LMFDB - Embedded newform 750.2.o.a.469.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(19,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("750.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.o (of order $50$, degree $20$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			469.9
Character	$\chi$	$=$	750.469
Dual form			750.2.o.a.379.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.998027 - 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(-1.31016 + 1.81204i) q^{5} +(-0.876307 + 0.481754i) q^{6} +(-2.59485 - 3.57150i) q^{7} +(0.982287 - 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +O(q^{10})$	\(q+(0.998027 - 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(-1.31016 + 1.81204i) q^{5} +(-0.876307 + 0.481754i) q^{6} +(-2.59485 - 3.57150i) q^{7} +(0.982287 - 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +(-1.19379 + 1.89073i) q^{10} +(-0.247899 - 3.94024i) q^{11} +(-0.844328 + 0.535827i) q^{12} +(2.91697 + 2.41313i) q^{13} +(-2.81398 - 3.40152i) q^{14} +(0.413935 - 2.19742i) q^{15} +(0.968583 - 0.248690i) q^{16} +(0.390191 - 3.08868i) q^{17} +(0.587785 - 0.809017i) q^{18} +(-0.674016 + 1.43236i) q^{19} +(-1.07272 + 1.96196i) q^{20} +(3.86856 + 2.12676i) q^{21} +(-0.494820 - 3.91690i) q^{22} +(-2.97937 - 7.52503i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(-1.56698 - 4.74811i) q^{25} +(3.06273 + 2.22521i) q^{26} +(-0.248690 + 0.968583i) q^{27} +(-3.02201 - 3.21812i) q^{28} +(5.46672 - 5.13360i) q^{29} +(0.275141 - 2.21908i) q^{30} +(-8.01388 - 1.01239i) q^{31} +(0.951057 - 0.309017i) q^{32} +(1.90198 + 3.45969i) q^{33} +(0.195481 - 3.10708i) q^{34} +(9.87135 - 0.0227459i) q^{35} +(0.535827 - 0.844328i) q^{36} +(-1.00164 - 3.90112i) q^{37} +(-0.582748 + 1.47185i) q^{38} +(-3.66681 - 0.941477i) q^{39} +(-0.947407 + 2.02544i) q^{40} +(10.1725 + 4.02758i) q^{41} +(3.99446 + 1.87965i) q^{42} +(7.03128 + 2.28460i) q^{43} +(-0.739788 - 3.87810i) q^{44} +(0.561077 + 2.16453i) q^{45} +(-3.44599 - 7.32310i) q^{46} +(-11.0639 - 2.11055i) q^{47} +(-0.770513 + 0.637424i) q^{48} +(-3.85926 + 11.8776i) q^{49} +(-1.86203 - 4.64035i) q^{50} +(0.962040 + 2.96086i) q^{51} +(3.19641 + 2.02850i) q^{52} +(2.77383 - 5.04558i) q^{53} +(-0.187381 + 0.982287i) q^{54} +(7.46467 + 4.71313i) q^{55} +(-3.21812 - 3.02201i) q^{56} -1.58302i q^{57} +(5.13360 - 5.46672i) q^{58} +(1.99641 + 3.14583i) q^{59} +(0.135261 - 2.23197i) q^{60} +(2.25272 - 0.891915i) q^{61} +(-8.06164 - 0.507195i) q^{62} +(-4.40590 - 0.277196i) q^{63} +(0.929776 - 0.368125i) q^{64} +(-8.19437 + 2.12409i) q^{65} +(2.11546 + 3.33344i) q^{66} +(-7.44291 + 7.92589i) q^{67} -3.11323i q^{68} +(5.89981 + 5.54029i) q^{69} +(9.85045 - 0.642528i) q^{70} +(1.94409 - 10.1913i) q^{71} +(0.481754 - 0.876307i) q^{72} +(-3.55645 - 2.25699i) q^{73} +(-1.24461 - 3.83052i) q^{74} +(3.43950 + 3.62903i) q^{75} +(-0.489179 + 1.50554i) q^{76} +(-13.4293 + 11.1097i) q^{77} +(-3.71869 - 0.709378i) q^{78} +(5.86407 + 12.4618i) q^{79} +(-0.818359 + 2.08093i) q^{80} +(-0.187381 - 0.982287i) q^{81} +(10.4053 + 3.38089i) q^{82} +(-15.1477 - 7.12795i) q^{83} +(4.10461 + 1.62513i) q^{84} +(5.08560 + 4.75369i) q^{85} +(7.16086 + 1.83860i) q^{86} +(-2.76066 + 6.97263i) q^{87} +(-0.981836 - 3.82400i) q^{88} +(-5.36521 + 8.45423i) q^{89} +(0.695881 + 2.12503i) q^{90} +(1.04939 - 16.6796i) q^{91} +(-3.89901 - 7.09228i) q^{92} +(7.68223 - 2.49611i) q^{93} +(-11.1746 - 1.41168i) q^{94} +(-1.71242 - 3.09796i) q^{95} +(-0.728969 + 0.684547i) q^{96} +(-2.40662 - 2.56279i) q^{97} +(-3.10584 + 12.0965i) q^{98} +(-3.19403 - 2.32060i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q+O(q^{10}) $ 240 * q	$ 240 q - 10 q^{11} + 20 q^{13} - 10 q^{17} + 10 q^{19} + 60 q^{23} - 60 q^{24} + 60 q^{25} + 10 q^{28} + 20 q^{29} + 10 q^{30} - 30 q^{31} - 10 q^{34} - 10 q^{35} + 20 q^{37} - 90 q^{38} - 20 q^{41} - 10 q^{42} - 10 q^{46} + 140 q^{47} + 50 q^{49} + 20 q^{50} + 10 q^{51} - 80 q^{52} + 30 q^{53} - 10 q^{55} - 30 q^{58} + 20 q^{59} + 40 q^{60} - 100 q^{61} - 10 q^{62} - 10 q^{63} - 20 q^{65} - 40 q^{66} - 10 q^{67} - 10 q^{69} + 10 q^{70} + 80 q^{71} + 20 q^{73} - 80 q^{75} + 10 q^{76} + 20 q^{77} + 140 q^{79} + 100 q^{82} - 70 q^{83} - 20 q^{85} + 20 q^{86} + 30 q^{87} - 10 q^{88} + 40 q^{89} + 10 q^{90} + 170 q^{91} + 120 q^{92} + 50 q^{93} - 30 q^{94} + 220 q^{95} - 60 q^{97} - 120 q^{98} - 20 q^{99}+O(q^{100}) $ 240 * q - 10 * q^11 + 20 * q^13 - 10 * q^17 + 10 * q^19 + 60 * q^23 - 60 * q^24 + 60 * q^25 + 10 * q^28 + 20 * q^29 + 10 * q^30 - 30 * q^31 - 10 * q^34 - 10 * q^35 + 20 * q^37 - 90 * q^38 - 20 * q^41 - 10 * q^42 - 10 * q^46 + 140 * q^47 + 50 * q^49 + 20 * q^50 + 10 * q^51 - 80 * q^52 + 30 * q^53 - 10 * q^55 - 30 * q^58 + 20 * q^59 + 40 * q^60 - 100 * q^61 - 10 * q^62 - 10 * q^63 - 20 * q^65 - 40 * q^66 - 10 * q^67 - 10 * q^69 + 10 * q^70 + 80 * q^71 + 20 * q^73 - 80 * q^75 + 10 * q^76 + 20 * q^77 + 140 * q^79 + 100 * q^82 - 70 * q^83 - 20 * q^85 + 20 * q^86 + 30 * q^87 - 10 * q^88 + 40 * q^89 + 10 * q^90 + 170 * q^91 + 120 * q^92 + 50 * q^93 - 30 * q^94 + 220 * q^95 - 60 * q^97 - 120 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{49}{50}\right)$	$1$

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 $

$2$	0.998027	−	0.0627905i	0.705711	−	0.0443996i
$2$	0.998027	−	0.0627905i	0.705711	−	0.0443996i
$3$	−0.904827	+	0.425779i	−0.522402	+	0.245824i
$3$	−0.904827	+	0.425779i	−0.522402	+	0.245824i
$4$	0.992115	−	0.125333i	0.496057	−	0.0626666i
$5$	−1.31016	+	1.81204i	−0.585920	+	0.810369i
$5$	−1.31016	+	1.81204i	−0.585920	+	0.810369i
$6$	−0.876307	+	0.481754i	−0.357751	+	0.196675i
$7$	−2.59485	−	3.57150i	−0.980759	−	1.34990i	−0.936419	−	0.350883i	$-0.885881\pi$
$7$	−2.59485	−	3.57150i	−0.980759	−	1.34990i	−0.0443402	−	0.999016i	$-0.514119\pi$
$8$	0.982287	−	0.187381i	0.347291	−	0.0662493i
$9$	0.637424	−	0.770513i	0.212475	−	0.256838i
$10$	−1.19379	+	1.89073i	−0.377510	+	0.597901i
$11$	−0.247899	−	3.94024i	−0.0747444	−	1.18803i	−0.839373	−	0.543557i	$-0.817077\pi$
$11$	−0.247899	−	3.94024i	−0.0747444	−	1.18803i	0.764628	−	0.644472i	$-0.222923\pi$
$12$	−0.844328	+	0.535827i	−0.243736	+	0.154680i
$13$	2.91697	+	2.41313i	0.809021	+	0.669281i	0.947028	−	0.321151i	$-0.104070\pi$
$13$	2.91697	+	2.41313i	0.809021	+	0.669281i	−0.138007	+	0.990431i	$0.544070\pi$
$14$	−2.81398	−	3.40152i	−0.752068	−	0.909094i
$15$	0.413935	−	2.19742i	0.106878	−	0.567372i
$16$	0.968583	−	0.248690i	0.242146	−	0.0621725i
$17$	0.390191	−	3.08868i	0.0946352	−	0.749115i	−0.871376	−	0.490615i	$-0.836772\pi$
$17$	0.390191	−	3.08868i	0.0946352	−	0.749115i	0.966011	−	0.258499i	$-0.0832280\pi$
$18$	0.587785	−	0.809017i	0.138542	−	0.190687i
$19$	−0.674016	+	1.43236i	−0.154630	+	0.328605i	−0.967100	−	0.254398i	$-0.918123\pi$
$19$	−0.674016	+	1.43236i	−0.154630	+	0.328605i	0.812470	+	0.583003i	$0.198123\pi$
$20$	−1.07272	+	1.96196i	−0.239867	+	0.438707i
$21$	3.86856	+	2.12676i	0.844188	+	0.464096i
$22$	−0.494820	−	3.91690i	−0.105496	−	0.835087i
$23$	−2.97937	−	7.52503i	−0.621241	−	1.56908i	−0.809604	−	0.586977i	$-0.800318\pi$
$23$	−2.97937	−	7.52503i	−0.621241	−	1.56908i	0.188362	−	0.982100i	$-0.439682\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	−1.56698	−	4.74811i	−0.313397	−	0.949622i
$26$	3.06273	+	2.22521i	0.600652	+	0.436399i
$27$	−0.248690	+	0.968583i	−0.0478604	+	0.186404i
$28$	−3.02201	−	3.21812i	−0.571107	−	0.608167i
$29$	5.46672	−	5.13360i	1.01515	−	0.953285i	0.0162308	−	0.999868i	$-0.494833\pi$
$29$	5.46672	−	5.13360i	1.01515	−	0.953285i	0.998914	+	0.0465835i	$0.0148333\pi$
$30$	0.275141	−	2.21908i	0.0502337	−	0.405146i
$31$	−8.01388	−	1.01239i	−1.43934	−	0.181830i	−0.633396	−	0.773828i	$-0.718340\pi$
$31$	−8.01388	−	1.01239i	−1.43934	−	0.181830i	−0.805940	+	0.591997i	$0.798340\pi$
$32$	0.951057	−	0.309017i	0.168125	−	0.0546270i
$33$	1.90198	+	3.45969i	0.331092	+	0.602255i
$34$	0.195481	−	3.10708i	0.0335248	−	0.532861i
$35$	9.87135	−	0.0227459i	1.66856	−	0.00384476i
$36$	0.535827	−	0.844328i	0.0893045	−	0.140721i
$37$	−1.00164	−	3.90112i	−0.164668	−	0.641340i	−0.996295	−	0.0860045i	$-0.972590\pi$
$37$	−1.00164	−	3.90112i	−0.164668	−	0.641340i	0.831627	−	0.555335i	$-0.187410\pi$
$38$	−0.582748	+	1.47185i	−0.0945341	+	0.238766i
$39$	−3.66681	−	0.941477i	−0.587160	−	0.150757i
$40$	−0.947407	+	2.02544i	−0.149798	+	0.320251i
$41$	10.1725	+	4.02758i	1.58868	+	0.629002i	0.985663	−	0.168728i	$-0.0539659\pi$
$41$	10.1725	+	4.02758i	1.58868	+	0.629002i	0.603015	+	0.797730i	$0.293966\pi$
$42$	3.99446	+	1.87965i	0.616359	+	0.290037i
$43$	7.03128	+	2.28460i	1.07226	+	0.348399i	0.791368	−	0.611341i	$-0.209369\pi$
$43$	7.03128	+	2.28460i	1.07226	+	0.348399i	0.280893	+	0.959739i	$0.409369\pi$
$44$	−0.739788	−	3.87810i	−0.111527	−	0.584646i
$45$	0.561077	+	2.16453i	0.0836404	+	0.322669i
$46$	−3.44599	−	7.32310i	−0.508084	−	1.07973i
$47$	−11.0639	−	2.11055i	−1.61383	−	0.307855i	−0.700060	−	0.714084i	$-0.746843\pi$
$47$	−11.0639	−	2.11055i	−1.61383	−	0.307855i	−0.913771	+	0.406229i	$0.866843\pi$
$48$	−0.770513	+	0.637424i	−0.111214	+	0.0920042i
$49$	−3.85926	+	11.8776i	−0.551323	+	1.69680i
$50$	−1.86203	−	4.64035i	−0.263330	−	0.656245i
$51$	0.962040	+	2.96086i	0.134713	+	0.414603i
$52$	3.19641	+	2.02850i	0.443263	+	0.281303i
$53$	2.77383	−	5.04558i	0.381015	−	0.693064i	−0.614371	−	0.789018i	$-0.710590\pi$
$53$	2.77383	−	5.04558i	0.381015	−	0.693064i	0.995386	+	0.0959536i	$0.0305900\pi$
$54$	−0.187381	+	0.982287i	−0.0254994	+	0.133672i
$55$	7.46467	+	4.71313i	1.00654	+	0.635518i
$56$	−3.21812	−	3.02201i	−0.430039	−	0.403833i
$57$		−	1.58302i		−	0.209676i
$58$	5.13360	−	5.46672i	0.674074	−	0.717816i
$59$	1.99641	+	3.14583i	0.259910	+	0.409553i	0.949074	−	0.315053i	$-0.102022\pi$
