LMFDB - Embedded newform 920.2.bf.a.509.131

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(29,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 11, 18]))

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

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

chi := DirichletCharacter("920.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bf (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$1400$
Relative dimension:	$140$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			509.131
Character	$\chi$	$=$	920.509
Dual form			920.2.bf.a.629.131

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38812 - 0.270430i) q^{2} +(1.18796 - 2.60128i) q^{3} +(1.85374 - 0.750777i) q^{4} +(1.05259 + 1.97283i) q^{5} +(0.945569 - 3.93214i) q^{6} +(1.18849 + 1.84933i) q^{7} +(2.37017 - 1.54347i) q^{8} +(-3.39080 - 3.91320i) q^{9} +O(q^{10})$	\(q+(1.38812 - 0.270430i) q^{2} +(1.18796 - 2.60128i) q^{3} +(1.85374 - 0.750777i) q^{4} +(1.05259 + 1.97283i) q^{5} +(0.945569 - 3.93214i) q^{6} +(1.18849 + 1.84933i) q^{7} +(2.37017 - 1.54347i) q^{8} +(-3.39080 - 3.91320i) q^{9} +(1.99462 + 2.45387i) q^{10} +(-0.231858 - 0.0333361i) q^{11} +(0.249192 - 5.71397i) q^{12} +(-1.88677 - 1.21256i) q^{13} +(2.14988 + 2.24569i) q^{14} +(6.38231 - 0.394417i) q^{15} +(2.87267 - 2.78348i) q^{16} +(-1.92098 + 6.54226i) q^{17} +(-5.76508 - 4.51500i) q^{18} +(-1.92021 - 6.53964i) q^{19} +(3.43237 + 2.86685i) q^{20} +(6.22252 - 0.894663i) q^{21} +(-0.330861 + 0.0164269i) q^{22} +(4.77887 + 0.402968i) q^{23} +(-1.19932 - 7.99905i) q^{24} +(-2.78413 + 4.15315i) q^{25} +(-2.94697 - 1.17293i) q^{26} +(-5.97587 + 1.75467i) q^{27} +(3.59159 + 2.53588i) q^{28} +(1.03289 - 3.51770i) q^{29} +(8.75273 - 2.27347i) q^{30} +(-3.95831 - 8.66749i) q^{31} +(3.23486 - 4.64065i) q^{32} +(-0.362155 + 0.563524i) q^{33} +(-0.897322 + 9.60091i) q^{34} +(-2.39743 + 4.29128i) q^{35} +(-9.22359 - 4.70829i) q^{36} +(3.44974 + 3.98121i) q^{37} +(-4.43400 - 8.55851i) q^{38} +(-5.39561 + 3.46755i) q^{39} +(5.53981 + 3.05131i) q^{40} +(-6.86408 + 7.92157i) q^{41} +(8.39564 - 2.92465i) q^{42} +(-1.97245 + 4.31906i) q^{43} +(-0.454831 + 0.112277i) q^{44} +(4.15096 - 10.8085i) q^{45} +(6.74261 - 0.732983i) q^{46} +7.47901i q^{47} +(-3.82798 - 10.7793i) q^{48} +(0.900390 - 1.97158i) q^{49} +(-2.74155 + 6.51797i) q^{50} +(14.7362 + 12.7690i) q^{51} +(-4.40794 - 0.831212i) q^{52} +(-3.29928 + 2.12032i) q^{53} +(-7.82068 + 4.05174i) q^{54} +(-0.178284 - 0.492505i) q^{55} +(5.67132 + 2.54882i) q^{56} +(-19.2926 - 2.77385i) q^{57} +(0.482480 - 5.16230i) q^{58} +(-2.74272 + 4.26775i) q^{59} +(11.5350 - 5.52284i) q^{60} +(-9.89220 + 4.51762i) q^{61} +(-7.83855 - 10.9610i) q^{62} +(3.20685 - 10.9215i) q^{63} +(3.23539 - 7.31657i) q^{64} +(0.406176 - 4.99860i) q^{65} +(-0.350320 + 0.880175i) q^{66} +(1.28963 + 8.96956i) q^{67} +(1.35079 + 13.5698i) q^{68} +(6.72536 - 11.9525i) q^{69} +(-2.16742 + 6.60514i) q^{70} +(1.38157 + 9.60902i) q^{71} +(-14.0767 - 4.04133i) q^{72} +(-1.89738 - 6.46189i) q^{73} +(5.86528 + 4.59347i) q^{74} +(7.49605 + 12.1761i) q^{75} +(-8.46938 - 10.6811i) q^{76} +(-0.213912 - 0.468402i) q^{77} +(-6.55201 + 6.27250i) q^{78} +(3.51294 + 2.25763i) q^{79} +(8.51507 + 2.73744i) q^{80} +(-0.324045 + 2.25378i) q^{81} +(-7.38591 + 12.8523i) q^{82} +(-7.86631 - 9.07821i) q^{83} +(10.8632 - 6.33019i) q^{84} +(-14.9288 + 3.09652i) q^{85} +(-1.56999 + 6.52877i) q^{86} +(-7.92347 - 6.86573i) q^{87} +(-0.600995 + 0.278854i) q^{88} +(3.74084 - 8.19131i) q^{89} +(2.83909 - 16.1259i) q^{90} -4.93039i q^{91} +(9.16130 - 2.84087i) q^{92} -27.2489 q^{93} +(2.02255 + 10.3817i) q^{94} +(10.8804 - 10.6718i) q^{95} +(-8.22873 - 13.9277i) q^{96} +(-0.414920 - 0.359530i) q^{97} +(0.716672 - 2.98027i) q^{98} +(0.655734 + 1.02034i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1400 q - 14 q^{4} - 14 q^{6} - 168 q^{9}+O(q^{10}) $ 1400 * q - 14 * q^4 - 14 * q^6 - 168 * q^9	$ 1400 q - 14 q^{4} - 14 q^{6} - 168 q^{9} - 5 q^{10} - 26 q^{14} - 6 q^{15} - 14 q^{16} - 27 q^{20} - 32 q^{24} - 18 q^{25} - 30 q^{26} - q^{30} - 52 q^{31} + 40 q^{34} + 26 q^{36} - 12 q^{39} + 15 q^{40} - 36 q^{41} - 142 q^{44} - 10 q^{46} + 80 q^{49} - 47 q^{50} + 46 q^{54} - 38 q^{55} + 14 q^{56} + 21 q^{60} - 26 q^{64} + 2 q^{65} - 104 q^{66} - 26 q^{70} - 36 q^{71} - 18 q^{74} - 96 q^{76} - 12 q^{79} + 82 q^{80} - 136 q^{81} - 82 q^{84} - 198 q^{86} - 52 q^{89} + 164 q^{90} - 38 q^{94} + 2 q^{95} - 432 q^{96}+O(q^{100}) $ 1400 * q - 14 * q^4 - 14 * q^6 - 168 * q^9 - 5 * q^10 - 26 * q^14 - 6 * q^15 - 14 * q^16 - 27 * q^20 - 32 * q^24 - 18 * q^25 - 30 * q^26 - q^30 - 52 * q^31 + 40 * q^34 + 26 * q^36 - 12 * q^39 + 15 * q^40 - 36 * q^41 - 142 * q^44 - 10 * q^46 + 80 * q^49 - 47 * q^50 + 46 * q^54 - 38 * q^55 + 14 * q^56 + 21 * q^60 - 26 * q^64 + 2 * q^65 - 104 * q^66 - 26 * q^70 - 36 * q^71 - 18 * q^74 - 96 * q^76 - 12 * q^79 + 82 * q^80 - 136 * q^81 - 82 * q^84 - 198 * q^86 - 52 * q^89 + 164 * q^90 - 38 * q^94 + 2 * q^95 - 432 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$	$-1$	$-1$

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 $

$2$	1.38812	−	0.270430i	0.981547	−	0.191223i
$2$	1.38812	−	0.270430i	0.981547	−	0.191223i
$3$	1.18796	−	2.60128i	0.685871	−	1.50185i	−0.170429	−	0.985370i	$-0.554515\pi$
$3$	1.18796	−	2.60128i	0.685871	−	1.50185i	0.856300	−	0.516478i	$-0.172757\pi$
$4$	1.85374	−	0.750777i	0.926868	−	0.375388i
$5$	1.05259	+	1.97283i	0.470731	+	0.882277i
$5$	1.05259	+	1.97283i	0.470731	+	0.882277i
$6$	0.945569	−	3.93214i	0.386027	−	1.60529i
$7$	1.18849	+	1.84933i	0.449209	+	0.698982i	0.989825	−	0.142287i	$-0.0454455\pi$
$7$	1.18849	+	1.84933i	0.449209	+	0.698982i	−0.540617	+	0.841269i	$0.681809\pi$
$8$	2.37017	−	1.54347i	0.837981	−	0.545699i
$9$	−3.39080	−	3.91320i	−1.13027	−	1.30440i
$10$	1.99462	+	2.45387i	0.630756	+	0.775981i
$11$	−0.231858	−	0.0333361i	−0.0699078	−	0.0100512i	0.107272	−	0.994230i	$-0.465788\pi$
$11$	−0.231858	−	0.0333361i	−0.0699078	−	0.0100512i	−0.177180	+	0.984178i	$0.556697\pi$
$12$	0.249192	−	5.71397i	0.0719354	−	1.64948i
$13$	−1.88677	−	1.21256i	−0.523297	−	0.336302i	0.252178	−	0.967681i	$-0.418853\pi$
$13$	−1.88677	−	1.21256i	−0.523297	−	0.336302i	−0.775475	+	0.631378i	$0.782489\pi$
$14$	2.14988	+	2.24569i	0.574581	+	0.600185i
$15$	6.38231	−	0.394417i	1.64791	−	0.101838i
$16$	2.87267	−	2.78348i	0.718167	−	0.695871i
$17$	−1.92098	+	6.54226i	−0.465906	+	1.58673i	0.306674	+	0.951815i	$0.400784\pi$
$17$	−1.92098	+	6.54226i	−0.465906	+	1.58673i	−0.772581	+	0.634917i	$0.781034\pi$
$18$	−5.76508	−	4.51500i	−1.35884	−	1.06420i
$19$	−1.92021	−	6.53964i	−0.440527	−	1.50030i	−0.818514	−	0.574486i	$-0.805202\pi$
$19$	−1.92021	−	6.53964i	−0.440527	−	1.50030i	0.377987	−	0.925811i	$-0.376616\pi$
$20$	3.43237	+	2.86685i	0.767502	+	0.641047i
$21$	6.22252	−	0.894663i	1.35786	−	0.195231i
$22$	−0.330861	+	0.0164269i	−0.0705398	+	0.00350222i
$23$	4.77887	+	0.402968i	0.996464	+	0.0840247i
$23$	4.77887	+	0.402968i	0.996464	+	0.0840247i
$24$	−1.19932	−	7.99905i	−0.244811	−	1.63280i
$25$	−2.78413	+	4.15315i	−0.556825	+	0.830630i
$26$	−2.94697	−	1.17293i	−0.577949	−	0.230030i
$27$	−5.97587	+	1.75467i	−1.15006	+	0.337687i
$28$	3.59159	+	2.53588i	0.678747	+	0.479236i
$29$	1.03289	−	3.51770i	0.191803	−	0.653220i	−0.806292	−	0.591518i	$-0.798529\pi$
$29$	1.03289	−	3.51770i	0.191803	−	0.653220i	0.998095	−	0.0617020i	$-0.0196529\pi$
$30$	8.75273	−	2.27347i	1.59802	−	0.415076i
$31$	−3.95831	−	8.66749i	−0.710933	−	1.55673i	−0.826190	−	0.563391i	$-0.809496\pi$
$31$	−3.95831	−	8.66749i	−0.710933	−	1.55673i	0.115257	−	0.993336i	$-0.463231\pi$
$32$	3.23486	−	4.64065i	0.571848	−	0.820359i
$33$	−0.362155	+	0.563524i	−0.0630431	+	0.0980970i
$34$	−0.897322	+	9.60091i	−0.153889	+	1.64654i
$35$	−2.39743	+	4.29128i	−0.405240	+	0.725359i
$36$	−9.22359	−	4.70829i	−1.53727	−	0.784716i
$37$	3.44974	+	3.98121i	0.567134	+	0.654507i	0.964788	−	0.263028i	$-0.0847211\pi$
$37$	3.44974	+	3.98121i	0.567134	+	0.654507i	−0.397654	+	0.917535i	$0.630176\pi$
$38$	−4.43400	−	8.55851i	−0.719289	−	1.38837i
$39$	−5.39561	+	3.46755i	−0.863989	+	0.555252i
$40$	5.53981	+	3.05131i	0.875921	+	0.482454i
$41$	−6.86408	+	7.92157i	−1.07199	+	1.23714i	−0.101796	+	0.994805i	$0.532459\pi$
$41$	−6.86408	+	7.92157i	−1.07199	+	1.23714i	−0.970193	+	0.242335i	$0.922087\pi$
$42$	8.39564	−	2.92465i	1.29547	−	0.451284i
$43$	−1.97245	+	4.31906i	−0.300796	+	0.658650i	−0.998322	−	0.0579087i	$-0.981557\pi$
$43$	−1.97245	+	4.31906i	−0.300796	+	0.658650i	0.697526	+	0.716559i	$0.254284\pi$
$44$	−0.454831	+	0.112277i	−0.0685684	+	0.0169264i
$45$	4.15096	−	10.8085i	0.618789	−	1.61123i
$46$	6.74261	−	0.732983i	0.994143	−	0.108072i
$47$			7.47901i			1.09093i	0.838135	+	0.545463i	$0.183646\pi$
$47$			7.47901i			1.09093i	−0.838135	+	0.545463i	$0.816354\pi$
$48$	−3.82798	−	10.7793i	−0.552522	−	1.55586i
$49$	0.900390	−	1.97158i	0.128627	−	0.281654i
$50$	−2.74155	+	6.51797i	−0.387714	+	0.921780i
$51$	14.7362	+	12.7690i	2.06348	+	1.78801i
$52$	−4.40794	−	0.831212i	−0.611271	−	0.115268i
$53$	−3.29928	+	2.12032i	−0.453191	+	0.291248i	−0.747255	−	0.664538i	$-0.768628\pi$
$53$	−3.29928	+	2.12032i	−0.453191	+	0.291248i	0.294064	+	0.955786i	$0.404992\pi$
$54$	−7.82068	+	4.05174i	−1.06426	+	0.551373i
$55$	−0.178284	−	0.492505i	−0.0240398	−	0.0664094i
$56$	5.67132	+	2.54882i	0.757863	+	0.340601i
$57$	−19.2926	−	2.77385i	−2.55536	−	0.367406i
$58$	0.482480	−	5.16230i	0.0633527	−	0.677843i
$59$	−2.74272	+	4.26775i	−0.357071	+	0.555614i	−0.972595	−	0.232504i	$-0.925308\pi$
$59$	−2.74272	+	4.26775i	−0.357071	+	0.555614i	0.615524	+	0.788118i	$0.288944\pi$
$60$	11.5350	−	5.52284i	1.48916	−	0.712995i
