LMFDB - Embedded newform 300.2.w.a.103.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(67,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 13]))

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

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

chi := DirichletCharacter("300.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			103.7
Character	$\chi$	$=$	300.103
Dual form			300.2.w.a.67.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12003 + 0.863445i) q^{2} +(-0.987688 + 0.156434i) q^{3} +(0.508925 - 1.93417i) q^{4} +(-1.70279 - 1.44932i) q^{5} +(0.971166 - 1.02803i) q^{6} +(1.87554 + 1.87554i) q^{7} +(1.10004 + 2.60575i) q^{8} +(0.951057 - 0.309017i) q^{9} +O(q^{10})$	\(q+(-1.12003 + 0.863445i) q^{2} +(-0.987688 + 0.156434i) q^{3} +(0.508925 - 1.93417i) q^{4} +(-1.70279 - 1.44932i) q^{5} +(0.971166 - 1.02803i) q^{6} +(1.87554 + 1.87554i) q^{7} +(1.10004 + 2.60575i) q^{8} +(0.951057 - 0.309017i) q^{9} +(3.15857 + 0.153014i) q^{10} +(-2.91356 - 0.946674i) q^{11} +(-0.200089 + 1.98997i) q^{12} +(-1.26064 + 2.47414i) q^{13} +(-3.72009 - 0.481232i) q^{14} +(1.90854 + 1.16510i) q^{15} +(-3.48199 - 1.96869i) q^{16} +(-0.901092 + 5.68927i) q^{17} +(-0.798391 + 1.16729i) q^{18} +(-3.66420 + 2.66220i) q^{19} +(-3.66981 + 2.55588i) q^{20} +(-2.14585 - 1.55905i) q^{21} +(4.08067 - 1.45540i) q^{22} +(-3.07781 - 6.04055i) q^{23} +(-1.49412 - 2.40158i) q^{24} +(0.798959 + 4.93575i) q^{25} +(-0.724334 - 3.85959i) q^{26} +(-0.891007 + 0.453990i) q^{27} +(4.58212 - 2.67310i) q^{28} +(-4.48892 + 6.17846i) q^{29} +(-3.14362 + 0.342980i) q^{30} +(1.14385 + 1.57437i) q^{31} +(5.59978 - 0.801520i) q^{32} +(3.02578 + 0.479237i) q^{33} +(-3.90312 - 7.15018i) q^{34} +(-0.475391 - 5.91190i) q^{35} +(-0.113673 - 1.99677i) q^{36} +(-4.87556 - 2.48422i) q^{37} +(1.80534 - 6.14557i) q^{38} +(0.858075 - 2.64088i) q^{39} +(1.90343 - 6.03133i) q^{40} +(-1.46647 - 4.51334i) q^{41} +(3.74957 - 0.106643i) q^{42} +(-0.964168 + 0.964168i) q^{43} +(-3.31381 + 5.15353i) q^{44} +(-2.06731 - 0.852193i) q^{45} +(8.66292 + 4.10806i) q^{46} +(1.87467 + 11.8362i) q^{47} +(3.74709 + 1.39975i) q^{48} +0.0353135i q^{49} +(-5.15661 - 4.83832i) q^{50} -5.76019i q^{51} +(4.14382 + 3.69743i) q^{52} +(1.98116 + 12.5085i) q^{53} +(0.605956 - 1.27782i) q^{54} +(3.58914 + 5.83466i) q^{55} +(-2.82403 + 6.95035i) q^{56} +(3.20263 - 3.20263i) q^{57} +(-0.307052 - 10.7960i) q^{58} +(1.89101 + 5.81992i) q^{59} +(3.22480 - 3.09849i) q^{60} +(2.51370 - 7.73638i) q^{61} +(-2.64052 - 0.775690i) q^{62} +(2.36332 + 1.20417i) q^{63} +(-5.57984 + 5.73283i) q^{64} +(5.73240 - 2.38586i) q^{65} +(-3.80276 + 2.07584i) q^{66} +(-1.31873 - 0.208866i) q^{67} +(10.5454 + 4.63827i) q^{68} +(3.98487 + 5.48470i) q^{69} +(5.63705 + 6.21102i) q^{70} +(7.46718 - 10.2777i) q^{71} +(1.85142 + 2.13828i) q^{72} +(-3.04977 + 1.55394i) q^{73} +(7.60576 - 1.42738i) q^{74} +(-1.56124 - 4.75000i) q^{75} +(3.28432 + 8.44202i) q^{76} +(-3.68898 - 7.24004i) q^{77} +(1.31919 + 3.69876i) q^{78} +(-0.348097 - 0.252907i) q^{79} +(3.07583 + 8.39877i) q^{80} +(0.809017 - 0.587785i) q^{81} +(5.53951 + 3.78884i) q^{82} +(1.82263 - 11.5076i) q^{83} +(-4.10754 + 3.35699i) q^{84} +(9.77992 - 8.38164i) q^{85} +(0.247389 - 1.91240i) q^{86} +(3.46713 - 6.80462i) q^{87} +(-0.738228 - 8.63339i) q^{88} +(2.37328 + 0.771124i) q^{89} +(3.05127 - 0.830528i) q^{90} +(-7.00472 + 2.27597i) q^{91} +(-13.2498 + 2.87881i) q^{92} +(-1.37605 - 1.37605i) q^{93} +(-12.3196 - 11.6382i) q^{94} +(10.0977 + 0.777436i) q^{95} +(-5.40545 + 1.66765i) q^{96} +(-12.2095 + 1.93379i) q^{97} +(-0.0304912 - 0.0395521i) q^{98} -3.06350 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{8}+O(q^{10}) $ 240 * q + 12 * q^8	$ 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) $ 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{20}\right)$

Coefficient data

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

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

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

$2$	−1.12003	+	0.863445i	−0.791979	+	0.610548i
$2$	−1.12003	+	0.863445i	−0.791979	+	0.610548i
$3$	−0.987688	+	0.156434i	−0.570242	+	0.0903175i
$3$	−0.987688	+	0.156434i	−0.570242	+	0.0903175i
$4$	0.508925	−	1.93417i	0.254463	−	0.967083i
$5$	−1.70279	−	1.44932i	−0.761509	−	0.648154i
$5$	−1.70279	−	1.44932i	−0.761509	−	0.648154i
$6$	0.971166	−	1.02803i	0.396477	−	0.419690i
$7$	1.87554	+	1.87554i	0.708888	+	0.708888i	0.966301	−	0.257413i	$-0.0828702\pi$
$7$	1.87554	+	1.87554i	0.708888	+	0.708888i	−0.257413	+	0.966301i	$0.582870\pi$
$8$	1.10004	+	2.60575i	0.388921	+	0.921271i
$9$	0.951057	−	0.309017i	0.317019	−	0.103006i
$10$	3.15857	+	0.153014i	0.998829	+	0.0483872i
$11$	−2.91356	−	0.946674i	−0.878472	−	0.285433i	−0.165149	−	0.986269i	$-0.552811\pi$
$11$	−2.91356	−	0.946674i	−0.878472	−	0.285433i	−0.713323	+	0.700836i	$0.752811\pi$
$12$	−0.200089	+	1.98997i	−0.0577608	+	0.574454i
$13$	−1.26064	+	2.47414i	−0.349637	+	0.686202i	−0.997117	−	0.0758808i	$-0.975823\pi$
$13$	−1.26064	+	2.47414i	−0.349637	+	0.686202i	0.647479	+	0.762083i	$0.275823\pi$
$14$	−3.72009	−	0.481232i	−0.994235	−	0.128615i
$15$	1.90854	+	1.16510i	0.492784	+	0.300827i
$16$	−3.48199	−	1.96869i	−0.870498	−	0.492173i
$17$	−0.901092	+	5.68927i	−0.218547	+	1.37985i	0.597502	+	0.801867i	$0.296160\pi$
$17$	−0.901092	+	5.68927i	−0.218547	+	1.37985i	−0.816049	+	0.577983i	$0.803840\pi$
$18$	−0.798391	+	1.16729i	−0.188182	+	0.275134i
$19$	−3.66420	+	2.66220i	−0.840625	+	0.610750i	−0.922545	−	0.385889i	$-0.873895\pi$
$19$	−3.66420	+	2.66220i	−0.840625	+	0.610750i	0.0819203	+	0.996639i	$0.473895\pi$
$20$	−3.66981	+	2.55588i	−0.820594	+	0.571511i
$21$	−2.14585	−	1.55905i	−0.468263	−	0.340213i
$22$	4.08067	−	1.45540i	0.870002	−	0.310292i
$23$	−3.07781	−	6.04055i	−0.641768	−	1.25954i	−0.951187	−	0.308615i	$-0.900134\pi$
$23$	−3.07781	−	6.04055i	−0.641768	−	1.25954i	0.309419	−	0.950926i	$-0.399866\pi$
$24$	−1.49412	−	2.40158i	−0.304986	−	0.490221i
$25$	0.798959	+	4.93575i	0.159792	+	0.987151i
$26$	−0.724334	−	3.85959i	−0.142054	−	0.756928i
$27$	−0.891007	+	0.453990i	−0.171474	+	0.0873705i
$28$	4.58212	−	2.67310i	0.865939	−	0.505168i
$29$	−4.48892	+	6.17846i	−0.833571	+	1.14731i	0.153677	+	0.988121i	$0.450888\pi$
$29$	−4.48892	+	6.17846i	−0.833571	+	1.14731i	−0.987248	+	0.159191i	$0.949112\pi$
$30$	−3.14362	+	0.342980i	−0.573944	+	0.0626193i
$31$	1.14385	+	1.57437i	0.205441	+	0.282765i	0.899288	−	0.437357i	$-0.144086\pi$
$31$	1.14385	+	1.57437i	0.205441	+	0.282765i	−0.693847	+	0.720123i	$0.744086\pi$
$32$	5.59978	−	0.801520i	0.989911	−	0.141690i
$33$	3.02578	+	0.479237i	0.526721	+	0.0834245i
$34$	−3.90312	−	7.15018i	−0.669380	−	1.22625i
$35$	−0.475391	−	5.91190i	−0.0803557	−	0.999294i
$36$	−0.113673	−	1.99677i	−0.0189456	−	0.332794i
$37$	−4.87556	−	2.48422i	−0.801538	−	0.408404i	0.00470480	−	0.999989i	$-0.498502\pi$
$37$	−4.87556	−	2.48422i	−0.801538	−	0.408404i	−0.806243	+	0.591585i	$0.798502\pi$
$38$	1.80534	−	6.14557i	0.292866	−	0.996943i
$39$	0.858075	−	2.64088i	0.137402	−	0.422880i
$40$	1.90343	−	6.03133i	0.300959	−	0.953637i
$41$	−1.46647	−	4.51334i	−0.229024	−	0.704865i	−0.997858	−	0.0654159i	$-0.979163\pi$
$41$	−1.46647	−	4.51334i	−0.229024	−	0.704865i	0.768834	−	0.639449i	$-0.220837\pi$
$42$	3.74957	−	0.106643i	0.578571	−	0.0164553i
$43$	−0.964168	+	0.964168i	−0.147034	+	0.147034i	−0.776792	−	0.629758i	$-0.783154\pi$
$43$	−0.964168	+	0.964168i	−0.147034	+	0.147034i	0.629758	+	0.776792i	$0.283154\pi$
$44$	−3.31381	+	5.15353i	−0.499576	+	0.776923i
$45$	−2.06731	−	0.852193i	−0.308176	−	0.127037i
$46$	8.66292	+	4.10806i	1.27728	+	0.605700i
$47$	1.87467	+	11.8362i	0.273449	+	1.72649i	0.616658	+	0.787231i	$0.288486\pi$
$47$	1.87467	+	11.8362i	0.273449	+	1.72649i	−0.343209	+	0.939259i	$0.611514\pi$
$48$	3.74709	+	1.39975i	0.540846	+	0.202036i
$49$			0.0353135i			0.00504478i
$50$	−5.15661	−	4.83832i	−0.729255	−	0.684242i
$51$		−	5.76019i		−	0.806587i
$52$	4.14382	+	3.69743i	0.574644	+	0.512741i
$53$	1.98116	+	12.5085i	0.272133	+	1.71818i	0.623399	+	0.781904i	$0.285751\pi$
$53$	1.98116	+	12.5085i	0.272133	+	1.71818i	−0.351266	+	0.936276i	$0.614249\pi$
$54$	0.605956	−	1.27782i	0.0824602	−	0.173889i
$55$	3.58914	+	5.83466i	0.483960	+	0.786745i
$56$	−2.82403	+	6.95035i	−0.377376	+	0.928780i
$57$	3.20263	−	3.20263i	0.424198	−	0.424198i
$58$	−0.307052	−	10.7960i	−0.0403179	−	1.41758i
$59$	1.89101	+	5.81992i	0.246188	+	0.757690i	0.995439	+	0.0954029i	$0.0304139\pi$
$59$	1.89101	+	5.81992i	0.246188	+	0.757690i	−0.749250	+	0.662287i	$0.769586\pi$
$60$	3.22480	−	3.09849i	0.416320	−	0.400014i
$61$	2.51370	−	7.73638i	0.321846	−	0.990542i	−0.650998	−	0.759080i	$-0.725649\pi$
$61$	2.51370	−	7.73638i	0.321846	−	0.990542i	0.972844	−	0.231462i	$-0.0743508\pi$
$62$	−2.64052	−	0.775690i	−0.335347	−	0.0985127i
$63$	2.36332	+	1.20417i	0.297750	+	0.151711i
$64$	−5.57984	+	5.73283i	−0.697481	+	0.716604i
$65$	5.73240	−	2.38586i	0.711017	−	0.295930i
$66$	−3.80276	+	2.07584i	−0.468087	+	0.255518i