$59$	1.99641	+	3.14583i	0.259910	+	0.409553i	−0.689164	+	0.724605i	$0.742022\pi$
$60$	0.135261	−	2.23197i	0.0174622	−	0.288147i
$61$	2.25272	−	0.891915i	0.288431	−	0.114198i	−0.219454	−	0.975623i	$-0.570428\pi$
$61$	2.25272	−	0.891915i	0.288431	−	0.114198i	0.507885	+	0.861425i	$0.330428\pi$
$62$	−8.06164	−	0.507195i	−1.02383	−	0.0644139i
$63$	−4.40590	−	0.277196i	−0.555092	−	0.0349234i
$64$	0.929776	−	0.368125i	0.116222	−	0.0460156i
$65$	−8.19437	+	2.12409i	−1.01639	+	0.263461i
$66$	2.11546	+	3.33344i	0.260395	+	0.410318i
$67$	−7.44291	+	7.92589i	−0.909296	+	0.968302i	−0.999619	−	0.0276105i	$-0.991210\pi$
$67$	−7.44291	+	7.92589i	−0.909296	+	0.968302i	0.0903226	+	0.995913i	$0.471210\pi$
$68$		−	3.11323i		−	0.377534i
$69$	5.89981	+	5.54029i	0.710254	+	0.666973i
$70$	9.85045	−	0.642528i	1.17735	−	0.0767968i
$71$	1.94409	−	10.1913i	0.230721	−	1.20948i	−0.658705	−	0.752401i	$-0.728895\pi$
$71$	1.94409	−	10.1913i	0.230721	−	1.20948i	0.889426	−	0.457080i	$-0.151105\pi$
$72$	0.481754	−	0.876307i	0.0567752	−	0.103274i
$73$	−3.55645	−	2.25699i	−0.416250	−	0.264161i	0.311168	−	0.950355i	$-0.399280\pi$
$73$	−3.55645	−	2.25699i	−0.416250	−	0.264161i	−0.727418	+	0.686194i	$0.759280\pi$
$74$	−1.24461	−	3.83052i	−0.144683	−	0.445289i
$75$	3.43950	+	3.62903i	0.397159	+	0.419044i
$76$	−0.489179	+	1.50554i	−0.0561127	+	0.172697i
$77$	−13.4293	+	11.1097i	−1.53041	+	1.26607i
$78$	−3.71869	−	0.709378i	−0.421059	−	0.0803213i
$79$	5.86407	+	12.4618i	0.659760	+	1.40206i	0.901954	+	0.431833i	$0.142133\pi$
$79$	5.86407	+	12.4618i	0.659760	+	1.40206i	−0.242194	+	0.970228i	$0.577867\pi$
$80$	−0.818359	+	2.08093i	−0.0914953	+	0.232656i
$81$	−0.187381	−	0.982287i	−0.0208201	−	0.109143i
$82$	10.4053	+	3.38089i	1.14908	+	0.373357i
$83$	−15.1477	−	7.12795i	−1.66267	−	0.782395i	−0.999422	−	0.0339981i	$-0.989176\pi$
$83$	−15.1477	−	7.12795i	−1.66267	−	0.782395i	−0.663251	−	0.748397i	$-0.730824\pi$
$84$	4.10461	+	1.62513i	0.447849	+	0.177316i
$85$	5.08560	+	4.75369i	0.551611	+	0.515610i
$86$	7.16086	+	1.83860i	0.772175	+	0.198261i
$87$	−2.76066	+	6.97263i	−0.295974	+	0.747545i
$88$	−0.981836	−	3.82400i	−0.104664	−	0.407640i
$89$	−5.36521	+	8.45423i	−0.568712	+	0.896146i	−0.999982	−	0.00607683i	$-0.998066\pi$
$89$	−5.36521	+	8.45423i	−0.568712	+	0.896146i	0.431270	+	0.902223i	$0.358066\pi$
$90$	0.695881	+	2.12503i	0.0733523	+	0.223998i
$91$	1.04939	−	16.6796i	0.110006	−	1.74850i
$92$	−3.89901	−	7.09228i	−0.406500	−	0.739421i
$93$	7.68223	−	2.49611i	0.796610	−	0.258834i
$94$	−11.1746	−	1.41168i	−1.15257	−	0.145603i
$95$	−1.71242	−	3.09796i	−0.175691	−	0.317844i
$96$	−0.728969	+	0.684547i	−0.0744000	+	0.0698663i
$97$	−2.40662	−	2.56279i	−0.244355	−	0.260212i	0.595086	−	0.803662i	$-0.297118\pi$
$97$	−2.40662	−	2.56279i	−0.244355	−	0.260212i	−0.839442	+	0.543450i	$0.817118\pi$
$98$	−3.10584	+	12.0965i	−0.313738	+	1.22193i
$99$	−3.19403	−	2.32060i	−0.321012	−	0.233229i
$100$	−2.14972	−	4.51428i	−0.214972	−	0.451428i
$101$	1.06129	−	0.771074i	0.105603	−	0.0767247i	−0.533731	−	0.845654i	$-0.679210\pi$
$101$	1.06129	−	0.771074i	0.105603	−	0.0767247i	0.639333	+	0.768930i	$0.279210\pi$
$102$	1.14606	+	2.89461i	0.113476	+	0.286609i
$103$	0.0904160	+	0.715716i	0.00890895	+	0.0705216i	0.995942	−	0.0899932i	$-0.0286845\pi$
$103$	0.0904160	+	0.715716i	0.00890895	+	0.0705216i	−0.987033	+	0.160515i	$0.948685\pi$
$104$	3.31748	+	1.82380i	0.325305	+	0.178838i
$105$	−8.92218	+	4.22360i	−0.870716	+	0.412181i
$106$	2.45154	−	5.20980i	0.238115	−	0.506020i
$107$	1.34364	−	1.84936i	0.129895	−	0.178785i	−0.739116	−	0.673578i	$-0.764756\pi$
$107$	1.34364	−	1.84936i	0.129895	−	0.178785i	0.869011	+	0.494794i	$0.164756\pi$
$108$	−0.125333	+	0.992115i	−0.0120602	+	0.0954663i
$109$	−12.6308	+	3.24303i	−1.20981	+	0.310626i	−0.799133	−	0.601154i	$-0.794708\pi$
$109$	−12.6308	+	3.24303i	−1.20981	+	0.310626i	−0.410677	+	0.911781i	$0.634708\pi$
$110$	7.74588	+	4.23512i	0.738541	+	0.403803i
$111$	2.56732	+	3.10336i	0.243679	+	0.294558i
$112$	−3.40152	−	2.81398i	−0.321413	−	0.265896i
$113$	−10.4595	+	6.63780i	−0.983947	+	0.624432i	−0.927441	−	0.373970i	$-0.877996\pi$
$113$	−10.4595	+	6.63780i	−0.983947	+	0.624432i	−0.0565067	+	0.998402i	$0.517996\pi$
$114$	−0.0993985	−	1.57989i	−0.00930952	−	0.147971i
$115$	17.5391	+	4.46022i	1.63553	+	0.415918i
$116$	4.78021	−	5.77828i	0.443831	−	0.536500i
$117$	3.71869	−	0.709378i	0.343793	−	0.0655820i
$118$	2.19000	+	3.01427i	0.201605	+	0.277486i
$119$	−12.0437	+	6.62108i	−1.10404	+	0.606953i
$120$	−0.00515241	−	2.23606i	−0.000470348	−	0.204124i
$121$	−4.55081	+	0.574900i	−0.413710	+	0.0522637i
$122$	2.19227	−	1.03160i	0.198479	−	0.0933971i
$123$	−10.9192	+	0.686979i	−0.984552	+	0.0619428i
$124$	−8.07758			−0.725388
$125$	10.6568	+	3.38133i	0.953170	+	0.302435i
$126$	−4.41462			−0.393285
$127$	14.5850	−	0.917608i	1.29421	−	0.0814245i	0.599299	−	0.800525i	$-0.295446\pi$
$127$	14.5850	−	0.917608i	1.29421	−	0.0814245i	0.694906	+	0.719101i	$0.255446\pi$
$128$	0.904827	−	0.425779i	0.0799762	−	0.0376339i
$129$	−7.33483	+	0.926605i	−0.645796	+	0.0815830i
$130$	−8.04482	+	2.63443i	−0.705578	+	0.231055i
$131$	3.12799	−	1.71962i	0.273293	−	0.150244i	−0.339214	−	0.940709i	$-0.610161\pi$
$131$	3.12799	−	1.71962i	0.273293	−	0.150244i	0.612507	+	0.790465i	$0.290161\pi$
$132$	2.32060	+	3.19403i	0.201982	+	0.278004i
$133$	6.86463	−	1.30950i	0.595239	−	0.113548i
$134$	−6.93055	+	8.37760i	−0.598708	+	0.723714i
$135$	−1.42929	−	1.71963i	−0.123014	−	0.148002i
$136$	−0.195481	−	3.10708i	−0.0167624	−	0.266430i
$137$	4.01449	−	2.54767i	0.342981	−	0.217662i	−0.353167	−	0.935560i	$-0.614895\pi$
$137$	4.01449	−	2.54767i	0.342981	−	0.217662i	0.696149	+	0.717898i	$0.254895\pi$
$138$	6.23605	+	5.15891i	0.530848	+	0.439156i
$139$	5.44543	+	6.58239i	0.461875	+	0.558311i	0.949104	−	0.314963i	$-0.101992\pi$
$139$	5.44543	+	6.58239i	0.461875	+	0.558311i	−0.487229	+	0.873274i	$0.661992\pi$
$140$	9.79066	−	1.25978i	0.827462	−	0.106470i
$141$	10.9095	−	2.80109i	0.918747	−	0.235894i
$142$	1.30034	−	10.2932i	0.109122	−	0.863789i
$143$	8.78519	−	12.0918i	0.734655	−	1.01117i
$144$	0.425779	−	0.904827i	0.0354816	−	0.0754023i
$145$	2.14002	+	16.6317i	0.177719	+	1.38119i
$146$	−3.69115	−	2.02922i	−0.305481	−	0.167940i
$147$	−1.56526	−	12.3903i	−0.129101	−	1.02194i
$148$	−1.48268	−	3.74482i	−0.121875	−	0.307822i
$149$	−3.80659	+	2.76565i	−0.311848	+	0.226571i	−0.732689	−	0.680563i	$-0.761735\pi$
$149$	−3.80659	+	2.76565i	−0.311848	+	0.226571i	0.420841	+	0.907134i	$0.361735\pi$
$150$	3.66058	+	3.40590i	0.298885	+	0.278091i
$151$	16.0328	+	11.6485i	1.30473	+	0.947942i	0.999990	−	0.00449290i	$-0.00143014\pi$
$151$	16.0328	+	11.6485i	1.30473	+	0.947942i	0.304741	+	0.952435i	$0.401430\pi$
$152$	−0.393680	+	1.53328i	−0.0319317	+	0.124366i
$153$	−2.13115	−	2.26945i	−0.172293	−	0.183474i
$154$	−12.7052	+	11.9310i	−1.02382	+	0.961428i
$155$	12.3339	−	13.1951i	0.990685	−	1.05986i
$156$	−3.75590	−	0.474480i	−0.300712	−	0.0379888i
$157$	−0.403537	+	0.131117i	−0.0322058	+	0.0104643i	−0.325076	−	0.945688i	$-0.605390\pi$
$157$	−0.403537	+	0.131117i	−0.0322058	+	0.0104643i	0.292870	+	0.956152i	$0.405390\pi$
$158$	6.63498	+	12.0690i	0.527851	+	0.960157i
$159$	−0.361534	+	5.74642i	−0.0286715	+	0.455721i
$160$	−0.686081	+	2.12821i	−0.0542395	+	0.168250i
$161$	−19.1446	+	30.1671i	−1.50881	+	2.37750i
$162$	−0.248690	−	0.968583i	−0.0195389	−	0.0760991i
$163$	−0.706173	+	1.78359i	−0.0553118	+	0.139702i	−0.954805	−	0.297233i	$-0.903936\pi$
$163$	−0.706173	+	1.78359i	−0.0553118	+	0.139702i	0.899493	+	0.436935i	$0.143936\pi$
$164$	10.5971	+	2.72087i	0.827493	+	0.212464i
$165$	−8.76099	−	1.08627i	−0.682042	−	0.0845657i
$166$	−15.5654	−	6.16276i	−1.20811	−	0.478323i
$167$	17.9376	+	8.44081i	1.38806	+	0.653170i	0.967214	−	0.253964i	$-0.0817344\pi$
$167$	17.9376	+	8.44081i	1.38806	+	0.653170i	0.420843	+	0.907134i	$0.361734\pi$
$168$	4.19855	+	1.36419i	0.323925	+	0.105250i
$169$	0.249570	+	1.30829i	0.0191977	+	0.100638i
$170$	5.37405	+	4.42499i	0.412171	+	0.339381i
$171$	0.674016	+	1.43236i	0.0515433	+	0.109535i
$172$	7.26217	+	1.38533i	0.553736	+	0.105631i
$173$	17.1086	−	14.1535i	1.30074	−	1.07607i	0.308569	−	0.951202i	$-0.400150\pi$
$173$	17.1086	−	14.1535i	1.30074	−	1.07607i	0.992174	−	0.124866i	$-0.0398501\pi$
$174$	−2.31740	+	7.13222i	−0.175682	+	0.540692i
$175$	−12.8918	+	17.9171i	−0.974528	+	1.35441i
$176$	−1.22001	−	3.75480i	−0.0919617	−	0.283029i
$177$	−3.14583	−	1.99641i	−0.236455	−	0.150059i
$178$	−4.82378	+	8.77443i	−0.361558	+	0.657671i
$179$	1.45869	−	7.64671i	0.109028	−	0.571542i	−0.885286	−	0.465047i	$-0.846037\pi$
$179$	1.45869	−	7.64671i	0.109028	−	0.571542i	0.994313	−	0.106495i	$-0.0339627\pi$
$180$	0.827940	+	2.07714i	0.0617110	+	0.154821i
$181$	−5.58294	−	5.24273i	−0.414977	−	0.389689i	0.448744	−	0.893661i	$-0.351872\pi$
$181$	−5.58294	−	5.24273i	−0.414977	−	0.389689i	−0.863720	+	0.503971i	$0.831872\pi$
$182$		−	16.7126i		−	1.23882i
$183$	−1.65856	+	1.76619i	−0.122604	+	0.130561i
$184$	−4.33665	−	6.83346i	−0.319702	−	0.503769i
$185$	8.38128	+	3.29606i	0.616204	+	0.242331i
$186$	7.51034	−	2.97355i	0.550685	−	0.218032i
$187$	−12.2669	−	0.771767i	−0.897043	−	0.0564372i
$188$	−11.2411	−	0.707233i	−0.819845	−	0.0515803i
$189$	4.10461	−	1.62513i	0.298566	−	0.118211i
$190$	−1.90357	−	2.98432i	−0.138099	−	0.216505i
$191$	2.07045	+	3.26251i	0.149813	+	0.236067i	0.910943	−	0.412532i	$-0.135355\pi$
$191$	2.07045	+	3.26251i	0.149813	+	0.236067i	−0.761130	+	0.648599i	$0.775355\pi$
$192$	−0.684547	+	0.728969i	−0.0494029	+	0.0526088i
$193$			4.45208i			0.320468i	0.987079	+	0.160234i	$0.0512249\pi$
$193$			4.45208i			0.320468i	−0.987079	+	0.160234i	$0.948775\pi$
$194$	−2.56279	−	2.40662i	−0.183998	−	0.172785i