$61$	−9.89220	+	4.51762i	−1.26657	+	0.578422i	−0.931489	−	0.363769i	$-0.881490\pi$
$61$	−9.89220	+	4.51762i	−1.26657	+	0.578422i	−0.335078	+	0.942190i	$0.608763\pi$
$62$	−7.83855	−	10.9610i	−0.995496	−	1.39205i
$63$	3.20685	−	10.9215i	0.404026	−	1.37598i
$64$	3.23539	−	7.31657i	0.404424	−	0.914572i
$65$	0.406176	−	4.99860i	0.0503799	−	0.620000i
$66$	−0.350320	+	0.880175i	−0.0431214	+	0.108342i
$67$	1.28963	+	8.96956i	0.157553	+	1.09581i	0.903124	+	0.429380i	$0.141268\pi$
$67$	1.28963	+	8.96956i	0.157553	+	1.09581i	−0.745571	+	0.666427i	$0.767823\pi$
$68$	1.35079	+	13.5698i	0.163807	+	1.64559i
$69$	6.72536	−	11.9525i	0.809638	−	1.43891i
$70$	−2.16742	+	6.60514i	−0.259056	+	0.789465i
$71$	1.38157	+	9.60902i	0.163962	+	1.14038i	0.891073	+	0.453861i	$0.149954\pi$
$71$	1.38157	+	9.60902i	0.163962	+	1.14038i	−0.727111	+	0.686520i	$0.759137\pi$
$72$	−14.0767	−	4.04133i	−1.65895	−	0.476275i
$73$	−1.89738	−	6.46189i	−0.222072	−	0.756307i	−0.992867	−	0.119224i	$-0.961959\pi$
$73$	−1.89738	−	6.46189i	−0.222072	−	0.756307i	0.770796	−	0.637082i	$-0.219859\pi$
$74$	5.86528	+	4.59347i	0.681825	+	0.533981i
$75$	7.49605	+	12.1761i	0.865570	+	1.40597i
$76$	−8.46938	−	10.6811i	−0.971504	−	1.22521i
$77$	−0.213912	−	0.468402i	−0.0243775	−	0.0533794i
$78$	−6.55201	+	6.27250i	−0.741869	+	0.710220i
$79$	3.51294	+	2.25763i	0.395236	+	0.254003i	0.723130	−	0.690711i	$-0.242703\pi$
$79$	3.51294	+	2.25763i	0.395236	+	0.254003i	−0.327894	+	0.944715i	$0.606339\pi$
$80$	8.51507	+	2.73744i	0.952014	+	0.306055i
$81$	−0.324045	+	2.25378i	−0.0360050	+	0.250420i
$82$	−7.38591	+	12.8523i	−0.815637	+	1.41930i
$83$	−7.86631	−	9.07821i	−0.863440	−	0.996463i	−0.999983	−	0.00582845i	$-0.998145\pi$
$83$	−7.86631	−	9.07821i	−0.863440	−	0.996463i	0.136543	−	0.990634i	$-0.456401\pi$
$84$	10.8632	−	6.33019i	1.18527	−	0.690680i
$85$	−14.9288	+	3.09652i	−1.61925	+	0.335865i
$86$	−1.56999	+	6.52877i	−0.169296	+	0.704015i
$87$	−7.92347	−	6.86573i	−0.849485	−	0.736083i
$88$	−0.600995	+	0.278854i	−0.0640663	+	0.0297259i
$89$	3.74084	−	8.19131i	0.396529	−	0.868277i	−0.601082	−	0.799188i	$-0.705263\pi$
$89$	3.74084	−	8.19131i	0.396529	−	0.868277i	0.997610	−	0.0690893i	$-0.0220093\pi$
$90$	2.83909	−	16.1259i	0.299266	−	1.69982i
$91$		−	4.93039i		−	0.516845i
$92$	9.16130	−	2.84087i	0.955132	−	0.296181i
$93$	−27.2489			−2.82558
$94$	2.02255	+	10.3817i	0.208610	+	1.07079i
$95$	10.8804	−	10.6718i	1.11631	−	1.09490i
$96$	−8.22873	−	13.9277i	−0.839841	−	1.42149i
$97$	−0.414920	−	0.359530i	−0.0421287	−	0.0365047i	0.633542	−	0.773708i	$-0.281600\pi$
$97$	−0.414920	−	0.359530i	−0.0421287	−	0.0365047i	−0.675671	+	0.737204i	$0.736146\pi$
$98$	0.716672	−	2.98027i	0.0723948	−	0.301053i
$99$	0.655734	+	1.02034i	0.0659037	+	0.102548i
$100$	−2.04294	+	9.78910i	−0.204294	+	0.978910i
$101$	13.0137	−	11.2764i	1.29491	−	1.12205i	0.309676	−	0.950842i	$-0.399779\pi$
$101$	13.0137	−	11.2764i	1.29491	−	1.12205i	0.985235	−	0.171205i	$-0.0547660\pi$
$102$	23.9086	+	13.7397i	2.36731	+	1.36043i
$103$	8.08845	+	1.16294i	0.796979	+	0.114588i	0.528762	−	0.848770i	$-0.322656\pi$
$103$	8.08845	+	1.16294i	0.796979	+	0.114588i	0.268217	+	0.963359i	$0.413566\pi$
$104$	−6.34351	+	0.0382196i	−0.622033	+	0.00374774i
$105$	8.31475	+	11.3343i	0.811437	+	1.10611i
$106$	−4.00638	+	3.83547i	−0.389134	+	0.372534i
$107$	−5.55987	−	12.1744i	−0.537493	−	1.17694i	−0.962382	−	0.271699i	$-0.912414\pi$
$107$	−5.55987	−	12.1744i	−0.537493	−	1.17694i	0.424890	−	0.905245i	$-0.360313\pi$
$108$	−9.76031	+	7.73924i	−0.939186	+	0.744709i
$109$	−2.13770	+	7.28035i	−0.204755	+	0.697331i	0.791524	+	0.611139i	$0.209288\pi$
$109$	−2.13770	+	7.28035i	−0.204755	+	0.697331i	−0.996278	+	0.0861926i	$0.972530\pi$
$110$	−0.380667	−	0.635442i	−0.0362952	−	0.0605870i
$111$	14.4544	−	4.24420i	1.37195	−	0.402841i
$112$	8.56174	+	2.00437i	0.809008	+	0.189395i
$113$	1.76190	−	0.253323i	0.165746	−	0.0238306i	−0.0589423	−	0.998261i	$-0.518773\pi$
$113$	1.76190	−	0.253323i	0.165746	−	0.0238306i	0.224688	+	0.974431i	$0.427864\pi$
$114$	−27.5305	+	1.36686i	−2.57846	+	0.128018i
$115$	4.23519	+	9.85207i	0.394933	+	0.918710i
$116$	−0.726302	−	7.29635i	−0.0674354	−	0.677449i
$117$	1.65271	+	11.4949i	0.152793	+	1.06270i
$118$	−2.65308	+	6.66585i	−0.244236	+	0.613641i
$119$	−14.3819	+	4.22291i	−1.31839	+	0.387113i
$120$	14.5184	−	10.7858i	1.32534	−	0.984600i
$121$	−10.5018	−	3.08360i	−0.954707	−	0.280327i
$122$	−12.5098	+	8.94613i	−1.13259	+	0.809945i
$123$	12.4519	+	27.2659i	1.12275	+	2.45848i
$124$	−13.8450	−	13.0954i	−1.24332	−	1.17600i
$125$	−11.1240	−	1.12106i	−0.994960	−	0.100271i
$126$	1.49797	−	16.0276i	0.133450	−	1.42785i
$127$	0.0194927	+	0.00280262i	0.00172969	+	0.000248693i	0.143180	−	0.989697i	$-0.454267\pi$
$127$	0.0194927	+	0.00280262i	0.00172969	+	0.000248693i	−0.141450	+	0.989945i	$0.545176\pi$
$128$	2.51248	−	11.0312i	0.222074	−	0.975030i
$129$	8.89188	+	10.2618i	0.782886	+	0.903499i
$130$	−0.787953	−	7.04849i	−0.0691080	−	0.618193i
$131$	6.06187	+	9.43246i	0.529628	+	0.824117i	0.998241	−	0.0592861i	$-0.0188824\pi$
$131$	6.06187	+	9.43246i	0.529628	+	0.824117i	−0.468613	+	0.883404i	$0.655246\pi$
$132$	−0.248259	+	1.31652i	−0.0216082	+	0.114589i
$133$	9.81182	−	11.3234i	0.850793	−	0.981867i
$134$	4.21579	+	12.1020i	0.364189	+	1.04546i
$135$	−9.75179	−	9.94243i	−0.839300	−	0.855708i
$136$	5.54474	+	18.4712i	0.475458	+	1.58390i
$137$			0.530751i			0.0453451i	0.999743	+	0.0226725i	$0.00721751\pi$
$137$			0.530751i			0.0453451i	−0.999743	+	0.0226725i	$0.992782\pi$
$138$	6.10328	−	18.4101i	0.519545	−	1.56718i
$139$			18.2571i			1.54855i	0.632849	+	0.774275i	$0.281885\pi$
$139$			18.2571i			1.54855i	−0.632849	+	0.774275i	$0.718115\pi$
$140$	−1.22241	+	9.75483i	−0.103312	+	0.824434i
$141$	19.4550	+	8.88479i	1.63841	+	0.748235i
$142$	4.51635	+	12.9648i	0.379003	+	1.08798i
$143$	0.397041	+	0.344038i	0.0332023	+	0.0287699i
$144$	−20.6330	−	1.80307i	−1.71941	−	0.150256i
$145$	8.02702	−	1.66496i	0.666608	−	0.138268i
$146$	−4.38128	−	8.45675i	−0.362597	−	0.699885i
$147$	−4.05899	−	4.68433i	−0.334780	−	0.386357i
$148$	9.38391	+	4.79013i	0.771352	+	0.393746i
$149$	−3.17553	−	0.456573i	−0.260150	−	0.0374039i	0.0110057	−	0.999939i	$-0.496497\pi$
$149$	−3.17553	−	0.456573i	−0.260150	−	0.0374039i	−0.271156	+	0.962536i	$0.587406\pi$
$150$	13.6982	+	14.8746i	1.11845	+	1.21451i
$151$	−1.59965	−	1.02803i	−0.130177	−	0.0836599i	0.473931	−	0.880562i	$-0.342834\pi$
$151$	−1.59965	−	1.02803i	−0.130177	−	0.0836599i	−0.604109	+	0.796902i	$0.706471\pi$
$152$	−14.6450	−	12.5363i	−1.18786	−	1.01683i
$153$	32.1148	−	14.6663i	2.59633	−	1.18570i
$154$	−0.423605	−	0.592349i	−0.0341351	−	0.0477328i
$155$	12.9330	−	16.9324i	1.03881	−	1.36004i
$156$	−7.39868	+	10.4788i	−0.592368	+	0.838977i
$157$	−1.17656	+	0.345469i	−0.0938997	+	0.0275714i	−0.328345	−	0.944558i	$-0.606491\pi$
$157$	−1.17656	+	0.345469i	−0.0938997	+	0.0275714i	0.234445	+	0.972129i	$0.424673\pi$
$158$	5.48690	+	2.18385i	0.436514	+	0.173738i
$159$	1.59611	+	11.1012i	0.126580	+	0.880382i
$160$	12.5602	+	1.49715i	0.992971	+	0.118360i
$161$	4.93444	+	9.31665i	0.388888	+	0.734255i
$162$	0.159678	+	3.21614i	0.0125455	+	0.252684i
$163$	0.621719	+	4.32415i	0.0486968	+	0.338694i	0.999576	+	0.0291302i	$0.00927376\pi$
$163$	0.621719	+	4.32415i	0.0486968	+	0.338694i	−0.950879	+	0.309563i	$0.899817\pi$
$164$	−6.77685	+	19.8379i	−0.529183	+	1.54908i
$165$	−1.49294	−	0.121313i	−0.116225	−	0.00944420i
$166$	−13.3744	−	10.4743i	−1.03805	−	0.812965i
$167$	3.04274	−	10.3626i	0.235454	−	0.801884i	−0.753979	−	0.656898i	$-0.771868\pi$
$167$	3.04274	−	10.3626i	0.235454	−	0.801884i	0.989434	−	0.144986i	$-0.0463137\pi$
$168$	13.3675	−	11.7248i	1.03133	−	0.904586i
$169$	−3.31077	−	7.24958i	−0.254675	−	0.557660i
$170$	−19.8855	+	8.33552i	−1.52515	+	0.639305i
$171$	−19.0798	+	29.6888i	−1.45907	+	2.27036i
$172$	−0.413748	+	9.48726i	−0.0315480	+	0.723397i
$173$	−0.698256	+	4.85647i	−0.0530874	+	0.369231i	0.945909	+	0.324433i	$0.105173\pi$
$173$	−0.698256	+	4.85647i	−0.0530874	+	0.369231i	−0.998996	+	0.0447979i	$0.985736\pi$
$174$	−12.8554	−	7.38768i	−0.974565	−	0.560059i
$175$	−10.9895	−	0.212781i	−0.830726	−	0.0160847i
$176$	−0.758841	+	0.549609i	−0.0571998	+	0.0414283i
$177$	7.84336	+	12.2045i	0.589543	+	0.917346i
$178$	2.97755	−	12.3821i	0.223177	−	0.928080i
$179$	6.03225	+	5.22697i	0.450871	+	0.390682i	0.850483	−	0.526002i	$-0.176310\pi$
$179$	6.03225	+	5.22697i	0.450871	+	0.390682i	−0.399612	+	0.916684i	$0.630855\pi$
$180$	−0.419954	−	23.1525i	−0.0313015	−	1.72568i
$181$	3.78958	+	1.73064i	0.281677	+	0.128638i	0.551244	−	0.834344i	$-0.314153\pi$
$181$	3.78958	+	1.73064i	0.281677	+	0.128638i	−0.269567	+	0.962982i	$0.586881\pi$
$182$	−1.33332	−	6.84395i	−0.0988326	−	0.507308i
$183$			31.0991i			2.29891i
$184$	11.9487	−	6.42095i	0.880870	−	0.473359i
$185$	−4.22311	+	10.9963i	−0.310489	+	0.808466i
$186$	−37.8246	+	7.36891i	−2.77344	+	0.540315i
$187$	0.663488	−	1.45284i	0.0485190	−	0.106242i
$188$	5.61507	+	13.8641i	0.409521	+	1.01114i
$189$	−10.3473	−	8.96595i	−0.752652	−	0.652177i
$190$	12.2173	−	17.7561i	0.886338	−	1.28816i
$191$	19.0972	−	12.2730i	1.38182	−	0.888044i	0.382469	−	0.923968i	$-0.375074\pi$
$191$	19.0972	−	12.2730i	1.38182	−	0.888044i	0.999355	+	0.0359245i	$0.0114376\pi$
$192$	−15.1889	−	17.1080i	−1.09616	−	1.23466i
$193$	7.60107	−	6.58637i	0.547137	−	0.474097i	−0.336883	−	0.941547i	$-0.609373\pi$
$193$	7.60107	−	6.58637i	0.547137	−	0.474097i	0.884020	+	0.467450i	$0.154827\pi$
$194$	−0.673184	−	0.386863i	−0.0483318	−	0.0277751i
$195$	−12.5202	−	6.99474i	−0.896592	−	0.500903i
$196$	0.188869	−	4.33078i	0.0134906	−	0.309341i
$197$	16.5458	+	10.6333i	1.17884	+	0.757593i	0.975172	−	0.221448i	$-0.0710783\pi$