$67$	−1.31873	−	0.208866i	−0.161108	−	0.0255170i	0.0753593	−	0.997156i	$-0.475990\pi$
$67$	−1.31873	−	0.208866i	−0.161108	−	0.0255170i	−0.236467	+	0.971639i	$0.575990\pi$
$68$	10.5454	+	4.63827i	1.27882	+	0.562473i
$69$	3.98487	+	5.48470i	0.479722	+	0.660280i
$70$	5.63705	+	6.21102i	0.673757	+	0.742359i
$71$	7.46718	−	10.2777i	0.886192	−	1.21974i	−0.0884755	−	0.996078i	$-0.528199\pi$
$71$	7.46718	−	10.2777i	0.886192	−	1.21974i	0.974667	−	0.223660i	$-0.0718005\pi$
$72$	1.85142	+	2.13828i	0.218191	+	0.251999i
$73$	−3.04977	+	1.55394i	−0.356949	+	0.181874i	−0.623264	−	0.782012i	$-0.714194\pi$
$73$	−3.04977	+	1.55394i	−0.356949	+	0.181874i	0.266315	+	0.963886i	$0.414194\pi$
$74$	7.60576	−	1.42738i	0.884152	−	0.165930i
$75$	−1.56124	−	4.75000i	−0.180277	−	0.548483i
$76$	3.28432	+	8.44202i	0.376738	+	0.968367i
$77$	−3.68898	−	7.24004i	−0.420399	−	0.825079i
$78$	1.31919	+	3.69876i	0.149369	+	0.418802i
$79$	−0.348097	−	0.252907i	−0.0391640	−	0.0284543i	0.568031	−	0.823007i	$-0.307705\pi$
$79$	−0.348097	−	0.252907i	−0.0391640	−	0.0284543i	−0.607195	+	0.794553i	$0.707705\pi$
$80$	3.07583	+	8.39877i	0.343888	+	0.939011i
$81$	0.809017	−	0.587785i	0.0898908	−	0.0653095i
$82$	5.53951	+	3.78884i	0.611736	+	0.418408i
$83$	1.82263	−	11.5076i	0.200060	−	1.26313i	−0.659348	−	0.751838i	$-0.729168\pi$
$83$	1.82263	−	11.5076i	0.200060	−	1.26313i	0.859408	−	0.511291i	$-0.170832\pi$
$84$	−4.10754	+	3.35699i	−0.448169	+	0.366277i
$85$	9.77992	−	8.38164i	1.06078	−	0.909116i
$86$	0.247389	−	1.91240i	0.0266766	−	0.206219i
$87$	3.46713	−	6.80462i	0.371715	−	0.729531i
$88$	−0.738228	−	8.63339i	−0.0786954	−	0.920322i
$89$	2.37328	+	0.771124i	0.251567	+	0.0817390i	0.432086	−	0.901832i	$-0.357778\pi$
$89$	2.37328	+	0.771124i	0.251567	+	0.0817390i	−0.180519	+	0.983571i	$0.557778\pi$
$90$	3.05127	−	0.830528i	0.321632	−	0.0875454i
$91$	−7.00472	+	2.27597i	−0.734294	+	0.238587i
$92$	−13.2498	+	2.87881i	−1.38139	+	0.300137i
$93$	−1.37605	−	1.37605i	−0.142690	−	0.142690i
$94$	−12.3196	−	11.6382i	−1.27067	−	1.20039i
$95$	10.0977	+	0.777436i	1.03600	+	0.0797633i
$96$	−5.40545	+	1.66765i	−0.551692	+	0.170204i
$97$	−12.2095	+	1.93379i	−1.23968	+	0.196346i	−0.741635	−	0.670804i	$-0.765949\pi$
$97$	−12.2095	+	1.93379i	−1.23968	+	0.196346i	−0.498047	+	0.867150i	$0.665949\pi$
$98$	−0.0304912	−	0.0395521i	−0.00308008	−	0.00399536i
$99$	−3.06350			−0.307893
$100$	9.95317	+	0.966609i	0.995317	+	0.0966609i
$101$	5.29258			0.526631			0.263315	−	0.964710i	$-0.415184\pi$
$101$	5.29258			0.526631			0.263315	+	0.964710i	$0.415184\pi$
$102$	4.97361	+	6.45157i	0.492460	+	0.638801i
$103$	5.18961	−	0.821954i	0.511348	−	0.0809895i	0.104572	−	0.994517i	$-0.466653\pi$
$103$	5.18961	−	0.821954i	0.511348	−	0.0809895i	0.406776	+	0.913528i	$0.366653\pi$
$104$	−7.83372	−	0.563261i	−0.768159	−	0.0552323i
$105$	1.39436	+	5.76475i	0.136076	+	0.562582i
$106$	−13.0194	−	12.2993i	−1.26455	−	1.19461i
$107$	−3.87709	−	3.87709i	−0.374812	−	0.374812i	0.494414	−	0.869226i	$-0.335383\pi$
$107$	−3.87709	−	3.87709i	−0.374812	−	0.374812i	−0.869226	+	0.494414i	$0.835383\pi$
$108$	0.424637	+	1.95440i	0.0408607	+	0.188062i
$109$	13.2787	−	4.31450i	1.27186	−	0.413254i	0.406156	−	0.913804i	$-0.366869\pi$
$109$	13.2787	−	4.31450i	1.27186	−	0.413254i	0.865708	+	0.500550i	$0.166869\pi$
$110$	−9.05785	−	3.43595i	−0.863632	−	0.327605i
$111$	5.20416	+	1.69093i	0.493957	+	0.160496i
$112$	−2.83826	−	10.2230i	−0.268190	−	0.965981i
$113$	−0.889930	+	1.74659i	−0.0837175	+	0.164305i	−0.929070	−	0.369904i	$-0.879391\pi$
$113$	−0.889930	+	1.74659i	−0.0837175	+	0.164305i	0.845352	+	0.534209i	$0.179391\pi$
$114$	−0.821739	+	6.35232i	−0.0769629	+	0.594950i
$115$	−3.51381	+	14.7465i	−0.327665	+	1.37512i
$116$	9.66565	+	11.8267i	0.897433	+	1.09808i
$117$	−0.434385	+	2.74260i	−0.0401589	+	0.253554i
$118$	−7.14317	−	4.88570i	−0.657582	−	0.449765i
$119$	−12.3605	+	8.98043i	−1.13308	+	0.823234i
$120$	−0.936488	+	6.25484i	−0.0854893	+	0.570986i
$121$	−1.30653	−	0.949249i	−0.118775	−	0.0862954i
$122$	3.86452	+	10.8354i	0.349877	+	0.980991i
$123$	2.15446	+	4.22836i	0.194261	+	0.381259i
$124$	3.62722	−	1.41115i	0.325734	−	0.126725i
$125$	5.79302	−	9.56248i	0.518143	−	0.855294i
$126$	−3.68672	+	0.691891i	−0.328439	+	0.0616386i
$127$	−10.9630	+	5.58595i	−0.972812	+	0.495673i	−0.866780	−	0.498690i	$-0.833815\pi$
$127$	−10.9630	+	5.58595i	−0.972812	+	0.495673i	−0.106032	+	0.994363i	$0.533815\pi$
$128$	1.29960	−	11.2388i	0.114869	−	0.993381i
$129$	0.801468	−	1.10313i	0.0705653	−	0.0971249i
$130$	−4.36039	+	7.62185i	−0.382431	+	0.668480i
$131$	0.398490	+	0.548475i	0.0348163	+	0.0479205i	0.826070	−	0.563567i	$-0.190571\pi$
$131$	0.398490	+	0.548475i	0.0348163	+	0.0479205i	−0.791254	+	0.611488i	$0.790571\pi$
$132$	2.46682	−	5.60847i	0.214709	−	0.488155i
$133$	−11.8654	−	1.87930i	−1.02886	−	0.162956i
$134$	1.65735	−	0.904712i	0.143174	−	0.0781552i
$135$	2.17517	+	0.518303i	0.187209	+	0.0446084i
$136$	−15.8160	+	3.91038i	−1.35621	+	0.335312i
$137$	−17.7950	−	9.06702i	−1.52033	−	0.774648i	−0.523338	−	0.852125i	$-0.675313\pi$
$137$	−17.7950	−	9.06702i	−1.52033	−	0.774648i	−0.996994	+	0.0774774i	$0.975313\pi$
$138$	−9.19890	−	2.70230i	−0.783063	−	0.230035i
$139$	−0.0167604	+	0.0515832i	−0.00142160	+	0.00437523i	−0.951765	−	0.306829i	$-0.900732\pi$
$139$	−0.0167604	+	0.0515832i	−0.00142160	+	0.00437523i	0.950343	+	0.311204i	$0.100732\pi$
$140$	−11.6765	−	2.08923i	−0.986847	−	0.176572i
$141$	−3.70319	−	11.3972i	−0.311864	−	0.959820i
$142$	0.510773	+	17.9588i	0.0428631	+	1.50707i
$143$	6.01514	−	6.01514i	0.503011	−	0.503011i
$144$	−3.91993	−	0.796341i	−0.326661	−	0.0663618i
$145$	16.5982	−	4.01474i	1.37841	−	0.333406i
$146$	2.07409	−	4.37376i	0.171653	−	0.361975i
$147$	−0.00552424	−	0.0348787i	−0.000455632	−	0.00287675i
$148$	−7.28620	+	8.16586i	−0.598922	+	0.671230i
$149$		−	1.12997i		−	0.0925708i	−0.998928	−	0.0462854i	$-0.985262\pi$
$149$		−	1.12997i		−	0.0925708i	0.998928	−	0.0462854i	$-0.0147384\pi$
$150$	5.85000	+	3.97209i	0.477651	+	0.324319i
$151$			5.68829i			0.462907i	0.972846	+	0.231453i	$0.0743481\pi$
$151$			5.68829i			0.462907i	−0.972846	+	0.231453i	$0.925652\pi$
$152$	−10.9678	−	6.61947i	−0.889603	−	0.536910i
$153$	0.901092	+	5.68927i	0.0728489	+	0.459950i
$154$	10.3831	+	4.92381i	0.836697	+	0.396772i
$155$	0.334036	−	4.33861i	0.0268304	−	0.348486i
$156$	−4.67121	−	3.00367i	−0.373996	−	0.240486i
$157$	−6.65160	+	6.65160i	−0.530856	+	0.530856i	−0.920827	−	0.389971i	$-0.872485\pi$
$157$	−6.65160	+	6.65160i	−0.530856	+	0.530856i	0.389971	+	0.920827i	$0.372485\pi$
$158$	0.608250	−	0.0172994i	0.0483898	−	0.00137627i
$159$	−3.91353	−	12.0446i	−0.310363	−	0.955200i
$160$	−10.6969	−	6.75105i	−0.845663	−	0.533717i
$161$	5.55673	−	17.1019i	0.437932	−	1.34782i
$162$	−0.398601	+	1.35688i	−0.0313171	+	0.106606i
$163$	−7.61012	−	3.87755i	−0.596070	−	0.303713i	0.129805	−	0.991540i	$-0.458565\pi$
$163$	−7.61012	−	3.87755i	−0.596070	−	0.303713i	−0.725875	+	0.687827i	$0.758565\pi$
$164$	−9.47586	+	0.539449i	−0.739941	+	0.0421239i
$165$	−4.45770	−	5.20136i	−0.347031	−	0.404925i
$166$	7.89482	+	14.4626i	0.612757	+	1.12252i
$167$	16.7839	+	2.65830i	1.29877	+	0.205706i	0.767256	−	0.641342i	$-0.221622\pi$
$167$	16.7839	+	2.65830i	1.29877	+	0.205706i	0.531518	+	0.847047i	$0.321622\pi$
$168$	1.70198	−	7.30656i	0.131311	−	0.563713i
$169$	3.10906	+	4.27925i	0.239158	+	0.329173i
$170$	−3.71670	+	17.8321i	−0.285058	+	1.36766i
$171$	−2.66220	+	3.66420i	−0.203583	+	0.280208i
$172$	1.37417	+	2.35555i	0.104780	+	0.179609i
$173$	14.2524	−	7.26195i	1.08359	−	0.552116i	0.181378	−	0.983413i	$-0.441944\pi$
$173$	14.2524	−	7.26195i	1.08359	−	0.552116i	0.902210	+	0.431298i	$0.141944\pi$
$174$	1.99214	+	10.6150i	0.151023	+	0.804724i
$175$	−7.75873	+	10.7557i	−0.586505	+	0.813054i
$176$	8.28129	+	9.03221i	0.624226	+	0.680829i
$177$	−2.77816	−	5.45245i	−0.208820	−	0.409831i
$178$	−3.32396	+	1.18551i	−0.249141	+	0.0888580i
$179$	2.73419	+	1.98651i	0.204363	+	0.148479i	0.685260	−	0.728299i	$-0.259689\pi$
$179$	2.73419	+	1.98651i	0.204363	+	0.148479i	−0.480896	+	0.876777i	$0.659689\pi$
$180$	−2.70039	+	3.56482i	−0.201275	+	0.265706i
$181$	−6.86505	+	4.98775i	−0.510275	+	0.370736i	−0.812928	−	0.582364i	$-0.802128\pi$
$181$	−6.86505	+	4.98775i	−0.510275	+	0.370736i	0.302653	+	0.953101i	$0.402128\pi$
$182$	5.88031	−	8.59734i	0.435877	−	0.637278i
$183$	−1.27252	+	8.03436i	−0.0940672	+	0.593917i
$184$	12.3544	−	14.6648i	0.910781	−	1.08110i
$185$	4.70161	+	11.2963i	0.345669	+	0.830523i
$186$	2.72936	+	0.353071i	0.200126	+	0.0258884i
$187$	8.01127	−	15.7230i	0.585842	−	1.14978i
$188$	23.8473	+	2.39782i	1.73924	+	0.174879i
$189$	−2.52260	−	0.819642i	−0.183492	−	0.0596202i
$190$	−11.9810	+	7.84807i	−0.869193	+	0.569359i
$191$	−23.0771	+	7.49819i	−1.66980	+	0.542550i	−0.982890	−	0.184194i	$-0.941033\pi$
$191$	−23.0771	+	7.49819i	−1.66980	+	0.542550i	−0.686908	+	0.726744i	$0.741033\pi$
$192$	4.61434	−	6.53513i	0.333011	−	0.471632i
$193$	−17.1394	−	17.1394i	−1.23372	−	1.23372i	−0.962525	−	0.271192i	$-0.912582\pi$
$193$	−17.1394	−	17.1394i	−1.23372	−	1.23372i	−0.271192	−	0.962525i	$-0.587418\pi$