$195$	6.51009	−	5.41093i	0.466197	−	0.387485i
$196$	−2.34017	+	12.2676i	−0.167155	+	0.876258i
$197$	0.255473	−	0.464703i	0.0182017	−	0.0331087i	−0.867049	−	0.498222i	$-0.833986\pi$
$197$	0.255473	−	0.464703i	0.0182017	−	0.0331087i	0.885251	+	0.465113i	$0.153986\pi$
$198$	−3.33344	−	2.11546i	−0.236897	−	0.150339i
$199$	−1.91383	−	5.89016i	−0.135668	−	0.417542i	0.860026	−	0.510251i	$-0.170447\pi$
$199$	−1.91383	−	5.89016i	−0.135668	−	0.417542i	−0.995693	+	0.0927087i	$0.970447\pi$
$200$	−2.42893	−	4.37039i	−0.171752	−	0.309033i
$201$	3.35986	−	10.3406i	0.236987	−	0.729370i
$202$	1.01078	−	0.836192i	0.0711184	−	0.0588342i
$203$	−32.5199	−	6.20351i	−2.28245	−	0.435401i
$204$	1.32555	+	2.81693i	0.0928069	+	0.197225i
$205$	−20.6257	+	13.1562i	−1.44056	+	0.918871i
$206$	0.135178	+	0.708627i	0.00941828	+	0.0493724i
$207$	−7.69725	−	2.50099i	−0.534996	−	0.173831i
$208$	3.42545	+	1.61189i	0.237512	+	0.111765i
$209$	5.81092	+	2.30071i	0.401950	+	0.159143i
$210$	−8.63937	+	4.77549i	−0.596173	+	0.329540i
$211$	6.44234	+	1.65411i	0.443509	+	0.113874i	0.463839	−	0.885920i	$-0.346472\pi$
$211$	6.44234	+	1.65411i	0.443509	+	0.113874i	−0.0203298	+	0.999793i	$0.506472\pi$
$212$	2.11958	−	5.35345i	0.145573	−	0.367676i
$213$	2.58017	+	10.0491i	0.176790	+	0.688552i
$214$	1.22487	−	1.93008i	0.0837303	−	0.131938i
$215$	−13.3519	+	9.74778i	−0.910590	+	0.664793i
$216$	−0.0627905	+	0.998027i	−0.00427235	+	0.0679071i
$217$	17.1790	+	31.2486i	1.16619	+	2.12129i
$218$	−12.4022	+	4.02973i	−0.839985	+	0.272928i
$219$	4.17895	+	0.527924i	0.282387	+	0.0356738i
$220$	7.99652	+	3.74039i	0.539125	+	0.252177i
$221$	8.59155	−	8.06800i	0.577930	−	0.542712i
$222$	2.75712	+	2.93603i	0.185046	+	0.197054i
$223$	6.67911	−	26.0134i	0.447267	−	1.74199i	−0.200068	−	0.979782i	$-0.564116\pi$
$223$	6.67911	−	26.0134i	0.447267	−	1.74199i	0.647334	−	0.762206i	$-0.275884\pi$
$224$	−3.57150	−	2.59485i	−0.238631	−	0.173375i
$225$	−4.65732	−	1.81918i	−0.310488	−	0.121279i
$226$	−10.0221	+	7.28146i	−0.666658	+	0.484356i
$227$	1.72688	+	4.36161i	0.114617	+	0.289490i	0.975749	−	0.218891i	$-0.0702440\pi$
$227$	1.72688	+	4.36161i	0.114617	+	0.289490i	−0.861132	+	0.508382i	$0.830244\pi$
$228$	−0.198405	−	1.57053i	−0.0131397	−	0.104011i
$229$	0.590709	+	0.324745i	0.0390352	+	0.0214598i	0.501152	−	0.865359i	$-0.332910\pi$
$229$	0.590709	+	0.324745i	0.0390352	+	0.0214598i	−0.462117	+	0.886819i	$0.652910\pi$
$230$	17.7845	+	3.35013i	1.17268	+	0.220901i
$231$	7.42093	−	15.7703i	0.488261	−	1.03761i
$232$	4.40795	−	6.06703i	0.289396	−	0.398320i
$233$	0.0157100	−	0.124357i	0.00102920	−	0.00814692i	−0.991592	−	0.129406i	$-0.958693\pi$
$233$	0.0157100	−	0.124357i	0.00102920	−	0.00814692i	0.992621	+	0.121259i	$0.0386931\pi$
$234$	3.66681	−	0.941477i	0.239707	−	0.0615463i
$235$	18.3198	−	17.2830i	1.19505	−	1.12742i
$236$	2.37494	+	2.87081i	0.154596	+	0.186874i
$237$	−10.6119	−	8.77896i	−0.689320	−	0.570255i
$238$	−11.6042	+	7.36424i	−0.752188	+	0.477353i
$239$	−0.654816	−	10.4080i	−0.0423565	−	0.673238i	−0.960723	−	0.277508i	$-0.910492\pi$
$239$	−0.654816	−	10.4080i	−0.0423565	−	0.673238i	0.918367	−	0.395730i	$-0.129508\pi$
$240$	−0.145546	−	2.23133i	−0.00939494	−	0.144031i
$241$	14.2950	−	17.2797i	0.920823	−	1.11308i	−0.0724599	−	0.997371i	$-0.523085\pi$
$241$	14.2950	−	17.2797i	0.920823	−	1.11308i	0.993283	−	0.115712i	$-0.0369151\pi$
$242$	−4.50573	+	0.859513i	−0.289639	+	0.0552516i
$243$	0.587785	+	0.809017i	0.0377064	+	0.0518985i
$244$	2.12317	−	1.16722i	0.135922	−	0.0747238i
$245$	−16.4664	−	22.5546i	−1.05200	−	1.44096i
$246$	−10.8545	+	1.37125i	−0.692060	+	0.0874275i
$247$	−5.42254	+	2.55165i	−0.345028	+	0.162358i
$248$	−8.06164	+	0.507195i	−0.511915	+	0.0322069i
$249$	16.7410			1.06092
$250$	10.8481	+	2.70551i	0.686091	+	0.171112i
$251$	26.0248			1.64267			0.821337	−	0.570444i	$-0.193229\pi$
$251$	26.0248			1.64267			0.821337	+	0.570444i	$0.193229\pi$
$252$	−4.40590	+	0.277196i	−0.277546	+	0.0174617i
$253$	−28.9119	+	13.6049i	−1.81767	+	0.855332i
$254$	14.4986	−	1.83159i	0.909720	−	0.114924i
$255$	−6.62561	−	2.13593i	−0.414912	−	0.133757i
$256$	0.876307	−	0.481754i	0.0547692	−	0.0301096i
$257$	−18.0855	−	24.8925i	−1.12814	−	1.55275i	−0.791555	−	0.611098i	$-0.790728\pi$
$257$	−18.0855	−	24.8925i	−1.12814	−	1.55275i	−0.336585	−	0.941653i	$-0.609272\pi$
$258$	−7.26217	+	1.38533i	−0.452123	+	0.0862471i
$259$	−11.3337	+	13.7001i	−0.704244	+	0.851285i
$260$	−7.86353	+	3.13437i	−0.487676	+	0.194385i
$261$	−0.470882	−	7.48446i	−0.0291469	−	0.463276i
$262$	3.01384	−	1.91264i	0.186195	−	0.118163i
$263$	−6.92479	−	5.72868i	−0.427001	−	0.353246i	0.398965	−	0.916966i	$-0.369369\pi$
$263$	−6.92479	−	5.72868i	−0.427001	−	0.353246i	−0.825966	+	0.563721i	$0.809369\pi$
$264$	2.51657	+	3.04201i	0.154884	+	0.187223i
$265$	5.50865	+	11.6368i	0.338393	+	0.714843i
$266$	6.76886	−	1.73795i	0.415025	−	0.106560i
$267$	1.25496	−	9.93401i	0.0768021	−	0.607951i
$268$	−6.39084	+	8.79624i	−0.390383	+	0.537316i
$269$	0.849177	−	1.80459i	0.0517753	−	0.110028i	−0.877265	−	0.480006i	$-0.840635\pi$
$269$	0.849177	−	1.80459i	0.0517753	−	0.110028i	0.929041	+	0.369978i	$0.120635\pi$
$270$	−1.53445	−	1.62649i	−0.0933834	−	0.0989852i
$271$	17.9231	+	9.85333i	1.08875	+	0.598547i	0.921898	−	0.387434i	$-0.126638\pi$
$271$	17.9231	+	9.85333i	1.08875	+	0.598547i	0.166856	+	0.985981i	$0.446638\pi$
$272$	−0.390191	−	3.08868i	−0.0236588	−	0.187279i
$273$	6.15232	+	15.5390i	0.372356	+	0.940463i
$274$	3.84660	−	2.79472i	0.232382	−	0.168835i
$275$	−18.3203	+	7.35135i	−1.10475	+	0.443303i
$276$	6.54768	+	4.75716i	0.394124	+	0.286348i
$277$	1.81241	−	7.05888i	0.108897	−	0.424127i	−0.890635	−	0.454720i	$-0.849739\pi$
$277$	1.81241	−	7.05888i	0.108897	−	0.424127i	0.999532	+	0.0305926i	$0.00973943\pi$
$278$	5.84800	+	6.22748i	0.350740	+	0.373500i
$279$	−5.88830	+	5.52948i	−0.352523	+	0.331041i
$280$	9.69224	−	1.87205i	0.579222	−	0.111876i
$281$	−13.6007	−	1.71817i	−0.811348	−	0.102497i	−0.291298	−	0.956632i	$-0.594087\pi$
$281$	−13.6007	−	1.71817i	−0.811348	−	0.102497i	−0.520051	+	0.854135i	$0.674087\pi$
$282$	10.7121	−	3.48057i	0.637897	−	0.207265i
$283$	3.55678	+	6.46976i	0.211429	+	0.384587i	0.960663	−	0.277718i	$-0.0895782\pi$
$283$	3.55678	+	6.46976i	0.211429	+	0.384587i	−0.749234	+	0.662305i	$0.769578\pi$
$284$	0.651454	−	10.3546i	0.0386567	−	0.614430i
$285$	2.86849	+	2.07400i	0.169915	+	0.122853i
$286$	8.00861	−	12.6195i	0.473559	−	0.746209i
$287$	−12.0116	−	46.7820i	−0.709021	−	2.76146i
$288$	0.368125	−	0.929776i	0.0216919	−	0.0547876i
$289$	7.07822	+	1.81738i	0.416366	+	0.106905i
$290$	3.18012	+	16.4645i	0.186743	+	0.966831i
$291$	3.26876	+	1.29419i	0.191618	+	0.0758670i
$292$	−3.81128	−	1.79345i	−0.223038	−	0.104954i
$293$	−0.503074	−	0.163459i	−0.0293899	−	0.00954935i	0.294285	−	0.955718i	$-0.404918\pi$
$293$	−0.503074	−	0.163459i	−0.0293899	−	0.00954935i	−0.323675	+	0.946168i	$0.604918\pi$
$294$	−2.34017	−	12.2676i	−0.136482	−	0.715462i
$295$	−8.31598	−	0.503962i	−0.484175	−	0.0293418i
$296$	−1.71489	−	3.64433i	−0.0996760	−	0.211822i
$297$	3.87810	+	0.739788i	0.225030	+	0.0429268i
$298$	−3.62542	+	2.99921i	−0.210015	+	0.173740i
$299$	9.46811	−	29.1399i	0.547555	−	1.68520i
$300$	3.86721	+	3.16933i	0.223274	+	0.182981i
$301$	−10.0856	−	31.0404i	−0.581327	−	1.78914i
$302$	16.7326	+	10.6188i	0.962852	+	0.611044i
$303$	−0.631979	+	1.14957i	−0.0363062	+	0.0660408i
$304$	−0.296628	+	1.55498i	−0.0170128	+	0.0891841i
$305$	−1.33523	+	5.25057i	−0.0764549	+	0.300647i
$306$	−2.26945	−	2.13115i	−0.129736	−	0.121830i
$307$			15.5262i			0.886130i	0.896490	+	0.443065i	$0.146109\pi$
$307$			15.5262i			0.886130i	−0.896490	+	0.443065i	$0.853891\pi$
$308$	−11.9310	+	12.7052i	−0.679832	+	0.723948i
$309$	−0.386548	−	0.609102i	−0.0219900	−	0.0346506i
$310$	11.4811	−	13.9435i	0.652080	−	0.791938i
$311$	−3.00505	+	1.18978i	−0.170401	+	0.0674665i	−0.451776	−	0.892131i	$-0.649209\pi$
$311$	−3.00505	+	1.18978i	−0.170401	+	0.0674665i	0.281375	+	0.959598i	$0.409209\pi$
$312$	−3.77828	−	0.237709i	−0.213903	−	0.0134576i
$313$	21.8968	+	1.37763i	1.23768	+	0.0778684i	0.668104	−	0.744068i	$-0.267106\pi$
$313$	21.8968	+	1.37763i	1.23768	+	0.0778684i	0.569579	+	0.821937i	$0.307106\pi$
$314$	−0.394508	+	0.156197i	−0.0222634	+	0.00881470i
$315$	6.27471	−	7.62051i	0.353540	−	0.429367i
$316$	7.37971	+	11.6286i	0.415141	+	0.654158i
$317$	−2.21289	+	2.35649i	−0.124288	+	0.132354i	−0.788103	−	0.615544i	$-0.788937\pi$
$317$	−2.21289	+	2.35649i	−0.124288	+	0.132354i	0.663814	+	0.747897i	$0.268937\pi$
$318$			5.75778i			0.322880i
$319$	−21.5828	−	20.2676i	−1.20841	−	1.13477i
$320$	−0.551095	+	2.16709i	−0.0308072	+	0.121144i
$321$	−0.428343	+	2.24545i	−0.0239077	+	0.125329i
$322$	−17.2126	+	31.3097i	−0.959223	+	1.74482i
$323$	4.16110	+	2.64071i	0.231530	+	0.146933i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	6.88695	−	17.6314i	0.382019	−	0.978015i
$326$	−0.592787	+	1.82441i	−0.0328315	+	0.101045i
$327$	10.0479	−	8.31231i	0.555648	−	0.459672i
$328$	10.7470	+	2.05010i	0.593404	+	0.113198i
$329$	21.1712	+	44.9911i	1.16721	+	2.48044i
$330$	−8.81191	−	0.534016i	−0.485080	−	0.0293966i
$331$	0.278844	+	1.46175i	0.0153267	+	0.0803451i	0.989129	−	0.147052i	$-0.0469785\pi$
$331$	0.278844	+	1.46175i	0.0153267	+	0.0803451i	−0.973802	+	0.227397i	$0.926978\pi$
$332$	−15.9216	−	5.17324i	−0.873811	−	0.283919i
$333$	−3.64433	−	1.71489i	−0.199708	−	0.0939754i
$334$	18.4323	+	7.29784i	1.00857	+	0.399320i
$335$	−4.61067	−	23.8710i	−0.251908	−	1.30421i
$336$	4.27592	+	1.09787i	0.233271	+	0.0598937i
$337$	2.28904	−	5.78147i	0.124692	−	0.314937i	−0.853999	−	0.520275i	$-0.825829\pi$
$337$	2.28904	−	5.78147i	0.124692	−	0.314937i	0.978691	+	0.205338i	$0.0658295\pi$
$338$	0.331226	+	1.29004i	0.0180163	+	0.0701689i
