
$350$	19.7990	+	52.3832i	0.0565685	+	0.149666i
$351$	−28.0000	−	284.366i	−0.0797721	−	0.810159i
$352$	264.000	−	63.4980i	0.750000	−	0.180392i
$353$		−	179.600i		−	0.508781i	−0.967102	−	0.254390i	$-0.918125\pi$
$353$		−	179.600i		−	0.508781i	0.967102	−	0.254390i	$-0.0818748\pi$
$354$	286.083	+	37.2608i	0.808145	+	0.105257i
$355$		−	507.984i		−	1.43094i
$356$	277.186	+	314.299i	0.778612	+	0.882863i
$357$	158.392	+	84.6640i	0.443675	+	0.237154i
$358$	226.000	+	597.940i	0.631285	+	1.67022i
$359$			329.266i			0.917175i	0.888649	+	0.458588i	$0.151644\pi$
$359$			329.266i			0.917175i	−0.888649	+	0.458588i	$0.848356\pi$
$360$	−41.6081	−	405.163i	−0.115578	−	1.12545i
$361$	333.000			0.922438
$362$	−217.789	+	82.3165i	−0.601627	+	0.227394i
$363$	−69.2965	+	129.642i	−0.190899	+	0.357140i
$364$	−112.000	−	126.996i	−0.307692	−	0.348890i
$365$	33.9411			0.0929894
$366$	−73.8091	+	566.696i	−0.201664	+	1.54835i
$367$	−228.000			−0.621253			−0.310627	−	0.950532i	$-0.600539\pi$
$367$	−228.000			−0.621253			−0.310627	+	0.950532i	$0.600539\pi$
$368$	−475.176	−	59.8665i	−1.29124	−	0.162681i
$369$	224.000	−	149.666i	0.607046	−	0.405600i
$370$	−560.000	+	211.660i	−1.51351	+	0.572054i
$371$	−203.647			−0.548913
$372$	−11.0294	−	46.7156i	−0.0296490	−	0.125580i
$373$		−	137.579i		−	0.368845i	−0.982847	−	0.184422i	$-0.940959\pi$
$373$		−	137.579i		−	0.368845i	0.982847	−	0.184422i	$-0.0590414\pi$
$374$	−237.588	+	89.7998i	−0.635262	+	0.240106i
$375$	144.000	−	269.399i	0.384000	−	0.718398i
$376$		0			0
$377$			179.600i			0.476391i
$378$	−95.7990	−	193.594i	−0.253436	−	0.512153i
$379$			164.037i			0.432814i	0.976303	+	0.216407i	$0.0694338\pi$
$379$			164.037i			0.432814i	−0.976303	+	0.216407i	$0.930566\pi$
$380$	79.1960	+	89.7998i	0.208410	+	0.236315i
$381$	107.480	−	201.077i	0.282100	−	0.527761i
$382$	−112.000	+	42.3320i	−0.293194	+	0.110817i
$383$		−	179.600i		−	0.468928i	−0.972125	−	0.234464i	$-0.924666\pi$
$383$		−	179.600i		−	0.468928i	0.972125	−	0.234464i	$-0.0753336\pi$
$384$	173.186	+	342.728i	0.451005	+	0.892522i
$385$	−192.000			−0.498701
$386$	−72.1249	−	190.825i	−0.186852	−	0.494364i
$387$	−39.5980	+	26.4575i	−0.102320	+	0.0683657i
$388$	−354.000	+	312.199i	−0.912371	+	0.804636i
$389$	−96.1665			−0.247215			−0.123607	−	0.992331i	$-0.539446\pi$
$389$	−96.1665			−0.247215			−0.123607	+	0.992331i	$0.539446\pi$
$390$	46.3919	−	356.191i	0.118954	−	0.913309i
$391$	448.000			1.14578
$392$	233.345	+	123.475i	0.595268	+	0.314986i
$393$	20.0000	−	37.4166i	0.0508906	−	0.0952076i
$394$	172.000	+	455.069i	0.436548	+	1.15500i
$395$	−701.450			−1.77582
$396$	295.279	+	78.2444i	0.745655	+	0.197587i
$397$			52.9150i			0.133287i	0.997777	+	0.0666436i	$0.0212291\pi$
$397$			52.9150i			0.133287i	−0.997777	+	0.0666436i	$0.978771\pi$
$398$	−132.936	−	351.716i	−0.334010	−	0.883708i
$399$	56.0000	+	29.9333i	0.140351	+	0.0750207i
$400$	14.0000	−	111.122i	0.0350000	−	0.277804i
$401$		−	134.700i		−	0.335909i	−0.985795	−	0.167955i	$-0.946284\pi$
$401$		−	134.700i		−	0.335909i	0.985795	−	0.167955i	$-0.0537162\pi$
$402$	36.9045	−	283.348i	0.0918024	−	0.704846i
$403$		−	42.3320i		−	0.105042i
$404$	−186.676	+	164.633i	−0.462070	+	0.407507i
$405$	175.362	−	423.320i	0.432994	−	1.04524i
$406$	48.0000	+	126.996i	0.118227	+	0.312798i
$407$		−	448.999i		−	1.10319i
$408$	−200.804	−	297.828i	−0.492167	−	0.729971i
$409$	−158.000			−0.386308			−0.193154	−	0.981168i	$-0.561872\pi$
$409$	−158.000			−0.386308			−0.193154	+	0.981168i	$0.561872\pi$
$410$	316.784	−	119.733i	0.772644	−	0.292032i
$411$		0			0
$412$	324.000	−	285.741i	0.786408	−	0.693546i
$413$	192.333			0.465697
$414$	−438.392	−	313.236i	−1.05892	−	0.756608i
$415$	16.0000			0.0385542
$416$	79.1960	+	329.266i	0.190375	+	0.791504i
$417$	−322.000	−	172.116i	−0.772182	−	0.412749i
$418$	−84.0000	+	31.7490i	−0.200957	+	0.0759546i
$419$	−330.926			−0.789799			−0.394900	−	0.918724i	$-0.629221\pi$
$419$	−330.926			−0.789799			−0.394900	+	0.918724i	$0.629221\pi$
$420$	−62.3919	−	264.264i	−0.148552	−	0.629199i
$421$		−	518.567i		−	1.23175i	−0.787843	−	0.615876i	$-0.788802\pi$
$421$		−	518.567i		−	1.23175i	0.787843	−	0.615876i	$-0.211198\pi$
$422$	−465.276	+	175.858i	−1.10255	+	0.416725i
$423$		0			0
$424$	360.000	+	190.494i	0.849057	+	0.449279i
$425$			104.766i			0.246509i
$426$	−69.5879	+	534.286i	−0.163352	+	1.25419i
$427$			380.988i			0.892244i
$428$	432.749	−	381.649i	1.01110	−	0.891703i
$429$	237.588	+	126.996i	0.553818	+	0.296028i
$430$	−56.0000	+	21.1660i	−0.130233	+	0.0492233i
$431$			359.199i			0.833409i	0.909042	+	0.416704i	$0.136815\pi$
$431$			359.199i			0.833409i	−0.909042	+	0.416704i	$0.863185\pi$
$432$	−11.7401	+	431.840i	−0.0271762	+	0.999631i
$433$	86.0000			0.198614			0.0993072	−	0.995057i	$-0.468337\pi$
$433$	86.0000			0.198614			0.0993072	+	0.995057i	$0.468337\pi$
$434$	−11.3137	−	29.9333i	−0.0260685	−	0.0689706i
$435$	−135.765	+	253.992i	−0.312102	+	0.583890i
$436$	−140.000	−	158.745i	−0.321101	−	0.364094i
$437$	158.392			0.362453
$438$	−35.6985	−	4.64954i	−0.0815034	−	0.0106154i
$439$	−156.000			−0.355353			−0.177677	−	0.984089i	$-0.556858\pi$
$439$	−156.000			−0.355353			−0.177677	+	0.984089i	$0.556858\pi$
$440$	339.411	+	179.600i	0.771389	+	0.408181i