$197$	16.5458	+	10.6333i	1.17884	+	0.757593i	0.203665	+	0.979041i	$0.434715\pi$
$198$	1.18617	+	1.23902i	0.0842971	+	0.0880535i
$199$	−4.32030	−	9.46013i	−0.306258	−	0.670611i	0.692448	−	0.721468i	$-0.256532\pi$
$199$	−4.32030	−	9.46013i	−0.306258	−	0.670611i	−0.998706	+	0.0508567i	$0.983805\pi$
$200$	−0.188579	+	14.1409i	−0.0133345	+	0.999911i
$201$	24.8644	+	7.30083i	1.75380	+	0.514961i
$202$	15.0150	−	19.1723i	1.05645	−	1.34896i
$203$	7.73298	−	2.27061i	0.542748	−	0.159365i
$204$	36.9036	+	12.6067i	2.58377	+	0.882646i
$205$	−22.8529	−	5.20353i	−1.59612	−	0.363430i
$206$	11.5422	−	0.573058i	0.804184	−	0.0399269i
$207$	−14.6273	−	20.0671i	−1.01667	−	1.39476i
$208$	−8.79520	+	1.76853i	−0.609837	+	0.122625i
$209$	0.227210	+	1.58028i	0.0157164	+	0.109310i
$210$	14.6070	+	13.4847i	1.00798	+	0.930534i
$211$	0.473400	+	1.61225i	0.0325902	+	0.110992i	0.974182	−	0.225765i	$-0.0724881\pi$
$211$	0.473400	+	1.61225i	0.0325902	+	0.110992i	−0.941592	+	0.336757i	$0.890670\pi$
$212$	−4.52410	+	6.40753i	−0.310717	+	0.440071i
$213$	26.6370	+	7.82133i	1.82514	+	0.535908i
$214$	−11.0101	−	15.3959i	−0.752633	−	1.05244i
$215$	−10.5969	+	0.654874i	−0.722706	+	0.0446621i
$216$	−11.4555	+	13.3824i	−0.779450	+	0.910560i
$217$	11.3246	−	17.6215i	0.768767	−	1.19623i
$218$	−0.998557	+	10.6841i	−0.0676308	+	0.723617i
$219$	−19.0632	−	2.74087i	−1.28817	−	0.185211i
$220$	−0.700253	−	0.779123i	−0.0472110	−	0.0525285i
$221$	11.5573	−	10.0145i	0.777429	−	0.673646i
$222$	18.9166	−	9.80034i	1.26960	−	0.657756i
$223$	7.98264	+	12.4212i	0.534557	+	0.831788i	0.998538	−	0.0540579i	$-0.0172156\pi$
$223$	7.98264	+	12.4212i	0.534557	+	0.831788i	−0.463980	+	0.885845i	$0.653579\pi$
$224$	12.4267	+	0.466947i	0.830296	+	0.0311992i
$225$	25.6925	−	3.18769i	1.71283	−	0.212512i
$226$	2.37722	−	0.828113i	0.158130	−	0.0550853i
$227$	−3.78292	+	8.28343i	−0.251081	+	0.549791i	−0.992641	−	0.121096i	$-0.961359\pi$
$227$	−3.78292	+	8.28343i	−0.251081	+	0.549791i	0.741560	+	0.670887i	$0.234086\pi$
$228$	−37.8459	+	9.34242i	−2.50640	+	0.618717i
$229$		−	5.30847i		−	0.350794i	−0.984498	−	0.175397i	$-0.943879\pi$
$229$		−	5.30847i		−	0.350794i	0.984498	−	0.175397i	$-0.0561208\pi$
$230$	8.54323	+	12.5305i	0.563324	+	0.826236i
$231$	−1.47256			−0.0968876
$232$	−2.98134	−	9.93177i	−0.195735	−	0.652052i
$233$	−0.962779	−	0.439687i	−0.0630738	−	0.0288048i	0.383628	−	0.923488i	$-0.374674\pi$
$233$	−0.962779	−	0.439687i	−0.0630738	−	0.0288048i	−0.446702	+	0.894683i	$0.647402\pi$
$234$	5.40271	+	15.5093i	0.353186	+	1.01387i
$235$	−14.7548	+	7.87230i	−0.962499	+	0.513532i
$236$	−1.88014	+	9.97045i	−0.122387	+	0.649021i
$237$	10.0460	−	6.45615i	0.652555	−	0.419372i
$238$	−18.8217	+	9.75118i	−1.22003	+	0.632075i
$239$	−7.89853	−	9.11539i	−0.510913	−	0.589625i	0.440419	−	0.897792i	$-0.354830\pi$
$239$	−7.89853	−	9.11539i	−0.510913	−	0.589625i	−0.951332	+	0.308167i	$0.900284\pi$
$240$	17.2364	−	18.8981i	1.11261	−	1.21987i
$241$	2.59157	−	18.0247i	0.166937	−	1.16108i	−0.718231	−	0.695805i	$-0.755048\pi$
$241$	2.59157	−	18.0247i	0.166937	−	1.16108i	0.885168	−	0.465271i	$-0.154043\pi$
$242$	−15.4116	−	1.44040i	−0.990694	−	0.0925925i
$243$	−10.2406	−	6.58124i	−0.656935	−	0.422187i
$244$	−14.9458	+	15.8013i	−0.956807	+	1.01157i
$245$	4.83733	−	0.298939i	0.309046	−	0.0190985i
$246$	24.6582	+	34.4809i	1.57215	+	2.19842i
$247$	−4.30668	+	14.6672i	−0.274027	+	0.933251i
$248$	−22.7599	−	14.4339i	−1.44525	−	0.916552i
$249$	−32.9598	+	9.67788i	−2.08874	+	0.613311i
$250$	−15.7446	+	1.45210i	−0.995774	+	0.0918387i
$251$	−4.92314	+	0.707841i	−0.310746	+	0.0446785i	−0.295924	−	0.955212i	$-0.595627\pi$
$251$	−4.92314	+	0.707841i	−0.310746	+	0.0446785i	−0.0148224	+	0.999890i	$0.504718\pi$
$252$	−2.25498	−	22.6533i	−0.142050	−	1.42702i
$253$	−1.09459	−	0.252740i	−0.0688160	−	0.0158897i
$254$	0.0278160	−	0.00138104i	0.00174533	−	8.66539e-5i
$255$	−9.67993	+	42.5124i	−0.606181	+	2.66223i
$256$	0.504451	−	15.9920i	0.0315282	−	0.999503i
$257$	0.174914	+	0.595701i	0.0109108	+	0.0371588i	0.964768	−	0.263100i	$-0.0847450\pi$
$257$	0.174914	+	0.595701i	0.0109108	+	0.0371588i	−0.953858	+	0.300259i	$0.902927\pi$
$258$	15.1181	+	11.8399i	0.941209	+	0.737120i
$259$	−3.26259	+	11.1114i	−0.202728	+	0.690427i
$260$	−2.99989	−	9.57104i	−0.186045	−	0.593570i
$261$	−17.2678	+	7.88592i	−1.06885	+	0.488126i
$262$	10.9654	+	11.4540i	0.677445	+	0.707633i
$263$	−2.36226	+	3.67575i	−0.145663	+	0.226656i	−0.906417	−	0.422384i	$-0.861193\pi$
$263$	−2.36226	+	3.67575i	−0.145663	+	0.226656i	0.760754	+	0.649041i	$0.224830\pi$
$264$	0.0114151	+	1.89462i	0.000702551	+	0.116606i
$265$	−7.65580	−	4.27710i	−0.470292	−	0.262740i
$266$	10.5578	−	18.3717i	0.647337	−	1.12644i
$267$	−16.8639	−	19.4619i	−1.03205	−	1.19105i
$268$	9.12477	+	15.6590i	0.557384	+	0.956524i
$269$	4.42660	+	6.88793i	0.269895	+	0.419964i	0.949573	−	0.313546i	$-0.101517\pi$
$269$	4.42660	+	6.88793i	0.269895	+	0.419964i	−0.679678	+	0.733510i	$0.737881\pi$
$270$	−16.2253	−	11.1641i	−0.987443	−	0.679424i
$271$	3.90750	−	4.50949i	0.237364	−	0.273932i	−0.624553	−	0.780983i	$-0.714719\pi$
$271$	3.90750	−	4.50949i	0.237364	−	0.273932i	0.861916	+	0.507050i	$0.169264\pi$
$272$	12.6919	+	24.1408i	0.769561	+	1.46375i
$273$	−12.8253	−	5.85712i	−0.776223	−	0.354489i
$274$	0.143531	+	0.736744i	0.00867102	+	0.0445083i
$275$	0.783971	−	0.870128i	0.0472752	−	0.0524707i
$276$	3.49341	−	27.2059i	0.210278	−	1.63760i
$277$	3.86566			0.232265			0.116132	−	0.993234i	$-0.462950\pi$
$277$	3.86566			0.232265			0.116132	+	0.993234i	$0.462950\pi$
$278$	4.93728	+	25.3430i	0.296118	+	1.51997i
$279$	−20.4957	+	44.8794i	−1.22705	+	2.68686i
$280$	0.941157	+	13.8714i	0.0562449	+	0.828976i
$281$	0.842814	−	0.972659i	0.0502780	−	0.0580240i	−0.730053	−	0.683390i	$-0.760505\pi$
$281$	0.842814	−	0.972659i	0.0502780	−	0.0580240i	0.780332	+	0.625366i	$0.215050\pi$
$282$	29.4085	+	7.07192i	1.75125	+	0.421127i
$283$	25.9306	−	16.6646i	1.54142	−	0.990607i	0.553990	−	0.832524i	$-0.313105\pi$
$283$	25.9306	−	16.6646i	1.54142	−	0.990607i	0.987426	−	0.158084i	$-0.0505316\pi$
$284$	9.77529	+	16.7753i	0.580057	+	0.995433i
$285$	−14.8347	−	40.9807i	−0.878735	−	2.42749i
$286$	0.644178	+	0.370193i	0.0380910	+	0.0218900i
$287$	−22.8075	−	3.27923i	−1.34629	−	0.193567i
$288$	−29.1286	+	3.07690i	−1.71642	+	0.181308i
$289$	−24.8097	−	15.9442i	−1.45939	−	0.937895i
$290$	10.6922	−	4.48191i	0.627867	−	0.263187i
$291$	−1.42815	+	0.652212i	−0.0837194	+	0.0382334i
$292$	−8.36868	−	10.5541i	−0.489740	−	0.617633i
$293$	−11.8075	−	3.46700i	−0.689803	−	0.202545i	−0.0820002	−	0.996632i	$-0.526131\pi$
$293$	−11.8075	−	3.46700i	−0.689803	−	0.202545i	−0.607803	+	0.794088i	$0.707949\pi$
$294$	−6.90114	−	5.40472i	−0.402483	−	0.315210i
$295$	−11.3065	−	0.918742i	−0.658290	−	0.0534912i
$296$	14.3214	+	4.11157i	0.832412	+	0.238980i
$297$	1.44405	−	0.207622i	0.0837920	−	0.0120475i
$298$	−4.53148	+	0.224983i	−0.262502	+	0.0130329i
$299$	−8.52803	−	6.55496i	−0.493188	−	0.379083i
$300$	23.0372	+	16.9434i	1.33005	+	0.978225i
$301$	−10.3316	+	1.48546i	−0.595505	+	0.0856207i
$302$	−2.49851	−	0.994434i	−0.143773	−	0.0572232i
$303$	−13.8733	−	47.2482i	−0.797002	−	2.71434i
$304$	−23.7191	−	13.4414i	−1.36038	−	0.770914i
$305$	−19.3249	−	14.7605i	−1.10654	−	0.845182i
$306$	40.6129	−	29.0434i	2.32168	−	1.66030i
$307$	−12.0951	−	26.4847i	−0.690306	−	1.51156i	−0.851342	−	0.524612i	$-0.824211\pi$
$307$	−12.0951	−	26.4847i	−0.690306	−	1.51156i	0.161035	−	0.986949i	$-0.448517\pi$
$308$	−0.748202	−	0.707693i	−0.0426328	−	0.0403246i
$309$	12.6339	−	19.6588i	0.718719	−	1.11835i
$310$	13.3735	−	27.0016i	0.759566	−	1.53359i
$311$	3.57587	−	24.8708i	0.202769	−	1.41029i	−0.593249	−	0.805019i	$-0.702155\pi$
$311$	3.57587	−	24.8708i	0.202769	−	1.41029i	0.796019	−	0.605272i	$-0.206936\pi$
$312$	−7.43644	+	16.5466i	−0.421006	+	0.936769i
$313$	−24.1411	+	20.9184i	−1.36453	+	1.18238i	−0.400595	+	0.916255i	$0.631197\pi$
$313$	−24.1411	+	20.9184i	−1.36453	+	1.18238i	−0.963940	+	0.266121i	$0.914258\pi$
$314$	−1.53978	+	0.797728i	−0.0868946	+	0.0450184i
$315$	24.9218	−	5.16928i	1.40419	−	0.291256i
$316$	8.20703	+	1.54761i	0.461682	+	0.0870600i
$317$	8.85957	−	10.2245i	0.497603	−	0.574265i	−0.450278	−	0.892888i	$-0.648675\pi$
$317$	8.85957	−	10.2245i	0.497603	−	0.574265i	0.947881	+	0.318624i	$0.103221\pi$
$318$	5.21768	+	14.9781i	0.292593	+	0.839931i
$319$	−0.356750	+	0.781173i	−0.0199741	+	0.0437373i
$320$	17.8399	−	1.31844i	0.997280	−	0.0737029i
$321$	−38.2739			−2.13624
$322$	9.36908	+	11.5982i	0.522118	+	0.646341i
$323$	46.4727			2.58581
$324$	1.09139	+	4.42120i	0.0606330	+	0.245622i
$325$	10.2889	−	4.46014i	0.570727	−	0.247404i
$326$	2.03240	+	5.83429i	0.112564	+	0.323132i
$327$	16.3987	+	14.2096i	0.906850	+	0.785790i
$328$	−4.04231	+	29.3699i	−0.223199	+	1.62168i
$329$	−13.8312	+	8.88876i	−0.762538	+	0.490053i
$330$	−2.10518	+	0.235339i	−0.115886	+	0.0129550i
$331$	18.9271	−	16.4004i	1.04033	−	0.901449i	0.0450958	−	0.998983i	$-0.485641\pi$
$331$	18.9271	−	16.4004i	1.04033	−	0.901449i	0.995232	+	0.0975333i	$0.0310952\pi$
$332$	−21.3978	−	10.9227i	−1.17435	−	0.599464i
$333$	3.88187	−	26.9990i	0.212725	−	1.47954i
$334$	1.42132	−	15.2074i	0.0777709	−	0.832111i
$335$	−16.3380	+	11.9855i	−0.892640	+	0.654836i
$336$	15.3850	−	19.8903i	0.839318	−	1.08511i
$337$	−2.64158	+	1.20637i	−0.143896	+	0.0657151i	−0.486062	−	0.873925i	$-0.661567\pi$
$337$	−2.64158	+	1.20637i	−0.143896	+	0.0657151i	0.342166	+	0.939640i	$0.388840\pi$
$338$	−6.55624	−	9.16793i	−0.356613	−	0.498670i
$339$	1.43411	−	4.88413i	0.0778902	−	0.265270i
$340$	−25.3492	+	16.9483i	−1.37475	+	0.919151i
$341$	0.628825	+	2.14158i	0.0340528	+	0.115973i