$339$	6.63780	−	10.4595i	0.360516	−	0.568082i
$340$	5.64130	+	4.07881i	0.305942	+	0.221205i
$341$	−2.00242	+	31.8276i	−0.108437	+	1.72356i
$342$	0.762624	+	1.38721i	0.0412380	+	0.0750117i
$343$	23.0451	−	7.48781i	1.24432	−	0.404304i
$344$	7.33483	+	0.926605i	0.395468	+	0.0499592i
$345$	−17.7689	+	3.43205i	−0.956646	+	0.184776i
$346$	16.1861	−	15.1998i	0.870172	−	0.817146i
$347$	17.7653	+	18.9181i	0.953689	+	1.01558i	0.999862	+	0.0166425i	$0.00529773\pi$
$347$	17.7653	+	18.9181i	0.953689	+	1.01558i	−0.0461721	+	0.998933i	$0.514702\pi$
$348$	−1.86499	+	7.26366i	−0.0999739	+	0.389373i
$349$	2.33985	+	1.70000i	0.125249	+	0.0909990i	0.648646	−	0.761090i	$-0.275335\pi$
$349$	2.33985	+	1.70000i	0.125249	+	0.0909990i	−0.523397	+	0.852089i	$0.675335\pi$
$350$	−11.7413	+	18.6912i	−0.627601	+	0.999088i
$351$	−3.06273	+	2.22521i	−0.163477	+	0.118773i
$352$	−1.45337	−	3.67079i	−0.0774648	−	0.195654i
$353$	3.05032	+	24.1458i	0.162352	+	1.28515i	0.837079	+	0.547082i	$0.184261\pi$
$353$	3.05032	+	24.1458i	0.162352	+	1.28515i	−0.674727	+	0.738067i	$0.735739\pi$
$354$	−3.26498	−	1.79494i	−0.173532	−	0.0953999i
$355$	15.9199	+	16.8749i	0.844942	+	0.895628i
$356$	−4.26331	+	9.06000i	−0.225955	+	0.480179i
$357$	8.07835	−	11.1189i	0.427551	−	0.588474i
$358$	0.975669	−	7.72322i	0.0515657	−	0.408185i
$359$	26.1966	−	6.72615i	1.38261	−	0.354993i	0.517114	−	0.855916i	$-0.327006\pi$
$359$	26.1966	−	6.72615i	1.38261	−	0.354993i	0.865491	+	0.500924i	$0.167006\pi$
$360$	0.956731	+	2.02106i	0.0504241	+	0.106519i
$361$	10.5137	+	12.7089i	0.553353	+	0.668889i
$362$	−5.90112	−	4.88183i	−0.310156	−	0.256583i
$363$	3.87291	−	2.45782i	0.203275	−	0.129002i
$364$	−1.04939	−	16.6796i	−0.0550032	−	0.874251i
$365$	8.74925	−	3.48742i	0.457957	−	0.182540i
$366$	−1.54439	+	1.86685i	−0.0807266	+	0.0975816i
$367$	−24.7897	+	4.72889i	−1.29401	+	0.246846i	−0.787997	−	0.615679i	$-0.788882\pi$
$367$	−24.7897	+	4.72889i	−1.29401	+	0.246846i	−0.506015	+	0.862525i	$0.668882\pi$
$368$	−4.75716	−	6.54768i	−0.247984	−	0.341321i
$369$	9.58750	−	5.27077i	0.499105	−	0.274385i
$370$	8.57170	+	2.76330i	0.445622	+	0.143657i
$371$	−25.2180	+	3.18577i	−1.30925	+	0.165397i
$372$	7.30881	−	3.43927i	0.378944	−	0.178318i
$373$	−25.3399	+	1.59425i	−1.31205	+	0.0825472i	−0.703345	−	0.710849i	$-0.748311\pi$
$373$	−25.3399	+	1.59425i	−1.31205	+	0.0825472i	−0.608705	+	0.793396i	$0.708311\pi$
$374$	−12.2911			−0.635559
$375$	−11.0822	+	1.47791i	−0.572284	+	0.0763190i
$376$	−11.2634			−0.580864
$377$	28.3343	−	1.78264i	1.45929	−	0.0918107i
$378$	3.99446	−	1.87965i	0.205453	−	0.0966788i
$379$	−34.7891	+	4.39488i	−1.78700	+	0.225750i	−0.947974	−	0.318349i	$-0.896872\pi$
$379$	−34.7891	+	4.39488i	−1.78700	+	0.225750i	−0.839021	+	0.544099i	$0.816872\pi$
$380$	−2.08720	−	2.85890i	−0.107071	−	0.146659i
$381$	−12.8062	+	7.04025i	−0.656080	+	0.360683i
$382$	2.27122	+	3.12607i	0.116206	+	0.159944i
$383$	20.2893	−	3.87038i	1.03673	−	0.197767i	0.359201	−	0.933260i	$-0.383049\pi$
$383$	20.2893	−	3.87038i	1.03673	−	0.197767i	0.677532	+	0.735493i	$0.263049\pi$
$384$	−0.637424	+	0.770513i	−0.0325284	+	0.0393201i
$385$	−2.53672	−	38.8899i	−0.129283	−	1.98201i
$386$	0.279549	+	4.44330i	0.0142287	+	0.226158i
$387$	6.24222	−	3.96144i	0.317310	−	0.201371i
$388$	−2.70885	−	2.24095i	−0.137521	−	0.113767i
$389$	−0.781992	−	0.945266i	−0.0396486	−	0.0479269i	0.750316	−	0.661079i	$-0.229901\pi$
$389$	−0.781992	−	0.945266i	−0.0396486	−	0.0479269i	−0.789965	+	0.613152i	$0.789901\pi$
$390$	6.15749	−	5.80902i	0.311797	−	0.294151i
$391$	−24.4049	+	6.26612i	−1.23421	+	0.316891i
$392$	−1.56526	+	12.3903i	−0.0790578	+	0.625807i
$393$	−2.09811	+	2.88779i	−0.105835	+	0.145670i
$394$	0.225789	−	0.479827i	0.0113751	−	0.0241733i
$395$	−30.2641	−	5.70095i	−1.52275	−	0.286846i
$396$	−3.45969	−	1.90198i	−0.173856	−	0.0955781i
$397$	−3.35787	−	26.5803i	−0.168527	−	1.33403i	−0.818691	−	0.574234i	$-0.805300\pi$
$397$	−3.35787	−	26.5803i	−0.168527	−	1.33403i	0.650164	−	0.759794i	$-0.274700\pi$
$398$	−2.27990	−	5.75837i	−0.114281	−	0.288641i
$399$	−5.65374	+	4.10769i	−0.283041	+	0.205641i
$400$	−2.69856	−	4.20925i	−0.134928	−	0.210462i
$401$	−4.72629	−	3.43385i	−0.236020	−	0.171478i	0.463488	−	0.886103i	$-0.346598\pi$
$401$	−4.72629	−	3.43385i	−0.236020	−	0.171478i	−0.699508	+	0.714625i	$0.746598\pi$
$402$	2.70394	−	10.5312i	0.134860	−	0.525247i
$403$	−20.9332	−	22.2916i	−1.04276	−	1.11042i
$404$	0.956283	−	0.898009i	0.0475768	−	0.0446776i
$405$	2.02544	+	0.947407i	0.100645	+	0.0470770i
$406$	−32.8453	−	4.14932i	−1.63008	−	0.205928i
$407$	−15.1230	+	4.91377i	−0.749621	+	0.243567i
$408$	1.49981	+	2.72814i	0.0742516	+	0.135063i
$409$	0.0389912	−	0.619747i	0.00192799	−	0.0306445i	−0.996945	−	0.0781054i	$-0.975113\pi$
$409$	0.0389912	−	0.619747i	0.00192799	−	0.0306445i	0.998873	+	0.0474609i	$0.0151129\pi$
$410$	−19.7589	+	14.4254i	−0.975823	+	0.712418i
$411$	−2.54767	+	4.01449i	−0.125667	+	0.198020i
$412$	0.179406	+	0.698741i	0.00883870	+	0.0344245i
$413$	6.05497	−	15.2931i	0.297946	−	0.752525i
$414$	−7.83910	−	2.01274i	−0.385271	−	0.0989208i
$415$	32.7620	−	18.1095i	1.60822	−	0.888959i
$416$	3.51990	+	1.39363i	0.172577	+	0.0683282i
$417$	−7.72982	−	3.63738i	−0.378531	−	0.178123i
$418$	5.94392	+	1.93130i	0.290727	+	0.0944628i
$419$	1.05055	+	5.50715i	0.0513225	+	0.269042i	0.998694	−	0.0510949i	$-0.0162711\pi$
$419$	1.05055	+	5.50715i	0.0513225	+	0.269042i	−0.947371	+	0.320137i	$0.896271\pi$
$420$	−8.32247	+	5.30854i	−0.406095	+	0.259030i
$421$	2.45940	+	5.22650i	0.119864	+	0.254724i	0.955751	−	0.294178i	$-0.0950459\pi$
$421$	2.45940	+	5.22650i	0.119864	+	0.254724i	−0.835887	+	0.548902i	$0.815046\pi$
$422$	6.53349	+	1.24633i	0.318046	+	0.0606704i
$423$	−8.67858	+	7.17955i	−0.421967	+	0.349081i
$424$	1.77925	−	5.47597i	0.0864081	−	0.265937i
$425$	−15.2768	+	2.98724i	−0.741034	+	0.144902i
$426$	3.20606	+	9.86725i	0.155334	+	0.478070i
$427$	−9.03093	−	5.73120i	−0.437037	−	0.277352i
$428$	1.10126	−	2.00318i	0.0532314	−	0.0968276i
$429$	−2.80065	+	14.6815i	−0.135217	+	0.708831i
$430$	−12.7135	+	10.5669i	−0.613097	+	0.509582i
$431$	8.82683	+	8.28895i	0.425174	+	0.399265i	0.867378	−	0.497650i	$-0.165803\pi$
$431$	8.82683	+	8.28895i	0.425174	+	0.399265i	−0.442205	+	0.896914i	$0.645803\pi$
$432$			1.00000i			0.0481125i
$433$	−10.8349	+	11.5380i	−0.520692	+	0.554481i	−0.934537	−	0.355867i	$-0.884186\pi$
$433$	−10.8349	+	11.5380i	−0.520692	+	0.554481i	0.413844	+	0.910348i	$0.364186\pi$
$434$	19.1073	+	30.1082i	0.917178	+	1.44524i
$435$	−9.01780	−	14.1377i	−0.432370	−	0.677849i
$436$	−12.1247	+	4.80052i	−0.580669	+	0.229903i
$437$	12.7867	+	0.804469i	0.611669	+	0.0384830i
$438$	4.20385	+	0.264484i	0.200868	+	0.0126375i
$439$	−28.1344	+	11.1392i	−1.34278	+	0.531645i	−0.926055	−	0.377388i	$-0.876822\pi$
$439$	−28.1344	+	11.1392i	−1.34278	+	0.531645i	−0.416726	+	0.909032i	$0.636822\pi$
$440$	8.21560	+	3.23091i	0.391663	+	0.154028i
$441$	6.69185	+	10.5447i	0.318659	+	0.502127i
$442$	8.06800	−	8.59155i	0.383756	−	0.408658i
$443$			19.7749i			0.939534i	0.882791	+	0.469767i	$0.155662\pi$
$443$			19.7749i			0.939534i	−0.882791	+	0.469767i	$0.844338\pi$
$444$	2.93603	+	2.75712i	0.139338	+	0.130847i
$445$	−8.29013	−	20.7983i	−0.392990	−	0.985936i
$446$	5.03254	−	26.3815i	0.238298	−	1.24920i
$447$	2.26675	−	4.12321i	0.107214	−	0.195021i
$448$	−3.72738	−	2.36547i	−0.176102	−	0.111758i
$449$	−1.11201	−	3.42240i	−0.0524788	−	0.161513i	0.921382	−	0.388658i	$-0.127061\pi$
$449$	−1.11201	−	3.42240i	−0.0524788	−	0.161513i	−0.973861	+	0.227144i	$0.927061\pi$
$450$	−4.76235	−	1.52315i	−0.224499	−	0.0718022i
$451$	13.3479	−	41.0806i	0.628527	−	1.93441i
$452$	−9.54509	+	7.89639i	−0.448963	+	0.371415i
$453$	−19.4666	−	3.71345i	−0.914621	−	0.174473i
$454$	1.99734	+	4.24457i	0.0937400	+	0.199208i
$455$	28.8493	+	23.7545i	1.35248	+	1.11363i
$456$	−0.296628	−	1.55498i	−0.0138909	−	0.0728185i
$457$	14.8117	+	4.81262i	0.692863	+	0.225125i	0.634218	−	0.773154i	$-0.281322\pi$
$457$	14.8117	+	4.81262i	0.692863	+	0.225125i	0.0586445	+	0.998279i	$0.481322\pi$
$458$	0.609934	+	0.287013i	0.0285004	+	0.0134113i
$459$	2.89461	+	1.14606i	0.135109	+	0.0534933i
$460$	17.9598	+	2.22682i	0.837380	+	0.103826i
$461$	21.0739	+	5.41086i	0.981509	+	0.252009i	0.705160	−	0.709049i	$-0.250875\pi$
$461$	21.0739	+	5.41086i	0.981509	+	0.252009i	0.276349	+	0.961057i	$0.410875\pi$
$462$	6.41606	−	16.2051i	0.298502	−	0.753931i
$463$	−6.38029	−	24.8496i	−0.296517	−	1.15486i	−0.925902	−	0.377765i	$-0.876693\pi$
$463$	−6.38029	−	24.8496i	−0.296517	−	1.15486i	0.629384	−	0.777094i	$-0.283307\pi$
$464$	4.01830	−	6.33183i	0.186545	−	0.293948i
$465$	−5.54187	+	17.1908i	−0.256998	+	0.797205i
$466$	0.00787053	−	0.125098i	0.000364595	−	0.00579507i
$467$	2.14578	+	3.90316i	0.0992949	+	0.180617i	0.921288	−	0.388880i	$-0.127138\pi$
$467$	2.14578	+	3.90316i	0.0992949	+	0.180617i	−0.821993	+	0.569497i	$0.807138\pi$
$468$	3.60046	−	1.16986i	0.166431	−	0.0540768i
$469$	47.6205	+	6.01587i	2.19891	+	0.277787i
$470$	17.1984	−	18.3992i	0.793304	−	0.848694i
$471$	0.309304	−	0.290456i	0.0142520	−	0.0133835i
$472$	2.55052	+	2.71602i	0.117397	+	0.125015i
$473$	7.25884	−	28.2713i	0.333762	−	1.29992i
$474$	−11.1422	−	8.09531i	−0.511780	−	0.371830i
$475$	7.85716	+	0.955824i	0.360511	+	0.0438562i
$476$	−11.1189	+	8.07835i	−0.509633	+	0.370270i
$477$	−2.11958	−	5.35345i	−0.0970489	−	0.245118i
$478$	−1.30705	−	10.3463i	−0.0597830	−	0.473231i
$479$	−14.5092	−	7.97651i	−0.662943	−	0.364456i	0.114488	−	0.993425i	$-0.463477\pi$
$479$	−14.5092	−	7.97651i	−0.662943	−	0.364456i	−0.777431	+	0.628969i	$0.783477\pi$
$480$	−0.285365	−	2.21778i	−0.0130251	−	0.101228i
$481$	6.49214	−	13.7965i	0.296016	−	0.629067i
$482$	13.1818	−	18.1432i	0.600415	−	0.826400i