$441$	165.000	+	246.949i	0.374150	+	0.559976i
$442$	−112.000	−	296.324i	−0.253394	−	0.670417i
$443$	212.132			0.478853			0.239427	−	0.970914i	$-0.423041\pi$
$443$	212.132			0.478853			0.239427	+	0.970914i	$0.423041\pi$
$444$	617.990	−	145.906i	1.39187	−	0.328617i
$445$			592.648i			1.33179i
$446$	132.936	+	351.716i	0.298063	+	0.788600i
$447$	−264.000	+	493.899i	−0.590604	+	1.10492i
$448$	144.000	+	211.660i	0.321429	+	0.472456i
$449$			493.899i			1.10000i	0.835166	+	0.549999i	$0.185372\pi$
$449$			493.899i			1.10000i	−0.835166	+	0.549999i	$0.814628\pi$
$450$	73.2513	−	102.520i	0.162781	−	0.227821i
$451$			253.992i			0.563175i
$452$	−237.588	−	269.399i	−0.525637	−	0.596016i
$453$	−84.8528	+	158.745i	−0.187313	+	0.350431i
$454$	−274.000	−	724.936i	−0.603524	−	1.59678i
$455$		−	239.466i		−	0.526299i
$456$	−70.9949	−	105.298i	−0.155691	−	0.230917i
$457$	194.000			0.424508			0.212254	−	0.977215i	$-0.431920\pi$
$457$	194.000			0.424508			0.212254	+	0.977215i	$0.431920\pi$
$458$	−455.377	+	172.116i	−0.994272	+	0.375800i
$459$	−39.5980	−	402.154i	−0.0862701	−	0.876153i
$460$	−448.000	−	507.984i	−0.973913	−	1.10431i
$461$	560.029			1.21481			0.607406	−	0.794391i	$-0.292210\pi$
$461$	560.029			1.21481			0.607406	+	0.794391i	$0.292210\pi$
$462$	201.941	+	26.3017i	0.437102	+	0.0569302i
$463$	−404.000			−0.872570			−0.436285	−	0.899808i	$-0.643706\pi$
$463$	−404.000			−0.872570			−0.436285	+	0.899808i	$0.643706\pi$
$464$	33.9411	−	269.399i	0.0731490	−	0.580602i
$465$	32.0000	−	59.8665i	0.0688172	−	0.128745i
$466$	196.000	−	74.0810i	0.420601	−	0.158972i
$467$	664.680			1.42330			0.711649	−	0.702535i	$-0.247949\pi$
$467$	664.680			1.42330			0.711649	+	0.702535i	$0.247949\pi$
$468$	−97.5879	+	368.278i	−0.208521	+	0.786919i
$469$		−	190.494i		−	0.406171i
$470$		0			0
$471$	−308.000	−	164.633i	−0.653928	−	0.349539i
$472$	−340.000	−	179.911i	−0.720339	−	0.381168i
$473$		−	44.8999i		−	0.0949258i
$474$	737.769	+	96.0904i	1.55647	+	0.202722i
$475$			37.0405i			0.0779800i
$476$	−158.392	−	179.600i	−0.332756	−	0.377310i
$477$	254.558	+	380.988i	0.533665	+	0.798717i
$478$	672.000	−	253.992i	1.40586	−	0.531364i
$479$		−	239.466i		−	0.499929i	−0.968255	−	0.249965i	$-0.919581\pi$
$479$		−	239.466i		−	0.499929i	0.968255	−	0.249965i	$-0.0804190\pi$
$480$	−136.902	+	525.519i	−0.285212	+	1.09483i
$481$	560.000			1.16424
$482$	86.2670	+	228.241i	0.178977	+	0.473529i
$483$	−316.784	−	169.328i	−0.655867	−	0.350576i
$484$	147.000	−	129.642i	0.303719	−	0.267855i
$485$	−667.509			−1.37631
$486$	−242.432	+	421.216i	−0.498831	+	0.866699i
$487$	500.000			1.02669			0.513347	−	0.858181i	$-0.328405\pi$
$487$	500.000			1.02669			0.513347	+	0.858181i	$0.328405\pi$
$488$	356.382	−	673.498i	0.730291	−	1.38012i
$489$	−770.000	−	411.582i	−1.57464	−	0.841682i
$490$	132.000	+	349.239i	0.269388	+	0.712733i
$491$	115.966			0.236182			0.118091	−	0.993003i	$-0.462322\pi$
$491$	115.966			0.236182			0.118091	+	0.993003i	$0.462322\pi$
$492$	−349.588	+	82.5368i	−0.710544	+	0.167758i
$493$			253.992i			0.515197i
$494$	−39.5980	−	104.766i	−0.0801579	−	0.212078i
$495$	240.000	+	359.199i	0.484848	+	0.725655i
$496$	−8.00000	+	63.4980i	−0.0161290	+	0.128020i
$497$			359.199i			0.722735i
$498$	−16.8284	−	2.19181i	−0.0337920	−	0.00440123i
$499$			333.365i			0.668065i	0.942561	+	0.334033i	$0.108410\pi$
$499$			333.365i			0.668065i	−0.942561	+	0.334033i	$0.891590\pi$
$500$	−305.470	+	269.399i	−0.610940	+	0.538799i
$501$	−871.156	−	465.652i	−1.73883	−	0.929446i
$502$	−114.000	−	301.616i	−0.227092	−	0.600828i
$503$		−	448.999i		−	0.892642i	−0.894873	−	0.446321i	$-0.852734\pi$
$503$		−	448.999i		−	0.892642i	0.894873	−	0.446321i	$-0.147266\pi$
$504$	29.4214	+	286.493i	0.0583757	+	0.568439i
$505$	−352.000			−0.697030
$506$	475.176	−	179.600i	0.939083	−	0.354940i
$507$	80.6102	−	150.808i	0.158994	−	0.297451i
$508$	−228.000	+	201.077i	−0.448819	+	0.395821i
$509$	−322.441			−0.633479			−0.316739	−	0.948513i	$-0.602588\pi$
$509$	−322.441			−0.633479			−0.316739	+	0.948513i	$0.602588\pi$
$510$	65.6081	−	503.730i	0.128643	−	0.987705i
$511$	−24.0000			−0.0469667
$512$	−56.5685	−	508.865i	−0.110485	−	0.993878i
$513$	−14.0000	−	142.183i	−0.0272904	−	0.277160i
$514$	−840.000	+	317.490i	−1.63424	+	0.617685i
$515$	610.940			1.18629
$516$	61.7990	−	14.5906i	0.119765	−	0.0282763i
$517$		0			0
$518$	395.980	−	149.666i	0.764440	−	0.288931i
$519$	−264.000	+	493.899i	−0.508671	+	0.951635i
$520$	−224.000	+	423.320i	−0.430769	+	0.814077i
$521$		−	179.600i		−	0.344721i	−0.985034	−	0.172360i	$-0.944861\pi$
$521$		−	179.600i		−	0.344721i	0.985034	−	0.172360i	$-0.0551394\pi$
$522$	177.588	−	248.545i	0.340207	−	0.476140i
$523$		−	555.608i		−	1.06235i	−0.847263	−	0.531174i	$-0.821751\pi$
$523$		−	555.608i		−	1.06235i	0.847263	−	0.531174i	$-0.178249\pi$
$524$	−42.4264	+	37.4166i	−0.0809664	+	0.0714057i
$525$	39.5980	−	74.0810i	0.0754247	−	0.141107i
$526$	−392.000	+	148.162i	−0.745247	+	0.281677i
$527$		−	59.8665i		−	0.113599i
$528$	−332.382	−	235.394i	−0.629511	−	0.445822i
$529$	−367.000			−0.693762
$530$	203.647	+	538.799i	0.384239	+	1.01660i
$531$	−240.416	−	359.822i	−0.452761	−	0.677631i
$532$	−56.0000	−	63.4980i	−0.105263	−	0.119357i
$533$	−316.784			−0.594341