$194$	12.0052	−	12.7081i	0.861924	−	0.912388i
$195$	−5.28859	+	3.25324i	−0.378724	+	0.232969i
$196$	0.0683021	+	0.0179719i	0.00487872	+	0.00128371i
$197$	12.7478	−	2.01906i	0.908247	−	0.143852i	0.315205	−	0.949024i	$-0.397927\pi$
$197$	12.7478	−	2.01906i	0.908247	−	0.143852i	0.593042	+	0.805172i	$0.297927\pi$
$198$	3.43121	−	2.64517i	0.243845	−	0.187984i
$199$	15.5227			1.10038			0.550189	−	0.835040i	$-0.314556\pi$
$199$	15.5227			1.10038			0.550189	+	0.835040i	$0.314556\pi$
$200$	−11.9824	+	7.51139i	−0.847287	+	0.531135i
$201$	1.33516			0.0941752
$202$	−5.92783	+	4.56985i	−0.417081	+	0.321533i
$203$	−20.0071	+	3.16882i	−1.40422	+	0.222407i
$204$	−11.1412	−	2.93150i	−0.780037	−	0.205246i
$205$	−4.04417	+	9.81063i	−0.282457	+	0.685204i
$206$	−5.10280	+	5.40156i	−0.355529	+	0.376344i
$207$	−4.79380	−	4.79380i	−0.333192	−	0.333192i
$208$	9.26033	−	6.13312i	0.642088	−	0.425255i
$209$	13.1961	−	4.28767i	0.912794	−	0.296585i
$210$	−6.53927	−	5.25272i	−0.451252	−	0.362472i
$211$	−1.95961	−	0.636716i	−0.134905	−	0.0438334i	0.240786	−	0.970578i	$-0.422595\pi$
$211$	−1.95961	−	0.636716i	−0.134905	−	0.0438334i	−0.375691	+	0.926745i	$0.622595\pi$
$212$	25.2018	+	2.53402i	1.73087	+	0.174037i
$213$	−5.76746	+	11.3193i	−0.395180	+	0.775585i
$214$	7.69010	+	0.994794i	0.525684	+	0.0680027i
$215$	3.03916	−	0.244386i	0.207269	−	0.0166670i
$216$	−2.16312	−	1.82233i	−0.147182	−	0.123994i
$217$	−0.807464	+	5.09813i	−0.0548143	+	0.346084i
$218$	−11.1471	+	16.2977i	−0.754979	+	1.10382i
$219$	2.76913	−	2.01189i	0.187121	−	0.135951i
$220$	13.1118	−	3.97259i	0.883997	−	0.267832i
$221$	−12.9401	−	9.40152i	−0.870444	−	0.632415i
$222$	−7.28883	+	2.59961i	−0.489194	+	0.174474i
$223$	9.43662	+	18.5204i	0.631923	+	1.24022i	0.955772	+	0.294110i	$0.0950231\pi$
$223$	9.43662	+	18.5204i	0.631923	+	1.24022i	−0.323849	+	0.946109i	$0.604977\pi$
$224$	12.0059	+	8.99934i	0.802179	+	0.601294i
$225$	2.28509	+	4.44729i	0.152339	+	0.296486i
$226$	−0.511335	−	2.72463i	−0.0340135	−	0.181240i
$227$	4.30929	−	2.19569i	0.286018	−	0.145733i	−0.305096	−	0.952322i	$-0.598688\pi$
$227$	4.30929	−	2.19569i	0.286018	−	0.145733i	0.591114	+	0.806588i	$0.298688\pi$
$228$	−4.56451	−	7.82431i	−0.302292	−	0.518177i
$229$	5.84117	−	8.03968i	0.385996	−	0.531277i	−0.571165	−	0.820835i	$-0.693508\pi$
$229$	5.84117	−	8.03968i	0.385996	−	0.531277i	0.957160	+	0.289558i	$0.0935083\pi$
$230$	−8.79721	−	19.5505i	−0.580071	−	1.28912i
$231$	4.77616	+	6.57381i	0.314248	+	0.432525i
$232$	−21.0375	−	4.90046i	−1.38118	−	0.321731i
$233$	−8.00740	−	1.26825i	−0.524582	−	0.0830856i	−0.111473	−	0.993767i	$-0.535557\pi$
$233$	−8.00740	−	1.26825i	−0.524582	−	0.0830856i	−0.413109	+	0.910682i	$0.635557\pi$
$234$	−1.88156	−	3.44686i	−0.123002	−	0.225328i
$235$	13.9623	−	22.8715i	0.910798	−	1.49197i
$236$	12.2191	−	0.695617i	0.795394	−	0.0452808i
$237$	0.383375	+	0.195339i	0.0249029	+	0.0126886i
$238$	6.09000	−	20.7309i	0.394756	−	1.34379i
$239$	−7.34407	+	22.6027i	−0.475049	+	1.46205i	0.370844	+	0.928695i	$0.379069\pi$
$239$	−7.34407	+	22.6027i	−0.475049	+	1.46205i	−0.845892	+	0.533354i	$0.820931\pi$
$240$	−4.35182	−	7.81420i	−0.280908	−	0.504404i
$241$	7.36630	+	22.6712i	0.474505	+	1.46038i	0.846624	+	0.532192i	$0.178632\pi$
$241$	7.36630	+	22.6712i	0.474505	+	1.46038i	−0.372118	+	0.928185i	$0.621368\pi$
$242$	2.28297	−	0.0649309i	0.146755	−	0.00417391i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−13.6841	−	8.79915i	−0.876038	−	0.563308i
$245$	0.0511804	−	0.0601313i	0.00326980	−	0.00384165i
$246$	−6.06401	−	2.87563i	−0.386627	−	0.183343i
$247$	−1.96742	−	12.4218i	−0.125184	−	0.790379i
$248$	−2.84414	+	4.71244i	−0.180603	+	0.299240i
$249$			11.6511i			0.738358i
$250$	1.76833	+	15.7122i	0.111839	+	0.993726i
$251$			1.75011i			0.110466i	0.998473	+	0.0552330i	$0.0175902\pi$
$251$			1.75011i			0.110466i	−0.998473	+	0.0552330i	$0.982410\pi$
$252$	3.53182	−	3.95822i	0.222484	−	0.249344i
$253$	3.24897	+	20.5132i	0.204261	+	1.28965i
$254$	7.45575	−	15.7224i	0.467815	−	0.986511i
$255$	−8.34834	+	9.80836i	−0.522793	+	0.614224i
$256$	8.24852	+	13.7099i	0.515532	+	0.856870i
$257$	0.796610	−	0.796610i	0.0496912	−	0.0496912i	−0.681825	−	0.731516i	$-0.738813\pi$
$257$	0.796610	−	0.796610i	0.0496912	−	0.0496912i	0.731516	+	0.681825i	$0.238813\pi$
$258$	0.0548223	+	1.92756i	0.00341309	+	0.120004i
$259$	−4.48506	−	13.8036i	−0.278688	−	0.857713i
$260$	−1.69729	−	12.3016i	−0.105262	−	0.762915i
$261$	−2.35996	+	7.26322i	−0.146078	+	0.449582i
$262$	−0.919899	−	0.270233i	−0.0568315	−	0.0166950i
$263$	11.0232	+	5.61660i	0.679719	+	0.346334i	0.759527	−	0.650476i	$-0.225431\pi$
$263$	11.0232	+	5.61660i	0.679719	+	0.346334i	−0.0798075	+	0.996810i	$0.525431\pi$
$264$	2.07970	+	8.41161i	0.127997	+	0.517699i
$265$	14.7554	−	24.1707i	0.906414	−	1.48479i
$266$	14.9123	−	8.14027i	0.914330	−	0.499112i
$267$	−2.46469	−	0.390368i	−0.150836	−	0.0238901i
$268$	−1.07511	+	2.44434i	−0.0656730	+	0.149312i
$269$	15.0035	+	20.6506i	0.914780	+	1.25909i	0.965508	+	0.260375i	$0.0838461\pi$
$269$	15.0035	+	20.6506i	0.914780	+	1.25909i	−0.0507271	+	0.998713i	$0.516154\pi$
$270$	−2.88378	+	1.29763i	−0.175501	+	0.0789710i
$271$	10.3796	−	14.2864i	0.630519	−	0.867835i	−0.367547	−	0.930005i	$-0.619802\pi$
$271$	10.3796	−	14.2864i	0.630519	−	0.867835i	0.998066	+	0.0621703i	$0.0198022\pi$
$272$	14.3380	−	18.0360i	0.869369	−	1.09359i
$273$	6.56244	−	3.34373i	0.397177	−	0.202372i
$274$	27.7598	−	5.20972i	1.67703	−	0.314730i
$275$	2.34473	−	15.1370i	0.141393	−	0.912794i
$276$	12.6363	−	4.91609i	0.760617	−	0.295914i
$277$	5.69164	+	11.1705i	0.341977	+	0.671168i	0.996383	−	0.0849753i	$-0.0270811\pi$
$277$	5.69164	+	11.1705i	0.341977	+	0.671168i	−0.654406	+	0.756144i	$0.727081\pi$
$278$	−0.0257671	−	0.0722463i	−0.00154541	−	0.00433304i
$279$	1.57437	+	1.14385i	0.0942551	+	0.0684803i
$280$	14.8820	−	7.74205i	0.889368	−	0.462676i
$281$	−11.8374	+	8.60034i	−0.706157	+	0.513053i	−0.881932	−	0.471377i	$-0.843757\pi$
$281$	−11.8374	+	8.60034i	−0.706157	+	0.513053i	0.175775	+	0.984430i	$0.443757\pi$
$282$	13.9886	+	9.56772i	0.833006	+	0.569749i
$283$	−2.48745	+	15.7051i	−0.147864	+	0.933574i	0.796492	+	0.604649i	$0.206686\pi$
$283$	−2.48745	+	15.7051i	−0.147864	+	0.933574i	−0.944356	+	0.328925i	$0.893314\pi$
$284$	−16.0785	−	19.6733i	−0.954085	−	1.16740i
$285$	−10.0950	+	0.811765i	−0.597977	+	0.0480848i
$286$	−1.54338	+	11.9309i	−0.0912621	+	0.705487i
$287$	5.71452	−	11.2154i	0.337318	−	0.662023i
$288$	5.07803	−	2.49272i	0.299226	−	0.146885i
$289$	−15.3879	−	4.99982i	−0.905168	−	0.294107i
$290$	−15.1240	+	18.8283i	−0.888109	+	1.10563i
$291$	11.7566	−	3.81996i	0.689186	−	0.223930i
$292$	1.45346	+	6.68960i	0.0850575	+	0.391479i
$293$	6.91192	+	6.91192i	0.403799	+	0.403799i	0.879569	−	0.475771i	$-0.157831\pi$
$293$	6.91192	+	6.91192i	0.403799	+	0.403799i	−0.475771	+	0.879569i	$0.657831\pi$
$294$	0.0363031	+	0.0342952i	0.00211724	+	0.00200014i
$295$	5.21493	−	12.6508i	0.303625	−	0.736555i
$296$	1.10997	−	15.4372i	0.0645156	−	0.897271i
$297$	3.02578	−	0.479237i	0.175574	−	0.0278082i
$298$	0.975667	+	1.26560i	0.0565189	+	0.0733141i
$299$	18.8251			1.08869
$300$	−9.98184	+	0.602310i	−0.576302	+	0.0347744i
$301$	−3.61667			−0.208462
$302$	−4.91153	−	6.37105i	−0.282627	−	0.366613i
$303$	−5.22741	+	0.827941i	−0.300307	+	0.0475640i
$304$	17.9997	−	2.05607i	1.03236	−	0.117924i
$305$	−15.4928	+	9.53024i	−0.887113	+	0.545700i
$306$	−5.92162	−	5.59410i	−0.338516	−	0.319793i
$307$	−16.6157	−	16.6157i	−0.948310	−	0.948310i	0.0504178	−	0.998728i	$-0.483945\pi$
$307$	−16.6157	−	16.6157i	−0.948310	−	0.948310i	−0.998728	+	0.0504178i	$0.983945\pi$
$308$	−15.8808	+	3.45047i	−0.904895	+	0.196609i
$309$	−4.99714	+	1.62367i	−0.284277	+	0.0923673i
$310$	3.37202	+	5.14779i	0.191518	+	0.292375i
$311$	11.5934	+	3.76691i	0.657399	+	0.213602i	0.618674	−	0.785648i	$-0.287670\pi$
$311$	11.5934	+	3.76691i	0.657399	+	0.213602i	0.0387251	+	0.999250i	$0.487670\pi$
$312$	7.82539	−	0.669138i	0.443025	−	0.0378825i
$313$	−10.5644	+	20.7338i	−0.597135	+	1.17194i	0.372648	+	0.927973i	$0.378450\pi$
$313$	−10.5644	+	20.7338i	−0.597135	+	1.17194i	−0.969783	+	0.243970i	$0.921550\pi$
$314$	1.70669	−	13.1933i	0.0963139	−	0.744540i
$315$	−2.27900	−	5.47565i	−0.128407	−	0.308518i
$316$	−0.666320	+	0.544566i	−0.0374834	+	0.0306342i
$317$	−1.97013	+	12.4389i	−0.110653	+	0.698638i	0.868526	+	0.495643i	$0.165068\pi$
$317$	−1.97013	+	12.4389i	−0.110653	+	0.698638i	−0.979180	+	0.202995i	$0.934932\pi$
$318$	14.7831	+	10.1112i	0.828997	+	0.567007i
$319$	18.9277	−	13.7518i	1.05975	−	0.769953i
$320$	17.8100	−	1.67482i	0.995608	−	0.0936251i
$321$	4.43586	+	3.22284i	0.247586	+	0.179882i
$322$	8.54282	+	23.9525i	0.476073	+	1.33482i
$323$	−11.8442	−	23.2455i	−0.659027	−	1.29341i
$324$	−0.725145	−	1.86391i	−0.0402858	−	0.103551i
$325$	−13.2189	−	4.24545i	−0.733254	−	0.235495i
$326$	11.8716	−	2.22796i	0.657507	−	0.123395i
$327$	−12.4402	+	6.33862i	−0.687947	+	0.350526i
$328$	10.1474	−	8.78608i	0.560299	−	0.485130i
$329$	−18.6833	+	25.7153i	−1.03004	+	1.41773i