$483$	4.47805	−	35.4474i	0.203758	−	1.61291i
$484$	−4.44287	+	1.14073i	−0.201948	+	0.0518516i
$485$	7.79693	−	1.00324i	0.354040	−	0.0455548i
$486$	0.637424	+	0.770513i	0.0289141	+	0.0349512i
$487$	4.67765	+	3.86969i	0.211964	+	0.175352i	0.737348	−	0.675514i	$-0.236078\pi$
$487$	4.67765	+	3.86969i	0.211964	+	0.175352i	−0.525383	+	0.850866i	$0.676078\pi$
$488$	2.04569	−	1.29823i	0.0926040	−	0.0587683i
$489$	−0.120451	−	1.91451i	−0.00544699	−	0.0865774i
$490$	−17.8501	−	21.4762i	−0.806388	−	0.970195i
$491$	22.3996	−	27.0764i	1.01088	−	1.22194i	0.0359651	−	0.999353i	$-0.488549\pi$
$491$	22.3996	−	27.0764i	1.01088	−	1.22194i	0.974913	−	0.222588i	$-0.0714505\pi$
$492$	−10.7470	+	2.05010i	−0.484513	+	0.0924257i
$493$	−13.7230	−	18.8880i	−0.618051	−	0.850675i
$494$	−5.25162	+	2.88710i	−0.236282	+	0.129897i
$495$	8.38969	−	2.74736i	0.377088	−	0.123485i
$496$	−8.01388	+	1.01239i	−0.359834	+	0.0454576i
$497$	−41.4427	+	19.5015i	−1.85896	+	0.874760i
$498$	16.7079	−	1.05117i	0.748700	−	0.0471042i
$499$	−4.29841			−0.192423			−0.0962117	−	0.995361i	$-0.530673\pi$
$499$	−4.29841			−0.192423			−0.0962117	+	0.995361i	$0.530673\pi$
$500$	10.9965	+	2.01902i	0.491780	+	0.0902933i
$501$	−19.8244			−0.885688
$502$	25.9735	−	1.63411i	1.15925	−	0.0729340i
$503$	−10.9693	+	5.16174i	−0.489095	+	0.230151i	−0.654481	−	0.756078i	$-0.727113\pi$
$503$	−10.9693	+	5.16174i	−0.489095	+	0.230151i	0.165386	+	0.986229i	$0.447113\pi$
$504$	−4.37980	+	0.553298i	−0.195092	+	0.0246459i
$505$	0.00675908	+	2.93333i	0.000300775	+	0.130532i
$506$	−28.0005	+	15.3934i	−1.24478	+	0.684322i
$507$	−0.782861	−	1.07752i	−0.0347681	−	0.0478541i
$508$	14.3549	−	2.73835i	0.636898	−	0.121495i
$509$	24.7276	−	29.8905i	1.09603	−	1.32487i	0.154482	−	0.987996i	$-0.450629\pi$
$509$	24.7276	−	29.8905i	1.09603	−	1.32487i	0.941548	−	0.336878i	$-0.109371\pi$
$510$	−6.74666	−	1.71569i	−0.298747	−	0.0759718i
$511$	1.16759	+	18.5584i	0.0516513	+	0.820974i
$512$	0.844328	−	0.535827i	0.0373144	−	0.0236804i
$513$	−1.21974	−	1.00905i	−0.0538527	−	0.0445508i
$514$	−19.6128	−	23.7078i	−0.865083	−	1.04571i
$515$	−1.41537	−	0.773863i	−0.0623685	−	0.0341005i
$516$	−7.16086	+	1.83860i	−0.315239	+	0.0809397i
$517$	−5.57334	+	44.1175i	−0.245115	+	1.94029i
$518$	−10.4511	+	14.3848i	−0.459197	+	0.632030i
$519$	−9.45407	+	20.0909i	−0.414988	+	0.881894i
$520$	−7.65121	+	3.62194i	−0.335528	+	0.158833i
$521$	24.3639	+	13.3941i	1.06740	+	0.586808i	0.915800	−	0.401634i	$-0.131558\pi$
$521$	24.3639	+	13.3941i	1.06740	+	0.586808i	0.151600	+	0.988442i	$0.451558\pi$
$522$	−0.939906	−	7.44012i	−0.0411386	−	0.325645i
$523$	4.71601	+	11.9113i	0.206217	+	0.520844i	0.995669	−	0.0929675i	$-0.0296353\pi$
$523$	4.71601	+	11.9113i	0.206217	+	0.520844i	−0.789452	+	0.613812i	$0.789635\pi$
$524$	2.88779	−	2.09811i	0.126154	−	0.0916562i
$525$	4.03612	−	21.7009i	0.176151	−	0.947106i
$526$	−7.27083	−	5.28257i	−0.317023	−	0.230331i
$527$	−6.25389	+	24.3573i	−0.272424	+	1.06102i
$528$	2.70262	+	2.87799i	0.117616	+	0.125249i
$529$	−30.9831	+	29.0951i	−1.34709	+	1.26500i
$530$	6.22846	+	11.2679i	0.270547	+	0.489448i
$531$	3.69646	+	0.466972i	0.160413	+	0.0202649i
$532$	6.64637	−	2.15954i	0.288157	−	0.0936279i
$533$	19.9538	+	36.2958i	0.864295	+	1.57215i
$534$	0.628719	−	9.99321i	0.0272073	−	0.432448i
$535$	1.59074	+	4.85769i	0.0687738	+	0.210016i
$536$	−5.82591	+	9.18017i	−0.251641	+	0.396523i
$537$	1.93595	+	7.54003i	0.0835425	+	0.325376i
$538$	0.734190	−	1.85435i	0.0316532	−	0.0799469i
$539$	47.7573	+	12.2620i	2.05705	+	0.528161i
$540$	−1.63355	−	1.52693i	−0.0702966	−	0.0657088i
$541$	6.06092	+	2.39969i	0.260579	+	0.103171i	0.494782	−	0.869017i	$-0.335248\pi$
$541$	6.06092	+	2.39969i	0.260579	+	0.103171i	−0.234203	+	0.972188i	$0.575248\pi$
$542$	18.5065	+	8.70849i	0.794921	+	0.374062i
$543$	7.28384	+	2.36666i	0.312580	+	0.101563i
$544$	−0.583361	−	3.05808i	−0.0250114	−	0.131114i
$545$	10.6718	−	27.1364i	0.457129	−	1.16239i
$546$	7.11589	+	15.1220i	0.304532	+	0.647163i
$547$	42.5854	+	8.12361i	1.82082	+	0.347340i	0.980770	−	0.195166i	$-0.0625246\pi$
$547$	42.5854	+	8.12361i	1.82082	+	0.347340i	0.840052	+	0.542507i	$0.182525\pi$
$548$	3.66353	−	3.03073i	0.156498	−	0.129467i
$549$	0.748705	−	2.30428i	0.0319540	−	0.0983442i
$550$	−17.8225	+	8.48718i	−0.759955	+	0.361895i
$551$	3.66848	+	11.2904i	0.156283	+	0.480988i
$552$	6.83346	+	4.33665i	0.290851	+	0.184580i
$553$	29.2909	−	53.2799i	1.24558	−	2.26569i
$554$	1.36561	−	7.15876i	0.0580190	−	0.304146i
$555$	−8.98701	+	0.586208i	−0.381477	+	0.0248831i
$556$	6.22748	+	5.84800i	0.264104	+	0.248010i
$557$		−	40.8569i		−	1.73116i	−0.500770	−	0.865580i	$-0.666950\pi$
$557$		−	40.8569i		−	1.73116i	0.500770	−	0.865580i	$-0.333050\pi$
$558$	−5.52948	+	5.88830i	−0.234082	+	0.249272i
$559$	14.9970	+	23.6315i	0.634305	+	0.999505i
$560$	9.55557	−	2.47694i	0.403797	−	0.104670i
$561$	11.4280	−	4.52467i	0.482491	−	0.191032i
$562$	−13.6817	−	0.860781i	−0.577129	−	0.0363099i
$563$	14.8881	+	0.936682i	0.627460	+	0.0394765i	0.373338	−	0.927696i	$-0.378213\pi$
$563$	14.8881	+	0.936682i	0.627460	+	0.0394765i	0.254123	+	0.967172i	$0.418213\pi$
$564$	10.4724	−	4.14633i	0.440969	−	0.174592i
$565$	1.67561	−	27.6496i	0.0704935	−	1.16323i
$566$	3.95600	+	6.23366i	0.166283	+	0.262020i
$567$	−3.02201	+	3.21812i	−0.126913	+	0.135148i
$568$		−	10.3750i		−	0.435327i
$569$	−25.6763	−	24.1117i	−1.07641	−	1.01081i	−0.999906	−	0.0137440i	$-0.995625\pi$
$569$	−25.6763	−	24.1117i	−1.07641	−	1.01081i	−0.0765014	−	0.997069i	$-0.524375\pi$
$570$	2.99306	+	1.88979i	0.125365	+	0.0791547i
$571$	6.20252	−	32.5147i	0.259567	−	1.36070i	−0.578745	−	0.815509i	$-0.696457\pi$
$571$	6.20252	−	32.5147i	0.259567	−	1.36070i	0.838312	−	0.545191i	$-0.183543\pi$
$572$	7.20042	−	13.0975i	0.301065	−	0.547634i
$573$	−3.26251	−	2.07045i	−0.136293	−	0.0864945i
$574$	−14.9253	−	45.9355i	−0.622972	−	1.91731i
$575$	−31.0610	+	25.9380i	−1.29534	+	1.08169i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	−5.19445	+	4.29722i	−0.216248	+	0.178896i	−0.739241	−	0.673441i	$-0.764815\pi$
$577$	−5.19445	+	4.29722i	−0.216248	+	0.178896i	0.522993	+	0.852337i	$0.324815\pi$
$578$	7.17837	+	1.36935i	0.298581	+	0.0569573i
$579$	−1.89561	−	4.02837i	−0.0787787	−	0.167413i
$580$	4.20766	+	16.2324i	0.174713	+	0.674013i
$581$	13.8484	+	72.5958i	0.574528	+	3.01178i
$582$	3.34357	+	1.08639i	0.138596	+	0.0450324i
$583$	−20.5685	−	9.67878i	−0.851858	−	0.400854i
$584$	−3.91637	−	1.55060i	−0.162060	−	0.0641643i
$585$	−3.58664	+	7.66782i	−0.148289	+	0.317025i
$586$	−0.512345	−	0.131548i	−0.0211648	−	0.00543419i
$587$	−16.4016	+	41.4257i	−0.676967	+	1.70982i	0.0270447	+	0.999634i	$0.491390\pi$
$587$	−16.4016	+	41.4257i	−0.676967	+	1.70982i	−0.704011	+	0.710189i	$0.748610\pi$
$588$	−3.10584	−	12.0965i	−0.128083	−	0.498850i
$589$	6.85159	−	10.7964i	0.282315	−	0.444857i
$590$	−8.33122	+	0.0191971i	−0.342991	+	0.000790331i
$591$	−0.0332976	+	0.529251i	−0.00136968	+	0.0217705i
$592$	−1.94034	−	3.52946i	−0.0797473	−	0.145060i
$593$	−22.0501	+	7.16450i	−0.905487	+	0.294211i	−0.724500	−	0.689275i	$-0.757929\pi$
$593$	−22.0501	+	7.16450i	−0.905487	+	0.294211i	−0.180987	+	0.983485i	$0.557929\pi$
$594$	3.91690	+	0.494820i	0.160712	+	0.0203027i
$595$	3.78146	−	30.4983i	0.155025	−	1.25031i
$596$	−3.42995	+	3.22094i	−0.140496	+	0.131935i
$597$	4.23959	+	4.51471i	0.173515	+	0.184775i
$598$	7.61972	−	29.6769i	0.311594	−	1.21358i
$599$	−15.1626	−	11.0163i	−0.619527	−	0.450113i	0.233229	−	0.972422i	$-0.425071\pi$
$599$	−15.1626	−	11.0163i	−0.619527	−	0.450113i	−0.852756	+	0.522309i	$0.825071\pi$
$600$	4.05859	+	2.92025i	0.165691	+	0.119219i
$601$	−11.7551	+	8.54055i	−0.479499	+	0.348376i	−0.801132	−	0.598488i	$-0.795768\pi$
$601$	−11.7551	+	8.54055i	−0.479499	+	0.348376i	0.321633	+	0.946865i	$0.395768\pi$
$602$	−12.0148	−	30.3459i	−0.489686	−	1.23681i
$603$	1.36272	+	10.7870i	0.0554941	+	0.439281i
$604$	17.3663	+	9.54722i	0.706626	+	0.388471i
$605$	4.92052	−	8.99945i	0.200048	−	0.365880i
$606$	−0.558550	+	1.18698i	−0.0226895	+	0.0482177i
$607$	−2.29472	+	3.15841i	−0.0931397	+	0.128196i	−0.853044	−	0.521840i	$-0.825246\pi$
$607$	−2.29472	+	3.15841i	−0.0931397	+	0.128196i	0.759904	+	0.650035i	$0.225246\pi$
$608$	−0.198405	+	1.57053i	−0.00804637	+	0.0636936i
$609$	32.0662	−	8.23321i	1.29939	−	0.333627i
$610$	−1.00291	+	5.32405i	−0.0406065	+	0.215564i
$611$	−27.1799	−	32.8549i	−1.09958	−	1.32917i
$612$	−2.39878	−	1.98445i	−0.0969651	−	0.0802165i
$613$	10.2541	−	6.50742i	0.414157	−	0.262832i	−0.312383	−	0.949956i	$-0.601127\pi$
$613$	10.2541	−	6.50742i	0.414157	−	0.262832i	0.726540	+	0.687124i	$0.241127\pi$
$614$	0.974901	+	15.4956i	0.0393438	+	0.625352i
$615$	13.0610	−	20.6861i	0.526672	−	0.834144i
$616$	−11.1097	+	13.4293i	−0.447622	+	0.541083i
$617$	1.50274	−	0.286664i	0.0604982	−	0.0115407i	−0.157043	−	0.987592i	$-0.550196\pi$
$617$	1.50274	−	0.286664i	0.0604982	−	0.0115407i	0.217542	+	0.976051i	$0.430196\pi$
$618$	−0.424031	−	0.583629i	−0.0170570	−	0.0234770i
$619$	11.1998	−	6.15716i	0.450159	−	0.247477i	−0.240512	−	0.970646i	$-0.577315\pi$
$619$	11.1998	−	6.15716i	0.450159	−	0.247477i	0.690671	+	0.723169i	$0.257315\pi$
$620$	10.5829	−	14.6369i	0.425019	−	0.587832i
$621$	8.02955	−	1.01437i	0.322215	−	0.0407052i
$622$	−2.92441	+	1.37612i	−0.117258	+	0.0551776i
$623$	44.1162	−	2.77555i	1.76748	−	0.111200i
$624$	−3.78575			−0.151551
$625$	−20.0891	+	14.8804i	−0.803565	+	0.595217i
$626$	21.9401			0.876904
$627$	−6.23747	+	0.392429i	−0.249101	+	0.0156721i
$628$	−0.383922	+	0.180660i	−0.0153202	+	0.00720912i
$629$	−12.4401	+	1.57155i	−0.496020	+	0.0626619i
$630$	5.78383	−	7.99946i	0.230433	−	0.318706i
$631$	−38.9025	+	21.3868i	−1.54868	+	0.851395i	−0.548802	+	0.835953i	$0.684916\pi$