$342$	−18.4563	+	46.3713i	−0.998003	+	2.50747i
$343$	19.9477	−	2.86805i	1.07708	−	0.154860i
$344$	1.99131	+	13.2813i	0.107364	+	0.716081i
$345$	30.6592	+	0.687003i	1.65064	+	0.0369870i
$346$	0.344076	+	6.93018i	0.0184976	+	0.372569i
$347$	−1.45223	−	10.1005i	−0.0779598	−	0.542222i	−0.990949	−	0.134239i	$-0.957141\pi$
$347$	−1.45223	−	10.1005i	−0.0779598	−	0.542222i	0.912989	−	0.407984i	$-0.133768\pi$
$348$	−19.8426	−	6.77848i	−1.06368	−	0.363365i
$349$	−8.56539	−	29.1711i	−0.458495	−	1.56149i	−0.786978	−	0.616981i	$-0.788356\pi$
$349$	−8.56539	−	29.1711i	−0.458495	−	1.56149i	0.328483	−	0.944510i	$-0.393463\pi$
$350$	−15.3122	+	2.67652i	−0.818472	+	0.143066i
$351$	13.4027	+	3.93540i	0.715386	+	0.210056i
$352$	−0.904729	+	0.968134i	−0.0482222	+	0.0516017i
$353$	27.2488	−	12.4441i	1.45031	−	0.662334i	0.474360	−	0.880331i	$-0.342679\pi$
$353$	27.2488	−	12.4441i	1.45031	−	0.662334i	0.975950	+	0.217997i	$0.0699522\pi$
$354$	14.1880	+	14.8202i	0.754081	+	0.787684i
$355$	−17.5028	+	12.8399i	−0.928950	+	0.681473i
$356$	0.784693	−	17.9931i	0.0415887	−	0.953630i
$357$	−6.10022	+	42.4280i	−0.322858	+	2.24553i
$358$	9.78700	+	5.62435i	0.517259	+	0.297256i
$359$	−8.36308	−	9.65151i	−0.441387	−	0.509387i	0.490846	−	0.871246i	$-0.336688\pi$
$359$	−8.36308	−	9.65151i	−0.441387	−	0.509387i	−0.932233	+	0.361859i	$0.882142\pi$
$360$	−6.84407	−	32.0248i	−0.360714	−	1.68785i
$361$	−23.0959	+	14.8428i	−1.21557	+	0.781202i
$362$	5.72840	+	1.37752i	0.301078	+	0.0724008i
$363$	−20.4970	+	23.6548i	−1.07581	+	1.24156i
$364$	−3.70162	−	9.13963i	−0.194018	−	0.479047i
$365$	10.7511	−	10.5449i	0.562736	−	0.551946i
$366$	8.41014	+	43.1692i	0.439605	+	2.25649i
$367$			14.7221i			0.768487i	0.923232	+	0.384243i	$0.125538\pi$
$367$			14.7221i			0.768487i	−0.923232	+	0.384243i	$0.874462\pi$
$368$	14.8498	−	12.1443i	0.774098	−	0.633066i
$369$	54.2734			2.82536
$370$	−2.88844	+	16.4062i	−0.150163	+	0.852920i
$371$	−7.84235	−	3.58148i	−0.407154	−	0.185941i
$372$	−50.5122	+	20.4578i	−2.61894	+	1.06069i
$373$	−20.3864	+	23.5272i	−1.05557	+	1.21819i	−0.0803937	+	0.996763i	$0.525618\pi$
$373$	−20.3864	+	23.5272i	−1.05557	+	1.21819i	−0.975176	+	0.221430i	$0.928928\pi$
$374$	0.528108	−	2.19613i	0.0273078	−	0.113559i
$375$	−16.1311	+	27.6048i	−0.833006	+	1.42551i
$376$	11.5436	+	17.7265i	0.595318	+	0.914175i
$377$	−6.21423	+	5.38466i	−0.320049	+	0.277324i
$378$	−16.7879	−	9.64758i	−0.863475	−	0.496218i
$379$	21.3384	+	3.06800i	1.09608	+	0.157592i	0.666550	−	0.745461i	$-0.267770\pi$
$379$	21.3384	+	3.06800i	1.09608	+	0.157592i	0.429529	+	0.903053i	$0.358680\pi$
$380$	12.1573	−	27.9515i	0.623656	−	1.43388i
$381$	0.0304470	−	0.0473764i	0.00155985	−	0.00242717i
$382$	23.1901	−	22.2008i	1.18651	−	1.13589i
$383$	−12.9203	+	5.90052i	−0.660199	+	0.301503i	−0.717196	−	0.696872i	$-0.754575\pi$
$383$	−12.9203	+	5.90052i	−0.660199	+	0.301503i	0.0569971	+	0.998374i	$0.481847\pi$
$384$	−25.7105	−	19.6403i	−1.31203	−	1.00227i
$385$	0.698917	−	0.915046i	0.0356201	−	0.0466351i
$386$	8.77002	−	11.1982i	0.446382	−	0.569973i
$387$	23.5895	−	6.92651i	1.19912	−	0.352094i
$388$	−1.03908	−	0.354961i	−0.0527512	−	0.0180204i
$389$	−20.4076	+	2.93417i	−1.03471	+	0.148768i	−0.638681	−	0.769471i	$-0.720520\pi$
$389$	−20.4076	+	2.93417i	−1.03471	+	0.148768i	−0.396025	+	0.918240i	$0.629611\pi$
$390$	−19.2711	−	6.32366i	−0.975832	−	0.320211i
$391$	−11.8164	+	30.4905i	−0.597583	+	1.54197i
$392$	−0.909000	−	6.06270i	−0.0459114	−	0.306213i
$393$	31.7377	−	4.56319i	1.60096	−	0.230183i
$394$	25.8430	+	10.2858i	1.30195	+	0.518192i
$395$	−0.756249	+	9.30678i	−0.0380510	+	0.468275i
$396$	1.98161	+	1.39913i	0.0995794	+	0.0703091i
$397$	8.33048	+	2.44605i	0.418095	+	0.122764i	0.484012	−	0.875061i	$-0.339179\pi$
$397$	8.33048	+	2.44605i	0.418095	+	0.122764i	−0.0659172	+	0.997825i	$0.520997\pi$
$398$	−8.55538	−	11.9634i	−0.428842	−	0.599672i
$399$	−17.7993	−	38.9751i	−0.891081	−	1.95120i
$400$	3.56235	+	19.6802i	0.178117	+	0.984009i
$401$	−1.24964	−	0.803095i	−0.0624040	−	0.0401046i	0.509067	−	0.860727i	$-0.329991\pi$
$401$	−1.24964	−	0.803095i	−0.0624040	−	0.0401046i	−0.571471	+	0.820622i	$0.693627\pi$
$402$	36.4890	+	3.41034i	1.81991	+	0.170092i
$403$	−3.04138	+	21.1533i	−0.151502	+	1.05372i
$404$	15.6579	−	30.6739i	0.779008	−	1.52608i
$405$	−4.78742	+	1.73301i	−0.237889	+	0.0861141i
$406$	10.1202	−	5.24310i	0.502259	−	0.260210i
$407$	−0.667131	−	1.03808i	−0.0330685	−	0.0514555i
$408$	54.6358	+	7.51974i	2.70487	+	0.372283i
$409$	−8.68096	+	10.0184i	−0.429246	+	0.495376i	−0.928631	−	0.371004i	$-0.879014\pi$
$409$	−8.68096	+	10.0184i	−0.429246	+	0.495376i	0.499386	+	0.866380i	$0.333559\pi$
$410$	−33.1297	−	1.04299i	−1.63616	−	0.0515095i
$411$	1.38063	+	0.630513i	0.0681014	+	0.0311009i
$412$	15.8670	−	3.91683i	0.781709	−	0.192968i
$413$	−11.1522			−0.548764
$414$	−25.7312	−	23.8997i	−1.26462	−	1.17461i
$415$	9.62980	−	25.0745i	0.472708	−	1.23086i
$416$	−11.7305	+	4.83341i	−0.575135	+	0.236977i
$417$	47.4919	+	21.6888i	2.32569	+	1.06211i
$418$	0.742749	+	2.13217i	0.0363290	+	0.104288i
$419$	1.19039	+	1.03148i	0.0581543	+	0.0503910i	0.683453	−	0.729994i	$-0.260477\pi$
$419$	1.19039	+	1.03148i	0.0581543	+	0.0503910i	−0.625299	+	0.780386i	$0.715023\pi$
$420$	23.9229	+	14.7682i	1.16732	+	0.720615i
$421$	−0.318249	−	0.495205i	−0.0155105	−	0.0241348i	0.833412	−	0.552653i	$-0.186384\pi$
$421$	−0.318249	−	0.495205i	−0.0155105	−	0.0241348i	−0.848922	+	0.528518i	$0.822748\pi$
$422$	1.09314	+	2.10997i	0.0532130	+	0.102712i
$423$	29.2668	−	25.3599i	1.42300	−	1.23304i
$424$	−4.54719	+	10.1178i	−0.220831	+	0.491366i
$425$	−21.8227	−	26.1926i	−1.05856	−	1.27053i
$426$	39.0904	+	3.65347i	1.89393	+	0.177011i
$427$	−20.1114	−	12.9248i	−0.973259	−	0.625476i
$428$	−19.4468	−	18.3939i	−0.939996	−	0.889103i
$429$	1.36661	−	0.624109i	0.0659805	−	0.0301323i
$430$	−14.5327	+	3.77477i	−0.700829	+	0.182036i
$431$	32.0200	+	9.40193i	1.54235	+	0.452875i	0.938804	−	0.344453i	$-0.111936\pi$
$431$	32.0200	+	9.40193i	1.54235	+	0.452875i	0.603547	+	0.797328i	$0.293754\pi$
$432$	−12.2826	+	21.6743i	−0.590946	+	1.04281i
$433$	0.0577843	+	0.196795i	0.00277694	+	0.00945737i	0.960870	−	0.277000i	$-0.0893404\pi$
$433$	0.0577843	+	0.196795i	0.00277694	+	0.00945737i	−0.958093	+	0.286458i	$0.907522\pi$
$434$	10.9546	−	27.5232i	0.525835	−	1.32116i
$435$	5.20478	−	22.8584i	0.249550	−	1.09598i
$436$	1.50318	+	15.1008i	0.0719893	+	0.723196i
$437$	−6.54118	−	32.0259i	−0.312907	−	1.53201i
$438$	−27.2031	+	1.35061i	−1.29982	+	0.0645345i
$439$	0.770987	+	5.36233i	0.0367972	+	0.255930i	0.999913	−	0.0131554i	$-0.00418763\pi$
$439$	0.770987	+	5.36233i	0.0367972	+	0.255930i	−0.963116	+	0.269086i	$0.913279\pi$
$440$	−1.18273	−	0.892145i	−0.0563845	−	0.0425313i
$441$	−10.7682	+	3.16184i	−0.512773	+	0.150564i
$442$	13.3347	−	17.0267i	0.634266	−	0.809877i
$443$	−10.8669	−	3.19082i	−0.516304	−	0.151600i	0.0131922	−	0.999913i	$-0.495801\pi$
$443$	−10.8669	−	3.19082i	−0.516304	−	0.151600i	−0.529496	+	0.848313i	$0.677619\pi$
$444$	23.6082	−	18.7196i	1.12040	−	0.888395i
$445$	20.0976	−	1.24200i	0.952719	−	0.0588765i
$446$	14.4399	+	15.0834i	0.683750	+	0.714219i
$447$	−4.96009	+	7.71805i	−0.234604	+	0.365051i
$448$	17.3760	−	2.71238i	0.820940	−	0.128148i
$449$	−2.91137	+	20.2490i	−0.137396	+	0.955610i	0.798163	+	0.602441i	$0.205805\pi$
$449$	−2.91137	+	20.2490i	−0.137396	+	0.955610i	−0.935559	+	0.353169i	$0.885104\pi$
$450$	34.8022	−	11.3729i	1.64059	−	0.536124i
$451$	1.85556	−	1.60786i	0.0873751	−	0.0757109i
$452$	3.07591	−	1.79239i	0.144679	−	0.0843069i
$453$	−4.57451	+	2.93986i	−0.214929	+	0.138127i
$454$	−3.01104	+	12.5214i	−0.141315	+	0.587658i
$455$	9.72682	−	5.18966i	0.456000	−	0.243295i
$456$	−50.0080	+	23.2030i	−2.34184	+	1.08658i
$457$	−35.0791	−	16.0201i	−1.64093	−	0.749389i	−0.641096	−	0.767460i	$-0.721520\pi$
$457$	−35.0791	−	16.0201i	−1.64093	−	0.749389i	−0.999837	+	0.0180715i	$0.994247\pi$
$458$	−1.43557	−	7.36878i	−0.0670798	−	0.344320i
$459$		−	42.4664i		−	1.98216i
$460$	15.2476	+	15.0834i	0.710924	+	0.703269i
$461$		−	13.4819i		−	0.627915i	−0.949437	−	0.313957i	$-0.898345\pi$
$461$		−	13.4819i		−	0.627915i	0.949437	−	0.313957i	$-0.101655\pi$
$462$	−2.04409	+	0.398225i	−0.0950997	+	0.0185271i
$463$	14.1330	+	6.45430i	0.656814	+	0.299957i	0.715804	−	0.698302i	$-0.246061\pi$
$463$	14.1330	+	6.45430i	0.656814	+	0.299957i	−0.0589896	+	0.998259i	$0.518788\pi$
$464$	−6.82430	−	12.9802i	−0.316810	−	0.602591i
$465$	−28.6818	−	53.7574i	−1.33009	−	2.49294i
$466$	−1.45535	−	0.349972i	−0.0674180	−	0.0162121i
$467$	5.02832	−	3.23151i	0.232683	−	0.149536i	−0.419104	−	0.907938i	$-0.637656\pi$
$467$	5.02832	−	3.23151i	0.232683	−	0.149536i	0.651787	+	0.758402i	$0.274019\pi$
$468$	11.6938	+	20.0676i	0.540544	+	0.927625i
$469$	−15.0550	+	13.0452i	−0.695175	+	0.602373i
$470$	−18.3525	+	14.9178i	−0.846538	+	0.688108i
$471$	−0.499049	+	3.47096i	−0.0229950	+	0.159934i
$472$	0.0864502	+	14.3486i	0.00397919	+	0.660447i
$473$	0.601308	−	0.935654i	0.0276482	−	0.0430214i
$474$	12.1990	−	11.6786i	0.560320	−	0.536416i
$475$	32.5062	+	10.2323i	1.49149	+	0.469488i
$476$	−23.4898	+	18.6257i	−1.07665	+	0.853709i
$477$	19.4844	+	5.72114i	0.892130	+	0.261953i
$478$	−13.4291	−	10.5172i	−0.614235	−	0.481046i
$479$	25.6679	−	7.53677i	1.17279	−	0.344364i	0.363403	−	0.931632i	$-0.381615\pi$
$479$	25.6679	−	7.53677i	1.17279	−	0.344364i	0.809392	+	0.587269i	$0.199797\pi$
$480$	18.8156	−	30.8940i	0.858809	−	1.41011i
$481$	−1.68144	−	11.6946i	−0.0766669	−	0.533230i
$482$	−1.27703	−	25.7213i	−0.0581673	−	1.17157i
$483$	30.0971	−	1.76800i	1.36947	−	0.0804469i
$484$	−21.7826	+	2.16831i	−0.990118	+	0.0985596i
$485$	0.272553	−	1.19700i	0.0123760	−	0.0543531i