$534$	81.1859	−	623.334i	0.152033	−	1.16729i
$535$	816.000			1.52523
$536$	−178.191	+	336.749i	−0.332446	+	0.628263i
$537$	452.000	−	845.615i	0.841713	−	1.57470i
$538$	−36.0000	−	95.2470i	−0.0669145	−	0.177039i
$539$	−280.014			−0.519507
$540$	−416.402	+	447.054i	−0.771115	+	0.827878i
$541$			772.559i			1.42802i	0.700135	+	0.714011i	$0.253123\pi$
$541$			772.559i			1.42802i	−0.700135	+	0.714011i	$0.746877\pi$
$542$	246.073	+	651.048i	0.454010	+	1.20120i
$543$	308.000	+	164.633i	0.567219	+	0.303191i
$544$	112.000	+	465.652i	0.205882	+	0.855978i
$545$		−	299.333i		−	0.549234i
$546$	−32.8040	+	251.865i	−0.0600807	+	0.461291i
$547$		−	502.693i		−	0.919000i	−0.888178	−	0.459500i	$-0.848029\pi$
$547$		−	502.693i		−	0.919000i	0.888178	−	0.459500i	$-0.151971\pi$
$548$		0			0
$549$	712.764	−	476.235i	1.29829	−	0.867459i
$550$	42.0000	+	111.122i	0.0763636	+	0.202039i
$551$			89.7998i			0.162976i
$552$	401.608	+	595.657i	0.727551	+	1.07909i
$553$	496.000			0.896926
$554$	−455.377	+	172.116i	−0.821980	+	0.310679i
$555$	791.960	+	423.320i	1.42695	+	0.762739i
$556$	322.000	+	365.114i	0.579137	+	0.656679i
$557$	−526.087			−0.944502			−0.472251	−	0.881464i	$-0.656558\pi$
$557$	−526.087			−0.944502			−0.472251	+	0.881464i	$0.656558\pi$
$558$	−41.8579	+	58.5826i	−0.0750141	+	0.104987i
$559$	56.0000			0.100179
$560$	−45.2548	+	359.199i	−0.0808122	+	0.641427i
$561$	336.000	+	179.600i	0.598930	+	0.320142i
$562$	588.000	−	222.243i	1.04626	−	0.395450i
$563$	8.48528			0.0150715			0.00753577	−	0.999972i	$-0.497601\pi$
$563$	8.48528			0.0150715			0.00753577	+	0.999972i	$0.497601\pi$
$564$		0			0
$565$		−	507.984i		−	0.899087i
$566$	−168.291	+	63.6082i	−0.297335	+	0.112382i
$567$	−124.000	+	299.333i	−0.218695	+	0.527923i
$568$	336.000	−	634.980i	0.591549	−	1.11792i
$569$			359.199i			0.631281i	0.948879	+	0.315641i	$0.102219\pi$
$569$			359.199i			0.631281i	−0.948879	+	0.315641i	$0.897781\pi$
$570$	23.1960	−	178.095i	0.0406947	−	0.312448i
$571$			5.29150i			0.00926708i	0.999989	+	0.00463354i	$0.00147491\pi$
$571$			5.29150i			0.00926708i	−0.999989	+	0.00463354i	$0.998525\pi$
$572$	−237.588	−	269.399i	−0.415363	−	0.470978i
$573$	158.392	+	84.6640i	0.276426	+	0.147756i
$574$	−224.000	+	84.6640i	−0.390244	+	0.147498i
$575$		−	209.533i		−	0.364405i
$576$	215.980	−	533.974i	0.374965	−	0.927039i
$577$	−18.0000			−0.0311958			−0.0155979	−	0.999878i	$-0.504965\pi$
$577$	−18.0000			−0.0311958			−0.0155979	+	0.999878i	$0.504965\pi$
$578$	45.9619	+	121.604i	0.0795189	+	0.210387i
$579$	−144.250	+	269.867i	−0.249136	+	0.466091i
$580$	288.000	−	253.992i	0.496552	−	0.437917i
$581$	−11.3137			−0.0194728
$582$	702.070	+	91.4409i	1.20631	+	0.157115i
$583$	−432.000			−0.740995
$584$	42.4264	+	22.4499i	0.0726480	+	0.0384417i
$585$	−448.000	+	299.333i	−0.765812	+	0.511680i
$586$	12.0000	+	31.7490i	0.0204778	+	0.0541792i
$587$	−121.622			−0.207193			−0.103597	−	0.994619i	$-0.533035\pi$
$587$	−121.622			−0.207193			−0.103597	+	0.994619i	$0.533035\pi$
$588$	−90.9929	−	385.404i	−0.154750	−	0.655449i
$589$		−	21.1660i		−	0.0359355i
$590$	−192.333	−	508.865i	−0.325988	−	0.862484i
$591$	344.000	−	643.565i	0.582064	−	1.08894i
$592$	−840.000	−	105.830i	−1.41892	−	0.178767i
$593$			718.398i			1.21146i	0.795669	+	0.605732i	$0.207120\pi$
$593$			718.398i			1.21146i	−0.795669	+	0.605732i	$0.792880\pi$
$594$	−203.220	−	410.674i	−0.342122	−	0.691371i
$595$		−	338.656i		−	0.569170i
$596$	560.029	−	493.899i	0.939645	−	0.828689i
$597$	−265.872	+	497.401i	−0.445347	+	0.833168i
$598$	224.000	+	592.648i	0.374582	+	0.991051i
$599$			688.465i			1.14936i	0.818379	+	0.574679i	$0.194873\pi$
$599$			688.465i			1.14936i	−0.818379	+	0.574679i	$0.805127\pi$
$600$	−139.296	+	93.9175i	−0.232161	+	0.156529i
$601$	−358.000			−0.595674			−0.297837	−	0.954617i	$-0.596265\pi$
$601$	−358.000			−0.595674			−0.297837	+	0.954617i	$0.596265\pi$
$602$	39.5980	−	14.9666i	0.0657774	−	0.0248615i
$603$	−356.382	+	238.118i	−0.591015	+	0.394888i
$604$	180.000	−	158.745i	0.298013	−	0.262823i
$605$	277.186			0.458158
$606$	370.225	+	48.2199i	0.610933	+	0.0795707i
$607$	−884.000			−1.45634			−0.728171	−	0.685395i	$-0.759629\pi$
$607$	−884.000			−1.45634			−0.728171	+	0.685395i	$0.759629\pi$
$608$	39.5980	+	164.633i	0.0651283	+	0.270778i
$609$	96.0000	−	179.600i	0.157635	−	0.294909i
$610$	1008.00	−	380.988i	1.65246	−	0.624571i
$611$		0			0
$612$	−138.010	+	520.824i	−0.225507	+	0.851019i
$613$		−	391.571i		−	0.638778i	−0.947624	−	0.319389i	$-0.896522\pi$
$613$		−	391.571i		−	0.638778i	0.947624	−	0.319389i	$-0.103478\pi$
$614$	−861.256	+	325.524i	−1.40270	+	0.530170i
$615$	−448.000	−	239.466i	−0.728455	−	0.389376i
$616$	−240.000	−	126.996i	−0.389610	−	0.206162i
$617$			104.766i			0.169800i	0.996389	+	0.0848998i	$0.0270570\pi$
$617$			104.766i			0.169800i	−0.996389	+	0.0848998i	$0.972943\pi$
$618$	−642.573	−	83.6916i	−1.03976	−	0.135423i
$619$			682.604i			1.10275i	0.834257	+	0.551376i	$0.185897\pi$
$619$			682.604i			1.10275i	−0.834257	+	0.551376i	$0.814103\pi$
$620$	−67.8823	+	59.8665i	−0.109488	+	0.0965589i
$621$	79.1960	+	804.308i	0.127530	+	1.29518i
$622$	−280.000	+	105.830i	−0.450161	+	0.170145i
$623$		−	419.066i		−	0.672658i
$624$	293.588	−	414.553i	0.470493	−	0.664348i