$631$	−38.9025	+	21.3868i	−1.54868	+	0.851395i	−0.999881	+	0.0154427i	$0.995084\pi$
$632$	8.09531	+	11.1422i	0.322014	+	0.443214i
$633$	−6.53349	+	1.24633i	−0.259683	+	0.0495372i
$634$	−2.06056	+	2.49079i	−0.0818354	+	0.0989220i
$635$	−17.4458	+	27.6307i	−0.692316	+	1.09649i
$636$	0.361534	+	5.74642i	0.0143358	+	0.227860i
$637$	−39.9194	+	25.3336i	−1.58167	+	1.00376i
$638$	−22.8128	−	18.8724i	−0.903169	−	0.747166i
$639$	−6.61330	−	7.99410i	−0.261618	−	0.316242i
$640$	−0.413935	+	2.19742i	−0.0163622	+	0.0868607i
$641$	−32.4154	+	8.32287i	−1.28033	+	0.328734i	−0.826795	−	0.562503i	$-0.809838\pi$
$641$	−32.4154	+	8.32287i	−1.28033	+	0.328734i	−0.453538	+	0.891237i	$0.649838\pi$
$642$	−0.286504	+	2.26792i	−0.0113074	+	0.0895075i
$643$	5.50945	−	7.58311i	0.217272	−	0.299049i	−0.686443	−	0.727183i	$-0.740829\pi$
$643$	5.50945	−	7.58311i	0.217272	−	0.299049i	0.903715	+	0.428135i	$0.140829\pi$
$644$	−15.2127	+	32.3287i	−0.599465	+	1.27393i
$645$	7.93073	−	14.5050i	0.312272	−	0.571134i
$646$	4.31870	+	2.37422i	0.169917	+	0.0934126i
$647$	2.74287	+	21.7120i	0.107833	+	0.853588i	0.949539	+	0.313650i	$0.101552\pi$
$647$	2.74287	+	21.7120i	0.107833	+	0.853588i	−0.841705	+	0.539937i	$0.818448\pi$
$648$	−0.368125	−	0.929776i	−0.0144613	−	0.0365251i
$649$	11.9004	−	8.64618i	0.467133	−	0.339392i
$650$	5.76628	−	18.0291i	0.226172	−	0.707158i
$651$	−28.8491	−	20.9601i	−1.13068	−	0.821490i
$652$	−0.477062	+	1.85803i	−0.0186832	+	0.0727662i
$653$	−19.5817	−	20.8524i	−0.766291	−	0.816017i	0.220944	−	0.975286i	$-0.429086\pi$
$653$	−19.5817	−	20.8524i	−0.766291	−	0.816017i	−0.987235	+	0.159269i	$0.949086\pi$
$654$	9.50610	−	8.92682i	0.371718	−	0.349066i
$655$	−0.982119	+	7.92101i	−0.0383746	+	0.309500i
$656$	10.8545	+	1.37125i	0.423798	+	0.0535382i
$657$	−4.00600	+	1.30163i	−0.156289	+	0.0507814i
$658$	23.9545	+	43.5730i	0.933842	+	1.69865i
$659$	0.141495	−	2.24900i	0.00551186	−	0.0876086i	−0.994309	−	0.106534i	$-0.966025\pi$
$659$	0.141495	−	2.24900i	0.00551186	−	0.0876086i	0.999821	+	0.0189257i	$0.00602461\pi$
$660$	−8.82805	+	0.0203419i	−0.343631	+	0.000791807i
$661$	4.20929	−	6.63278i	0.163722	−	0.257985i	−0.752555	−	0.658529i	$-0.771179\pi$
$661$	4.20929	−	6.63278i	0.163722	−	0.257985i	0.916277	+	0.400544i	$0.131179\pi$
$662$	0.370078	+	1.44136i	0.0143835	+	0.0560200i
$663$	−4.33868	+	10.9582i	−0.168500	+	0.425583i
$664$	−16.2150	−	4.16331i	−0.629265	−	0.161568i
$665$	−6.62087	+	14.1546i	−0.256746	+	0.548893i
$666$	−3.74482	−	1.48268i	−0.145109	−	0.0574526i
$667$	−54.9178	−	25.8424i	−2.12643	−	1.00062i
$668$	18.8541	+	6.12607i	0.729488	+	0.237025i
$669$	5.03254	+	26.3815i	0.194569	+	1.01997i
$670$	−6.10045	−	23.5344i	−0.235681	−	0.909213i
$671$	−4.07281	−	8.65516i	−0.157229	−	0.334129i
$672$	4.33642	+	0.827216i	0.167281	+	0.0319106i
$673$	18.3107	−	15.1479i	0.705826	−	0.583910i	−0.213719	−	0.976895i	$-0.568558\pi$
$673$	18.3107	−	15.1479i	0.705826	−	0.583910i	0.919545	+	0.392985i	$0.128558\pi$
$674$	1.92151	−	5.91379i	0.0740137	−	0.227791i
$675$	4.98863	−	0.336946i	0.192013	−	0.0129691i
$676$	0.411574	+	1.26670i	0.0158298	+	0.0487190i
$677$	−1.27468	−	0.808937i	−0.0489899	−	0.0310900i	0.511106	−	0.859518i	$-0.329236\pi$
$677$	−1.27468	−	0.808937i	−0.0489899	−	0.0310900i	−0.560096	+	0.828428i	$0.689236\pi$
$678$	5.96795	−	10.8557i	0.229198	−	0.416909i
$679$	−2.90820	+	15.2453i	−0.111606	+	0.585061i
$680$	5.88627	+	3.71655i	0.225728	+	0.142523i
$681$	−3.41962	−	3.21123i	−0.131040	−	0.123055i
$682$			31.8906i			1.22115i
$683$	−23.5711	+	25.1007i	−0.901924	+	0.960452i	−0.999395	−	0.0347869i	$-0.988925\pi$
$683$	−23.5711	+	25.1007i	−0.901924	+	0.960452i	0.0974707	+	0.995238i	$0.468925\pi$
$684$	0.848223	+	1.33659i	0.0324326	+	0.0511056i
$685$	−0.643121	+	10.6123i	−0.0245724	+	0.405474i
$686$	22.5295	−	8.92005i	0.860179	−	0.340569i
$687$	−0.672759	−	0.0423264i	−0.0256674	−	0.00161485i
$688$	7.37854	+	0.464218i	0.281304	+	0.0176982i
$689$	20.2668	−	8.02420i	0.772104	−	0.305697i
$690$	−17.5184	+	4.54100i	−0.666912	+	0.172873i
$691$	−5.23068	−	8.24223i	−0.198984	−	0.313549i	0.730153	−	0.683284i	$-0.239449\pi$
$691$	−5.23068	−	8.24223i	−0.198984	−	0.313549i	−0.929138	+	0.369734i	$0.879449\pi$
$692$	15.1998	−	16.1861i	0.577809	−	0.615305i
$693$			17.4291i			0.662075i
$694$	18.9181	+	17.7653i	0.718121	+	0.674360i
$695$	−19.0619	+	1.24338i	−0.723060	+	0.0471640i
$696$	−1.40522	+	7.36643i	−0.0532648	+	0.279224i
$697$	16.4091	−	29.8481i	0.621540	−	1.13058i
$698$	2.44198	+	1.54973i	0.0924303	+	0.0586580i
$699$	0.0387340	+	0.119211i	0.00146505	+	0.00450897i
$700$	−10.5445	+	19.3916i	−0.398546	+	0.732933i
$701$	−0.532176	+	1.63787i	−0.0201000	+	0.0618614i	−0.960603	−	0.277923i	$-0.910354\pi$
$701$	−0.532176	+	1.63787i	−0.0201000	+	0.0618614i	0.940503	+	0.339784i	$0.110354\pi$
$702$	−2.91697	+	2.41313i	−0.110094	+	0.0910776i
$703$	6.26291	+	1.19471i	0.236210	+	0.0450595i
$704$	−1.68099	−	3.57229i	−0.0633547	−	0.134636i
$705$	−9.21748	+	23.4383i	−0.347150	+	0.882739i
$706$	4.56042	+	23.9066i	0.171634	+	0.899736i
$707$	−5.50778	−	1.78959i	−0.207141	−	0.0673043i
$708$	−3.37124	−	1.58639i	−0.126699	−	0.0596201i
$709$	−7.25381	−	2.87199i	−0.272423	−	0.107860i	0.227941	−	0.973675i	$-0.426801\pi$
$709$	−7.25381	−	2.87199i	−0.272423	−	0.107860i	−0.500364	+	0.865815i	$0.666801\pi$
$710$	16.9481	+	15.8420i	0.636051	+	0.594540i
$711$	13.3399	+	3.42510i	0.500284	+	0.128451i
$712$	−3.68602	+	9.30982i	−0.138139	+	0.348900i
$713$	16.2581	+	63.3210i	0.608869	+	2.37139i
$714$	7.36424	−	11.6042i	0.275600	−	0.434276i
$715$	10.4008	+	31.7612i	0.388969	+	1.18780i
$716$	0.488799	−	7.76924i	0.0182673	−	0.290350i
$717$	5.02401	+	9.13863i	0.187625	+	0.341288i
$718$	25.7226	−	8.35778i	0.959959	−	0.311910i
$719$	−19.8733	−	2.51059i	−0.741151	−	0.0936291i	−0.254314	−	0.967122i	$-0.581850\pi$
$719$	−19.8733	−	2.51059i	−0.741151	−	0.0936291i	−0.486837	+	0.873493i	$0.661850\pi$
$720$	1.08175	+	1.95699i	0.0403143	+	0.0729329i
$721$	2.32156	−	2.18009i	0.0864596	−	0.0811909i
$722$	11.2910	+	12.0236i	0.420206	+	0.447474i
$723$	−5.57718	+	21.7217i	−0.207417	+	0.807837i
$724$	−6.19601	−	4.50166i	−0.230273	−	0.167303i
$725$	−32.9412	−	17.9124i	−1.22340	−	0.665248i
$726$	3.71094	−	2.69616i	0.137726	−	0.100064i
$727$	4.06975	+	10.2790i	0.150939	+	0.381228i	0.985497	−	0.169691i	$-0.0542771\pi$
$727$	4.06975	+	10.2790i	0.150939	+	0.381228i	−0.834558	+	0.550920i	$0.814277\pi$
$728$	−2.09465	−	16.5808i	−0.0776328	−	0.614527i
$729$	−0.876307	−	0.481754i	−0.0324558	−	0.0178427i
$730$	8.51301	−	4.02991i	0.315081	−	0.149153i
$731$	9.79995	−	20.8259i	0.362464	−	0.770275i
$732$	−1.42412	+	1.96014i	−0.0526371	+	0.0724487i
$733$	−2.40417	+	19.0310i	−0.0888002	+	0.702926i	0.883374	+	0.468668i	$0.155266\pi$
$733$	−2.40417	+	19.0310i	−0.0888002	+	0.702926i	−0.972175	+	0.234258i	$0.924734\pi$
$734$	−24.4439	+	6.27611i	−0.902239	+	0.231656i
$735$	24.5026	+	13.3970i	0.903790	+	0.494154i
$736$	−5.15891	−	6.23605i	−0.190160	−	0.229864i
$737$	33.0750	+	27.3621i	1.21833	+	1.00789i
$738$	9.23763	−	5.86238i	0.340042	−	0.215797i
$739$	3.35810	+	53.3754i	0.123530	+	1.96345i	0.241424	+	0.970420i	$0.422386\pi$
$739$	3.35810	+	53.3754i	0.123530	+	1.96345i	−0.117894	+	0.993026i	$0.537614\pi$
$740$	8.72830	+	2.21962i	0.320859	+	0.0815949i
$741$	3.82002	−	4.61761i	0.140332	−	0.169632i
$742$	−24.9682	+	4.76293i	−0.916610	+	0.174853i
$743$	12.1525	+	16.7265i	0.445833	+	0.613637i	0.971496	−	0.237056i	$-0.0761826\pi$
$743$	12.1525	+	16.7265i	0.445833	+	0.613637i	−0.525663	+	0.850693i	$0.676183\pi$
$744$	7.07844	−	3.89140i	0.259508	−	0.142666i
$745$	−0.0242432	−	10.5211i	−0.000888200	−	0.385465i
$746$	−25.1898	+	3.18221i	−0.922264	+	0.116509i
$747$	−15.1477	+	7.12795i	−0.554224	+	0.260798i
$748$	−12.2669	+	0.771767i	−0.448521	+	0.0282186i
$749$	−10.0915			−0.368737
$750$	−10.9676	+	2.17085i	−0.400479	+	0.0792684i
$751$	1.87141			0.0682887			0.0341443	−	0.999417i	$-0.489129\pi$
$751$	1.87141			0.0682887			0.0341443	+	0.999417i	$0.489129\pi$
$752$	−11.2411	+	0.707233i	−0.409923	+	0.0257901i
$753$	−23.5480	+	11.0808i	−0.858136	+	0.403808i
$754$	28.1664	−	3.55825i	1.02576	−	0.129584i
$755$	−42.1130	+	13.7907i	−1.53265	+	0.501896i
$756$	3.86856	−	2.12676i	0.140698	−	0.0773494i
$757$	25.2208	+	34.7135i	0.916667	+	1.26168i	0.964838	+	0.262845i	$0.0846608\pi$
$757$	25.2208	+	34.7135i	0.916667	+	1.26168i	−0.0481709	+	0.998839i	$0.515339\pi$
$758$	−34.4445	+	6.57064i	−1.25108	+	0.238656i
$759$	20.3676	−	24.6201i	0.739295	−	0.893654i
$760$	−2.26259	−	2.72221i	−0.0820728	−	0.0987448i
$761$	1.90939	+	30.3489i	0.0692154	+	1.10015i	0.867360	+	0.497681i	$0.165815\pi$
$761$	1.90939	+	30.3489i	0.0692154	+	1.10015i	−0.798145	+	0.602466i	$0.794185\pi$
$762$	−12.3388	+	7.83046i	−0.446989	+	0.283668i
$763$	44.3574	+	36.6957i	1.60585	+	1.32847i
$764$	2.46303	+	2.97729i	0.0891093	+	0.107715i
$765$	6.90447	−	0.888405i	0.249632	−	0.0321204i
$766$	20.0062	−	5.13672i	0.722854	−	0.185597i
$767$	−1.76784	+	13.9939i	−0.0638329	+	0.505290i
$768$	−0.587785	+	0.809017i	−0.0212099	+	0.0291929i
$769$	−2.35050	+	4.99507i	−0.0847613	+	0.180127i	−0.942714	−	0.333601i	$-0.891736\pi$
$769$	−2.35050	+	4.99507i	−0.0847613	+	0.180127i	0.857953	+	0.513728i	$0.171736\pi$
$770$	−4.97364	−	38.6539i	−0.179237	−	1.39299i
$771$	26.9629	+	14.8230i	0.971046	+	0.533837i
$772$	0.557994	+	4.41698i	0.0200826	+	0.158971i
$773$	5.06708	+	12.7980i	0.182250	+	0.460311i	0.991965	−	0.126512i	$-0.0403783\pi$
$773$	5.06708	+	12.7980i	0.182250	+	0.460311i	−0.809715	+	0.586823i	$0.800378\pi$
$774$	5.98117	−	4.34557i	0.214989	−	0.156198i
$775$	7.75068	+	39.6372i	0.278413	+	1.42381i
$776$	−2.84421	−	2.06644i	−0.102101	−	0.0741809i
$777$	4.42184	−	17.2219i	0.158633	−	0.617833i