$486$	−15.9949	−	6.36616i	−0.725544	−	0.288775i
$487$	1.23376	+	4.20181i	0.0559071	+	0.190402i	0.982712	−	0.185141i	$-0.0592743\pi$
$487$	1.23376	+	4.20181i	0.0559071	+	0.190402i	−0.926805	+	0.375543i	$0.877456\pi$
$488$	−16.4734	+	25.9758i	−0.745715	+	1.17587i
$489$	11.9869	+	3.51967i	0.542066	+	0.159165i
$490$	6.63394	−	1.72312i	0.299691	−	0.0778427i
$491$	−21.5019	+	9.81960i	−0.970369	+	0.443153i	−0.836572	−	0.547856i	$-0.815444\pi$
$491$	−21.5019	+	9.81960i	−0.970369	+	0.443153i	−0.133796	+	0.991009i	$0.542717\pi$
$492$	43.5532	+	41.1951i	1.96353	+	1.85722i
$493$	21.0295	+	13.5149i	0.947122	+	0.608678i
$494$	−2.01172	+	21.5244i	−0.0905116	+	0.968430i
$495$	−1.32275	+	2.36765i	−0.0594530	+	0.106418i
$496$	−35.4967	−	13.8809i	−1.59385	−	0.623273i
$497$	−16.1283	+	13.9753i	−0.723453	+	0.626876i
$498$	−43.1349	+	22.3473i	−1.93292	+	1.00141i
$499$	−1.64348	−	2.55731i	−0.0735724	−	0.114481i	0.802518	−	0.596628i	$-0.203493\pi$
$499$	−1.64348	−	2.55731i	−0.0735724	−	0.114481i	−0.876090	+	0.482147i	$0.839857\pi$
$500$	−21.4626	+	6.27348i	−0.959837	+	0.280559i
$501$	−23.3414	−	20.2254i	−1.04282	−	0.903606i
$502$	−6.64247	+	2.31393i	−0.296468	+	0.103276i
$503$	−7.86686	−	3.59267i	−0.350766	−	0.160189i	0.232238	−	0.972659i	$-0.425395\pi$
$503$	−7.86686	−	3.59267i	−0.350766	−	0.160189i	−0.583003	+	0.812470i	$0.698123\pi$
$504$	−9.25630	−	30.8356i	−0.412308	−	1.37353i
$505$	35.9445	+	13.8044i	1.59951	+	0.614288i
$506$	−1.58776	−	0.0548244i	−0.0705846	−	0.00243724i
$507$	−22.7913			−1.01219
$508$	0.0382384	−	0.00943932i	0.00169655	−	0.000418802i
$509$	34.7155	+	15.8540i	1.53874	+	0.702718i	0.990991	−	0.133927i	$-0.0427586\pi$
$509$	34.7155	+	15.8540i	1.53874	+	0.702718i	0.547746	+	0.836645i	$0.315486\pi$
$510$	−1.94023	+	61.6300i	−0.0859149	+	2.72902i
$511$	9.69516	−	11.1888i	0.428889	−	0.494964i
$512$	−3.62449	−	22.3352i	−0.160181	−	0.987088i
$513$	22.9499	+	35.7107i	1.01326	+	1.57667i
$514$	0.403896	+	0.779600i	0.0178151	+	0.0343867i
$515$	6.21950	+	17.1812i	0.274064	+	0.757096i
$516$	24.1875	+	12.3468i	1.06479	+	0.543537i
$517$	0.249321	−	1.73407i	0.0109651	−	0.0762642i
$518$	−1.52401	+	16.3062i	−0.0669612	+	0.716452i
$519$	11.8035	+	7.58567i	0.518118	+	0.332974i
$520$	−6.75250	−	12.4745i	−0.296117	−	0.547041i
$521$	−3.06425	−	6.70978i	−0.134247	−	0.293961i	0.830555	−	0.556936i	$-0.188023\pi$
$521$	−3.06425	−	6.70978i	−0.134247	−	0.293961i	−0.964802	+	0.262976i	$0.915296\pi$
$522$	−21.8371	+	15.6163i	−0.955783	+	0.683507i
$523$	−37.4289	−	10.9901i	−1.63665	−	0.480564i	−0.671226	−	0.741252i	$-0.734232\pi$
$523$	−37.4289	−	10.9901i	−1.63665	−	0.480564i	−0.965423	+	0.260689i	$0.916050\pi$
$524$	18.3188	+	12.9342i	0.800259	+	0.565032i
$525$	−13.6086	+	28.3339i	−0.593928	+	1.23659i
$526$	−2.28506	+	5.74120i	−0.0996334	+	0.250328i
$527$	64.3088	−	9.24621i	2.80134	−	0.402771i
$528$	0.528208	+	2.62687i	0.0229873	+	0.114320i
$529$	22.6752	+	3.85147i	0.985880	+	0.167455i
$530$	−11.7838	−	3.86676i	−0.511856	−	0.167961i
$531$	26.0006	−	3.73832i	1.12833	−	0.162229i
$532$	9.68714	−	28.3572i	0.419991	−	1.22944i
$533$	22.5563	−	6.62312i	0.977021	−	0.286879i
$534$	−28.6721	−	22.4550i	−1.24076	−	0.971721i
$535$	18.1658	−	23.7833i	0.785377	−	1.02824i
$536$	16.9009	+	19.2689i	0.730008	+	0.832288i
$537$	20.7629	−	9.48210i	0.895985	−	0.409183i
$538$	8.00734	+	8.36416i	0.345221	+	0.360605i
$539$	−0.274487	+	0.427111i	−0.0118230	+	0.0183970i
$540$	−25.5418	−	11.1092i	−1.09914	−	0.478065i
$541$	−25.2039	−	3.62377i	−1.08360	−	0.155798i	−0.422698	−	0.906270i	$-0.638917\pi$
$541$	−25.2039	−	3.62377i	−1.08360	−	0.155798i	−0.660902	+	0.750472i	$0.729826\pi$
$542$	4.20456	−	7.31641i	0.180601	−	0.314267i
$543$	9.00377	−	7.80181i	0.386389	−	0.334808i
$544$	24.1463	+	30.0779i	1.03526	+	1.28958i
$545$	−16.6130	+	3.44587i	−0.711624	+	0.147605i
$546$	−19.3870	−	4.66202i	−0.829685	−	0.199516i
$547$	−24.0241	+	27.7252i	−1.02719	+	1.18545i	−0.0447294	+	0.998999i	$0.514243\pi$
$547$	−24.0241	+	27.7252i	−1.02719	+	1.18545i	−0.982465	+	0.186446i	$0.940303\pi$
$548$	0.398475	+	0.983871i	0.0170220	+	0.0420289i
$549$	51.2209	+	23.3918i	2.18605	+	0.998337i
$550$	0.852934	−	1.41985i	0.0363692	−	0.0605425i
$551$	−24.9878			−1.06452
$552$	−2.50805	−	38.7097i	−0.106750	−	1.64760i
$553$			9.17977i			0.390364i
$554$	5.36599	−	1.04539i	0.227979	−	0.0444144i
$555$	23.5876	+	24.0487i	1.00124	+	1.02081i
$556$	13.7070	+	33.8439i	0.581308	+	1.43530i
$557$	29.1743	−	33.6689i	1.23615	−	1.42660i	0.368351	−	0.929687i	$-0.379922\pi$
$557$	29.1743	−	33.6689i	1.23615	−	1.42660i	0.867802	−	0.496910i	$-0.165532\pi$
$558$	−16.3137	+	67.8405i	−0.690616	+	2.87192i
$559$	8.95866	−	5.75738i	0.378911	−	0.243511i
$560$	5.05768	+	19.0006i	0.213726	+	0.802923i
$561$	−2.99103	−	3.45183i	−0.126281	−	0.145736i
$562$	0.906887	−	1.57809i	0.0382547	−	0.0665675i
$563$	−2.87844	+	20.0200i	−0.121312	+	0.843743i	0.834761	+	0.550613i	$0.185606\pi$
$563$	−2.87844	+	20.0200i	−0.121312	+	0.843743i	−0.956073	+	0.293130i	$0.905303\pi$
$564$	42.7349	+	1.86371i	1.79946	+	0.0784762i
$565$	2.35432	+	3.20929i	0.0990469	+	0.135016i
$566$	31.4881	−	30.1448i	1.32354	−	1.26708i
$567$	−4.55312	+	2.07934i	−0.191213	+	0.0873241i
$568$	18.1058	+	20.6426i	0.759703	+	0.866144i
$569$	28.5455	+	8.38171i	1.19669	+	0.351379i	0.818586	−	0.574384i	$-0.194758\pi$
$569$	28.5455	+	8.38171i	1.19669	+	0.351379i	0.378103	+	0.925764i	$0.376577\pi$
$570$	−31.6748	−	52.8742i	−1.32671	−	2.21466i
$571$	−9.73454	−	33.1528i	−0.407378	−	1.38740i	−0.866566	−	0.499062i	$-0.833678\pi$
$571$	−9.73454	−	33.1528i	−0.407378	−	1.38740i	0.459188	−	0.888339i	$-0.348140\pi$
$572$	0.994305	+	0.339666i	0.0415740	+	0.0142022i
$573$	−9.23875	−	64.2569i	−0.385954	−	2.68437i
$574$	−32.5463	+	1.61589i	−1.35846	+	0.0674459i
$575$	−14.9786	+	18.7255i	−0.624649	+	0.780905i
$576$	−39.6018	+	12.1483i	−1.65007	+	0.506181i
$577$	−23.5129	+	3.38065i	−0.978856	+	0.140738i	−0.613128	−	0.789983i	$-0.710089\pi$
$577$	−23.5129	+	3.38065i	−0.978856	+	0.140738i	−0.365728	+	0.930722i	$0.619180\pi$
$578$	−38.7505	−	15.4232i	−1.61181	−	0.641519i
$579$	−8.10317	−	27.5969i	−0.336756	−	1.14689i
$580$	13.6300	−	9.11290i	0.565953	−	0.378393i
$581$	7.43956	−	25.3368i	0.308645	−	1.05115i
$582$	−1.80606	+	1.29156i	−0.0748634	+	0.0535369i
$583$	0.835646	−	0.381627i	0.0346089	−	0.0158054i
$584$	−14.4709	−	12.3872i	−0.598808	−	0.512586i
$585$	−20.9378	+	15.3598i	−0.865671	+	0.635051i
$586$	−17.3278	−	1.61950i	−0.715805	−	0.0669007i
$587$	1.96337	−	13.6556i	0.0810371	−	0.563626i	−0.908338	−	0.418238i	$-0.862648\pi$
$587$	1.96337	−	13.6556i	0.0810371	−	0.563626i	0.989375	−	0.145388i	$-0.0464430\pi$
$588$	−11.0412	−	5.63611i	−0.455331	−	0.232429i
$589$	−49.0815	+	42.5294i	−2.02237	+	1.75239i
$590$	−15.9432	+	1.78229i	−0.656371	+	0.0733759i
$591$	47.3160	−	30.4081i	1.94632	−	1.25082i
$592$	20.9916	+	1.83441i	0.862749	+	0.0753939i
$593$	−24.1448	−	20.9216i	−0.991508	−	0.859147i	−0.00147754	−	0.999999i	$-0.500470\pi$
$593$	−24.1448	−	20.9216i	−0.991508	−	0.859147i	−0.990031	+	0.140852i	$0.955016\pi$
$594$	1.94836	−	0.678717i	0.0799420	−	0.0278481i
$595$	−23.4693	−	23.9281i	−0.962146	−	0.980956i
$596$	−6.22939	+	1.53775i	−0.255166	+	0.0629888i
$597$	−29.7408			−1.21721
$598$	−13.6106	−	6.79281i	−0.556577	−	0.277779i
$599$	9.23980			0.377528			0.188764	−	0.982022i	$-0.439552\pi$
$599$	9.23980			0.377528			0.188764	+	0.982022i	$0.439552\pi$
$600$	36.5603	+	17.2894i	1.49257	+	0.705837i
$601$	−6.86960	+	15.0423i	−0.280217	+	0.613589i	−0.996442	−	0.0842800i	$-0.973141\pi$
$601$	−6.86960	+	15.0423i	−0.280217	+	0.613589i	0.716225	+	0.697869i	$0.245868\pi$
$602$	−13.9398	+	4.85598i	−0.568143	+	0.197915i
$603$	30.7268	−	35.4606i	1.25129	−	1.44407i
$604$	−3.73714	−	0.704719i	−0.152062	−	0.0286746i
$605$	−4.97060	−	23.9640i	−0.202084	−	0.974275i
$606$	−32.0351	−	61.8343i	−1.30134	−	2.51185i
$607$	−13.6419	+	11.8207i	−0.553706	+	0.479789i	−0.886191	−	0.463319i	$-0.846658\pi$
$607$	−13.6419	+	11.8207i	−0.553706	+	0.479789i	0.332485	+	0.943108i	$0.392113\pi$
$608$	−36.5599	−	12.2438i	−1.48270	−	0.496552i
$609$	3.28002	−	22.8130i	0.132913	−	0.924430i
$610$	−30.8169	−	15.2632i	−1.24774	−	0.617990i
$611$	9.06872	−	14.1112i	0.366881	−	0.570878i
$612$	48.5212	−	51.2986i	1.96135	−	2.07362i
$613$	−4.79241	−	10.4939i	−0.193563	−	0.423845i	0.787819	−	0.615906i	$-0.211210\pi$
$613$	−4.79241	−	10.4939i	−0.193563	−	0.423845i	−0.981383	+	0.192061i	$0.938483\pi$
$614$	−23.9517	−	33.4929i	−0.966613	−	1.35166i
$615$	−40.6843	+	53.2652i	−1.64055	+	2.14786i
$616$	−1.22997	−	0.780025i	−0.0495570	−	0.0314281i
$617$	−3.90726	−	13.3069i	−0.157301	−	0.535716i	0.842696	−	0.538390i	$-0.180967\pi$
$617$	−3.90726	−	13.3069i	−0.157301	−	0.535716i	−0.999996	+	0.00267349i	$0.999149\pi$
$618$	12.2210	−	30.7053i	0.491602	−	1.23515i
$619$	−6.69032	+	0.961923i	−0.268907	+	0.0386630i	−0.275449	−	0.961316i	$-0.588827\pi$
$619$	−6.69032	+	0.961923i	−0.268907	+	0.0386630i	0.00654235	+	0.999979i	$0.497917\pi$
$620$	11.2620	−	41.0979i	0.452293	−	1.65053i
$621$	−29.2650	+	5.97727i	−1.17436	+	0.239860i
$622$	−1.76207	−	35.4905i	−0.0706524	−	1.42304i
$623$	19.5944	−	2.81725i	0.785034	−	0.112871i
$624$	−5.84794	+	24.9797i	−0.234105	+	0.999989i
$625$	−9.49730	−	23.1258i	−0.379892	−	0.925031i
$626$	−27.8537	+	35.5656i	−1.11326	+	1.42149i
$627$	4.38066	+	1.28628i	0.174947	+	0.0513690i
$628$	−1.92166	+	1.52374i	−0.0766826	+	0.0608039i
$629$	−32.6730	+	14.9213i	−1.30276	+	0.594950i
$630$	33.1965	−	13.9152i	1.32258	−	0.554394i
$631$	5.46792	+	3.51402i	0.217674	+	0.139891i	0.644934	−	0.764238i	$-0.276885\pi$
$631$	5.46792	+	3.51402i	0.217674	+	0.139891i	−0.427260	+	0.904129i	$0.640521\pi$
$632$	11.8108	−	0.0711602i	0.469810	−	0.00283060i