$625$	−751.000			−1.20160
$626$	−397.394	−	1051.41i	−0.634815	−	1.67956i
$627$	118.794	+	63.4980i	0.189464	+	0.101273i
$628$	308.000	+	349.239i	0.490446	+	0.556113i
$629$	791.960			1.25908
$630$	−236.784	+	331.393i	−0.375847	+	0.526021i
$631$	−428.000			−0.678288			−0.339144	−	0.940734i	$-0.610137\pi$
$631$	−428.000			−0.678288			−0.339144	+	0.940734i	$0.610137\pi$
$632$	−876.812	−	463.966i	−1.38736	−	0.734123i
$633$	658.000	+	351.716i	1.03949	+	0.555633i
$634$	−4.00000	−	10.5830i	−0.00630915	−	0.0166924i
$635$	−429.921			−0.677041
$636$	−140.382	−	594.593i	−0.220726	−	0.934895i
$637$		−	349.239i		−	0.548256i
$638$	101.823	+	269.399i	0.159598	+	0.422256i
$639$	672.000	−	448.999i	1.05164	−	0.702659i
$640$	416.000	−	592.648i	0.650000	−	0.926013i
$641$		−	793.231i		−	1.23749i	−0.785592	−	0.618745i	$-0.787641\pi$
$641$		−	793.231i		−	1.23749i	0.785592	−	0.618745i	$-0.212359\pi$
$642$	−858.250	−	111.782i	−1.33684	−	0.174116i
$643$			851.932i			1.32493i	0.749092	+	0.662467i	$0.230490\pi$
$643$			851.932i			1.32493i	−0.749092	+	0.662467i	$0.769510\pi$
$644$	316.784	+	359.199i	0.491900	+	0.557763i
$645$	79.1960	+	42.3320i	0.122784	+	0.0656310i
$646$	−56.0000	−	148.162i	−0.0866873	−	0.229353i
$647$		−	448.999i		−	0.693970i	−0.937871	−	0.346985i	$-0.887205\pi$
$647$		−	448.999i		−	0.693970i	0.937871	−	0.346985i	$-0.112795\pi$
$648$	499.203	−	413.159i	0.770375	−	0.637591i
$649$	408.000			0.628659
$650$	−138.593	+	52.3832i	−0.213220	+	0.0805895i
$651$	−22.6274	+	42.3320i	−0.0347579	+	0.0650261i
$652$	770.000	+	873.098i	1.18098	+	1.33911i
$653$	1103.09			1.68926			0.844630	−	0.535351i	$-0.179821\pi$
$653$	1103.09			1.68926			0.844630	+	0.535351i	$0.179821\pi$
$654$	−41.0051	+	314.831i	−0.0626989	+	0.481393i
$655$	−80.0000			−0.122137
$656$	475.176	+	59.8665i	0.724353	+	0.0912599i
$657$	30.0000	+	44.8999i	0.0456621	+	0.0683408i
$658$		0			0
$659$	−924.896			−1.40348			−0.701742	−	0.712431i	$-0.747594\pi$
$659$	−924.896			−1.40348			−0.701742	+	0.712431i	$0.747594\pi$
$660$	−132.353	−	560.588i	−0.200535	−	0.849375i
$661$		−	433.903i		−	0.656435i	−0.944602	−	0.328217i	$-0.893552\pi$
$661$		−	433.903i		−	0.656435i	0.944602	−	0.328217i	$-0.106448\pi$
$662$	782.060	−	295.591i	1.18136	−	0.446512i
$663$	−224.000	+	419.066i	−0.337858	+	0.632075i
$664$	20.0000	+	10.5830i	0.0301205	+	0.0159383i
$665$		−	119.733i		−	0.180050i
$666$	−774.975	−	553.727i	−1.16363	−	0.831423i
$667$		−	507.984i		−	0.761596i
$668$	871.156	+	987.798i	1.30413	+	1.47874i
$669$	265.872	−	497.401i	0.397417	−	0.743500i
$670$	−504.000	+	190.494i	−0.752239	+	0.284320i
$671$			808.198i			1.20447i
$672$	96.8040	−	371.598i	0.144054	−	0.552973i
$673$	566.000			0.841010			0.420505	−	0.907290i	$-0.361853\pi$
$673$	566.000			0.841010			0.420505	+	0.907290i	$0.361853\pi$
$674$	−35.3553	−	93.5414i	−0.0524560	−	0.138786i
$675$	−188.090	+	18.5203i	−0.278652	+	0.0274374i
$676$	−171.000	+	150.808i	−0.252959	+	0.223088i
$677$	−797.616			−1.17816			−0.589082	−	0.808074i	$-0.700510\pi$
$677$	−797.616			−1.17816			−0.589082	+	0.808074i	$0.700510\pi$
$678$	−69.5879	+	534.286i	−0.102637	+	0.788032i
$679$	472.000			0.695140
$680$	−316.784	+	598.665i	−0.465859	+	0.880390i
$681$	−548.000	+	1025.21i	−0.804699	+	1.50545i
$682$	−24.0000	−	63.4980i	−0.0351906	−	0.0931056i
$683$	404.465			0.592189			0.296094	−	0.955159i	$-0.404316\pi$
$683$	404.465			0.592189			0.296094	+	0.955159i	$0.404316\pi$
$684$	−48.7939	+	184.139i	−0.0713362	+	0.269209i
$685$		0			0
$686$	−231.931	−	613.632i	−0.338092	−	0.894507i
$687$	644.000	+	344.232i	0.937409	+	0.501066i
$688$	−84.0000	−	10.5830i	−0.122093	−	0.0153823i
$689$		−	538.799i		−	0.782001i
$690$	−131.216	+	1007.46i	−0.190168	+	1.46009i
$691$		−	121.705i		−	0.176128i	−0.996115	−	0.0880641i	$-0.971932\pi$
$691$		−	121.705i		−	0.176128i	0.996115	−	0.0880641i	$-0.0280680\pi$
$692$	560.029	−	493.899i	0.809290	−	0.713727i
$693$	−169.706	−	253.992i	−0.244885	−	0.366511i
$694$	254.000	+	672.021i	0.365994	+	0.968330i
$695$			688.465i			0.990597i
$696$	−337.706	+	227.690i	−0.485209	+	0.327141i
$697$	−448.000			−0.642755
$698$	217.789	−	82.3165i	0.312018	−	0.117932i
$699$	−277.186	−	148.162i	−0.396546	−	0.211963i
$700$	−84.0000	+	74.0810i	−0.120000	+	0.105830i
$701$	333.754			0.476112			0.238056	−	0.971251i	$-0.423490\pi$
$701$	333.754			0.476112			0.238056	+	0.971251i	$0.423490\pi$
$702$	512.201	−	253.460i	0.729631	−	0.361055i
$703$	280.000			0.398293
$704$	305.470	+	448.999i	0.433906	+	0.637783i
$705$		0			0
$706$	336.000	−	126.996i	0.475921	−	0.179881i
$707$	248.902			0.352053
$708$	132.583	+	561.560i	0.187264	+	0.793164i
$709$			370.405i			0.522433i	0.965280	+	0.261217i	$0.0841237\pi$
$709$			370.405i			0.522433i	−0.965280	+	0.261217i	$0.915876\pi$
$710$	950.352	−	359.199i	1.33852	−	0.505914i
$711$	−620.000	−	927.931i	−0.872011	−	1.30511i
$712$	−392.000	+	740.810i	−0.550562	+	1.04046i
$713$			119.733i			0.167929i
$714$	−46.3919	+	356.191i	−0.0649747	+	0.498866i
$715$		−	507.984i		−	0.710467i
$716$	−958.837	+	845.615i	−1.33916	+	1.18103i
$717$	−950.352	−	507.984i	−1.32546	−	0.708486i
$718$	−616.000	+	232.826i	−0.857939	+	0.324270i
$719$		−	1017.73i		−	1.41548i	−0.706473	−	0.707740i	$-0.749715\pi$