$778$	−0.839803	−	0.894299i	−0.0301084	−	0.0320622i
$779$	−12.6254	+	11.8560i	−0.452350	+	0.424785i
$780$	5.78059	−	6.18419i	0.206978	−	0.221430i
$781$	−40.6380	−	5.13378i	−1.45414	−	0.183701i
$782$	−23.9633	+	7.78615i	−0.856926	+	0.278432i
$783$	3.61280	+	6.57165i	0.129111	+	0.234852i
$784$	−0.784180	+	12.4642i	−0.0280064	+	0.445149i
$785$	0.291107	−	0.903010i	0.0103901	−	0.0322298i
$786$	−1.91264	+	3.01384i	−0.0682216	+	0.107500i
$787$	0.777563	+	3.02841i	0.0277171	+	0.107951i	0.980937	−	0.194328i	$-0.0622526\pi$
$787$	0.777563	+	3.02841i	0.0277171	+	0.107951i	−0.953219	+	0.302279i	$0.902253\pi$
$788$	0.195215	−	0.493058i	0.00695426	−	0.0175645i
$789$	8.70489	+	2.23504i	0.309902	+	0.0795694i
$790$	−30.5624	−	3.78940i	−1.08736	−	0.134821i
$791$	50.8477	+	20.1320i	1.80794	+	0.715813i
$792$	−3.57229	−	1.68099i	−0.126936	−	0.0597314i
$793$	8.72341	+	2.83441i	0.309778	+	0.100653i
$794$	−5.02024	−	26.3170i	−0.178162	−	0.933956i
$795$	−9.93908	−	8.18382i	−0.352503	−	0.290250i
$796$	−2.63697	−	5.60385i	−0.0934649	−	0.198623i
$797$	2.92487	+	0.557948i	0.103604	+	0.0197635i	0.238923	−	0.971039i	$-0.423206\pi$
$797$	2.92487	+	0.557948i	0.103604	+	0.0197635i	−0.135319	+	0.990802i	$0.543206\pi$
$798$	−5.38466	+	4.45458i	−0.190615	+	0.157690i
$799$	−10.8358	+	33.3492i	−0.383344	+	1.17981i
$800$	−2.95754	−	4.03150i	−0.104565	−	0.142535i
$801$	3.09418	+	9.52290i	0.109327	+	0.336475i
$802$	−4.93258	−	3.13031i	−0.174175	−	0.110535i
$803$	−8.01145	+	14.5728i	−0.282718	+	0.514262i
$804$	2.03735	−	10.6802i	0.0718518	−	0.376660i
$805$	−29.5816	−	74.2144i	−1.04261	−	2.61571i
$806$	−22.2916	−	20.9332i	−0.785189	−	0.737341i
$807$			1.99441i			0.0702065i
$808$	0.898009	−	0.956283i	0.0315919	−	0.0336419i
$809$	6.76666	+	10.6626i	0.237903	+	0.374875i	0.942211	−	0.335019i	$-0.108743\pi$
$809$	6.76666	+	10.6626i	0.237903	+	0.374875i	−0.704308	+	0.709894i	$0.748743\pi$
$810$	2.08093	+	0.818359i	0.0731166	+	0.0287542i
$811$	−29.3248	+	11.6105i	−1.02973	+	0.407701i	−0.821397	−	0.570356i	$-0.806805\pi$
$811$	−29.3248	+	11.6105i	−1.02973	+	0.407701i	−0.208337	+	0.978057i	$0.566805\pi$
$812$	−33.0410	−	2.07876i	−1.15951	−	0.0729503i
$813$	−20.4127	−	1.28426i	−0.715904	−	0.0450409i
$814$	−14.7847	+	5.85366i	−0.518202	+	0.205171i
$815$	−2.30674	−	3.61640i	−0.0808016	−	0.126677i
$816$	1.66815	+	2.62859i	0.0583970	+	0.0920189i
$817$	−8.01156	+	8.53145i	−0.280289	+	0.298478i
$818$		−	0.620972i		−	0.0217118i
$819$	−12.1830	−	11.4406i	−0.425708	−	0.399766i
$820$	−18.8141	+	15.6376i	−0.657018	+	0.546088i
$821$	0.340735	−	1.78619i	0.0118917	−	0.0623386i	−0.975847	−	0.218456i	$-0.929898\pi$
$821$	0.340735	−	1.78619i	0.0118917	−	0.0623386i	0.987738	+	0.156118i	$0.0498979\pi$
$822$	−2.29057	+	4.16654i	−0.0798930	+	0.145325i
$823$	27.5590	+	17.4895i	0.960647	+	0.609645i	0.920997	−	0.389569i	$-0.127376\pi$
$823$	27.5590	+	17.4895i	0.960647	+	0.609645i	0.0396493	+	0.999214i	$0.487376\pi$
$824$	0.222926	+	0.686097i	0.00776601	+	0.0239013i
$825$	13.4466	−	14.4521i	0.468151	−	0.503157i
$826$	5.08276	−	15.6431i	0.176852	−	0.544294i
$827$	24.4122	−	20.1955i	0.848895	−	0.702267i	−0.107544	−	0.994200i	$-0.534299\pi$
$827$	24.4122	−	20.1955i	0.848895	−	0.702267i	0.956439	+	0.291934i	$0.0942986\pi$
$828$	−7.95002	−	1.51655i	−0.276282	−	0.0527036i
$829$	−13.5643	−	28.8255i	−0.471107	−	1.00115i	−0.989301	−	0.145890i	$-0.953396\pi$
$829$	−13.5643	−	28.8255i	−0.471107	−	1.00115i	0.518194	−	0.855263i	$-0.326604\pi$
$830$	31.5602	−	20.1309i	1.09547	−	0.698753i
$831$	1.36561	+	7.15876i	0.0473723	+	0.248334i
$832$	3.60046	+	1.16986i	0.124823	+	0.0405576i
$833$	35.1802	+	16.5545i	1.21892	+	0.573581i
$834$	−7.94296	−	3.14484i	−0.275042	−	0.108897i
$835$	−38.7962	+	21.4450i	−1.34260	+	0.742133i
$836$	6.05346	+	1.55426i	0.209363	+	0.0537553i
$837$	2.97355	−	7.51034i	0.102781	−	0.259595i
$838$	1.39427	+	5.43032i	0.0481642	+	0.187587i
$839$	14.4779	−	22.8136i	0.499834	−	0.787612i	−0.496948	−	0.867780i	$-0.665546\pi$
$839$	14.4779	−	22.8136i	0.499834	−	0.787612i	0.996781	+	0.0801688i	$0.0255459\pi$
$840$	−7.97272	+	5.82064i	−0.275085	+	0.200831i
$841$	1.71034	−	27.1851i	0.0589774	−	0.937418i
$842$	2.78272	+	5.06176i	0.0958990	+	0.174440i
$843$	13.0378	−	4.23625i	0.449046	−	0.145904i
$844$	6.59886	+	0.833630i	0.227142	+	0.0286947i
$845$	−2.69765	−	1.26183i	−0.0928020	−	0.0434084i
$846$	−8.21065	+	7.71031i	−0.282288	+	0.265086i
$847$	13.8619	+	14.7614i	0.476300	+	0.507208i
$848$	1.43190	−	5.57689i	0.0491717	−	0.191511i
$849$	−5.97296	−	4.33961i	−0.204991	−	0.148935i
$850$	−15.0591	+	3.94058i	−0.516523	+	0.135161i
$851$	−26.3718	+	19.1602i	−0.904012	+	0.656803i
$852$	3.81931	+	9.64647i	0.130847	+	0.330483i
$853$	−1.73495	−	13.7335i	−0.0594035	−	0.470227i	−0.993555	−	0.113351i	$-0.963842\pi$
$853$	−1.73495	−	13.7335i	−0.0594035	−	0.470227i	0.934151	−	0.356877i	$-0.116158\pi$
$854$	−9.37298	−	5.15284i	−0.320737	−	0.176326i
$855$	−3.47856	−	0.655266i	−0.118964	−	0.0224096i
$856$	0.973306	−	2.06838i	0.0332669	−	0.0706958i
$857$	1.24693	−	1.71625i	0.0425943	−	0.0586260i	−0.787189	−	0.616712i	$-0.788464\pi$
$857$	1.24693	−	1.71625i	0.0425943	−	0.0586260i	0.829783	+	0.558086i	$0.188464\pi$
$858$	−1.87326	+	14.8284i	−0.0639521	+	0.506233i
$859$	35.4245	−	9.09546i	1.20867	−	0.310333i	0.409989	−	0.912091i	$-0.365533\pi$
$859$	35.4245	−	9.09546i	1.20867	−	0.310333i	0.798679	+	0.601758i	$0.205533\pi$
$860$	−12.0249	+	11.3444i	−0.410044	+	0.386839i
$861$	30.7872	+	37.2154i	1.04923	+	1.26830i
$862$	9.32988	+	7.71835i	0.317777	+	0.262888i
$863$	33.6259	−	21.3397i	1.14464	−	0.726410i	0.178375	−	0.983963i	$-0.442916\pi$
$863$	33.6259	−	21.3397i	1.14464	−	0.726410i	0.966264	+	0.257552i	$0.0829159\pi$
$864$	0.0627905	+	0.998027i	0.00213618	+	0.0339536i
$865$	3.23172	+	49.5447i	0.109882	+	1.68457i
$866$	−10.0890	+	12.1956i	−0.342840	+	0.414422i
$867$	−7.17837	+	1.36935i	−0.243790	+	0.0465055i
$868$	20.9601	+	28.8491i	0.711431	+	0.979201i
$869$	47.6488	−	26.1951i	1.61637	−	0.888609i
$870$	−9.88772	−	13.5435i	−0.335225	−	0.459169i
$871$	−40.8369	+	5.15890i	−1.38371	+	0.174803i
$872$	−11.7994	+	5.55236i	−0.399577	+	0.188027i
$873$	−3.50870	+	0.220749i	−0.118752	+	0.00747122i
$874$	12.8119			0.433371
$875$	−15.5762	−	46.8346i	−0.526573	−	1.58330i
$876$	4.21216			0.142316
$877$	17.9440	−	1.12894i	0.605924	−	0.0381215i	0.243135	−	0.969993i	$-0.421824\pi$
$877$	17.9440	−	1.12894i	0.605924	−	0.0381215i	0.362790	+	0.931871i	$0.381824\pi$
$878$	−27.3794	+	12.8838i	−0.924011	+	0.434807i
$879$	0.524792	−	0.0662967i	0.0177008	−	0.00223613i
$880$	8.40226	+	2.70867i	0.283240	+	0.0913093i
$881$	17.3837	−	9.55678i	0.585672	−	0.321976i	−0.161223	−	0.986918i	$-0.551544\pi$
$881$	17.3837	−	9.55678i	0.585672	−	0.321976i	0.746895	+	0.664942i	$0.231544\pi$
$882$	7.34075	+	10.1037i	0.247176	+	0.340208i
$883$	39.7966	−	7.59160i	1.33926	−	0.255478i	0.532537	−	0.846407i	$-0.321239\pi$
$883$	39.7966	−	7.59160i	1.33926	−	0.255478i	0.806724	+	0.590929i	$0.201239\pi$
$884$	7.51261	−	9.08119i	0.252676	−	0.305433i
$885$	7.73910	−	3.08477i	0.260147	−	0.103694i
$886$	1.24168	+	19.7359i	0.0417149	+	0.663040i
$887$	15.8090	−	10.0327i	0.530815	−	0.336865i	−0.243258	−	0.969962i	$-0.578216\pi$
$887$	15.8090	−	10.0327i	0.530815	−	0.336865i	0.774073	+	0.633096i	$0.218216\pi$
$888$	3.10336	+	2.56732i	0.104142	+	0.0861537i
$889$	−41.1229	−	49.7091i	−1.37922	−	1.66719i
$890$	−9.57971	−	20.2368i	−0.321113	−	0.678338i
$891$	−3.82400	+	0.981836i	−0.128109	+	0.0328928i
$892$	3.36610	−	26.6454i	0.112705	−	0.892155i
$893$	10.4803	−	14.4249i	0.350709	−	0.482710i
$894$	2.00338	−	4.25740i	0.0670031	−	0.142389i
$895$	11.9450	+	12.6616i	0.399279	+	0.423230i
$896$	−3.86856	−	2.12676i	−0.129239	−	0.0710500i
$897$	3.84014	+	30.3979i	0.128219	+	1.01495i
$898$	−1.32471	−	3.34583i	−0.0442060	−	0.111652i
$899$	−49.0069	+	35.6056i	−1.63447	+	1.18751i
$900$	−4.84859	−	1.22112i	−0.161620	−	0.0407039i
$901$	−14.5019	−	10.5362i	−0.483127	−	0.351012i
$902$	10.7421	−	41.8376i	0.357672	−	1.39304i
$903$	22.3421	+	23.7919i	0.743499	+	0.791746i
$904$	−9.03044	+	8.48015i	−0.300348	+	0.282045i
$905$	16.8146	−	3.24772i	0.558935	−	0.107958i
$906$	−19.6614	−	2.48381i	−0.653205	−	0.0825190i
$907$	26.6708	−	8.66587i	0.885590	−	0.287746i	0.169313	−	0.985562i	$-0.445845\pi$
$907$	26.6708	−	8.66587i	0.885590	−	0.287746i	0.716276	+	0.697817i	$0.245845\pi$
$908$	2.25992	+	4.11078i	0.0749982	+	0.136421i
$909$	0.0823705	−	1.30924i	0.00273206	−	0.0434248i
$910$	30.2839	+	21.8961i	1.00390	+	0.725850i
$911$	−23.9547	+	37.7466i	−0.793655	+	1.25060i	0.170526	+	0.985353i	$0.445453\pi$
$911$	−23.9547	+	37.7466i	−0.793655	+	1.25060i	−0.964181	+	0.265246i	$0.914547\pi$
$912$	−0.393680	−	1.53328i	−0.0130361	−	0.0507721i
$913$	−24.3308	+	61.4525i	−0.805231	+	2.03378i
$914$	15.0847	+	3.87308i	0.498956	+	0.128110i
$915$	−1.02743	−	5.31937i	−0.0339659	−	0.175853i
$916$	0.626753	+	0.248149i	0.0207085	+	0.00819907i
$917$	−14.2583	−	6.70944i	−0.470850	−	0.221565i
$918$	2.96086	+	0.962040i	0.0977228	+	0.0317521i
$919$	−6.51967	−	34.1773i	−0.215064	−	1.12741i	−0.911974	−	0.410247i	$-0.865442\pi$
$919$	−6.51967	−	34.1773i	−0.215064	−	1.12741i	0.696910	−	0.717159i	$-0.254558\pi$
$920$	18.0642	+	1.09472i	0.595559	+	0.0360918i
$921$	−6.61075	−	14.0486i	−0.217832	−	0.462916i
$922$	21.3721	+	4.07694i	0.703851	+	0.134267i
$923$	30.2637	−	25.0363i	0.996141	−	0.824079i
$924$	5.38587	−	16.5760i	0.177182	−	0.545311i
$925$	−16.9534	+	10.8689i	−0.557424	+	0.357366i
$926$	−7.92802	−	24.3999i	−0.260531	−	0.801832i
$927$	0.609102	+	0.386548i	0.0200055	+	0.0126959i
$928$	3.61280	−	6.57165i	0.118596	−	0.215725i
$929$	0.601716	−	3.15430i	0.0197417	−	0.103489i	−0.971053	−	0.238866i	$-0.923224\pi$
$929$	0.601716	−	3.15430i	0.0197417	−	0.103489i	0.990794	+	0.135376i	$0.0432244\pi$