$330$	9.48383	+	1.97669i	0.522068	+	0.108813i
$331$	6.91545	+	9.51830i	0.380108	+	0.523173i	0.955613	−	0.294625i	$-0.0951946\pi$
$331$	6.91545	+	9.51830i	0.380108	+	0.523173i	−0.575505	+	0.817798i	$0.695195\pi$
$332$	−21.3301	−	9.38180i	−1.17064	−	0.514893i
$333$	−5.40460	−	0.856005i	−0.296171	−	0.0469088i
$334$	−21.0937	+	11.5146i	−1.15419	+	0.630049i
$335$	1.94280	+	2.26691i	0.106146	+	0.123854i
$336$	4.40254	+	9.65312i	0.240178	+	0.526621i
$337$	14.1885	+	7.22941i	0.772898	+	0.393811i	0.795516	−	0.605933i	$-0.207200\pi$
$337$	14.1885	+	7.22941i	0.772898	+	0.393811i	−0.0226179	+	0.999744i	$0.507200\pi$
$338$	−7.17713	−	2.10838i	−0.390384	−	0.114681i
$339$	0.605747	−	1.86430i	0.0328997	−	0.101255i
$340$	−11.2342	−	23.1816i	−0.609262	−	1.25720i
$341$	−1.84225	−	5.66988i	−0.0997637	−	0.307041i
$342$	−0.182100	−	6.40266i	−0.00984686	−	0.346216i
$343$	13.0626	−	13.0626i	0.705312	−	0.705312i
$344$	−3.57300	−	1.45176i	−0.192643	−	0.0782736i
$345$	1.16369	−	15.1146i	0.0626512	−	0.813743i
$346$	−9.69276	+	20.4397i	−0.521086	+	1.09885i
$347$	3.91892	+	24.7431i	0.210379	+	1.32828i	0.836248	+	0.548351i	$0.184744\pi$
$347$	3.91892	+	24.7431i	0.210379	+	1.32828i	−0.625870	+	0.779928i	$0.715256\pi$
$348$	−11.3967	−	10.1690i	−0.610930	−	0.545117i
$349$		−	3.77373i		−	0.202003i	−0.994886	−	0.101002i	$-0.967795\pi$
$349$		−	3.77373i		−	0.202003i	0.994886	−	0.101002i	$-0.0322047\pi$
$350$	−0.596956	−	18.7459i	−0.0319086	−	1.00201i
$351$		−	2.77679i		−	0.148214i
$352$	−17.0741	−	2.96589i	−0.910052	−	0.158082i
$353$	−2.35188	−	14.8492i	−0.125178	−	0.790341i	−0.967779	−	0.251803i	$-0.918977\pi$
$353$	−2.35188	−	14.8492i	−0.125178	−	0.790341i	0.842601	−	0.538539i	$-0.181023\pi$
$354$	7.81951	+	3.70811i	0.415602	+	0.197084i
$355$	−27.6107	+	6.67840i	−1.46542	+	0.354453i
$356$	2.69930	−	4.19786i	0.143063	−	0.222486i
$357$	10.8035	−	10.8035i	0.571780	−	0.571780i
$358$	−4.77761	+	0.135882i	−0.252505	+	0.00718157i
$359$	−8.66676	−	26.6735i	−0.457414	−	1.40778i	−0.868278	−	0.496079i	$-0.834773\pi$
$359$	−8.66676	−	26.6735i	−0.457414	−	1.40778i	0.410864	−	0.911697i	$-0.365227\pi$
$360$	−0.0535135	−	6.32433i	−0.00282041	−	0.333321i
$361$	0.467740	−	1.43956i	0.0246179	−	0.0757661i
$362$	3.38240	−	11.5140i	0.177775	−	0.605163i
$363$	1.43894	+	0.733176i	0.0755247	+	0.0384818i
$364$	0.837228	+	14.7066i	0.0438827	+	0.770835i
$365$	7.44525	+	1.77407i	0.389702	+	0.0928588i
$366$	−5.51197	−	10.0975i	−0.288115	−	0.527802i
$367$	−25.9476	−	4.10970i	−1.35445	−	0.214524i	−0.563356	−	0.826214i	$-0.690490\pi$
$367$	−25.9476	−	4.10970i	−1.35445	−	0.214524i	−0.791098	+	0.611690i	$0.790490\pi$
$368$	−1.17505	+	27.0924i	−0.0612538	+	1.41229i
$369$	−2.78940	−	3.83927i	−0.145210	−	0.199865i
$370$	−15.0197	−	8.59263i	−0.780837	−	0.446710i
$371$	−19.7445	+	27.1760i	−1.02509	+	1.41091i
$372$	−3.36181	+	1.96120i	−0.174302	+	0.101684i
$373$	22.7635	−	11.5986i	1.17865	−	0.600552i	0.248823	−	0.968549i	$-0.419956\pi$
$373$	22.7635	−	11.5986i	1.17865	−	0.600552i	0.929827	+	0.367997i	$0.119956\pi$
$374$	4.60310	+	24.5275i	0.238021	+	1.26829i
$375$	−4.22579	+	10.3510i	−0.218219	+	0.534522i
$376$	−28.7800	+	17.9052i	−1.48421	+	0.923389i
$377$	−9.62747	−	18.8950i	−0.495840	−	0.973141i
$378$	3.53310	−	1.26010i	0.181723	−	0.0648127i
$379$	−18.5839	−	13.5020i	−0.954593	−	0.693553i	−0.00270450	−	0.999996i	$-0.500861\pi$
$379$	−18.5839	−	13.5020i	−0.954593	−	0.693553i	−0.951889	+	0.306444i	$0.900861\pi$
$380$	6.64267	−	19.1350i	0.340762	−	0.981604i
$381$	9.95423	−	7.23217i	0.509971	−	0.370515i
$382$	19.3727	−	28.3240i	0.991193	−	1.44918i
$383$	−3.48028	+	21.9736i	−0.177834	+	1.12280i	0.723707	+	0.690107i	$0.242437\pi$
$383$	−3.48028	+	21.9736i	−0.177834	+	1.12280i	−0.901541	+	0.432693i	$0.857563\pi$
$384$	0.474541	+	11.3038i	0.0242163	+	0.576842i
$385$	−4.21156	+	17.6747i	−0.214641	+	0.900788i
$386$	33.9954	+	4.39766i	1.73032	+	0.223835i
$387$	−0.619034	+	1.21492i	−0.0314673	+	0.0617580i
$388$	−2.47343	+	24.5993i	−0.125569	+	1.24884i
$389$	−25.2281	−	8.19711i	−1.27912	−	0.415610i	−0.410847	−	0.911704i	$-0.634767\pi$
$389$	−25.2281	−	8.19711i	−1.27912	−	0.415610i	−0.868269	+	0.496094i	$0.834767\pi$
$390$	3.11438	−	8.21013i	0.157703	−	0.415736i
$391$	37.1397	−	12.0674i	1.87823	−	0.610275i
$392$	−0.0920180	+	0.0388461i	−0.00464761	+	0.00196202i
$393$	−0.479385	−	0.479385i	−0.0241818	−	0.0241818i
$394$	−12.5346	+	13.2685i	−0.631484	+	0.668456i
$395$	0.226192	+	0.935150i	0.0113809	+	0.0470525i
$396$	−1.55909	+	5.92532i	−0.0783474	+	0.297758i
$397$	−31.3701	+	4.96854i	−1.57442	+	0.249364i	−0.881689	−	0.471831i	$-0.843593\pi$
$397$	−31.3701	+	4.96854i	−1.57442	+	0.249364i	−0.692732	+	0.721195i	$0.743593\pi$
$398$	−17.3859	+	13.4030i	−0.871477	+	0.671833i
$399$	12.0133			0.601418
$400$	6.93500	−	18.7592i	0.346750	−	0.937958i
$401$	1.93725			0.0967417			0.0483708	−	0.998829i	$-0.484597\pi$
$401$	1.93725			0.0967417			0.0483708	+	0.998829i	$0.484597\pi$
$402$	−1.49542	+	1.15284i	−0.0745848	+	0.0574985i
$403$	−5.33718	+	0.845327i	−0.265864	+	0.0421087i
$404$	2.69352	−	10.2367i	0.134008	−	0.509296i
$405$	−2.22947	−	0.171650i	−0.110783	−	0.00852935i
$406$	19.6724	−	20.8242i	0.976326	−	1.03349i
$407$	11.8535	+	11.8535i	0.587557	+	0.587557i
$408$	15.0096	−	6.33641i	0.743086	−	0.313699i
$409$	11.2145	−	3.64381i	0.554520	−	0.180175i	−0.0183337	−	0.999832i	$-0.505836\pi$
$409$	11.2145	−	3.64381i	0.554520	−	0.180175i	0.572854	+	0.819657i	$0.305836\pi$
$410$	−3.94136	−	14.4801i	−0.194650	−	0.715121i
$411$	18.9943	+	6.17163i	0.936922	+	0.304424i
$412$	1.05133	−	10.4559i	0.0517953	−	0.515124i
$413$	−7.36885	+	14.4622i	−0.362597	+	0.711637i
$414$	9.50838	+	1.23001i	0.467312	+	0.0604516i
$415$	−19.7818	+	16.9535i	−0.971050	+	0.832214i
$416$	−5.07622	+	14.8651i	−0.248882	+	0.728819i
$417$	0.00848465	−	0.0535700i	0.000415495	−	0.00262333i
$418$	−11.0778	+	16.1964i	−0.541835	+	0.792193i
$419$	−24.8894	+	18.0832i	−1.21593	+	0.883421i	−0.995755	−	0.0920401i	$-0.970661\pi$
$419$	−24.8894	+	18.0832i	−1.21593	+	0.883421i	−0.220170	+	0.975462i	$0.570661\pi$
$420$	11.8596	+	0.236896i	0.578689	+	0.0115593i
$421$	13.5139	+	9.81844i	0.658628	+	0.478522i	0.866199	−	0.499698i	$-0.166556\pi$
$421$	13.5139	+	9.81844i	0.658628	+	0.478522i	−0.207571	+	0.978220i	$0.566556\pi$
$422$	2.74459	−	0.978877i	0.133604	−	0.0476510i
$423$	5.44051	+	10.6776i	0.264527	+	0.519163i
$424$	−30.4148	+	18.9222i	−1.47707	+	0.918945i
$425$	−28.8008	+	0.0979274i	−1.39704	+	0.00475017i
$426$	−3.31386	−	17.6578i	−0.160557	−	0.855524i
$427$	19.2244	−	9.79535i	0.930336	−	0.474030i
$428$	−9.47207	+	5.52578i	−0.457850	+	0.267099i
$429$	−5.00011	+	6.88206i	−0.241408	+	0.332269i
$430$	−3.19293	+	2.89786i	−0.153977	+	0.139747i
$431$	−10.2982	−	14.1742i	−0.496046	−	0.682749i	0.485443	−	0.874269i	$-0.338658\pi$
$431$	−10.2982	−	14.1742i	−0.496046	−	0.682749i	−0.981489	+	0.191519i	$0.938658\pi$
$432$	3.99624	+	0.173325i	0.192269	+	0.00833912i
$433$	21.0372	+	3.33196i	1.01098	+	0.160124i	0.639885	−	0.768471i	$-0.278982\pi$
$433$	21.0372	+	3.33196i	1.01098	+	0.160124i	0.371096	+	0.928594i	$0.378982\pi$
$434$	−3.49757	−	6.40725i	−0.167889	−	0.307558i
$435$	−15.7658	+	6.56184i	−0.755913	+	0.314616i
$436$	−1.58711	−	27.8789i	−0.0760087	−	1.33516i
$437$	27.3588	+	13.9400i	1.30875	+	0.666842i
$438$	−1.36435	+	4.64437i	−0.0651910	+	0.221917i
$439$	−3.66634	+	11.2838i	−0.174985	+	0.538547i	−0.999633	−	0.0270987i	$-0.991373\pi$
$439$	−3.66634	+	11.2838i	−0.174985	+	0.538547i	0.824648	+	0.565646i	$0.191373\pi$
$440$	−11.2555	+	15.7707i	−0.536583	+	0.751840i
$441$	0.0109125	+	0.0335851i	0.000519641	+	0.00159929i
$442$	22.6109	−	0.643086i	1.07549	−	0.0305885i
$443$	−4.55801	+	4.55801i	−0.216558	+	0.216558i	−0.807046	−	0.590488i	$-0.798935\pi$
$443$	−4.55801	+	4.55801i	−0.216558	+	0.216558i	0.590488	+	0.807046i	$0.298935\pi$
$444$	5.91907	−	9.20514i	0.280907	−	0.436857i
$445$	−2.92358	−	4.75269i	−0.138591	−	0.225299i
$446$	−26.5606	−	12.5954i	−1.25768	−	0.596408i
$447$	0.176766	+	1.11606i	0.00836076	+	0.0527877i
$448$	−21.2174	+	0.286929i	−1.00243	+	0.0135561i
$449$		−	15.7982i		−	0.745562i	−0.927919	−	0.372781i	$-0.878404\pi$
$449$		−	15.7982i		−	0.745562i	0.927919	−	0.372781i	$-0.121596\pi$
$450$	−6.39935	−	3.00804i	−0.301668	−	0.141800i
$451$			14.5382i			0.684575i
$452$	2.92528	+	2.61015i	0.137593	+	0.122771i
$453$	−0.889845	−	5.61826i	−0.0418086	−	0.263969i
$454$	−2.93067	+	6.18008i	−0.137543	+	0.290045i
$455$	15.2261	+	6.27657i	0.713813	+	0.294250i
$456$	11.8682	+	4.82224i	0.555781	+	0.225822i
$457$	29.8131	−	29.8131i	1.39460	−	1.39460i	0.579929	−	0.814667i	$-0.303080\pi$
$457$	29.8131	−	29.8131i	1.39460	−	1.39460i	0.814667	−	0.579929i	$-0.196920\pi$
$458$	0.399550	+	14.0482i	0.0186697	+	0.656429i
$459$	−1.78000	−	5.47826i	−0.0830831	−	0.255703i
$460$	26.7339	+	14.3011i	1.24647	+	0.666795i
$461$	−7.67255	+	23.6137i	−0.357346	+	1.09980i	0.597290	+	0.802025i	$0.296244\pi$
$461$	−7.67255	+	23.6137i	−0.357346	+	1.09980i	−0.954636	+	0.297774i	$0.903756\pi$
$462$	−11.0256	−	3.23891i	−0.512955	−	0.150688i