$719$		−	1017.73i		−	1.41548i	0.706473	−	0.707740i	$-0.250285\pi$
$720$	728.569	−	364.335i	1.01190	−	0.506021i
$721$	−432.000			−0.599168
$722$	235.467	+	622.986i	0.326131	+	0.862861i
$723$	172.534	−	322.782i	0.238636	−	0.446448i
$724$	−308.000	−	349.239i	−0.425414	−	0.482375i
$725$	118.794			0.163854
$726$	−291.538	−	37.9712i	−0.401567	−	0.0523019i
$727$	1140.00			1.56809			0.784044	−	0.620705i	$-0.213154\pi$
$727$	1140.00			1.56809			0.784044	+	0.620705i	$0.213154\pi$
$728$	158.392	−	299.333i	0.217571	−	0.411171i
$729$	715.000	−	142.183i	0.980796	−	0.195038i
$730$	24.0000	+	63.4980i	0.0328767	+	0.0869836i
$731$	79.1960			0.108339
$732$	−1112.38	+	262.630i	−1.51965	+	0.358785i
$733$		−	370.405i		−	0.505328i	−0.967554	−	0.252664i	$-0.918693\pi$
$733$		−	370.405i		−	0.505328i	0.967554	−	0.252664i	$-0.0813067\pi$
$734$	−161.220	−	426.549i	−0.219646	−	0.581129i
$735$	264.000	−	493.899i	0.359184	−	0.671971i
$736$	−224.000	−	931.304i	−0.304348	−	1.26536i
$737$		−	404.099i		−	0.548303i
$738$	438.392	+	313.236i	0.594027	+	0.424438i
$739$		−	5.29150i		−	0.00716036i	−0.999994	−	0.00358018i	$-0.998860\pi$
$739$		−	5.29150i		−	0.00716036i	0.999994	−	0.00358018i	$-0.00113961\pi$
$740$	−791.960	−	897.998i	−1.07022	−	1.21351i
$741$	−79.1960	+	148.162i	−0.106877	+	0.199949i
$742$	−144.000	−	380.988i	−0.194070	−	0.513461i
$743$			748.331i			1.00718i	0.863944	+	0.503588i	$0.167987\pi$
$743$			748.331i			1.00718i	−0.863944	+	0.503588i	$0.832013\pi$
$744$	79.5980	−	53.6671i	0.106987	−	0.0721332i
$745$	1056.00			1.41745
$746$	257.387	−	97.2831i	0.345023	−	0.130406i
$747$	14.1421	+	21.1660i	0.0189319	+	0.0283347i
$748$	−336.000	−	380.988i	−0.449198	−	0.509342i
$749$	−576.999			−0.770359
$750$	605.823	+	78.9052i	0.807765	+	0.105207i
$751$	−1108.00			−1.47537			−0.737683	−	0.675147i	$-0.764080\pi$
$751$	−1108.00			−1.47537			−0.737683	+	0.675147i	$0.764080\pi$
$752$		0			0
$753$	−228.000	+	426.549i	−0.302789	+	0.566466i
$754$	−336.000	+	126.996i	−0.445623	+	0.168430i
$755$	339.411			0.449551
$756$	294.441	−	316.115i	0.389472	−	0.418142i
$757$			1047.72i			1.38404i	0.721879	+	0.692019i	$0.243279\pi$
$757$			1047.72i			1.38404i	−0.721879	+	0.692019i	$0.756721\pi$
$758$	−306.884	+	115.991i	−0.404861	+	0.153023i
$759$	−672.000	−	359.199i	−0.885375	−	0.473253i
$760$	−112.000	+	211.660i	−0.147368	+	0.278500i
$761$		−	1287.13i		−	1.69137i	−0.533685	−	0.845683i	$-0.679193\pi$
$761$		−	1287.13i		−	1.69137i	0.533685	−	0.845683i	$-0.320807\pi$
$762$	452.181	+	58.8941i	0.593413	+	0.0772889i
$763$			211.660i			0.277405i
$764$	−158.392	−	179.600i	−0.207319	−	0.235078i
$765$	−633.568	+	423.320i	−0.828193	+	0.553360i
$766$	336.000	−	126.996i	0.438642	−	0.165791i
$767$			508.865i			0.663449i
$768$	−518.725	+	566.347i	−0.675423	+	0.737430i
$769$	538.000			0.699610			0.349805	−	0.936823i	$-0.386248\pi$
$769$	538.000			0.699610			0.349805	+	0.936823i	$0.386248\pi$
$770$	−135.765	−	359.199i	−0.176318	−	0.466492i
$771$	1187.94	+	634.980i	1.54078	+	0.823580i
$772$	306.000	−	269.867i	0.396373	−	0.349568i
$773$	62.2254			0.0804986			0.0402493	−	0.999190i	$-0.487185\pi$
$773$	62.2254			0.0804986			0.0402493	+	0.999190i	$0.487185\pi$
$774$	−77.4975	−	55.3727i	−0.100126	−	0.0715410i
$775$	−28.0000			−0.0361290
$776$	−834.386	−	441.516i	−1.07524	−	0.568963i
$777$	−560.000	−	299.333i	−0.720721	−	0.385241i
$778$	−68.0000	−	179.911i	−0.0874036	−	0.231248i
$779$	−158.392			−0.203327
$780$	699.176	−	165.074i	0.896379	−	0.211633i
$781$			761.976i			0.975642i
$782$	316.784	+	838.131i	0.405094	+	1.07178i
$783$	−456.000	+	44.8999i	−0.582375	+	0.0573434i
$784$	−66.0000	+	523.859i	−0.0841837	+	0.668187i
$785$			658.532i			0.838894i
$786$	84.1421	+	10.9591i	0.107051	+	0.0139428i
$787$		−	1476.33i		−	1.87589i	−0.346778	−	0.937947i	$-0.612724\pi$
$787$		−	1476.33i		−	1.87589i	0.346778	−	0.937947i	$-0.387276\pi$
$788$	−729.734	+	643.565i	−0.926059	+	0.816707i
$789$	554.372	+	296.324i	0.702626	+	0.375569i
$790$	−496.000	−	1312.29i	−0.627848	−	1.66113i
$791$			359.199i			0.454108i
$792$	62.4121	+	607.744i	0.0788032	+	0.767353i
$793$	−1008.00			−1.27112
$794$	−98.9949	+	37.4166i	−0.124679	+	0.0471241i
$795$	407.294	−	761.976i	0.512319	−	0.958461i
$796$	564.000	−	497.401i	0.708543	−	0.624876i
$797$	−1250.16			−1.56859			−0.784294	−	0.620389i	$-0.786975\pi$
$797$	−1250.16			−1.56859			−0.784294	+	0.620389i	$0.786975\pi$
$798$	−16.4020	+	125.932i	−0.0205539	+	0.157810i
$799$		0			0
$800$	217.789	−	52.3832i	0.272236	−	0.0654790i
$801$	−784.000	+	523.832i	−0.978777	+	0.653973i
$802$	252.000	−	95.2470i	0.314214	−	0.118762i
$803$	−50.9117			−0.0634019
$804$	556.191	−	131.315i	0.691780	−	0.163327i
$805$			677.312i			0.841382i
$806$	79.1960	−	29.9333i	0.0982580	−	0.0371380i
$807$	−72.0000	+	134.700i	−0.0892193	+	0.166914i
$808$	−440.000	−	232.826i	−0.544554	−	0.288151i
$809$			448.999i			0.555005i	0.960725	+	0.277502i	$0.0895066\pi$
$809$			448.999i			0.555005i	−0.960725	+	0.277502i	$0.910493\pi$
$810$	915.960	+	28.7406i	1.13081	+	0.0354822i
$811$			1391.67i			1.71599i	0.513661	+	0.857993i	$0.328289\pi$
$811$			1391.67i			1.71599i	−0.513661	+	0.857993i	$0.671711\pi$
$812$	−203.647	+	179.600i	−0.250796	+	0.221182i
$813$	492.146	−	920.721i	0.605346	−	1.13250i