$633$	4.75630	+	0.683852i	0.189046	+	0.0271807i
$634$	9.53311	−	16.5887i	0.378608	−	0.658821i
$635$	0.0149886	+	0.0414057i	0.000594805	+	0.00164314i
$636$	11.2933	+	19.3804i	0.447808	+	0.768481i
$637$	−4.08948	+	2.62815i	−0.162031	+	0.104131i
$638$	−0.283958	+	1.18083i	−0.0112420	+	0.0467497i
$639$	32.9174	−	37.9887i	1.30219	−	1.50281i
$640$	24.4073	−	6.65459i	0.964783	−	0.263046i
$641$	−15.5403	+	34.0284i	−0.613804	+	1.34404i	0.306138	+	0.951987i	$0.400963\pi$
$641$	−15.5403	+	34.0284i	−0.613804	+	1.34404i	−0.919942	+	0.392055i	$0.871764\pi$
$642$	−53.1287	+	10.3504i	−2.09682	+	0.408498i
$643$	−27.6873			−1.09188			−0.545941	−	0.837824i	$-0.683828\pi$
$643$	−27.6873			−1.09188			−0.545941	+	0.837824i	$0.683828\pi$
$644$	16.1419	+	13.5659i	0.636079	+	0.534573i
$645$	−10.8853	+	28.3436i	−0.428607	+	1.11603i
$646$	64.5096	−	12.5676i	2.53810	−	0.494467i
$647$	16.4307	+	7.50365i	0.645957	+	0.294999i	0.711326	−	0.702862i	$-0.248095\pi$
$647$	16.4307	+	7.50365i	0.645957	+	0.294999i	−0.0653686	+	0.997861i	$0.520822\pi$
$648$	2.71061	+	5.84199i	0.106483	+	0.229495i
$649$	0.778191	−	0.898080i	0.0305467	−	0.0352527i
$650$	13.0761	−	8.97364i	0.512886	−	0.351975i
$651$	−32.3851	−	50.3923i	−1.26927	−	1.97503i
$652$	4.39897	+	7.54906i	0.172277	+	0.295644i
$653$	25.7697	+	29.7398i	1.00845	+	1.16381i	0.986452	+	0.164051i	$0.0524562\pi$
$653$	25.7697	+	29.7398i	1.00845	+	1.16381i	0.0219945	+	0.999758i	$0.492998\pi$
$654$	26.6060	+	15.2898i	1.04038	+	0.597879i
$655$	−12.2280	+	21.8875i	−0.477788	+	0.855216i
$656$	2.33132	+	41.8621i	0.0910229	+	1.63444i
$657$	−18.8530	+	29.3358i	−0.735525	+	1.14450i
$658$	−16.7955	+	16.0790i	−0.654757	+	0.626825i
$659$	−3.24367	+	1.48133i	−0.126355	+	0.0577046i	−0.477590	−	0.878583i	$-0.658489\pi$
$659$	−3.24367	+	1.48133i	−0.126355	+	0.0577046i	0.351234	+	0.936288i	$0.385762\pi$
$660$	−2.85859	+	0.895981i	−0.111270	+	0.0348760i
$661$	−3.71529	+	12.6531i	−0.144508	+	0.492149i	−0.999656	−	0.0262355i	$-0.991648\pi$
$661$	−3.71529	+	12.6531i	−0.144508	+	0.492149i	0.855148	+	0.518384i	$0.173466\pi$
$662$	21.8379	−	27.8842i	0.848753	−	1.08375i
$663$	−12.3207	−	41.9606i	−0.478498	−	1.62961i
$664$	−32.6564	−	9.37545i	−1.26732	−	0.363838i
$665$	32.6670	+	7.43816i	1.26677	+	0.288440i
$666$	−1.91285	−	38.5276i	−0.0741215	−	1.49291i
$667$	6.35356	−	16.3944i	0.246011	−	0.634794i
$668$	−2.13958	−	21.4940i	−0.0827829	−	0.831627i
$669$	41.7942	−	6.00909i	1.61586	−	0.232325i
$670$	−19.4378	+	21.0555i	−0.750948	+	0.813445i
$671$	2.44418	−	0.717677i	0.0943567	−	0.0277056i
$672$	15.9772	−	31.7707i	0.616332	−	1.22558i
$673$	−6.07206	+	20.6795i	−0.234061	+	0.797137i	0.755764	+	0.654844i	$0.227266\pi$
$673$	−6.07206	+	20.6795i	−0.234061	+	0.797137i	−0.989825	+	0.142293i	$0.954552\pi$
$674$	−3.34058	+	2.38894i	−0.128674	+	0.0920186i
$675$	9.35014	−	29.7039i	0.359887	−	1.14330i
$676$	−11.5801	−	10.9532i	−0.445389	−	0.421275i
$677$	19.2967	+	12.4013i	0.741634	+	0.476619i	0.856102	−	0.516808i	$-0.172880\pi$
$677$	19.2967	+	12.4013i	0.741634	+	0.476619i	−0.114467	+	0.993427i	$0.536516\pi$
$678$	0.669897	−	7.16757i	0.0257272	−	0.275269i
$679$	0.171761	−	1.19462i	0.00659158	−	0.0458455i
$680$	−30.6043	+	30.3814i	−1.17362	+	1.16507i
$681$	17.0535	+	19.6808i	0.653493	+	0.754171i
$682$	1.45203	+	2.80271i	0.0556011	+	0.107321i
$683$	15.0210	−	9.65342i	0.574763	−	0.369378i	−0.220735	−	0.975334i	$-0.570846\pi$
$683$	15.0210	−	9.65342i	0.574763	−	0.369378i	0.795498	+	0.605956i	$0.207209\pi$
$684$	−13.0793	+	69.3599i	−0.500100	+	2.65204i
$685$	−1.04708	+	0.558661i	−0.0400069	+	0.0213453i
$686$	26.9142	−	9.37565i	1.02759	−	0.357964i
$687$	−13.8088	−	6.30627i	−0.526839	−	0.240599i
$688$	6.35584	+	17.8975i	0.242314	+	0.682336i
$689$	8.79599			0.335101
$690$	42.7443	−	7.33753i	1.62725	−	0.279335i
$691$		−	21.2892i		−	0.809880i	−0.914343	−	0.404940i	$-0.867292\pi$
$691$		−	21.2892i		−	0.809880i	0.914343	−	0.404940i	$-0.132708\pi$
$692$	2.35175	+	9.52685i	0.0894000	+	0.362157i
$693$	−1.10762	+	2.42534i	−0.0420748	+	0.0921311i
$694$	−4.74734	−	13.6279i	−0.180206	−	0.517309i
$695$	−36.0182	+	19.2172i	−1.36625	+	0.728950i
$696$	−29.3770	−	4.04328i	−1.11353	−	0.153260i
$697$	−38.6392	−	60.1237i	−1.46356	−	2.27735i
$698$	−19.7785	−	38.1765i	−0.748627	−	1.44500i
$699$	−2.28749	+	1.98212i	−0.0865209	+	0.0749708i
$700$	−20.5313	+	7.85620i	−0.776011	+	0.296937i
$701$	−1.71520	−	0.246608i	−0.0647821	−	0.00931426i	0.109848	−	0.993948i	$-0.464964\pi$
$701$	−1.71520	−	0.246608i	−0.0647821	−	0.00931426i	−0.174630	+	0.984634i	$0.555873\pi$
$702$	19.6688	+	1.83829i	0.742352	+	0.0693818i
$703$	19.4115	−	30.2049i	0.732118	−	1.13920i
$704$	−0.994057	+	1.58855i	−0.0374649	+	0.0598707i
$705$	2.94985	+	47.7334i	0.111098	+	1.79774i
$706$	34.4593	−	24.6428i	1.29689	−	0.927444i
$707$	36.3206	+	10.6647i	1.36598	+	0.401087i
$708$	23.7024	+	16.7353i	0.890789	+	0.628951i
$709$	14.9525	+	50.9235i	0.561552	+	1.91247i	0.359770	+	0.933041i	$0.382855\pi$
$709$	14.9525	+	50.9235i	0.561552	+	1.91247i	0.201783	+	0.979430i	$0.435327\pi$
$710$	−20.8236	+	22.5566i	−0.781495	+	0.846534i
$711$	−3.07714	−	21.4020i	−0.115402	−	0.802637i
$712$	−3.77662	−	25.1887i	−0.141535	−	0.943985i
$713$	−15.4235	−	43.0159i	−0.577616	−	1.61096i
$714$	3.00598	+	60.5446i	0.112496	+	2.26583i
$715$	−0.260809	+	1.14542i	−0.00975371	+	0.0428365i
$716$	15.1065	+	5.16055i	0.564556	+	0.192859i
$717$	−33.0948	+	9.71751i	−1.23595	+	0.362907i
$718$	−14.2190	−	11.1358i	−0.530648	−	0.415584i
$719$	−14.5531	−	4.27317i	−0.542738	−	0.159362i	−0.00113906	−	0.999999i	$-0.500363\pi$
$719$	−14.5531	−	4.27317i	−0.542738	−	0.159362i	−0.541599	+	0.840637i	$0.682181\pi$
$720$	−18.1608	−	42.6033i	−0.676814	−	1.58773i
$721$	7.46241	+	16.3404i	0.277915	+	0.608548i
$722$	−28.0459	+	26.8494i	−1.04376	+	0.999232i
$723$	−43.8087	−	28.1541i	−1.62926	−	1.04706i
$724$	8.32421	+	0.363026i	0.309367	+	0.0134918i
$725$	11.7338	+	14.0834i	0.435783	+	0.523046i
$726$	−22.0553	+	38.3787i	−0.818548	+	1.42437i
$727$	−16.3805	+	14.1938i	−0.607519	+	0.526418i	−0.903396	−	0.428808i	$-0.858934\pi$
$727$	−16.3805	+	14.1938i	−0.607519	+	0.526418i	0.295877	+	0.955226i	$0.404388\pi$
$728$	−7.60991	−	11.6858i	−0.282042	−	0.433106i
$729$	−35.0316	+	22.5134i	−1.29747	+	0.833831i
$730$	12.0721	−	17.5450i	0.446807	−	0.649368i
$731$	−24.4674	−	21.2011i	−0.904959	−	0.784151i
$732$	23.3485	+	57.6496i	0.862986	+	2.13079i
$733$	−12.9170	+	28.2843i	−0.477101	+	1.04471i	0.506149	+	0.862446i	$0.331069\pi$
$733$	−12.9170	+	28.2843i	−0.477101	+	1.04471i	−0.983250	+	0.182260i	$0.941659\pi$
$734$	3.98129	+	20.4360i	0.146952	+	0.754306i
$735$	4.96895	−	12.9384i	0.183282	−	0.477239i
$736$	17.3290	−	20.8735i	0.638756	−	0.769409i
$737$		−	2.12265i		−	0.0781890i
$738$	75.3378	−	14.6771i	2.77322	−	0.540273i
$739$	28.4237	+	12.9807i	1.04558	+	0.477502i	0.862744	−	0.505640i	$-0.168744\pi$
$739$	28.4237	+	12.9807i	1.04558	+	0.477502i	0.182840	+	0.983143i	$0.441471\pi$
$740$	0.427253	+	23.5549i	0.0157061	+	0.865895i
$741$	33.0373	+	28.6269i	1.21365	+	1.05164i
$742$	−11.8546	−	2.85071i	−0.435197	−	0.104653i
$743$	−12.3547	−	19.2242i	−0.453248	−	0.705268i	0.537154	−	0.843484i	$-0.319500\pi$
$743$	−12.3547	−	19.2242i	−0.453248	−	0.705268i	−0.990402	+	0.138216i	$0.955863\pi$
$744$	−64.5844	+	42.0579i	−2.36778	+	1.54192i
$745$	−2.44178	−	6.74538i	−0.0894600	−	0.247131i
$746$	−21.9363	+	38.1716i	−0.803145	+	1.39756i
$747$	−8.85169	+	61.5648i	−0.323866	+	2.25254i
$748$	0.139176	−	3.19130i	0.00508877	−	0.116686i
$749$	15.9067	−	24.7513i	0.581217	−	0.904391i
$750$	−14.9267	+	42.6810i	−0.545045	+	1.55849i
$751$	−15.8441	−	34.6937i	−0.578158	−	1.26599i	−0.942338	−	0.334661i	$-0.891378\pi$
$751$	−15.8441	−	34.6937i	−0.578158	−	1.26599i	0.364180	−	0.931329i	$-0.381349\pi$
$752$	20.8177	+	21.4847i	0.759143	+	0.783467i
$753$	−4.00722	+	13.6473i	−0.146031	+	0.497337i
$754$	−7.16990	+	9.15505i	−0.261112	+	0.333407i
$755$	0.344365	−	4.23792i	0.0125327	−	0.154234i
$756$	−25.9125	−	8.85202i	−0.942429	−	0.321945i
$757$	−0.653855	−	4.54766i	−0.0237648	−	0.165288i	0.974483	−	0.224462i	$-0.0720624\pi$
$757$	−0.653855	−	4.54766i	−0.0237648	−	0.165288i	−0.998248	+	0.0591742i	$0.981153\pi$
$758$	30.4498	−	1.51180i	1.10599	−	0.0549111i
$759$	−1.95778	+	2.54707i	−0.0710627	+	0.0924529i
$760$	9.31683	−	42.0876i	0.337957	−	1.52668i
$761$	−3.34561	−	23.2692i	−0.121278	−	0.843509i	−0.956111	−	0.293005i	$-0.905345\pi$
$761$	−3.34561	−	23.2692i	−0.121278	−	0.843509i	0.834833	−	0.550504i	$-0.185564\pi$
$762$	0.0294520	−	0.0739978i	0.00106693	−	0.00268066i
$763$	−16.0044	+	4.69933i	−0.579400	+	0.170127i
$764$	26.1868	−	37.0886i	0.947406	−	1.34182i
$765$	62.7378	+	47.9195i	2.26829	+	1.73253i
$766$	−16.3393	+	11.6847i	−0.590362	+	0.422184i
$767$	10.3498	−	4.72658i	0.373708	−	0.170667i
$768$	−41.0005	−	20.3102i	−1.47948	−	0.732881i
$769$	28.1764	+	18.1079i	1.01607	+	0.652986i	0.938956	−	0.344037i	$-0.111794\pi$
$769$	28.1764	+	18.1079i	1.01607	+	0.652986i	0.0771097	+	0.997023i	$0.475431\pi$
$770$	0.722723	−	1.45920i	0.0260451	−	0.0525859i
$771$	1.75737	+	0.252672i	0.0632903	+	0.00909977i
$772$	9.14548	−	17.9161i	0.329153	−	0.644814i
$773$	2.76563	+	3.19171i	0.0994727	+	0.114798i	0.803303	−	0.595570i	$-0.203074\pi$
$773$	2.76563	+	3.19171i	0.0994727	+	0.114798i	−0.703830	+	0.710368i	$0.748528\pi$
$774$	30.8719	−	15.9941i	1.10967	−	0.574896i
$775$	47.0178	+	7.69192i	1.68893	+	0.276302i
$776$	−1.53835	−	0.211730i	−0.0552237	−	0.00760066i
$777$	25.0279	+	21.6868i	0.897871	+	0.778010i
$778$	−27.5346	+	9.59180i	−0.987165	+	0.343883i
$779$	64.9847	+	29.6775i	2.32832	+	1.06331i
$780$	−28.4607	−	3.56649i	−1.01906	−	0.127701i
$781$		−	2.27398i		−	0.0813695i