$463$	−7.34620	−	3.74307i	−0.341407	−	0.173955i	0.274877	−	0.961479i	$-0.411363\pi$
$463$	−7.34620	−	3.74307i	−0.341407	−	0.173955i	−0.616284	+	0.787524i	$0.711363\pi$
$464$	27.7938	−	12.6761i	1.29030	−	0.588471i
$465$	0.348786	+	4.33745i	0.0161745	+	0.201145i
$466$	10.0636	−	5.49348i	0.466186	−	0.254480i
$467$	11.4787	+	1.81805i	0.531172	+	0.0841294i	0.416259	−	0.909246i	$-0.363341\pi$
$467$	11.4787	+	1.81805i	0.531172	+	0.0841294i	0.114913	+	0.993376i	$0.463341\pi$
$468$	5.08358	+	2.23595i	0.234988	+	0.103357i
$469$	−2.08159	−	2.86506i	−0.0961189	−	0.132296i
$470$	4.11019	+	37.6724i	0.189589	+	1.73770i
$471$	5.52917	−	7.61025i	0.254771	−	0.350662i
$472$	−13.0851	+	11.3296i	−0.602290	+	0.521488i
$473$	3.72192	−	1.89641i	0.171134	−	0.0871971i
$474$	−0.598055	+	0.112238i	−0.0274696	+	0.00515525i
$475$	−16.0675	−	15.9586i	−0.737227	−	0.732231i
$476$	11.0791	+	28.4776i	0.507808	+	1.30527i
$477$	5.74954	+	11.2841i	0.263254	+	0.516664i
$478$	−11.2907	−	31.6569i	−0.516422	−	1.44795i
$479$	−2.26075	−	1.64253i	−0.103296	−	0.0750491i	0.534938	−	0.844891i	$-0.320335\pi$
$479$	−2.26075	−	1.64253i	−0.103296	−	0.0750491i	−0.638234	+	0.769842i	$0.720335\pi$
$480$	11.6213	+	4.99457i	0.530437	+	0.227970i
$481$	12.2926	−	8.93111i	0.560495	−	0.407224i
$482$	−27.8258	−	19.0319i	−1.26743	−	0.866880i
$483$	−2.81300	+	17.7606i	−0.127996	+	0.808134i
$484$	−2.50093	+	2.04395i	−0.113679	+	0.0929067i
$485$	23.5928	+	14.4025i	1.07129	+	0.653986i
$486$	0.181431	−	1.40253i	0.00822990	−	0.0636199i
$487$	−14.7690	+	28.9857i	−0.669245	+	1.31347i	0.267534	+	0.963548i	$0.413791\pi$
$487$	−14.7690	+	28.9857i	−0.669245	+	1.31347i	−0.936780	+	0.349920i	$0.886209\pi$
$488$	22.9242	−	1.96022i	1.03773	−	0.0887348i
$489$	8.12301	+	2.63932i	0.367335	+	0.119354i
$490$	−0.00540344	+	0.111540i	−0.000244103	+	0.00503887i
$491$	−15.9391	+	5.17893i	−0.719321	+	0.233722i	−0.645729	−	0.763567i	$-0.723446\pi$
$491$	−15.9391	+	5.17893i	−0.719321	+	0.233722i	−0.0735925	+	0.997288i	$0.523446\pi$
$492$	9.27481	−	2.01516i	0.418141	−	0.0908504i
$493$	−31.1060	−	31.1060i	−1.40094	−	1.40094i
$494$	12.9291	+	12.2140i	0.581707	+	0.549533i
$495$	5.21649	+	4.43999i	0.234464	+	0.199562i
$496$	−0.883417	−	7.73382i	−0.0396666	−	0.347259i
$497$	33.2813	−	5.27123i	1.49287	−	0.236447i
$498$	−10.0601	−	13.0495i	−0.450803	−	0.584764i
$499$	41.5528			1.86016			0.930079	−	0.367359i	$-0.119738\pi$
$499$	41.5528			1.86016			0.930079	+	0.367359i	$0.119738\pi$
$500$	−15.5472	−	16.0712i	−0.695292	−	0.718727i
$501$	−16.9931			−0.759194
$502$	−1.51112	−	1.96017i	−0.0674448	−	0.0874868i
$503$	8.35723	−	1.32366i	0.372630	−	0.0590189i	0.0326893	−	0.999466i	$-0.489593\pi$
$503$	8.35723	−	1.32366i	0.372630	−	0.0590189i	0.339941	+	0.940447i	$0.389593\pi$
$504$	−0.538033	+	7.48285i	−0.0239659	+	0.333313i
$505$	−9.01212	−	7.67062i	−0.401034	−	0.341338i
$506$	−21.3510	−	20.1700i	−0.949166	−	0.896668i
$507$	−3.74020	−	3.74020i	−0.166108	−	0.166108i
$508$	5.22478	+	24.0472i	0.231812	+	1.06692i
$509$	21.4866	−	6.98141i	0.952376	−	0.309446i	0.208695	−	0.977981i	$-0.433078\pi$
$509$	21.4866	−	6.98141i	0.952376	−	0.309446i	0.743681	+	0.668535i	$0.233078\pi$
$510$	0.881387	−	18.1940i	0.0390285	−	0.805643i
$511$	−8.63444	−	2.80550i	−0.381965	−	0.124108i
$512$	−21.0763	−	8.23335i	−0.931451	−	0.363866i
$513$	2.05621	−	4.03555i	0.0907840	−	0.178174i
$514$	−0.204396	+	1.58005i	−0.00901554	+	0.0696932i
$515$	−10.0281	−	6.12178i	−0.441890	−	0.269758i
$516$	−1.72574	−	2.11158i	−0.0759715	−	0.0929572i
$517$	5.74306	−	36.2603i	0.252580	−	1.59472i
$518$	16.9420	+	11.5878i	0.744390	+	0.509139i
$519$	−12.9409	+	9.40210i	−0.568042	+	0.412707i
$520$	12.5228	+	12.3127i	0.549161	+	0.539946i
$521$	−9.58644	−	6.96496i	−0.419990	−	0.305140i	0.357644	−	0.933858i	$-0.383580\pi$
$521$	−9.58644	−	6.96496i	−0.419990	−	0.305140i	−0.777634	+	0.628718i	$0.783580\pi$
$522$	−3.62817	−	10.1727i	−0.158801	−	0.445247i
$523$	−2.25878	−	4.43311i	−0.0987696	−	0.193846i	0.836334	−	0.548220i	$-0.184694\pi$
$523$	−2.25878	−	4.43311i	−0.0987696	−	0.193846i	−0.935104	+	0.354373i	$0.884694\pi$
$524$	1.26364	−	0.491614i	0.0552025	−	0.0214762i
$525$	5.98065	−	11.8370i	0.261017	−	0.516609i
$526$	−17.1959	+	3.22718i	−0.749777	+	0.140712i
$527$	−9.98773	+	5.08900i	−0.435072	+	0.221680i
$528$	−9.59228	−	7.62553i	−0.417451	−	0.331859i
$529$	−13.4962	+	18.5759i	−0.586792	+	0.807650i
$530$	4.34366	+	39.8123i	0.188676	+	1.72933i
$531$	3.59691	+	4.95072i	0.156093	+	0.214843i
$532$	−9.67348	+	21.9933i	−0.419399	+	0.953529i
$533$	13.0153	+	2.06142i	0.563755	+	0.0892900i
$534$	3.09758	−	1.69090i	0.134045	−	0.0731724i
$535$	0.982720	+	12.2210i	0.0424867	+	0.528359i
$536$	−0.906394	−	3.66603i	−0.0391503	−	0.158348i
$537$	−3.01129	−	1.53433i	−0.129947	−	0.0662111i
$538$	−34.6350	−	10.1745i	−1.49322	−	0.438654i
$539$	0.0334303	−	0.102888i	0.00143995	−	0.00443170i
$540$	2.10948	−	3.94336i	0.0907776	−	0.169695i
$541$	−2.92452	−	9.00075i	−0.125735	−	0.386973i	0.868299	−	0.496041i	$-0.165213\pi$
$541$	−2.92452	−	9.00075i	−0.125735	−	0.386973i	−0.994034	+	0.109068i	$0.965213\pi$
$542$	0.709992	+	24.9634i	0.0304968	+	1.07227i
$543$	6.00027	−	6.00027i	0.257496	−	0.257496i
$544$	−0.485856	+	32.5809i	−0.0208309	+	1.39690i
$545$	−28.8638	−	11.8983i	−1.23639	−	0.509668i
$546$	−4.46299	+	9.41138i	−0.190998	+	0.402770i
$547$	−2.16103	−	13.6442i	−0.0923989	−	0.583384i	−0.989833	−	0.142235i	$-0.954571\pi$
$547$	−2.16103	−	13.6442i	−0.0923989	−	0.583384i	0.897434	−	0.441149i	$-0.145429\pi$
$548$	−26.5935	+	29.8041i	−1.13602	+	1.27317i
$549$		−	8.13451i		−	0.347172i
$550$	10.4438	+	18.9784i	0.445325	+	0.809241i
$551$		−	34.5895i		−	1.47356i
$552$	−9.90825	+	16.4169i	−0.421723	+	0.698751i
$553$	−0.178532	−	1.12721i	−0.00759196	−	0.0479338i
$554$	−16.0199	−	7.59682i	−0.680619	−	0.322758i
$555$	−6.41087	−	10.4218i	−0.272126	−	0.442379i
$556$	0.0912406	+	0.0586693i	0.00386946	+	0.00248813i
$557$	−20.2567	+	20.2567i	−0.858304	+	0.858304i	−0.991138	−	0.132834i	$-0.957592\pi$
$557$	−20.2567	+	20.2567i	−0.858304	+	0.858304i	0.132834	+	0.991138i	$0.457592\pi$
$558$	−2.75099	+	0.0782418i	−0.116459	+	0.00331224i
$559$	−1.17002	−	3.60095i	−0.0494865	−	0.152304i
$560$	−9.98339	+	21.5211i	−0.421875	+	0.909432i
$561$	−5.45302	+	16.7827i	−0.230227	+	0.708565i
$562$	5.83224	−	19.8535i	0.246018	−	0.837470i
$563$	−18.7194	−	9.53800i	−0.788928	−	0.401979i	0.0126118	−	0.999920i	$-0.495985\pi$
$563$	−18.7194	−	9.53800i	−0.788928	−	0.401979i	−0.801540	+	0.597942i	$0.795985\pi$
$564$	−23.9288	+	1.36224i	−1.00758	+	0.0573605i
$565$	4.04672	−	1.68427i	0.170247	−	0.0708578i
$566$	−10.7745	−	19.7380i	−0.452887	−	0.829649i
$567$	2.61976	+	0.414929i	0.110020	+	0.0174254i
$568$	34.9953	+	8.15177i	1.46837	+	0.342041i
$569$	−22.8243	−	31.4149i	−0.956843	−	1.31698i	−0.948420	−	0.317016i	$-0.897319\pi$
$569$	−22.8243	−	31.4149i	−0.956843	−	1.31698i	−0.00842243	−	0.999965i	$-0.502681\pi$
$570$	10.6058	−	9.62569i	0.444227	−	0.403176i
$571$	4.66625	−	6.42254i	0.195276	−	0.268775i	−0.700139	−	0.714007i	$-0.746879\pi$
$571$	4.66625	−	6.42254i	0.195276	−	0.268775i	0.895415	+	0.445232i	$0.146879\pi$
$572$	−8.57302	−	14.6955i	−0.358456	−	0.614451i
$573$	21.6200	−	11.0159i	0.903187	−	0.460197i
$574$	3.28344	+	17.4957i	0.137048	+	0.730257i
$575$	27.3556	−	20.0175i	1.14081	−	0.834786i
$576$	−3.53521	+	7.17651i	−0.147300	+	0.299021i
$577$	9.74625	+	19.1281i	0.405742	+	0.796313i	0.999968	−	0.00798495i	$-0.00254172\pi$
$577$	9.74625	+	19.1281i	0.405742	+	0.796313i	−0.594226	+	0.804298i	$0.702542\pi$
$578$	21.5519	−	7.68663i	0.896441	−	0.319722i
$579$	19.6095	+	14.2472i	0.814944	+	0.592091i
$580$	0.682085	−	34.1469i	0.0283220	−	1.41787i
$581$	25.0015	−	18.1647i	1.03724	−	0.753597i
$582$	−9.86942	+	14.4297i	−0.409101	+	0.598129i
$583$	6.06928	−	38.3199i	0.251364	−	1.58705i
$584$	−7.40402	−	6.23755i	−0.306381	−	0.258112i
$585$	4.71456	−	4.04050i	0.194923	−	0.167054i
$586$	−13.7096	−	1.77348i	−0.566339	−	0.0732618i
$587$	11.3820	−	22.3385i	0.469787	−	0.922009i	−0.527581	−	0.849505i	$-0.676901\pi$
$587$	11.3820	−	22.3385i	0.469787	−	0.922009i	0.997368	−	0.0725046i	$-0.0230992\pi$
$588$	−0.0702726	−	0.00706584i	−0.00289799	−	0.000291390i
$589$	−8.38257	−	2.72366i	−0.345398	−	0.112226i
$590$	5.08236	+	18.6720i	0.209237	+	0.768714i
$591$	−12.2751	+	3.98841i	−0.504928	+	0.164061i
$592$	12.0860	+	18.2485i	0.496732	+	0.750010i
$593$	−28.1891	−	28.1891i	−1.15759	−	1.15759i	−0.984993	−	0.172594i	$-0.944785\pi$
$593$	−28.1891	−	28.1891i	−1.15759	−	1.15759i	−0.172594	−	0.984993i	$-0.555215\pi$
$594$	−2.97517	+	3.14936i	−0.122073	+	0.129220i
$595$	34.0628	+	2.62254i	1.39644	+	0.107514i
$596$	−2.18555	−	0.575070i	−0.0895236	−	0.0235558i
$597$	−15.3316	+	2.42829i	−0.627482	+	0.0993834i
$598$	−21.0847	+	16.2545i	−0.862217	+	0.664695i
$599$	11.5491			0.471885			0.235943	−	0.971767i	$-0.424182\pi$
$599$	11.5491			0.471885			0.235943	+	0.971767i	$0.424182\pi$
$600$	10.6599	−	9.29338i	0.435188	−	0.379401i
$601$	10.4058			0.424462			0.212231	−	0.977220i	$-0.431927\pi$
$601$	10.4058			0.424462			0.212231	+	0.977220i	$0.431927\pi$