$814$	840.000	−	317.490i	1.03194	−	0.390037i
$815$			1646.33i			2.02004i
$816$	415.196	−	586.266i	0.508819	−	0.718464i
$817$	28.0000			0.0342717
$818$	−111.723	−	295.591i	−0.136581	−	0.361358i
$819$	316.784	−	211.660i	0.386793	−	0.258437i
$820$	448.000	+	507.984i	0.546341	+	0.619493i
$821$	469.519			0.571887			0.285943	−	0.958247i	$-0.407693\pi$
$821$	469.519			0.571887			0.285943	+	0.958247i	$0.407693\pi$
$822$		0			0
$823$	1268.00			1.54070			0.770352	−	0.637618i	$-0.220080\pi$
$823$	1268.00			1.54070			0.770352	+	0.637618i	$0.220080\pi$
$824$	763.675	+	404.099i	0.926790	+	0.490411i
$825$	84.0000	−	157.150i	0.101818	−	0.190484i
$826$	136.000	+	359.822i	0.164649	+	0.435620i
$827$	1145.51			1.38514			0.692571	−	0.721349i	$-0.256478\pi$
$827$	1145.51			1.38514			0.692571	+	0.721349i	$0.256478\pi$
$828$	276.020	−	1041.65i	0.333358	−	1.25803i
$829$		−	1217.05i		−	1.46809i	−0.679101	−	0.734044i	$-0.737630\pi$
$829$		−	1217.05i		−	1.46809i	0.679101	−	0.734044i	$-0.262370\pi$
$830$	11.3137	+	29.9333i	0.0136310	+	0.0360642i
$831$	644.000	+	344.232i	0.774970	+	0.414239i
$832$	−560.000	+	380.988i	−0.673077	+	0.457918i
$833$		−	493.899i		−	0.592916i
$834$	94.3116	−	724.111i	0.113083	−	0.868239i
$835$			1862.61i			2.23067i
$836$	−118.794	−	134.700i	−0.142098	−	0.161124i
$837$	107.480	−	10.5830i	0.128411	−	0.0126440i
$838$	−234.000	−	619.106i	−0.279236	−	0.738790i
$839$		−	1227.26i		−	1.46277i	−0.681965	−	0.731385i	$-0.738874\pi$
$839$		−	1227.26i		−	1.46277i	0.681965	−	0.731385i	$-0.261126\pi$
$840$	450.274	−	303.587i	0.536041	−	0.361413i
$841$	−553.000			−0.657551
$842$	970.151	−	366.682i	1.15220	−	0.435490i
$843$	−831.558	−	444.486i	−0.986427	−	0.527267i
$844$	−658.000	−	746.102i	−0.779621	−	0.884007i
$845$	−322.441			−0.381587
$846$		0			0
$847$	−196.000			−0.231405
$848$	−101.823	+	808.198i	−0.120075	+	0.953064i
$849$	238.000	+	127.216i	0.280330	+	0.149843i
$850$	−196.000	+	74.0810i	−0.230588	+	0.0871542i
$851$	−1583.92			−1.86124
$852$	−1048.76	+	247.610i	−1.23094	+	0.290622i
$853$			1047.72i			1.22827i	0.789200	+	0.614137i	$0.210496\pi$
$853$			1047.72i			1.22827i	−0.789200	+	0.614137i	$0.789504\pi$
$854$	−712.764	+	269.399i	−0.834618	+	0.315456i
$855$	−224.000	+	149.666i	−0.261988	+	0.175048i
$856$	1020.00	+	539.733i	1.19159	+	0.630530i
$857$			359.199i			0.419135i	0.977794	+	0.209568i	$0.0672057\pi$
$857$			359.199i			0.419135i	−0.977794	+	0.209568i	$0.932794\pi$
$858$	−69.5879	+	534.286i	−0.0811048	+	0.622711i
$859$		−	513.276i		−	0.597527i	−0.954327	−	0.298764i	$-0.903426\pi$
$859$		−	513.276i		−	0.597527i	0.954327	−	0.298764i	$-0.0965742\pi$
$860$	−79.1960	−	89.7998i	−0.0920883	−	0.104418i
$861$	316.784	+	169.328i	0.367925	+	0.196664i
$862$	−672.000	+	253.992i	−0.779582	+	0.294654i
$863$		−	538.799i		−	0.624332i	−0.950028	−	0.312166i	$-0.898945\pi$
$863$		−	538.799i		−	0.624332i	0.950028	−	0.312166i	$-0.101055\pi$
$864$	−816.201	+	283.394i	−0.944677	+	0.328002i
$865$	1056.00			1.22081
$866$	60.8112	+	160.891i	0.0702208	+	0.185787i
$867$	91.9239	−	171.974i	0.106025	−	0.198355i
$868$	48.0000	−	42.3320i	0.0552995	−	0.0487696i
$869$	1052.17			1.21079
$870$	−571.176	−	74.3926i	−0.656524	−	0.0855087i
$871$	504.000			0.578645
$872$	197.990	−	374.166i	0.227053	−	0.429089i
$873$	−590.000	−	883.031i	−0.675830	−	1.01149i
$874$	112.000	+	296.324i	0.128146	+	0.339044i
$875$	407.294			0.465478
$876$	−16.5442	−	70.0735i	−0.0188860	−	0.0799925i
$877$		−	1344.04i		−	1.53254i	−0.642516	−	0.766272i	$-0.722109\pi$
$877$		−	1344.04i		−	1.53254i	0.642516	−	0.766272i	$-0.277891\pi$
$878$	−110.309	−	291.849i	−0.125636	−	0.332402i
$879$	24.0000	−	44.8999i	0.0273038	−	0.0510806i
$880$	−96.0000	+	761.976i	−0.109091	+	0.865882i
$881$			748.331i			0.849411i	0.905331	+	0.424706i	$0.139622\pi$
$881$			748.331i			0.849411i	−0.905331	+	0.424706i	$0.860378\pi$
$882$	−345.327	+	483.306i	−0.391528	+	0.547966i
$883$		−	418.029i		−	0.473419i	−0.971581	−	0.236709i	$-0.923931\pi$
$883$		−	418.029i		−	0.473419i	0.971581	−	0.236709i	$-0.0760689\pi$
$884$	475.176	−	419.066i	0.537529	−	0.474056i
$885$	−384.666	+	719.644i	−0.434651	+	0.813157i
$886$	150.000	+	396.863i	0.169300	+	0.447926i
$887$		−	1167.40i		−	1.31612i	−0.752966	−	0.658059i	$-0.771378\pi$
$887$		−	1167.40i		−	1.31612i	0.752966	−	0.658059i	$-0.228622\pi$
$888$	709.949	+	1052.98i	0.799493	+	1.18579i
$889$	304.000			0.341957
$890$	−1108.74	+	419.066i	−1.24578	+	0.470860i
$891$	−263.044	+	634.980i	−0.295223	+	0.712660i
$892$	−564.000	+	497.401i	−0.632287	+	0.557625i
$893$		0			0
$894$	−1110.68	−	144.660i	−1.24237	−	0.161812i
$895$	−1808.00			−2.02011
$896$	−294.156	+	419.066i	−0.328300	+	0.467707i
$897$	448.000	−	838.131i	0.499443	−	0.934372i
$898$	−924.000	+	349.239i	−1.02895	+	0.388908i
$899$	−67.8823			−0.0755086
$900$	243.593	+	64.5483i	0.270659	+	0.0717203i
$901$		−	761.976i		−	0.845701i
$902$	−475.176	+	179.600i	−0.526802	+	0.199113i
$903$	−56.0000	−	29.9333i	−0.0620155	−	0.0331487i
$904$	336.000	−	634.980i	0.371681	−	0.702412i
$905$		−	658.532i		−	0.727659i
$906$	−356.985	−	46.4954i	−0.394023	−	0.0513194i
$907$		−	597.940i		−	0.659250i	−0.944112	−	0.329625i	$-0.893078\pi$
$907$		−	597.940i		−	0.659250i	0.944112	−	0.329625i	$-0.106922\pi$