$782$	−8.15705	+	45.5199i	−0.291696	+	1.62779i
$783$			22.8337i			0.816009i
$784$	−2.90133	−	8.16991i	−0.103619	−	0.291783i
$785$	−1.91998	−	1.95752i	−0.0685271	−	0.0698668i
$786$	42.8216	−	14.9171i	1.52740	−	0.532074i
$787$	14.2444	−	16.4389i	0.507759	−	0.585985i	−0.442765	−	0.896638i	$-0.646002\pi$
$787$	14.2444	−	16.4389i	0.507759	−	0.585985i	0.950523	+	0.310653i	$0.100548\pi$
$788$	38.6547	+	7.28918i	1.37702	+	0.259666i
$789$	6.75536	+	10.5116i	0.240497	+	0.374221i
$790$	1.46707	+	13.1234i	0.0521960	+	0.466910i
$791$	2.56249	+	2.95727i	0.0911116	+	0.105148i
$792$	3.12907	+	1.40627i	0.111187	+	0.0499698i
$793$	24.1422	+	3.47113i	0.857315	+	0.123263i
$794$	12.2252	+	1.14259i	0.433855	+	0.0405490i
$795$	−20.2207	+	14.8338i	−0.717156	+	0.526101i
$796$	−15.1111	−	14.2930i	−0.535600	−	0.506602i
$797$	7.77680	+	17.0288i	0.275468	+	0.603192i	0.995913	−	0.0903211i	$-0.0287893\pi$
$797$	7.77680	+	17.0288i	0.275468	+	0.603192i	−0.720444	+	0.693513i	$0.756062\pi$
$798$	−35.2476	−	49.2885i	−1.24775	−	1.74479i
$799$	−48.9296	−	14.3670i	−1.73101	−	0.508269i
$800$	10.2671	+	26.3550i	0.362996	+	0.931791i
$801$	−44.7387	+	13.1365i	−1.58076	+	0.464154i
$802$	−1.95183	−	0.776849i	−0.0689214	−	0.0274315i
$803$	0.224508	+	1.56149i	0.00792273	+	0.0551038i
$804$	51.5732	−	5.13377i	1.81885	−	0.181054i
$805$	−13.1863	+	19.5414i	−0.464755	+	0.688744i
$806$	1.49869	+	30.1857i	0.0527890	+	1.06324i
$807$	23.1761	−	3.33221i	0.815836	−	0.117299i
$808$	13.4398	−	46.8133i	0.472811	−	1.64689i
$809$	3.95401	−	1.16100i	0.139016	−	0.0408187i	−0.211485	−	0.977381i	$-0.567830\pi$
$809$	3.95401	−	1.16100i	0.139016	−	0.0408187i	0.350500	+	0.936563i	$0.386012\pi$
$810$	−6.17683	+	3.70029i	−0.217032	+	0.130015i
$811$	−6.12008	+	20.8431i	−0.214905	+	0.731900i	0.779513	+	0.626386i	$0.215467\pi$
$811$	−6.12008	+	20.8431i	−0.214905	+	0.731900i	−0.994418	+	0.105513i	$0.966351\pi$
$812$	12.6302	−	10.0148i	0.443232	−	0.351452i
$813$	−7.08848	−	15.5216i	−0.248604	−	0.544366i
$814$	−1.20678	−	1.26056i	−0.0422977	−	0.0441826i
$815$	−7.87640	+	5.77809i	−0.275898	+	0.202398i
$816$	77.8744	−	4.33687i	2.72615	−	0.151821i
$817$	32.0326	+	4.60560i	1.12068	+	0.161129i
$818$	−9.34092	+	16.2542i	−0.326598	+	0.568316i
$819$	−19.2936	+	16.7180i	−0.674172	+	0.584174i
$820$	−46.2700	+	7.51148i	−1.61582	+	0.262312i
$821$	−10.4829	−	16.3117i	−0.365855	−	0.569282i	0.608708	−	0.793394i	$-0.291688\pi$
$821$	−10.4829	−	16.3117i	−0.365855	−	0.569282i	−0.974563	+	0.224113i	$0.928052\pi$
$822$	2.08698	+	0.501861i	0.0727919	+	0.0175044i
$823$	26.9792	+	23.3776i	0.940434	+	0.814891i	0.982887	−	0.184208i	$-0.0589719\pi$
$823$	26.9792	+	23.3776i	0.940434	+	0.814891i	−0.0424533	+	0.999098i	$0.513517\pi$
$824$	20.9660	−	9.72792i	0.730384	−	0.338888i
$825$	−1.33212	−	3.07301i	−0.0463783	−	0.106988i
$826$	−15.4806	+	3.01589i	−0.538637	+	0.104936i
$827$	38.8654			1.35148			0.675741	−	0.737139i	$-0.263824\pi$
$827$	38.8654			1.35148			0.675741	+	0.737139i	$0.263824\pi$
$828$	−42.1811	−	26.2171i	−1.46589	−	0.911109i
$829$		−	10.2989i		−	0.357697i	−0.983877	−	0.178848i	$-0.942763\pi$
$829$		−	10.2989i		−	0.357697i	0.983877	−	0.178848i	$-0.0572372\pi$
$830$	6.58639	−	37.4105i	0.228617	−	1.29854i
$831$	4.59226	−	10.0557i	0.159304	−	0.348827i
$832$	−14.9762	+	9.88162i	−0.519206	+	0.342583i
$833$	11.1690	+	9.67795i	0.386981	+	0.335321i
$834$	71.7895	+	17.2634i	2.48587	+	0.597782i
$835$	23.6465	−	4.90474i	0.818320	−	0.169736i
$836$	1.60762	+	2.75884i	0.0556009	+	0.0954164i
$837$	38.8629	+	44.8502i	1.34330	+	1.55025i
$838$	1.93134	+	1.10990i	0.0667171	+	0.0383407i
$839$	−7.43669	+	51.7233i	−0.256743	+	1.78569i	0.298920	+	0.954278i	$0.403374\pi$
$839$	−7.43669	+	51.7233i	−0.256743	+	1.78569i	−0.555663	+	0.831408i	$0.687535\pi$
$840$	37.2015	+	14.0305i	1.28357	+	0.484099i
$841$	13.0890	+	8.41181i	0.451346	+	0.290062i
$842$	−0.575685	−	0.601339i	−0.0198394	−	0.0207235i
$843$	−1.52892	−	3.34787i	−0.0526589	−	0.115307i
$844$	2.08800	+	2.63327i	0.0718719	+	0.0906410i
$845$	10.8173	−	14.1624i	0.372127	−	0.487202i
$846$	33.7677	−	43.1171i	1.16096	−	1.48240i
$847$	−6.77870	−	23.0861i	−0.232919	−	0.793249i
$848$	−3.57587	+	15.2745i	−0.122796	+	0.524527i
$849$	−12.5446	−	87.2497i	−0.430530	−	2.99440i
$850$	−37.3758	−	30.4568i	−1.28198	−	1.04466i
$851$	14.8816	+	20.4158i	0.510134	+	0.699846i
$852$	55.2500	−	5.49976i	1.89283	−	0.188419i
$853$	7.61326	+	52.9514i	0.260673	+	1.81302i	0.527809	+	0.849363i	$0.323014\pi$
$853$	7.61326	+	52.9514i	0.260673	+	1.81302i	−0.267136	+	0.963659i	$0.586077\pi$
$854$	−31.4122	−	12.5024i	−1.07490	−	0.427824i
$855$	−78.6542	−	6.39128i	−2.68992	−	0.218577i
$856$	−31.9687	−	20.2739i	−1.09267	−	0.692948i
$857$	−9.04455	+	30.8029i	−0.308956	+	1.05221i	0.647919	+	0.761709i	$0.275639\pi$
$857$	−9.04455	+	30.8029i	−0.308956	+	1.05221i	−0.956875	+	0.290499i	$0.906179\pi$
$858$	1.72823	−	1.23591i	0.0590010	−	0.0421932i
$859$	39.4227	−	18.0037i	1.34508	−	0.614279i	0.392837	−	0.919608i	$-0.371494\pi$
$859$	39.4227	−	18.0037i	1.34508	−	0.614279i	0.952247	+	0.305329i	$0.0987664\pi$
$860$	−19.1523	+	9.16990i	−0.653087	+	0.312691i
$861$	−35.6247	+	55.4331i	−1.21409	+	1.88916i
$862$	46.9901	+	4.39180i	1.60049	+	0.149585i
$863$	10.0240	+	1.44124i	0.341221	+	0.0490602i	0.310796	−	0.950477i	$-0.399405\pi$
$863$	10.0240	+	1.44124i	0.341221	+	0.0490602i	0.0304259	+	0.999537i	$0.490314\pi$
$864$	−11.1883	+	33.4081i	−0.380633	+	1.13657i
$865$	−10.3160	+	3.73432i	−0.350754	+	0.126971i
$866$	0.133431	+	0.257548i	0.00453416	+	0.00875184i
$867$	−70.9484	+	45.5957i	−2.40953	+	1.54851i
$868$	7.76309	−	41.1679i	0.263497	−	1.39733i
$869$	−0.739242	−	0.640556i	−0.0250771	−	0.0217294i
$870$	1.04324	−	33.1377i	0.0353691	−	1.12347i
$871$	8.44286	−	18.4873i	0.286075	−	0.626418i
$872$	6.17029	+	20.5551i	0.208953	+	0.696085i
$873$			2.84276i			0.0962127i
$874$	−17.7407	−	42.6868i	−0.600088	−	1.44390i
$875$	−11.1476	−	21.9043i	−0.376857	−	0.740502i
$876$	−37.3959	+	9.23134i	−1.26349	+	0.311898i
$877$	0.833202	−	1.82446i	0.0281352	−	0.0616076i	−0.895043	−	0.445981i	$-0.852855\pi$
$877$	0.833202	−	1.82446i	0.0281352	−	0.0616076i	0.923178	+	0.384373i	$0.125582\pi$
$878$	2.52036	+	7.23504i	0.0850579	+	0.244171i
$879$	−23.0456	+	26.5960i	−0.777307	+	0.897060i
$880$	−1.88303	−	0.918555i	−0.0634769	−	0.0309645i
$881$	−2.40541	+	1.54586i	−0.0810403	+	0.0520814i	−0.580533	−	0.814236i	$-0.697156\pi$
$881$	−2.40541	+	1.54586i	−0.0810403	+	0.0520814i	0.499493	+	0.866318i	$0.333520\pi$
$882$	−14.0925	+	7.30105i	−0.474519	+	0.245839i
$883$	−15.7337	−	18.1576i	−0.529480	−	0.611052i	0.426499	−	0.904488i	$-0.359747\pi$
$883$	−15.7337	−	18.1576i	−0.529480	−	0.611052i	−0.955979	+	0.293436i	$0.905201\pi$
$884$	13.9056	−	27.2411i	0.467695	−	0.916218i
$885$	−15.8216	+	28.3199i	−0.531838	+	0.951963i
$886$	−15.9475	−	1.49048i	−0.535766	−	0.0500738i
$887$	5.16216	−	8.03247i	0.173328	−	0.269704i	−0.743711	−	0.668502i	$-0.766936\pi$
$887$	5.16216	−	8.03247i	0.173328	−	0.269704i	0.917039	+	0.398798i	$0.130572\pi$
$888$	27.7086	−	32.3694i	0.929839	−	1.08625i
$889$	0.0179839	+	0.0393793i	0.000603162	+	0.00132074i
$890$	27.5620	−	7.15904i	0.923880	−	0.239972i
$891$	0.150265	−	0.511754i	0.00503406	−	0.0171444i
$892$	24.1233	+	17.0325i	0.807707	+	0.570290i
$893$	48.9101	−	14.3613i	1.63671	−	0.480582i
$894$	−4.79799	+	12.0549i	−0.160469	+	0.403177i
$895$	−3.96247	+	17.4024i	−0.132451	+	0.581700i
$896$	23.3864	−	8.46410i	0.781286	−	0.282766i
$897$	−27.1822	+	14.3967i	−0.907589	+	0.480692i
$898$	1.43462	+	28.8953i	0.0478740	+	0.964249i
$899$	−34.5781	+	4.97158i	−1.15324	+	0.165811i
$900$	45.2339	−	25.1985i	1.50780	−	0.839949i
$901$	−7.53382	−	25.6578i	−0.250988	−	0.854786i
$902$	2.14093	−	2.73369i	0.0712851	−	0.0910219i
$903$	−8.40949	+	28.6401i	−0.279850	+	0.953083i
$904$	3.78501	−	3.31986i	0.125887	−	0.110417i
$905$	0.574593	+	9.29785i	0.0191001	+	0.309071i
$906$	−5.55493	+	5.31796i	−0.184550	+	0.176677i
$907$	31.4313	+	20.1997i	1.04366	+	0.670718i	0.945889	−	0.324491i	$-0.105193\pi$
$907$	31.4313	+	20.1997i	1.04366	+	0.670718i	0.0977694	+	0.995209i	$0.468829\pi$
$908$	−0.793519	+	18.1954i	−0.0263338	+	0.603836i
$909$	−88.2538	−	12.6890i	−2.92719	−	0.420867i
$910$	12.0985	−	9.83427i	0.401062	−	0.326003i
$911$	5.98212	+	6.90373i	0.198196	+	0.228731i	0.846144	−	0.532954i	$-0.178918\pi$
$911$	5.98212	+	6.90373i	0.198196	+	0.228731i	−0.647948	+	0.761685i	$0.724373\pi$
$912$	−63.1421	+	45.7322i	−2.09085	+	1.51434i
$913$	1.52123	+	2.36709i	0.0503455	+	0.0783391i
$914$	−53.0263	−	12.7513i	−1.75395	−	0.421776i
$915$	−61.3533	+	32.7345i	−2.02828	+	1.08217i
$916$	−3.98548	−	9.84050i	−0.131684	−	0.325139i
$917$	−10.2393	+	22.4208i	−0.338130	+	0.740401i
$918$	−11.4842	−	58.9483i	−0.379034	−	1.94558i
$919$	12.6337			0.416746			0.208373	−	0.978049i	$-0.433183\pi$
$919$	12.6337			0.416746			0.208373	+	0.978049i	$0.433183\pi$
$920$	25.2445	+	16.8142i	0.832286	+	0.554347i
$921$	−83.2626			−2.74360
$922$	−3.64591	−	18.7144i	−0.120072	−	0.616328i
$923$	9.04477	−	19.8053i	0.297712	−	0.651899i
$924$	−2.72974	+	1.10557i	−0.0898020	+	0.0363705i
$925$	−26.1391	+	3.24309i	−0.859448	+	0.106632i
$926$	21.3636	+	5.13735i	0.702052	+	0.168824i
$927$	−22.8755	−	35.5950i	−0.751331	−	1.16909i
$928$	−12.9832	−	16.1725i	−0.426193	−	0.530890i
$929$	−10.4184	−	12.0235i	−0.341816	−	0.394477i	0.558650	−	0.829404i	$-0.311320\pi$
$929$	−10.4184	−	12.0235i	−0.341816	−	0.394477i	−0.900466	+	0.434927i	$0.856774\pi$
$930$	−54.3513	−	66.8652i	−1.78225	−	2.19259i
$931$	−14.6224	−	2.10238i	−0.479229	−	0.0689027i
$932$	−2.11484	−	0.0922302i	−0.0692740	−	0.00302110i
$933$	−60.4477	−	38.8474i	−1.97897	−	1.27181i
$934$	6.10600	−	5.84552i	0.199795	−	0.191271i