$602$	4.05078	−	3.12280i	0.165097	−	0.127276i
$603$	−1.31873	+	0.208866i	−0.0537027	+	0.00850567i
$604$	11.0021	+	2.89492i	0.447669	+	0.117792i
$605$	0.848977	+	3.50994i	0.0345158	+	0.142700i
$606$	5.13997	−	5.44090i	0.208797	−	0.221022i
$607$	16.1166	+	16.1166i	0.654154	+	0.654154i	0.953991	−	0.299837i	$-0.0969322\pi$
$607$	16.1166	+	16.1166i	0.654154	+	0.654154i	−0.299837	+	0.953991i	$0.596932\pi$
$608$	−18.3849	+	17.8446i	−0.745607	+	0.723696i
$609$	19.2651	−	6.25960i	0.780660	−	0.253652i
$610$	9.12348	−	24.0513i	0.369399	−	0.973808i
$611$	−31.6477	−	10.2830i	−1.28033	−	0.416004i
$612$	11.4626	+	1.15255i	0.463347	+	0.0465891i
$613$	15.0439	−	29.5254i	0.607619	−	1.19252i	−0.358284	−	0.933613i	$-0.616638\pi$
$613$	15.0439	−	29.5254i	0.607619	−	1.19252i	0.965903	−	0.258906i	$-0.0833619\pi$
$614$	32.9569	+	4.26331i	1.33003	+	0.172053i
$615$	2.45966	−	10.3225i	0.0991830	−	0.416243i
$616$	14.8077	−	17.5769i	0.596619	−	0.708192i
$617$	−4.40691	+	27.8241i	−0.177415	+	1.12016i	0.724828	+	0.688930i	$0.241919\pi$
$617$	−4.40691	+	27.8241i	−0.177415	+	1.12016i	−0.902243	+	0.431227i	$0.858081\pi$
$618$	4.19499	−	6.13331i	0.168747	−	0.246718i
$619$	26.0513	−	18.9274i	1.04709	−	0.760756i	0.0754341	−	0.997151i	$-0.475966\pi$
$619$	26.0513	−	18.9274i	1.04709	−	0.760756i	0.971657	+	0.236394i	$0.0759657\pi$
$620$	−8.22160	−	2.85411i	−0.330187	−	0.114624i
$621$	5.48470	+	3.98487i	0.220093	+	0.159907i
$622$	−16.2374	+	5.79118i	−0.651060	+	0.232205i
$623$	3.00490	+	5.89745i	0.120389	+	0.236276i
$624$	−8.18689	+	7.50625i	−0.327738	+	0.300490i
$625$	−23.7233	+	7.88693i	−0.948933	+	0.315477i
$626$	−6.07007	−	32.3442i	−0.242609	−	1.29273i
$627$	−12.3629	+	6.29921i	−0.493727	+	0.251566i
$628$	9.48013	+	16.2505i	0.378298	+	0.648464i
$629$	18.5267	−	25.4999i	0.738710	−	1.01675i
$630$	7.28047	+	4.16509i	0.290061	+	0.165941i
$631$	−2.63098	−	3.62123i	−0.104738	−	0.144159i	0.753431	−	0.657527i	$-0.228398\pi$
$631$	−2.63098	−	3.62123i	−0.104738	−	0.144159i	−0.858168	+	0.513368i	$0.828398\pi$
$632$	0.276094	−	1.18526i	0.0109824	−	0.0471471i
$633$	2.03509	+	0.322326i	0.0808875	+	0.0128113i
$634$	−8.53371	−	15.6330i	−0.338917	−	0.620866i
$635$	26.7635	+	6.37725i	1.06208	+	0.253073i
$636$	−25.2880	+	1.43961i	−1.00273	+	0.0570844i
$637$	−0.0873703	−	0.0445174i	−0.00346174	−	0.00176384i
$638$	−9.32566	+	31.7455i	−0.369206	+	1.25681i
$639$	3.92573	−	12.0822i	0.155300	−	0.477963i
$640$	−18.5016	+	17.2538i	−0.731338	+	0.682015i
$641$	10.1109	+	31.1181i	0.399356	+	1.22909i	0.925517	+	0.378707i	$0.123631\pi$
$641$	10.1109	+	31.1181i	0.399356	+	1.22909i	−0.526160	+	0.850385i	$0.676369\pi$
$642$	−7.75104	+	0.220450i	−0.305909	+	0.00870047i
$643$	−20.7316	+	20.7316i	−0.817573	+	0.817573i	−0.985756	−	0.168183i	$-0.946210\pi$
$643$	−20.7316	+	20.7316i	−0.817573	+	0.817573i	0.168183	+	0.985756i	$0.446210\pi$
$644$	−30.2499	−	19.4512i	−1.19201	−	0.766485i
$645$	−2.96351	+	0.716806i	−0.116688	+	0.0282242i
$646$	33.3370	+	15.8088i	1.31163	+	0.621989i
$647$	1.54895	+	9.77971i	0.0608957	+	0.384480i	0.999247	+	0.0387973i	$0.0123527\pi$
$647$	1.54895	+	9.77971i	0.0608957	+	0.384480i	−0.938351	+	0.345683i	$0.887647\pi$
$648$	2.42157	+	1.46151i	0.0951282	+	0.0574135i
$649$		−	18.7469i		−	0.735880i
$650$	18.4713	−	6.65879i	0.724503	−	0.261179i
$651$		−	5.16168i		−	0.202302i
$652$	−11.3728	+	12.7458i	−0.445393	+	0.499166i
$653$	0.873916	+	5.51769i	0.0341990	+	0.215924i	0.998870	−	0.0475352i	$-0.0151366\pi$
$653$	0.873916	+	5.51769i	0.0341990	+	0.215924i	−0.964671	+	0.263459i	$0.915137\pi$
$654$	8.46036	−	17.8409i	0.330826	−	0.697634i
$655$	0.116370	−	1.51147i	0.00454697	−	0.0590582i
$656$	−3.77912	+	18.6024i	−0.147550	+	0.726303i
$657$	−2.42031	+	2.42031i	−0.0944253	+	0.0944253i
$658$	−1.27798	−	44.9339i	−0.0498209	−	1.75171i
$659$	11.9644	+	36.8226i	0.466066	+	1.43440i	0.857636	+	0.514256i	$0.171932\pi$
$659$	11.9644	+	36.8226i	0.466066	+	1.43440i	−0.391570	+	0.920148i	$0.628068\pi$
$660$	−12.3289	+	5.97482i	−0.479903	+	0.232570i
$661$	−9.93403	+	30.5738i	−0.386389	+	1.18918i	0.549079	+	0.835771i	$0.314979\pi$
$661$	−9.93403	+	30.5738i	−0.386389	+	1.18918i	−0.935468	+	0.353412i	$0.885021\pi$
$662$	−15.9640	−	4.68965i	−0.620460	−	0.182269i
$663$	14.2515	+	7.26150i	0.553482	+	0.282013i
$664$	31.9910	−	7.90950i	1.24149	−	0.306948i
$665$	17.4806	+	20.3968i	0.677867	+	0.790954i
$666$	6.79242	−	3.70783i	0.263201	−	0.143675i
$667$	51.1373	+	8.09936i	1.98005	+	0.313608i
$668$	13.6833	−	31.1099i	0.529423	−	1.20368i
$669$	−12.2177	−	16.8162i	−0.472362	−	0.650151i
$670$	−4.13333	−	0.861501i	−0.159685	−	0.0332827i
$671$	−14.6477	+	20.1608i	−0.565466	+	0.778298i
$672$	−13.2659	−	7.01041i	−0.511743	−	0.270432i
$673$	25.8524	−	13.1724i	0.996535	−	0.507760i	0.121900	−	0.992542i	$-0.461101\pi$
$673$	25.8524	−	13.1724i	0.996535	−	0.507760i	0.874635	+	0.484782i	$0.161101\pi$
$674$	−22.1337	+	4.15386i	−0.852559	+	0.160001i
$675$	−2.95266	−	4.03507i	−0.113648	−	0.155310i
$676$	9.85906	−	3.83561i	0.379195	−	0.147524i
$677$	2.17299	+	4.26473i	0.0835147	+	0.163907i	0.928987	−	0.370113i	$-0.120681\pi$
$677$	2.17299	+	4.26473i	0.0835147	+	0.163907i	−0.845472	+	0.534019i	$0.820681\pi$
$678$	0.931265	+	2.61109i	0.0357650	+	0.100278i
$679$	−26.5262	−	19.2724i	−1.01798	−	0.739608i
$680$	32.5987	+	16.2639i	1.25010	+	0.623693i
$681$	−3.91276	+	2.84278i	−0.149937	+	0.108936i
$682$	6.95900	+	4.75974i	0.266474	+	0.182260i
$683$	5.72483	−	36.1452i	0.219055	−	1.38306i	−0.595679	−	0.803222i	$-0.703117\pi$
$683$	5.72483	−	36.1452i	0.219055	−	1.38306i	0.814734	−	0.579835i	$-0.196883\pi$
$684$	5.73231	+	7.01393i	0.219180	+	0.268184i
$685$	17.1601	+	41.2298i	0.655655	+	1.57531i
$686$	−3.35163	+	25.9092i	−0.127966	+	0.989219i
$687$	−4.51157	+	8.85446i	−0.172127	+	0.337819i
$688$	5.25537	−	1.45908i	0.200359	−	0.0556267i
$689$	−33.4453	−	10.8671i	−1.27417	−	0.414002i
$690$	11.7473	+	17.9336i	0.447211	+	0.682719i
$691$	−3.63597	+	1.18140i	−0.138319	+	0.0449425i	−0.377358	−	0.926067i	$-0.623167\pi$
$691$	−3.63597	+	1.18140i	−0.138319	+	0.0449425i	0.239039	+	0.971010i	$0.423167\pi$
$692$	−6.79242	−	31.2622i	−0.258209	−	1.18841i
$693$	−5.74572	−	5.74572i	−0.218262	−	0.218262i
$694$	−25.7536	−	24.3292i	−0.977593	−	0.923523i
$695$	0.103300	−	0.0635440i	0.00391838	−	0.00241036i
$696$	21.5451	+	1.54914i	0.816664	+	0.0587199i
$697$	26.9990	−	4.27622i	1.02266	−	0.161973i
$698$	3.25841	+	4.22668i	0.123333	+	0.159982i
$699$	8.10721			0.306643
$700$	16.8547	+	20.4805i	0.637047	+	0.774090i
$701$	22.6934			0.857118			0.428559	−	0.903514i	$-0.359021\pi$
$701$	22.6934			0.857118			0.428559	+	0.903514i	$0.359021\pi$
$702$	2.39760	+	3.11008i	0.0904917	+	0.117382i
$703$	24.4785	−	3.87702i	0.923225	−	0.146224i
$704$	21.6843	−	11.4207i	0.817260	−	0.430433i
$705$	−10.2125	+	24.7741i	−0.384624	+	0.933048i
$706$	15.4556	+	14.6008i	0.581679	+	0.549507i
$707$	9.92645	+	9.92645i	0.373322	+	0.373322i
$708$	−11.9598	+	2.59854i	−0.449478	+	0.0976590i
$709$	−23.3358	+	7.58226i	−0.876394	+	0.284758i	−0.712459	−	0.701714i	$-0.752419\pi$
$709$	−23.3358	+	7.58226i	−0.876394	+	0.284758i	−0.163935	+	0.986471i	$0.552419\pi$
$710$	25.1583	−	31.3203i	0.944173	−	1.17543i
$711$	−0.409212	−	0.132961i	−0.0153467	−	0.00498643i
$712$	0.601332	+	7.03242i	0.0225359	+	0.263551i
$713$	5.98951	−	11.7551i	0.224309	−	0.440231i
$714$	−2.77198	+	21.4284i	−0.103739	+	0.801937i
$715$	−18.9603	+	1.52465i	−0.709077	+	0.0570187i
$716$	5.23373	−	4.27740i	0.195594	−	0.159854i
$717$	3.71781	−	23.4733i	0.138844	−	0.876627i
$718$	32.7381	+	22.3918i	1.22178	+	0.835656i
$719$	−30.8564	+	22.4185i	−1.15075	+	0.836068i	−0.988580	−	0.150695i	$-0.951849\pi$
$719$	−30.8564	+	22.4185i	−1.15075	+	0.836068i	−0.162168	+	0.986763i	$0.551849\pi$
$720$	5.52065	+	7.03722i	0.205742	+	0.262262i
$721$	11.2749	+	8.19173i	0.419901	+	0.305076i
$722$	0.719096	+	2.01621i	0.0267620	+	0.0750356i
$723$	−10.8222	−	21.2397i	−0.402481	−	0.789913i
$724$	6.15333	+	15.8165i	0.228687	+	0.587816i
$725$	−34.0818	−	17.2198i	−1.26577	−	0.639529i
$726$	−2.24471	+	0.421267i	−0.0833090	+	0.0156347i
$727$	−17.5691	+	8.95193i	−0.651603	+	0.332009i	−0.748353	−	0.663300i	$-0.769155\pi$
$727$	−17.5691	+	8.95193i	−0.651603	+	0.332009i	0.0967500	+	0.995309i	$0.469155\pi$
$728$	−13.6360	−	15.7489i	−0.505386	−	0.583693i
$729$	0.587785	−	0.809017i	0.0217698	−	0.0299636i
$730$	−9.87070	+	4.44156i	−0.365331	+	0.164390i
$731$	−4.61661	−	6.35421i	−0.170751	−	0.235019i
$732$	14.8922	+	6.55015i	0.550430	+	0.242100i
$733$	11.6075	+	1.83845i	0.428732	+	0.0679046i	0.367072	−	0.930193i	$-0.380360\pi$
$733$	11.6075	+	1.83845i	0.428732	+	0.0679046i	0.0616607	+	0.998097i	$0.480360\pi$
$734$	32.6105	−	17.8014i	1.20368	−	0.657060i
$735$	−0.0411437	+	0.0673973i	−0.00151761	+	0.00248599i
$736$	−22.0767	−	31.3588i	−0.813758	−	1.15590i
$737$	3.64446	+	1.85695i	0.134246	+	0.0684015i
$738$	6.43920	+	1.89160i	0.237030	+	0.0696309i
$739$	−11.7485	+	36.1581i	−0.432175	+	1.33010i	0.463779	+	0.885951i	$0.346493\pi$
$739$	−11.7485	+	36.1581i	−0.432175	+	1.33010i	−0.895954	+	0.444147i	$0.853507\pi$