$908$	1162.48	−	1025.21i	1.28027	−	1.12909i
$909$	−311.127	−	465.652i	−0.342274	−	0.512269i
$910$	448.000	−	169.328i	0.492308	−	0.186075i
$911$		−	359.199i		−	0.394291i	−0.980374	−	0.197146i	$-0.936833\pi$
$911$		−	359.199i		−	0.394291i	0.980374	−	0.197146i	$-0.0631671\pi$
$912$	146.794	−	207.276i	0.160958	−	0.227277i
$913$	−24.0000			−0.0262870
$914$	137.179	+	362.941i	0.150086	+	0.397091i
$915$	−1425.53	−	761.976i	−1.55795	−	0.832761i
$916$	−644.000	−	730.227i	−0.703057	−	0.797191i
$917$	56.5685			0.0616887
$918$	724.362	−	358.447i	0.789065	−	0.390465i
$919$	−780.000			−0.848749			−0.424374	−	0.905487i	$-0.639506\pi$
$919$	−780.000			−0.848749			−0.424374	+	0.905487i	$0.639506\pi$
$920$	633.568	−	1197.33i	0.688661	−	1.30145i
$921$	1218.00	+	651.048i	1.32248	+	0.706893i
$922$	396.000	+	1047.72i	0.429501	+	1.13635i
$923$	−950.352			−1.02963
$924$	93.5879	+	396.395i	0.101286	+	0.428999i
$925$		−	370.405i		−	0.400438i
$926$	−285.671	−	755.815i	−0.308500	−	0.816215i
$927$	540.000	+	808.198i	0.582524	+	0.871842i
$928$	528.000	−	126.996i	0.568966	−	0.136849i
$929$			1361.96i			1.46605i	0.680200	+	0.733027i	$0.261893\pi$
$929$			1361.96i			1.46605i	−0.680200	+	0.733027i	$0.738107\pi$
$930$	134.627	+	17.5345i	0.144761	+	0.0188543i
$931$		−	174.620i		−	0.187561i
$932$	277.186	+	314.299i	0.297410	+	0.337231i
$933$	395.980	+	211.660i	0.424416	+	0.226860i
$934$	470.000	+	1243.50i	0.503212	+	1.33137i
$935$		−	718.398i		−	0.768340i
$936$	−757.990	+	77.8416i	−0.809818	+	0.0831641i
$937$	566.000			0.604055			0.302028	−	0.953299i	$-0.402336\pi$
$937$	566.000			0.604055			0.302028	+	0.953299i	$0.402336\pi$
$938$	356.382	−	134.700i	0.379938	−	0.143603i
$939$	−794.788	+	1486.91i	−0.846420	+	1.58351i
$940$		0			0
$941$	424.264			0.450865			0.225433	−	0.974259i	$-0.427620\pi$
$941$	424.264			0.450865			0.225433	+	0.974259i	$0.427620\pi$
$942$	90.2111	−	692.628i	0.0957655	−	0.735274i
$943$	896.000			0.950159
$944$	96.1665	−	763.298i	0.101871	−	0.808579i
$945$	608.000	−	59.8665i	0.643386	−	0.0633508i
$946$	84.0000	−	31.7490i	0.0887949	−	0.0335613i
$947$	466.690			0.492809			0.246405	−	0.969167i	$-0.420751\pi$
$947$	466.690			0.492809			0.246405	+	0.969167i	$0.420751\pi$
$948$	341.913	+	1448.19i	0.360667	+	1.52762i
$949$		−	63.4980i		−	0.0669105i
$950$	−69.2965	+	26.1916i	−0.0729436	+	0.0275701i
$951$	−8.00000	+	14.9666i	−0.00841220	+	0.0157378i
$952$	224.000	−	423.320i	0.235294	−	0.444664i
$953$			897.998i			0.942285i	0.882057	+	0.471143i	$0.156158\pi$
$953$			897.998i			0.942285i	−0.882057	+	0.471143i	$0.843842\pi$
$954$	−532.764	+	745.635i	−0.558452	+	0.781588i
$955$		−	338.656i		−	0.354614i
$956$	950.352	+	1077.60i	0.994092	+	1.12719i
$957$	203.647	−	380.988i	0.212797	−	0.398107i
$958$	448.000	−	169.328i	0.467641	−	0.176752i
$959$		0			0
$960$	−1079.96	+	115.478i	−1.12496	+	0.120290i
$961$	−945.000			−0.983351
$962$	395.980	+	1047.66i	0.411621	+	1.08905i
$963$	721.249	+	1079.47i	0.748960	+	1.12094i
$964$	−366.000	+	322.782i	−0.379668	+	0.334836i
$965$	576.999			0.597927
$966$	92.7838	−	712.381i	0.0960495	−	0.737455i
$967$	692.000			0.715615			0.357808	−	0.933795i	$-0.383524\pi$
$967$	692.000			0.715615			0.357808	+	0.933795i	$0.383524\pi$
$968$	346.482	+	183.341i	0.357936	+	0.189402i
$969$	−112.000	+	209.533i	−0.115583	+	0.216236i
$970$	−472.000	−	1248.79i	−0.486598	−	1.28742i
$971$	449.720			0.463151			0.231576	−	0.972817i	$-0.425612\pi$
$971$	449.720			0.463151			0.231576	+	0.972817i	$0.425612\pi$
$972$	−959.448	−	155.704i	−0.987086	−	0.160190i
$973$		−	486.818i		−	0.500327i
$974$	353.553	+	935.414i	0.362991	+	0.960384i
$975$	196.000	+	104.766i	0.201026	+	0.107453i
$976$	1512.00	+	190.494i	1.54918	+	0.195178i
$977$		−	883.031i		−	0.903819i	−0.892064	−	0.451909i	$-0.850743\pi$
$977$		−	883.031i		−	0.903819i	0.892064	−	0.451909i	$-0.149257\pi$
$978$	225.528	−	1731.57i	0.230601	−	1.77052i
$979$		−	888.972i		−	0.908041i
$980$	−560.029	+	493.899i	−0.571458	+	0.503978i
$981$	395.980	−	264.575i	0.403649	−	0.269699i
$982$	82.0000	+	216.952i	0.0835031	+	0.220928i
$983$		−	329.266i		−	0.334960i	−0.985875	−	0.167480i	$-0.946437\pi$
$983$		−	329.266i		−	0.334960i	0.985875	−	0.167480i	$-0.0535630\pi$
$984$	−401.608	−	595.657i	−0.408138	−	0.605342i
$985$	−1376.00			−1.39695
$986$	−475.176	+	179.600i	−0.481923	+	0.182150i
$987$		0			0
$988$	168.000	−	148.162i	0.170040	−	0.149962i
$989$	−158.392			−0.160154
$990$	−502.294	+	702.991i	−0.507368	+	0.710092i
$991$	−340.000			−0.343088			−0.171544	−	0.985176i	$-0.554876\pi$
$991$	−340.000			−0.343088			−0.171544	+	0.985176i	$0.554876\pi$
$992$	−124.451	+	29.9333i	−0.125454	+	0.0301747i
$993$	−1106.00	−	591.182i	−1.11380	−	0.595349i
$994$	−672.000	+	253.992i	−0.676056	+	0.255525i
$995$	1063.49			1.06883
$996$	−7.79899	−	33.0329i	−0.00783031	−	0.0331656i
$997$			1555.70i			1.56038i	0.625541	+	0.780191i	$0.284878\pi$
$997$			1555.70i			1.56038i	−0.625541	+	0.780191i	$0.715122\pi$
$998$	−623.668	+	235.724i	−0.624918	+	0.236197i
$999$	140.000	+	1421.83i	0.140140	+	1.42325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	24.3.h.c.5.4	yes	4
3.2	odd	2	inner	24.3.h.c.5.1	✓	4
4.3	odd	2		96.3.h.c.17.2		4
8.3	odd	2		96.3.h.c.17.3		4
8.5	even	2	inner	24.3.h.c.5.2	yes	4