$930$	−4.45152	+	17.5049i	−0.145971	+	0.574007i
$931$	−14.4117	−	13.5335i	−0.472325	−	0.443543i
$932$		−	0.125346i		−	0.00410584i
$933$	2.21247	−	2.35604i	0.0724329	−	0.0771332i
$934$	2.38663	+	3.76072i	0.0780928	+	0.123055i
$935$	17.4700	−	21.2169i	0.571330	−	0.693868i
$936$	3.51990	−	1.39363i	0.115051	−	0.0455521i
$937$	−6.32985	−	0.398241i	−0.206787	−	0.0130100i	−0.0409410	−	0.999162i	$-0.513036\pi$
$937$	−6.32985	−	0.398241i	−0.206787	−	0.0130100i	−0.165846	+	0.986152i	$0.553036\pi$
$938$	47.9043	+	3.01388i	1.56413	+	0.0984068i
$939$	−20.3994	+	8.07670i	−0.665710	+	0.263573i
$940$	16.0092	−	19.4428i	0.522162	−	0.634155i
$941$	8.27648	+	13.0416i	0.269805	+	0.425145i	0.952033	−	0.305994i	$-0.0989888\pi$
$941$	8.27648	+	13.0416i	0.269805	+	0.425145i	−0.682228	+	0.731140i	$0.738989\pi$
$942$	0.290456	−	0.309304i	0.00946358	−	0.0100777i
$943$		−	88.5480i		−	2.88352i
$944$	2.71602	+	2.55052i	0.0883990	+	0.0830122i
$945$	−2.43287	+	9.56688i	−0.0791414	+	0.311211i
$946$	5.46935	−	28.6713i	0.177824	−	0.932185i
$947$	−2.22002	+	4.03821i	−0.0721411	+	0.131224i	−0.909917	−	0.414789i	$-0.863855\pi$
$947$	−2.22002	+	4.03821i	−0.0721411	+	0.131224i	0.837776	+	0.546014i	$0.183855\pi$
$948$	−11.6286	−	7.37971i	−0.377678	−	0.239682i
$949$	−4.92764	−	15.1657i	−0.159958	−	0.492300i
$950$	7.90167	+	0.460583i	0.256364	+	0.0149433i
$951$	0.998940	−	3.07442i	0.0323929	−	0.0996950i
$952$	−10.5897	+	8.76057i	−0.343214	+	0.283932i
$953$	−14.6532	−	2.79524i	−0.474663	−	0.0905468i	−0.0555016	−	0.998459i	$-0.517676\pi$
$953$	−14.6532	−	2.79524i	−0.474663	−	0.0905468i	−0.419161	+	0.907912i	$0.637676\pi$
$954$	−2.45154	−	5.20980i	−0.0793717	−	0.168673i
$955$	−8.62443	−	0.522654i	−0.279080	−	0.0169127i
$956$	−1.95412	−	10.2439i	−0.0632008	−	0.331310i
$957$	28.1582	+	9.14917i	0.910227	+	0.295751i
$958$	−14.9814	−	7.04973i	−0.484028	−	0.227766i
$959$	−19.5160	−	7.72693i	−0.630205	−	0.249516i
$960$	−0.424057	−	2.19549i	−0.0136864	−	0.0708591i
$961$	33.1713	+	8.51695i	1.07004	+	0.274740i
$962$	5.61304	−	14.1769i	0.180972	−	0.457082i
$963$	−0.568490	−	2.21412i	−0.0183193	−	0.0713491i
$964$	12.0166	−	18.9351i	0.387028	−	0.609858i
$965$	−8.06736	−	5.83292i	−0.259697	−	0.187768i
$966$	2.24345	−	35.6586i	0.0721818	−	1.14730i
$967$	20.8362	+	37.9008i	0.670046	+	1.21881i	0.964737	+	0.263216i	$0.0847832\pi$
$967$	20.8362	+	37.9008i	0.670046	+	1.21881i	−0.294691	+	0.955592i	$0.595217\pi$
$968$	−4.36247	+	1.41745i	−0.140215	+	0.0455587i
$969$	−4.88943	−	0.617679i	−0.157071	−	0.0198427i
$970$	7.71855	−	1.49083i	0.247828	−	0.0478678i
$971$	27.6850	−	25.9980i	0.888455	−	0.834315i	−0.0985290	−	0.995134i	$-0.531414\pi$
$971$	27.6850	−	25.9980i	0.888455	−	0.834315i	0.986984	+	0.160820i	$0.0514137\pi$
$972$	0.684547	+	0.728969i	0.0219569	+	0.0233817i
$973$	9.37896	−	36.5286i	0.300676	−	1.17105i
$974$	4.91139	+	3.56834i	0.157371	+	0.114337i
$975$	1.27559	+	18.8857i	0.0408517	+	0.604827i
$976$	1.96014	−	1.42412i	0.0627424	−	0.0455850i
$977$	17.3518	+	43.8258i	0.555135	+	1.40211i	0.888310	+	0.459245i	$0.151880\pi$
$977$	17.3518	+	43.8258i	0.555135	+	1.40211i	−0.333175	+	0.942865i	$0.608120\pi$
$978$	−0.240427	−	1.90317i	−0.00768800	−	0.0608568i
$979$	34.6417	+	19.0445i	1.10715	+	0.608664i
$980$	−19.1634	−	20.3130i	−0.612153	−	0.648874i
$981$	−5.55236	+	11.7994i	−0.177273	+	0.376725i
$982$	20.6552	−	28.4295i	0.659134	−	0.907220i
$983$	2.49685	−	19.7646i	0.0796373	−	0.630394i	−0.900895	−	0.434037i	$-0.857089\pi$
$983$	2.49685	−	19.7646i	0.0796373	−	0.630394i	0.980532	−	0.196357i	$-0.0629112\pi$
$984$	−10.5971	+	2.72087i	−0.337822	+	0.0867381i
$985$	0.507352	+	1.07176i	0.0161656	+	0.0341491i
$986$	−14.8819	−	17.9891i	−0.473935	−	0.572890i
$987$	−38.3126	−	31.6949i	−1.21950	−	1.00886i
$988$	−5.05998	+	3.21116i	−0.160979	+	0.102161i
$989$	−3.75709	−	59.7173i	−0.119469	−	1.89890i
$990$	8.20062	−	3.26874i	0.260633	−	0.103887i
$991$	31.3867	−	37.9399i	0.997030	−	1.20520i	0.0183456	−	0.999832i	$-0.494160\pi$
$991$	31.3867	−	37.9399i	0.997030	−	1.20520i	0.978684	−	0.205370i	$-0.0658399\pi$
$992$	−7.93450	+	1.51359i	−0.251921	+	0.0480564i
$993$	−0.874689	−	1.20391i	−0.0277574	−	0.0382048i
$994$	−40.1364	+	22.0652i	−1.27305	+	0.699865i
$995$	13.1806	+	4.24909i	0.417854	+	0.134705i
$996$	16.6090	−	2.09820i	0.526275	−	0.0664840i
$997$	−33.5897	+	15.8061i	−1.06380	+	0.500585i	−0.876343	−	0.481688i	$-0.840024\pi$
$997$	−33.5897	+	15.8061i	−1.06380	+	0.500585i	−0.187455	+	0.982273i	$0.560024\pi$
$998$	−4.28993	+	0.269899i	−0.135795	+	0.00854352i
$999$	4.02765			0.127429

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.a.469.9	yes	240
125.4	even	50	inner	750.2.o.a.379.9	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.a.379.9	✓	240	125.4	even	50	inner
750.2.o.a.469.9	yes	240	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.o (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.998027 - 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(-1.31016 + 1.81204i) q^{5} +(-0.876307 + 0.481754i) q^{6} +(-2.59485 - 3.57150i) q^{7} +(0.982287 - 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +O(q^{10})\)	\(q+(0.998027 - 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(-1.31016 + 1.81204i) q^{5} +(-0.876307 + 0.481754i) q^{6} +(-2.59485 - 3.57150i) q^{7} +(0.982287 - 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +(-1.19379 + 1.89073i) q^{10} +(-0.247899 - 3.94024i) q^{11} +(-0.844328 + 0.535827i) q^{12} +(2.91697 + 2.41313i) q^{13} +(-2.81398 - 3.40152i) q^{14} +(0.413935 - 2.19742i) q^{15} +(0.968583 - 0.248690i) q^{16} +(0.390191 - 3.08868i) q^{17} +(0.587785 - 0.809017i) q^{18} +(-0.674016 + 1.43236i) q^{19} +(-1.07272 + 1.96196i) q^{20} +(3.86856 + 2.12676i) q^{21} +(-0.494820 - 3.91690i) q^{22} +(-2.97937 - 7.52503i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(-1.56698 - 4.74811i) q^{25} +(3.06273 + 2.22521i) q^{26} +(-0.248690 + 0.968583i) q^{27} +(-3.02201 - 3.21812i) q^{28} +(5.46672 - 5.13360i) q^{29} +(0.275141 - 2.21908i) q^{30} +(-8.01388 - 1.01239i) q^{31} +(0.951057 - 0.309017i) q^{32} +(1.90198 + 3.45969i) q^{33} +(0.195481 - 3.10708i) q^{34} +(9.87135 - 0.0227459i) q^{35} +(0.535827 - 0.844328i) q^{36} +(-1.00164 - 3.90112i) q^{37} +(-0.582748 + 1.47185i) q^{38} +(-3.66681 - 0.941477i) q^{39} +(-0.947407 + 2.02544i) q^{40} +(10.1725 + 4.02758i) q^{41} +(3.99446 + 1.87965i) q^{42} +(7.03128 + 2.28460i) q^{43} +(-0.739788 - 3.87810i) q^{44} +(0.561077 + 2.16453i) q^{45} +(-3.44599 - 7.32310i) q^{46} +(-11.0639 - 2.11055i) q^{47} +(-0.770513 + 0.637424i) q^{48} +(-3.85926 + 11.8776i) q^{49} +(-1.86203 - 4.64035i) q^{50} +(0.962040 + 2.96086i) q^{51} +(3.19641 + 2.02850i) q^{52} +(2.77383 - 5.04558i) q^{53} +(-0.187381 + 0.982287i) q^{54} +(7.46467 + 4.71313i) q^{55} +(-3.21812 - 3.02201i) q^{56} -1.58302i q^{57} +(5.13360 - 5.46672i) q^{58} +(1.99641 + 3.14583i) q^{59} +(0.135261 - 2.23197i) q^{60} +(2.25272 - 0.891915i) q^{61} +(-8.06164 - 0.507195i) q^{62} +(-4.40590 - 0.277196i) q^{63} +(0.929776 - 0.368125i) q^{64} +(-8.19437 + 2.12409i) q^{65} +(2.11546 + 3.33344i) q^{66} +(-7.44291 + 7.92589i) q^{67} -3.11323i q^{68} +(5.89981 + 5.54029i) q^{69} +(9.85045 - 0.642528i) q^{70} +(1.94409 - 10.1913i) q^{71} +(0.481754 - 0.876307i) q^{72} +(-3.55645 - 2.25699i) q^{73} +(-1.24461 - 3.83052i) q^{74} +(3.43950 + 3.62903i) q^{75} +(-0.489179 + 1.50554i) q^{76} +(-13.4293 + 11.1097i) q^{77} +(-3.71869 - 0.709378i) q^{78} +(5.86407 + 12.4618i) q^{79} +(-0.818359 + 2.08093i) q^{80} +(-0.187381 - 0.982287i) q^{81} +(10.4053 + 3.38089i) q^{82} +(-15.1477 - 7.12795i) q^{83} +(4.10461 + 1.62513i) q^{84} +(5.08560 + 4.75369i) q^{85} +(7.16086 + 1.83860i) q^{86} +(-2.76066 + 6.97263i) q^{87} +(-0.981836 - 3.82400i) q^{88} +(-5.36521 + 8.45423i) q^{89} +(0.695881 + 2.12503i) q^{90} +(1.04939 - 16.6796i) q^{91} +(-3.89901 - 7.09228i) q^{92} +(7.68223 - 2.49611i) q^{93} +(-11.1746 - 1.41168i) q^{94} +(-1.71242 - 3.09796i) q^{95} +(-0.728969 + 0.684547i) q^{96} +(-2.40662 - 2.56279i) q^{97} +(-3.10584 + 12.0965i) q^{98} +(-3.19403 - 2.32060i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q+O(q^{10}) \) 240 * q	\( 240 q - 10 q^{11} + 20 q^{13} - 10 q^{17} + 10 q^{19} + 60 q^{23} - 60 q^{24} + 60 q^{25} + 10 q^{28} + 20 q^{29} + 10 q^{30} - 30 q^{31} - 10 q^{34} - 10 q^{35} + 20 q^{37} - 90 q^{38} - 20 q^{41} - 10 q^{42} - 10 q^{46} + 140 q^{47} + 50 q^{49} + 20 q^{50} + 10 q^{51} - 80 q^{52} + 30 q^{53} - 10 q^{55} - 30 q^{58} + 20 q^{59} + 40 q^{60} - 100 q^{61} - 10 q^{62} - 10 q^{63} - 20 q^{65} - 40 q^{66} - 10 q^{67} - 10 q^{69} + 10 q^{70} + 80 q^{71} + 20 q^{73} - 80 q^{75} + 10 q^{76} + 20 q^{77} + 140 q^{79} + 100 q^{82} - 70 q^{83} - 20 q^{85} + 20 q^{86} + 30 q^{87} - 10 q^{88} + 40 q^{89} + 10 q^{90} + 170 q^{91} + 120 q^{92} + 50 q^{93} - 30 q^{94} + 220 q^{95} - 60 q^{97} - 120 q^{98} - 20 q^{99}+O(q^{100}) \) 240 * q - 10 * q^11 + 20 * q^13 - 10 * q^17 + 10 * q^19 + 60 * q^23 - 60 * q^24 + 60 * q^25 + 10 * q^28 + 20 * q^29 + 10 * q^30 - 30 * q^31 - 10 * q^34 - 10 * q^35 + 20 * q^37 - 90 * q^38 - 20 * q^41 - 10 * q^42 - 10 * q^46 + 140 * q^47 + 50 * q^49 + 20 * q^50 + 10 * q^51 - 80 * q^52 + 30 * q^53 - 10 * q^55 - 30 * q^58 + 20 * q^59 + 40 * q^60 - 100 * q^61 - 10 * q^62 - 10 * q^63 - 20 * q^65 - 40 * q^66 - 10 * q^67 - 10 * q^69 + 10 * q^70 + 80 * q^71 + 20 * q^73 - 80 * q^75 + 10 * q^76 + 20 * q^77 + 140 * q^79 + 100 * q^82 - 70 * q^83 - 20 * q^85 + 20 * q^86 + 30 * q^87 - 10 * q^88 + 40 * q^89 + 10 * q^90 + 170 * q^91 + 120 * q^92 + 50 * q^93 - 30 * q^94 + 220 * q^95 - 60 * q^97 - 120 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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