$740$	24.2418	−	3.34471i	0.891145	−	0.122954i
$741$	3.88639	+	11.9611i	0.142770	+	0.439401i
$742$	−1.35057	−	47.4862i	−0.0495811	−	1.74327i
$743$	23.1808	−	23.1808i	0.850422	−	0.850422i	−0.139763	−	0.990185i	$-0.544634\pi$
$743$	23.1808	−	23.1808i	0.850422	−	0.850422i	0.990185	+	0.139763i	$0.0446339\pi$
$744$	2.07194	−	5.09934i	0.0759609	−	0.186951i
$745$	−1.63769	+	1.92410i	−0.0600001	+	0.0704935i
$746$	−15.4810	+	32.6458i	−0.566800	+	1.19525i
$747$	−1.82263	−	11.5076i	−0.0666866	−	0.421043i
$748$	−26.3338	−	23.4970i	−0.962857	−	0.859134i
$749$		−	14.5433i		−	0.531400i
$750$	−4.20449	−	15.2421i	−0.153526	−	0.556564i
$751$		−	6.42557i		−	0.234473i	−0.993104	−	0.117236i	$-0.962597\pi$
$751$		−	6.42557i		−	0.234473i	0.993104	−	0.117236i	$-0.0374035\pi$
$752$	16.7743	−	44.9043i	0.611694	−	1.63749i
$753$	−0.273778	−	1.72856i	−0.00997701	−	0.0629924i
$754$	27.0978	+	12.8501i	0.986844	+	0.467973i
$755$	8.24414	−	9.68595i	0.300035	−	0.352508i
$756$	−2.86914	+	4.46199i	−0.104349	+	0.162281i
$757$	−13.6083	+	13.6083i	−0.494602	+	0.494602i	−0.909753	−	0.415150i	$-0.863729\pi$
$757$	−13.6083	+	13.6083i	−0.494602	+	0.494602i	0.415150	+	0.909753i	$0.363729\pi$
$758$	32.4728	−	0.923570i	1.17947	−	0.0335456i
$759$	−6.41794	−	19.7524i	−0.232957	−	0.716966i
$760$	9.08204	+	27.1673i	0.329440	+	0.985462i
$761$	2.47261	−	7.60993i	0.0896322	−	0.275860i	−0.896185	−	0.443680i	$-0.853673\pi$
$761$	2.47261	−	7.60993i	0.0896322	−	0.275860i	0.985818	+	0.167820i	$0.0536728\pi$
$762$	−4.90443	+	16.6952i	−0.177669	+	0.604802i
$763$	32.9967	+	16.8126i	1.19456	+	0.608659i
$764$	2.75825	+	48.4509i	0.0997899	+	1.75289i
$765$	6.71119	−	10.9936i	0.242644	−	0.397474i
$766$	−15.0750	−	27.6161i	−0.544682	−	0.997810i
$767$	−16.7832	−	2.65819i	−0.606005	−	0.0959817i
$768$	−10.2917	−	12.2508i	−0.371369	−	0.442062i
$769$	21.7509	+	29.9376i	0.784358	+	1.07958i	0.994788	+	0.101967i	$0.0325137\pi$
$769$	21.7509	+	29.9376i	0.784358	+	1.07958i	−0.210430	+	0.977609i	$0.567486\pi$
$770$	−10.5441	−	23.4326i	−0.379983	−	0.844454i
$771$	−0.662185	+	0.911419i	−0.0238480	+	0.0328240i
$772$	−41.8730	+	24.4277i	−1.50704	+	0.879172i
$773$	44.7020	−	22.7768i	1.60782	−	0.819226i	0.608143	−	0.793827i	$-0.291915\pi$
$773$	44.7020	−	22.7768i	1.60782	−	0.819226i	0.999677	−	0.0253983i	$-0.00808540\pi$
$774$	−0.355684	−	1.89525i	−0.0127848	−	0.0681233i
$775$	−6.85682	+	6.90360i	−0.246304	+	0.247985i
$776$	−18.4698	−	29.6875i	−0.663027	−	1.06572i
$777$	6.58920	+	12.9320i	0.236386	+	0.463934i
$778$	35.3340	−	12.6021i	1.26678	−	0.451807i
$779$	17.3888	+	12.6337i	0.623019	+	0.452650i
$780$	3.60080	+	11.8847i	0.128929	+	0.425539i
$781$	−31.4857	+	22.8757i	−1.12665	+	0.818558i
$782$	−31.1779	+	45.5839i	−1.11492	+	1.63008i
$783$	1.19469	−	7.54298i	0.0426947	−	0.269564i
$784$	0.0695213	−	0.122961i	0.00248290	−	0.00439147i
$785$	20.9665	−	1.68597i	0.748328	−	0.0601749i
$786$	0.950847	+	0.123002i	0.0339156	+	0.00438733i
$787$	−15.6617	+	30.7377i	−0.558278	+	1.09568i	0.423544	+	0.905876i	$0.360786\pi$
$787$	−15.6617	+	30.7377i	−0.558278	+	1.09568i	−0.981822	+	0.189806i	$0.939214\pi$
$788$	2.58250	−	25.6840i	0.0919978	−	0.914954i
$789$	−11.7661	−	3.82304i	−0.418885	−	0.136104i
$790$	−1.06079	−	0.852090i	−0.0377413	−	0.0303160i
$791$	−4.94489	+	1.60669i	−0.175820	+	0.0571274i
$792$	−3.36996	−	7.98271i	−0.119746	−	0.283653i
$793$	15.9720	+	15.9720i	0.567182	+	0.567182i
$794$	30.8453	−	32.6513i	1.09466	−	1.15875i
$795$	−10.7926	+	26.1814i	−0.382773	+	0.928557i
$796$	7.89991	−	30.0235i	0.280005	−	1.06416i
$797$	6.88757	−	1.09088i	0.243970	−	0.0386411i	−0.0332517	−	0.999447i	$-0.510586\pi$
$797$	6.88757	−	1.09088i	0.243970	−	0.0386411i	0.277222	+	0.960806i	$0.410586\pi$
$798$	−13.4553	+	10.3728i	−0.476311	+	0.367195i
$799$	−69.0287			−2.44206
$800$	8.43010	+	26.9988i	0.298049	+	0.954551i
$801$	2.49541			0.0881710
$802$	−2.16978	+	1.67271i	−0.0766174	+	0.0590654i
$803$	10.3568	−	1.64035i	0.365482	−	0.0578867i
$804$	0.679498	−	2.58243i	0.0239641	−	0.0910752i
$805$	−34.2479	+	21.0673i	−1.20708	+	0.742526i
$806$	5.24790	−	5.55515i	0.184849	−	0.195672i
$807$	−18.0493	−	18.0493i	−0.635364	−	0.635364i
$808$	5.82202	+	13.7911i	0.204818	+	0.485170i
$809$	−8.24083	+	2.67761i	−0.289732	+	0.0941397i	−0.450277	−	0.892889i	$-0.648675\pi$
$809$	−8.24083	+	2.67761i	−0.289732	+	0.0941397i	0.160545	+	0.987029i	$0.448675\pi$
$810$	2.64528	−	1.73277i	0.0929456	−	0.0608834i
$811$	−25.8508	−	8.39942i	−0.907743	−	0.294944i	−0.182314	−	0.983240i	$-0.558359\pi$
$811$	−25.8508	−	8.39942i	−0.907743	−	0.294944i	−0.725429	+	0.688297i	$0.758359\pi$
$812$	−4.05311	+	40.3098i	−0.142236	+	1.41459i
$813$	−8.01698	+	15.7342i	−0.281168	+	0.551823i
$814$	−23.5111	−	3.04141i	−0.824064	−	0.106601i
$815$	7.33860	+	17.6321i	0.257060	+	0.617626i
$816$	−11.3400	+	20.0569i	−0.396980	+	0.702132i
$817$	0.966098	−	6.09971i	0.0337995	−	0.213402i
$818$	−9.41431	+	13.7643i	−0.329163	+	0.481256i
$819$	−5.95857	+	4.32916i	−0.208209	+	0.151273i
$820$	16.9172	+	12.8150i	0.590774	+	0.447518i
$821$	17.7303	+	12.8818i	0.618792	+	0.449579i	0.852500	−	0.522728i	$-0.175086\pi$
$821$	17.7303	+	12.8818i	0.618792	+	0.449579i	−0.233707	+	0.972307i	$0.575086\pi$
$822$	−26.6031	+	9.48817i	−0.927888	+	0.330938i
$823$	8.21349	+	16.1199i	0.286304	+	0.561904i	0.988704	−	0.149878i	$-0.0478882\pi$
$823$	8.21349	+	16.1199i	0.286304	+	0.561904i	−0.702400	+	0.711782i	$0.747888\pi$
$824$	7.85056	+	12.6186i	0.273487	+	0.439591i
$825$	0.0520817	+	15.3174i	0.00181325	+	0.533284i
$826$	−4.23398	−	22.5606i	−0.147319	−	0.784985i
$827$	23.6776	−	12.0643i	0.823351	−	0.419518i	0.00904858	−	0.999959i	$-0.497120\pi$
$827$	23.6776	−	12.0643i	0.823351	−	0.419518i	0.814302	+	0.580441i	$0.197120\pi$
$828$	−11.7117	+	6.83232i	−0.407010	+	0.237440i
$829$	3.93521	−	5.41635i	0.136676	−	0.188118i	−0.735193	−	0.677858i	$-0.762908\pi$
$829$	3.93521	−	5.41635i	0.136676	−	0.188118i	0.871868	+	0.489740i	$0.162908\pi$
$830$	7.51775	−	36.0689i	0.260945	−	1.25197i
$831$	−7.36901	−	10.1426i	−0.255628	−	0.351842i
$832$	−7.14965	−	21.0323i	−0.247870	−	0.729164i
$833$	−0.200908	−	0.0318207i	−0.00696104	−	0.00110252i
$834$	0.0367517	+	0.0673259i	0.00127261	+	0.00233131i
$835$	−24.7266	−	28.8516i	−0.855699	−	0.998452i
$836$	−1.57724	−	27.7056i	−0.0545501	−	0.958217i
$837$	−1.73392	−	0.883479i	−0.0599332	−	0.0305375i
$838$	12.2630	−	41.7443i	0.423617	−	1.44203i
$839$	7.61135	−	23.4253i	0.262773	−	0.808732i	−0.729425	−	0.684061i	$-0.760212\pi$
$839$	7.61135	−	23.4253i	0.262773	−	0.808732i	0.992198	−	0.124672i	$-0.0397877\pi$
$840$	−13.4876	+	9.97479i	−0.465367	+	0.344163i
$841$	−9.06154	−	27.8886i	−0.312467	−	0.961674i
$842$	−23.6137	+	0.671604i	−0.813780	+	0.0231450i
$843$	10.3462	−	10.3462i	0.356343	−	0.356343i
$844$	−2.22881	+	3.46617i	−0.0767188	+	0.119311i
$845$	0.907933	−	11.7927i	0.0312338	−	0.405680i
$846$	−15.3131	−	7.26163i	−0.526474	−	0.249660i
$847$	−0.670094	−	4.23081i	−0.0230247	−	0.145372i
$848$	17.7271	−	47.4549i	0.608750	−	1.62961i
$849$		−	15.9009i		−	0.545718i
$850$	32.1731	−	24.9776i	1.10353	−	0.856723i
$851$			37.0970i			1.27167i
$852$	18.9582	+	16.9159i	0.649496	+	0.579529i
$853$	1.79974	+	11.3631i	0.0616219	+	0.389066i	0.999152	+	0.0411626i	$0.0131062\pi$
$853$	1.79974	+	11.3631i	0.0616219	+	0.389066i	−0.937531	+	0.347903i	$0.886894\pi$
$854$	−13.0742	+	27.5703i	−0.447389	+	0.943437i
$855$	9.84374	−	2.38098i	0.336649	−	0.0814278i
$856$	5.83778	−	14.3676i	0.199531	−	0.491076i
$857$	−3.84290	+	3.84290i	−0.131271	+	0.131271i	−0.769690	−	0.638418i	$-0.779589\pi$
$857$	−3.84290	+	3.84290i	−0.131271	+	0.131271i	0.638418	+	0.769690i	$0.279589\pi$
$858$	−0.342019	−	12.0254i	−0.0116763	−	0.410541i
$859$	13.7094	+	42.1931i	0.467758	+	1.43961i	0.855481	+	0.517834i	$0.173262\pi$
$859$	13.7094	+	42.1931i	0.467758	+	1.43961i	−0.387723	+	0.921776i	$0.626738\pi$
$860$	1.07402	−	6.00260i	0.0366238	−	0.204687i
$861$	−3.88969	+	11.9712i	−0.132560	+	0.407979i
$862$	23.7729	+	6.98362i	0.809709	+	0.237863i
$863$	−30.0592	−	15.3159i	−1.02323	−	0.521359i	−0.139923	−	0.990162i	$-0.544685\pi$
$863$	−30.0592	−	15.3159i	−1.02323	−	0.521359i	−0.883303	+	0.468803i	$0.844685\pi$
$864$	−4.62556	+	3.25641i	−0.157365	+	0.110785i
$865$	−34.7936	−	8.29067i	−1.18302	−	0.281891i
$866$	−26.4392	+	14.4325i	−0.898439	+	0.490438i
$867$	15.9806	+	2.53107i	0.542728	+	0.0859597i
$868$	9.44969	+	4.15634i	0.320743	+	0.141075i
$869$	0.774782	+	1.06640i	0.0262827	+	0.0361750i
$870$	11.9924	−	20.9624i	0.406579	−	0.710691i
$871$	2.17920	−	2.99940i	0.0738392	−	0.101631i
$872$	25.8495	+	29.8547i	0.875374	+	1.01101i
$873$	−11.0143	+	5.61207i	−0.372778	+	0.189940i
$874$	−42.6791	+	8.00964i	−1.44364	+	0.270930i
$875$	28.7999	−	7.06978i	0.973613	−	0.239002i
$876$	−2.48205	−	6.37986i	−0.0838608	−	0.215556i
$877$	−4.72327	−	9.26995i	−0.159494	−	0.313024i	0.797406	−	0.603443i	$-0.206205\pi$
$877$	−4.72327	−	9.26995i	−0.159494	−	0.313024i	−0.956899	+	0.290420i	$0.906205\pi$
$878$	−5.63656	−	15.8039i	−0.190225	−	0.533355i
$879$	−7.90809	−	5.74556i	−0.266733	−	0.193793i