12.11	even	2		96.3.h.c.17.4		4
16.3	odd	4		768.3.e.l.257.1		4
16.5	even	4		768.3.e.i.257.1		4
16.11	odd	4		768.3.e.l.257.4		4
16.13	even	4		768.3.e.i.257.4		4
24.5	odd	2	inner	24.3.h.c.5.3	yes	4
24.11	even	2		96.3.h.c.17.1		4
48.5	odd	4		768.3.e.i.257.2		4
48.11	even	4		768.3.e.l.257.3		4
48.29	odd	4		768.3.e.i.257.3		4
48.35	even	4		768.3.e.l.257.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.3.h.c.5.1	✓	4	3.2	odd	2	inner
24.3.h.c.5.2	yes	4	8.5	even	2	inner
24.3.h.c.5.3	yes	4	24.5	odd	2	inner
24.3.h.c.5.4	yes	4	1.1	even	1	trivial
96.3.h.c.17.1		4	24.11	even	2
96.3.h.c.17.2		4	4.3	odd	2
96.3.h.c.17.3		4	8.3	odd	2
96.3.h.c.17.4		4	12.11	even	2
768.3.e.i.257.1		4	16.5	even	4
768.3.e.i.257.2		4	48.5	odd	4
768.3.e.i.257.3		4	48.29	odd	4
768.3.e.i.257.4		4	16.13	even	4
768.3.e.l.257.1		4	16.3	odd	4
768.3.e.l.257.2		4	48.35	even	4
768.3.e.l.257.3		4	48.11	even	4
768.3.e.l.257.4		4	16.11	odd	4

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:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	24.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.87083i) q^{2} +(1.41421 - 2.64575i) q^{3} +(-3.00000 + 2.64575i) q^{4} -5.65685 q^{5} +(5.94975 + 0.774923i) q^{6} +4.00000 q^{7} +(-7.07107 - 3.74166i) q^{8} +(-5.00000 - 7.48331i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 1.87083i) q^{2} +(1.41421 - 2.64575i) q^{3} +(-3.00000 + 2.64575i) q^{4} -5.65685 q^{5} +(5.94975 + 0.774923i) q^{6} +4.00000 q^{7} +(-7.07107 - 3.74166i) q^{8} +(-5.00000 - 7.48331i) q^{9} +(-4.00000 - 10.5830i) q^{10} +8.48528 q^{11} +(2.75736 + 11.6789i) q^{12} +10.5830i q^{13} +(2.82843 + 7.48331i) q^{14} +(-8.00000 + 14.9666i) q^{15} +(2.00000 - 15.8745i) q^{16} +14.9666i q^{17} +(10.4645 - 14.6456i) q^{18} +5.29150i q^{19} +(16.9706 - 14.9666i) q^{20} +(5.65685 - 10.5830i) q^{21} +(6.00000 + 15.8745i) q^{22} -29.9333i q^{23} +(-19.8995 + 13.4168i) q^{24} +7.00000 q^{25} +(-19.7990 + 7.48331i) q^{26} +(-26.8701 + 2.64575i) q^{27} +(-12.0000 + 10.5830i) q^{28} +16.9706 q^{29} +(-33.6569 - 4.38362i) q^{30} -4.00000 q^{31} +(31.1127 - 7.48331i) q^{32} +(12.0000 - 22.4499i) q^{33} +(-28.0000 + 10.5830i) q^{34} -22.6274 q^{35} +(34.7990 + 9.22119i) q^{36} -52.9150i q^{37} +(-9.89949 + 3.74166i) q^{38} +(28.0000 + 14.9666i) q^{39} +(40.0000 + 21.1660i) q^{40} +29.9333i q^{41} +(23.7990 + 3.09969i) q^{42} -5.29150i q^{43} +(-25.4558 + 22.4499i) q^{44} +(28.2843 + 42.3320i) q^{45} +(56.0000 - 21.1660i) q^{46} +(-39.1716 - 27.7414i) q^{48} -33.0000 q^{49} +(4.94975 + 13.0958i) q^{50} +(39.5980 + 21.1660i) q^{51} +(-28.0000 - 31.7490i) q^{52} -50.9117 q^{53} +(-23.9497 - 48.3984i) q^{54} -48.0000 q^{55} +(-28.2843 - 14.9666i) q^{56} +(14.0000 + 7.48331i) q^{57} +(12.0000 + 31.7490i) q^{58} +48.0833 q^{59} +(-15.5980 - 66.0659i) q^{60} +95.2470i q^{61} +(-2.82843 - 7.48331i) q^{62} +(-20.0000 - 29.9333i) q^{63} +(36.0000 + 52.9150i) q^{64} -59.8665i q^{65} +(50.4853 + 6.57544i) q^{66} -47.6235i q^{67} +(-39.5980 - 44.8999i) q^{68} +(-79.1960 - 42.3320i) q^{69} +(-16.0000 - 42.3320i) q^{70} +89.7998i q^{71} +(7.35534 + 71.6233i) q^{72} -6.00000 q^{73} +(98.9949 - 37.4166i) q^{74} +(9.89949 - 18.5203i) q^{75} +(-14.0000 - 15.8745i) q^{76} +33.9411 q^{77} +(-8.20101 + 62.9662i) q^{78} +124.000 q^{79} +(-11.3137 + 89.7998i) q^{80} +(-31.0000 + 74.8331i) q^{81} +(-56.0000 + 21.1660i) q^{82} -2.82843 q^{83} +(11.0294 + 46.7156i) q^{84} -84.6640i q^{85} +(9.89949 - 3.74166i) q^{86} +(24.0000 - 44.8999i) q^{87} +(-60.0000 - 31.7490i) q^{88} -104.766i q^{89} +(-59.1960 + 82.8483i) q^{90} +42.3320i q^{91} +(79.1960 + 89.7998i) q^{92} +(-5.65685 + 10.5830i) q^{93} -29.9333i q^{95} +(24.2010 - 92.8995i) q^{96} +118.000 q^{97} +(-23.3345 - 61.7373i) q^{98} +(-42.4264 - 63.4980i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 12 q^{4} + 4 q^{6} + 16 q^{7} - 20 q^{9}+O(q^{10}) \) 4 * q - 12 * q^4 + 4 * q^6 + 16 * q^7 - 20 * q^9	\( 4 q - 12 q^{4} + 4 q^{6} + 16 q^{7} - 20 q^{9} - 16 q^{10} + 28 q^{12} - 32 q^{15} + 8 q^{16} + 56 q^{18} + 24 q^{22} - 40 q^{24} + 28 q^{25} - 48 q^{28} - 112 q^{30} - 16 q^{31} + 48 q^{33} - 112 q^{34} + 60 q^{36} + 112 q^{39} + 160 q^{40} + 16 q^{42} + 224 q^{46} - 168 q^{48} - 132 q^{49} - 112 q^{52} - 76 q^{54} - 192 q^{55} + 56 q^{57} + 48 q^{58} + 96 q^{60} - 80 q^{63} + 144 q^{64} + 168 q^{66} - 64 q^{70} - 112 q^{72} - 24 q^{73} - 56 q^{76} - 112 q^{78} + 496 q^{79} - 124 q^{81} - 224 q^{82} + 112 q^{84} + 96 q^{87} - 240 q^{88} + 80 q^{90} + 176 q^{96} + 472 q^{97}+O(q^{100}) \) 4 * q - 12 * q^4 + 4 * q^6 + 16 * q^7 - 20 * q^9 - 16 * q^10 + 28 * q^12 - 32 * q^15 + 8 * q^16 + 56 * q^18 + 24 * q^22 - 40 * q^24 + 28 * q^25 - 48 * q^28 - 112 * q^30 - 16 * q^31 + 48 * q^33 - 112 * q^34 + 60 * q^36 + 112 * q^39 + 160 * q^40 + 16 * q^42 + 224 * q^46 - 168 * q^48 - 132 * q^49 - 112 * q^52 - 76 * q^54 - 192 * q^55 + 56 * q^57 + 48 * q^58 + 96 * q^60 - 80 * q^63 + 144 * q^64 + 168 * q^66 - 64 * q^70 - 112 * q^72 - 24 * q^73 - 56 * q^76 - 112 * q^78 + 496 * q^79 - 124 * q^81 - 224 * q^82 + 112 * q^84 + 96 * q^87 - 240 * q^88 + 80 * q^90 + 176 * q^96 + 472 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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