$935$	3.56458	−	0.220285i	0.116574	−	0.00720410i
$936$	21.6592	+	24.6938i	0.707952	+	0.807143i
$937$	7.74467	−	26.3759i	0.253007	−	0.861664i	−0.730824	−	0.682566i	$-0.760864\pi$
$937$	7.74467	−	26.3759i	0.253007	−	0.861664i	0.983831	−	0.179098i	$-0.0573179\pi$
$938$	−17.3703	+	22.1796i	−0.567159	+	0.724190i
$939$	25.7358	+	87.6479i	0.839855	+	2.86028i
$940$	−21.4412	+	25.6707i	−0.699335	+	0.837287i
$941$	−0.315436	+	0.0453529i	−0.0102829	+	0.00147846i	−0.147454	−	0.989069i	$-0.547108\pi$
$941$	−0.315436	+	0.0453529i	−0.0102829	+	0.00147846i	0.137171	+	0.990547i	$0.456199\pi$
$942$	0.245914	+	4.95306i	0.00801231	+	0.161379i
$943$	−35.9947	+	35.0901i	−1.17215	+	1.14269i
$944$	4.00029	+	19.8941i	0.130198	+	0.647499i
$945$	6.79693	−	29.8508i	0.221104	−	0.971048i
$946$	0.581657	−	1.46141i	0.0189113	−	0.0475145i
$947$	−17.6090	+	5.17046i	−0.572215	+	0.168017i	−0.555023	−	0.831835i	$-0.687291\pi$
$947$	−17.6090	+	5.17046i	−0.572215	+	0.168017i	−0.0171913	+	0.999852i	$0.505472\pi$
$948$	13.7754	−	19.5103i	0.447405	−	0.633664i
$949$	−4.25547	+	14.4928i	−0.138138	+	0.470456i
$950$	47.8895	+	5.41291i	1.55374	+	0.175618i
$951$	−16.0719	−	35.1925i	−0.521167	−	1.14120i
$952$	−27.5696	+	32.2070i	−0.893535	+	1.04384i
$953$	−23.3635	+	36.3543i	−0.756818	+	1.17763i	0.222426	+	0.974950i	$0.428602\pi$
$953$	−23.3635	+	36.3543i	−0.756818	+	1.17763i	−0.979244	+	0.202683i	$0.935034\pi$
$954$	28.5938	+	2.67244i	0.925759	+	0.0865235i
$955$	44.3140	+	24.7571i	1.43397	+	0.801121i
$956$	−21.4854	−	10.9675i	−0.694887	−	0.354714i
$957$	1.60824	+	1.85601i	0.0519871	+	0.0599963i
$958$	33.5918	−	17.4033i	1.08530	−	0.562274i
$959$	−0.981535	+	0.630794i	−0.0316954	+	0.0203694i
$960$	17.7635	−	47.9728i	0.573315	−	1.54831i
$961$	−39.1565	+	45.1890i	−1.26311	+	1.45771i
$962$	−5.49661	−	15.7788i	−0.177218	−	0.508730i
$963$	−28.7884	+	63.0379i	−0.927694	+	2.03137i
$964$	−8.72848	−	35.3588i	−0.281125	−	1.13883i
$965$	20.9946	+	8.06291i	0.675839	+	0.259554i
$966$	41.3002	−	10.5934i	1.32881	−	0.340836i
$967$			22.3270i			0.717988i	0.933340	+	0.358994i	$0.116880\pi$
$967$			22.3270i			0.717988i	−0.933340	+	0.358994i	$0.883120\pi$
$968$	−29.6504	+	8.90054i	−0.953001	+	0.286074i
$969$	55.2079	−	120.889i	1.77353	−	3.88350i
$970$	0.0546302	−	1.73529i	0.00175407	−	0.0557167i
$971$	−30.3383	−	26.2883i	−0.973602	−	0.843631i	0.0141122	−	0.999900i	$-0.495508\pi$
$971$	−30.3383	−	26.2883i	−0.973602	−	0.843631i	−0.987715	+	0.156269i	$0.950053\pi$
$972$	−23.9244	−	4.51146i	−0.767376	−	0.144705i
$973$	−33.7635	+	21.6985i	−1.08241	+	0.695622i
$974$	2.84890	+	5.49896i	0.0912847	+	0.176198i
$975$	0.620809	−	32.0629i	0.0198818	−	1.02683i
$976$	−15.8423	+	40.5124i	−0.507100	+	1.29677i
$977$	35.6809	+	5.13014i	1.14153	+	0.164128i	0.687038	−	0.726621i	$-0.258911\pi$
$977$	35.6809	+	5.13014i	1.14153	+	0.164128i	0.454495	+	0.890749i	$0.349820\pi$
$978$	17.5910	+	1.64410i	0.562499	+	0.0525724i
$979$	−1.14041	+	1.77451i	−0.0364477	+	0.0567137i
$980$	8.74269	−	4.18591i	0.279275	−	0.133714i
$981$	35.7380	−	16.3210i	1.14103	−	0.521089i
$982$	−27.1917	+	19.4455i	−0.867721	+	0.620532i
$983$	−4.25816	+	14.5020i	−0.135814	+	0.462541i	−0.999111	−	0.0421559i	$-0.986577\pi$
$983$	−4.25816	+	14.5020i	−0.135814	+	0.462541i	0.863297	+	0.504696i	$0.168396\pi$
$984$	71.5973	+	45.4056i	2.28244	+	1.44748i
$985$	−3.56190	+	43.8345i	−0.113492	+	1.39668i
$986$	32.8463	+	13.0732i	1.04604	+	0.416335i
$987$	6.69119	+	46.5383i	0.212983	+	1.48133i
$988$	3.02835	+	30.4224i	0.0963446	+	0.967867i
$989$	−11.1665	+	19.8454i	−0.355075	+	0.631047i
$990$	−1.19584	+	3.64428i	−0.0380063	+	0.115823i
$991$	4.60342	+	32.0175i	0.146232	+	1.01707i	0.922315	+	0.386438i	$0.126295\pi$
$991$	4.60342	+	32.0175i	0.146232	+	1.01707i	−0.776083	+	0.630631i	$0.782796\pi$
$992$	−53.0274	−	9.66899i	−1.68362	−	0.306991i
$993$	−20.1774	−	68.7178i	−0.640309	−	2.18069i
$994$	−18.6086	+	23.7609i	−0.590230	+	0.753649i
$995$	14.1158	−	18.4808i	0.447500	−	0.585881i
$996$	−53.8329	+	42.6857i	−1.70576	+	1.35255i
$997$	−13.8601	−	30.3495i	−0.438955	−	0.961177i	−0.991789	−	0.127886i	$-0.959181\pi$
$997$	−13.8601	−	30.3495i	−0.438955	−	0.961177i	0.552834	−	0.833291i	$-0.313546\pi$
$998$	−2.97292	−	3.10540i	−0.0941062	−	0.0982997i
$999$	−27.6009	−	17.7380i	−0.873254	−	0.561206i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bf.a.509.131	yes	1400
5.4	even	2	inner	920.2.bf.a.509.10	yes	1400
8.5	even	2	inner	920.2.bf.a.509.138	yes	1400
23.8	even	11	inner	920.2.bf.a.629.3	yes	1400
40.29	even	2	inner	920.2.bf.a.509.3	✓	1400
115.54	even	22	inner	920.2.bf.a.629.138	yes	1400
184.77	even	22	inner	920.2.bf.a.629.10	yes	1400
920.629	even	22	inner	920.2.bf.a.629.131	yes	1400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bf.a.509.3	✓	1400	40.29	even	2	inner
920.2.bf.a.509.10	yes	1400	5.4	even	2	inner
920.2.bf.a.509.131	yes	1400	1.1	even	1	trivial
920.2.bf.a.509.138	yes	1400	8.5	even	2	inner
920.2.bf.a.629.3	yes	1400	23.8	even	11	inner
920.2.bf.a.629.10	yes	1400	184.77	even	22	inner
920.2.bf.a.629.131	yes	1400	920.629	even	22	inner
920.2.bf.a.629.138	yes	1400	115.54	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bf (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38812 - 0.270430i) q^{2} +(1.18796 - 2.60128i) q^{3} +(1.85374 - 0.750777i) q^{4} +(1.05259 + 1.97283i) q^{5} +(0.945569 - 3.93214i) q^{6} +(1.18849 + 1.84933i) q^{7} +(2.37017 - 1.54347i) q^{8} +(-3.39080 - 3.91320i) q^{9} +O(q^{10})\)	\(q+(1.38812 - 0.270430i) q^{2} +(1.18796 - 2.60128i) q^{3} +(1.85374 - 0.750777i) q^{4} +(1.05259 + 1.97283i) q^{5} +(0.945569 - 3.93214i) q^{6} +(1.18849 + 1.84933i) q^{7} +(2.37017 - 1.54347i) q^{8} +(-3.39080 - 3.91320i) q^{9} +(1.99462 + 2.45387i) q^{10} +(-0.231858 - 0.0333361i) q^{11} +(0.249192 - 5.71397i) q^{12} +(-1.88677 - 1.21256i) q^{13} +(2.14988 + 2.24569i) q^{14} +(6.38231 - 0.394417i) q^{15} +(2.87267 - 2.78348i) q^{16} +(-1.92098 + 6.54226i) q^{17} +(-5.76508 - 4.51500i) q^{18} +(-1.92021 - 6.53964i) q^{19} +(3.43237 + 2.86685i) q^{20} +(6.22252 - 0.894663i) q^{21} +(-0.330861 + 0.0164269i) q^{22} +(4.77887 + 0.402968i) q^{23} +(-1.19932 - 7.99905i) q^{24} +(-2.78413 + 4.15315i) q^{25} +(-2.94697 - 1.17293i) q^{26} +(-5.97587 + 1.75467i) q^{27} +(3.59159 + 2.53588i) q^{28} +(1.03289 - 3.51770i) q^{29} +(8.75273 - 2.27347i) q^{30} +(-3.95831 - 8.66749i) q^{31} +(3.23486 - 4.64065i) q^{32} +(-0.362155 + 0.563524i) q^{33} +(-0.897322 + 9.60091i) q^{34} +(-2.39743 + 4.29128i) q^{35} +(-9.22359 - 4.70829i) q^{36} +(3.44974 + 3.98121i) q^{37} +(-4.43400 - 8.55851i) q^{38} +(-5.39561 + 3.46755i) q^{39} +(5.53981 + 3.05131i) q^{40} +(-6.86408 + 7.92157i) q^{41} +(8.39564 - 2.92465i) q^{42} +(-1.97245 + 4.31906i) q^{43} +(-0.454831 + 0.112277i) q^{44} +(4.15096 - 10.8085i) q^{45} +(6.74261 - 0.732983i) q^{46} +7.47901i q^{47} +(-3.82798 - 10.7793i) q^{48} +(0.900390 - 1.97158i) q^{49} +(-2.74155 + 6.51797i) q^{50} +(14.7362 + 12.7690i) q^{51} +(-4.40794 - 0.831212i) q^{52} +(-3.29928 + 2.12032i) q^{53} +(-7.82068 + 4.05174i) q^{54} +(-0.178284 - 0.492505i) q^{55} +(5.67132 + 2.54882i) q^{56} +(-19.2926 - 2.77385i) q^{57} +(0.482480 - 5.16230i) q^{58} +(-2.74272 + 4.26775i) q^{59} +(11.5350 - 5.52284i) q^{60} +(-9.89220 + 4.51762i) q^{61} +(-7.83855 - 10.9610i) q^{62} +(3.20685 - 10.9215i) q^{63} +(3.23539 - 7.31657i) q^{64} +(0.406176 - 4.99860i) q^{65} +(-0.350320 + 0.880175i) q^{66} +(1.28963 + 8.96956i) q^{67} +(1.35079 + 13.5698i) q^{68} +(6.72536 - 11.9525i) q^{69} +(-2.16742 + 6.60514i) q^{70} +(1.38157 + 9.60902i) q^{71} +(-14.0767 - 4.04133i) q^{72} +(-1.89738 - 6.46189i) q^{73} +(5.86528 + 4.59347i) q^{74} +(7.49605 + 12.1761i) q^{75} +(-8.46938 - 10.6811i) q^{76} +(-0.213912 - 0.468402i) q^{77} +(-6.55201 + 6.27250i) q^{78} +(3.51294 + 2.25763i) q^{79} +(8.51507 + 2.73744i) q^{80} +(-0.324045 + 2.25378i) q^{81} +(-7.38591 + 12.8523i) q^{82} +(-7.86631 - 9.07821i) q^{83} +(10.8632 - 6.33019i) q^{84} +(-14.9288 + 3.09652i) q^{85} +(-1.56999 + 6.52877i) q^{86} +(-7.92347 - 6.86573i) q^{87} +(-0.600995 + 0.278854i) q^{88} +(3.74084 - 8.19131i) q^{89} +(2.83909 - 16.1259i) q^{90} -4.93039i q^{91} +(9.16130 - 2.84087i) q^{92} -27.2489 q^{93} +(2.02255 + 10.3817i) q^{94} +(10.8804 - 10.6718i) q^{95} +(-8.22873 - 13.9277i) q^{96} +(-0.414920 - 0.359530i) q^{97} +(0.716672 - 2.98027i) q^{98} +(0.655734 + 1.02034i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1400 q - 14 q^{4} - 14 q^{6} - 168 q^{9}+O(q^{10}) \) 1400 * q - 14 * q^4 - 14 * q^6 - 168 * q^9	\( 1400 q - 14 q^{4} - 14 q^{6} - 168 q^{9} - 5 q^{10} - 26 q^{14} - 6 q^{15} - 14 q^{16} - 27 q^{20} - 32 q^{24} - 18 q^{25} - 30 q^{26} - q^{30} - 52 q^{31} + 40 q^{34} + 26 q^{36} - 12 q^{39} + 15 q^{40} - 36 q^{41} - 142 q^{44} - 10 q^{46} + 80 q^{49} - 47 q^{50} + 46 q^{54} - 38 q^{55} + 14 q^{56} + 21 q^{60} - 26 q^{64} + 2 q^{65} - 104 q^{66} - 26 q^{70} - 36 q^{71} - 18 q^{74} - 96 q^{76} - 12 q^{79} + 82 q^{80} - 136 q^{81} - 82 q^{84} - 198 q^{86} - 52 q^{89} + 164 q^{90} - 38 q^{94} + 2 q^{95} - 432 q^{96}+O(q^{100}) \) 1400 * q - 14 * q^4 - 14 * q^6 - 168 * q^9 - 5 * q^10 - 26 * q^14 - 6 * q^15 - 14 * q^16 - 27 * q^20 - 32 * q^24 - 18 * q^25 - 30 * q^26 - q^30 - 52 * q^31 + 40 * q^34 + 26 * q^36 - 12 * q^39 + 15 * q^40 - 36 * q^41 - 142 * q^44 - 10 * q^46 + 80 * q^49 - 47 * q^50 + 46 * q^54 - 38 * q^55 + 14 * q^56 + 21 * q^60 - 26 * q^64 + 2 * q^65 - 104 * q^66 - 26 * q^70 - 36 * q^71 - 18 * q^74 - 96 * q^76 - 12 * q^79 + 82 * q^80 - 136 * q^81 - 82 * q^84 - 198 * q^86 - 52 * q^89 + 164 * q^90 - 38 * q^94 + 2 * q^95 - 432 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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