$880$	−1.01072	−	27.3821i	−0.0340715	−	0.923052i
$881$	−41.0084	+	29.7944i	−1.38161	+	1.00380i	−0.384882	+	0.922966i	$0.625758\pi$
$881$	−41.0084	+	29.7944i	−1.38161	+	1.00380i	−0.996728	+	0.0808323i	$0.974242\pi$
$882$	−0.0412212	−	0.0281939i	−0.00138799	−	0.000949339i
$883$	−2.28368	+	14.4186i	−0.0768518	+	0.485223i	0.919002	+	0.394253i	$0.128997\pi$
$883$	−2.28368	+	14.4186i	−0.0768518	+	0.485223i	−0.995854	+	0.0909700i	$0.971003\pi$
$884$	−24.7696	+	20.2436i	−0.833093	+	0.680865i
$885$	−3.17172	+	13.3108i	−0.106616	+	0.447438i
$886$	1.16951	−	9.04070i	0.0392904	−	0.303728i
$887$	−19.7248	+	38.7121i	−0.662294	+	1.29982i	0.278367	+	0.960475i	$0.410207\pi$
$887$	−19.7248	+	38.7121i	−0.662294	+	1.29982i	−0.940660	+	0.339349i	$0.889793\pi$
$888$	1.31861	+	15.4208i	0.0442497	+	0.517488i
$889$	−31.0383	−	10.0850i	−1.04099	−	0.338239i
$890$	7.37817	+	2.79880i	0.247317	+	0.0938159i
$891$	−2.91356	+	0.946674i	−0.0976080	+	0.0317148i
$892$	40.6241	−	8.82648i	1.36019	−	0.295533i
$893$	−38.3795	−	38.3795i	−1.28432	−	1.28432i
$894$	−1.16164	−	1.09739i	−0.0388510	−	0.0367022i
$895$	−1.77667	−	7.34531i	−0.0593874	−	0.245527i
$896$	23.5163	−	18.6414i	0.785625	−	0.622766i
$897$	−18.5934	+	2.94490i	−0.620814	+	0.0983274i
$898$	13.6409	+	17.6944i	0.455201	+	0.590470i
$899$	−14.8618			−0.495669
$900$	9.76473	−	2.15640i	0.325491	−	0.0718800i
$901$	−72.9496			−2.43030
$902$	−12.5529	−	16.2831i	−0.417966	−	0.542169i
$903$	3.57215	−	0.565772i	0.118874	−	0.0188277i
$904$	−5.53012	−	0.397627i	−0.183929	−	0.0132249i
$905$	18.9185	+	1.45656i	0.628873	+	0.0484178i
$906$	5.84771	+	5.52428i	0.194277	+	0.183532i
$907$	−0.872558	−	0.872558i	−0.0289728	−	0.0289728i	0.692472	−	0.721445i	$-0.256522\pi$
$907$	−0.872558	−	0.872558i	−0.0289728	−	0.0289728i	−0.721445	+	0.692472i	$0.756522\pi$
$908$	−2.05373	−	9.45233i	−0.0681554	−	0.313687i
$909$	5.03354	−	1.63550i	0.166952	−	0.0542460i
$910$	−22.4732	+	6.11701i	−0.744979	+	0.202777i
$911$	7.76948	+	2.52446i	0.257414	+	0.0836390i	0.434881	−	0.900488i	$-0.356790\pi$
$911$	7.76948	+	2.52446i	0.257414	+	0.0836390i	−0.177467	+	0.984127i	$0.556790\pi$
$912$	−17.4565	+	4.84654i	−0.578042	+	0.160485i
$913$	−16.2043	+	31.8028i	−0.536286	+	1.05252i
$914$	−7.64952	+	59.1334i	−0.253024	+	1.95596i
$915$	13.8112	−	11.8365i	0.456583	−	0.391303i
$916$	−12.5774	−	15.3894i	−0.415568	−	0.508480i
$917$	−0.281302	+	1.77607i	−0.00928942	+	0.0586511i
$918$	6.72382	+	4.59888i	0.221919	+	0.151786i
$919$	−16.1445	+	11.7297i	−0.532559	+	0.386927i	−0.821314	−	0.570476i	$-0.806759\pi$
$919$	−16.1445	+	11.7297i	−0.532559	+	0.386927i	0.288755	+	0.957403i	$0.406759\pi$
$920$	−42.2909	+	7.06554i	−1.39429	+	0.232944i
$921$	19.0104	+	13.8119i	0.626416	+	0.455118i
$922$	−11.7957	−	33.0728i	−0.388469	−	1.08920i
$923$	16.0150	+	31.4313i	0.527141	+	1.03457i
$924$	15.1455	−	5.89230i	0.498252	−	0.193842i
$925$	8.36614	−	26.0494i	0.275077	−	0.856498i
$926$	11.4599	−	2.15069i	0.376595	−	0.0706761i
$927$	4.68162	−	2.38540i	0.153765	−	0.0783469i
$928$	−20.1848	+	38.1960i	−0.662598	+	1.25385i
$929$	−3.28252	+	4.51800i	−0.107696	+	0.148231i	−0.859463	−	0.511198i	$-0.829202\pi$
$929$	−3.28252	+	4.51800i	−0.107696	+	0.148231i	0.751767	+	0.659429i	$0.229202\pi$
$930$	−4.13580	−	4.55691i	−0.135618	−	0.149427i
$931$	−0.0940114	−	0.129396i	−0.00308110	−	0.00424077i
$932$	−6.52817	+	14.8422i	−0.213837	+	0.486172i
$933$	−12.0399	−	1.90693i	−0.394168	−	0.0624301i
$934$	−14.4263	+	7.87499i	−0.472043	+	0.257677i
$935$	−36.4291	+	15.1620i	−1.19136	+	0.495852i
$936$	−7.62437	+	1.88506i	−0.249210	+	0.0616151i
$937$	28.6540	+	14.6000i	0.936087	+	0.476960i	0.854352	−	0.519694i	$-0.173954\pi$
$937$	28.6540	+	14.6000i	0.936087	+	0.476960i	0.0817343	+	0.996654i	$0.473954\pi$
$938$	4.80526	+	1.41161i	0.156897	+	0.0460907i
$939$	7.19085	−	22.1312i	0.234665	−	0.722223i
$940$	−37.1316	−	38.6452i	−1.21110	−	1.26047i
$941$	8.23440	+	25.3429i	0.268434	+	0.826155i	0.990882	+	0.134730i	$0.0430167\pi$
$941$	8.23440	+	25.3429i	0.268434	+	0.826155i	−0.722448	+	0.691425i	$0.756983\pi$
$942$	0.378208	+	13.2978i	0.0123227	+	0.433267i
$943$	−22.7495	+	22.7495i	−0.740825	+	0.740825i
$944$	4.87316	−	23.9877i	0.158608	−	0.780734i
$945$	3.10752	+	5.05172i	0.101088	+	0.164332i
$946$	−2.53120	+	5.33770i	−0.0822965	+	0.173544i
$947$	3.58370	+	22.6266i	0.116455	+	0.735266i	0.974947	+	0.222439i	$0.0714018\pi$
$947$	3.58370	+	22.6266i	0.116455	+	0.735266i	−0.858492	+	0.512827i	$0.828598\pi$
$948$	0.572927	−	0.642097i	0.0186078	−	0.0208543i
$949$		−	9.50450i		−	0.308529i
$950$	31.7754	+	4.00068i	1.03093	+	0.129799i
$951$		−	12.5940i		−	0.408387i
$952$	−36.9977	−	22.3296i	−1.19910	−	0.723705i
$953$	7.63828	+	48.2262i	0.247428	+	1.56220i	0.728207	+	0.685358i	$0.240354\pi$
$953$	7.63828	+	48.2262i	0.247428	+	1.56220i	−0.480779	+	0.876842i	$0.659646\pi$
$954$	−16.1829	−	7.67411i	−0.523940	−	0.248458i
$955$	50.1626	+	20.6782i	1.62322	+	0.669130i
$956$	39.9798	+	25.7077i	1.29304	+	0.831448i
$957$	−16.5434	+	16.5434i	−0.534774	+	0.534774i
$958$	3.95034	−	0.112353i	0.127630	−	0.00362996i
$959$	−16.3697	−	50.3809i	−0.528607	−	1.62688i
$960$	−17.3287	+	4.44029i	−0.559281	+	0.143310i
$961$	8.40927	−	25.8811i	0.271267	−	0.834873i
$962$	−6.05655	+	20.6171i	−0.195271	+	0.664722i
$963$	−4.88542	−	2.48924i	−0.157430	−	0.0802147i
$964$	47.5987	−	2.70973i	1.53305	−	0.0872746i
$965$	4.34429	+	54.0250i	0.139848	+	1.73913i
$966$	−12.1846	−	22.3212i	−0.392034	−	0.718173i
$967$	−43.3805	−	6.87079i	−1.39502	−	0.220950i	−0.586754	−	0.809765i	$-0.699595\pi$
$967$	−43.3805	−	6.87079i	−1.39502	−	0.220950i	−0.808268	+	0.588815i	$0.799595\pi$
$968$	1.03628	−	4.44869i	0.0333072	−	0.142986i
$969$	15.3347	+	21.1065i	0.492623	+	0.678037i
$970$	−38.8604	+	4.23980i	−1.24773	+	0.136132i
$971$	17.3975	−	23.9456i	0.558313	−	0.768452i	−0.432797	−	0.901491i	$-0.642473\pi$
$971$	17.3975	−	23.9456i	0.558313	−	0.768452i	0.991111	+	0.133039i	$0.0424735\pi$
$972$	1.00780	+	1.72753i	0.0323251	+	0.0554104i
$973$	−0.128181	+	0.0653116i	−0.00410930	+	0.00209379i
$974$	−8.48593	−	45.2170i	−0.271907	−	1.44885i
$975$	13.7203	+	2.12529i	0.439402	+	0.0680637i
$976$	−23.9832	+	21.9893i	−0.767684	+	0.703860i
$977$	−22.2885	−	43.7437i	−0.713073	−	1.39948i	−0.908128	−	0.418692i	$-0.862489\pi$
$977$	−22.2885	−	43.7437i	−0.713073	−	1.39948i	0.195056	−	0.980792i	$-0.437511\pi$
$978$	−11.3769	+	4.05765i	−0.363793	+	0.129749i
$979$	−6.18469	−	4.49344i	−0.197663	−	0.143611i
$980$	−0.0902568	−	0.129594i	−0.00288315	−	0.00413972i
$981$	11.2955	−	8.20666i	0.360637	−	0.262018i
$982$	13.3805	−	19.5631i	0.426989	−	0.624283i
$983$	3.27845	−	20.6993i	0.104566	−	0.660207i	−0.878609	−	0.477542i	$-0.841528\pi$
$983$	3.27845	−	20.6993i	0.104566	−	0.660207i	0.983175	−	0.182665i	$-0.0584722\pi$
$984$	−8.64807	+	10.2653i	−0.275690	+	0.327247i
$985$	−24.6331	−	15.0376i	−0.784876	−	0.479139i
$986$	61.6979	+	7.98127i	1.96486	+	0.254175i
$987$	14.4305	−	28.3215i	0.459328	−	0.901482i
$988$	−25.0271	−	2.51645i	−0.796217	−	0.0800589i
$989$	8.79163	+	2.85657i	0.279557	+	0.0908337i
$990$	−9.67629	−	0.468757i	−0.307533	−	0.0148981i
$991$	11.0600	−	3.59363i	0.351334	−	0.114155i	−0.128033	−	0.991770i	$-0.540866\pi$
$991$	11.0600	−	3.59363i	0.351334	−	0.114155i	0.479367	+	0.877615i	$0.340866\pi$
$992$	7.66718	+	7.89932i	0.243433	+	0.250804i
$993$	−8.31930	−	8.31930i	−0.264005	−	0.264005i
$994$	−32.7245	+	34.6405i	−1.03796	+	1.09873i
$995$	−26.4319	−	22.4974i	−0.837948	−	0.713215i
$996$	22.5351	+	5.92953i	0.714053	+	0.187884i
$997$	15.9677	−	2.52904i	0.505703	−	0.0800955i	0.101630	−	0.994822i	$-0.467594\pi$
$997$	15.9677	−	2.52904i	0.505703	−	0.0800955i	0.404073	+	0.914727i	$0.367594\pi$
$998$	−46.5403	+	35.8786i	−1.47321	+	1.13572i
$999$	5.47197			0.173126

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.103.7	yes	240
3.2	odd	2		900.2.bj.f.703.24		240
4.3	odd	2	inner	300.2.w.a.103.28	yes	240
12.11	even	2		900.2.bj.f.703.3		240
25.17	odd	20	inner	300.2.w.a.67.28	yes	240
75.17	even	20		900.2.bj.f.667.3		240
100.67	even	20	inner	300.2.w.a.67.7	✓	240
300.167	odd	20		900.2.bj.f.667.24		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.67.7	✓	240	100.67	even	20	inner
300.2.w.a.67.28	yes	240	25.17	odd	20	inner
300.2.w.a.103.7	yes	240	1.1	even	1	trivial
300.2.w.a.103.28	yes	240	4.3	odd	2	inner
900.2.bj.f.667.3		240	75.17	even	20
900.2.bj.f.667.24		240	300.167	odd	20
900.2.bj.f.703.3		240	12.11	even	2
900.2.bj.f.703.24		240	3.2	odd	2

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12003 + 0.863445i) q^{2} +(-0.987688 + 0.156434i) q^{3} +(0.508925 - 1.93417i) q^{4} +(-1.70279 - 1.44932i) q^{5} +(0.971166 - 1.02803i) q^{6} +(1.87554 + 1.87554i) q^{7} +(1.10004 + 2.60575i) q^{8} +(0.951057 - 0.309017i) q^{9} +O(q^{10})\)	\(q+(-1.12003 + 0.863445i) q^{2} +(-0.987688 + 0.156434i) q^{3} +(0.508925 - 1.93417i) q^{4} +(-1.70279 - 1.44932i) q^{5} +(0.971166 - 1.02803i) q^{6} +(1.87554 + 1.87554i) q^{7} +(1.10004 + 2.60575i) q^{8} +(0.951057 - 0.309017i) q^{9} +(3.15857 + 0.153014i) q^{10} +(-2.91356 - 0.946674i) q^{11} +(-0.200089 + 1.98997i) q^{12} +(-1.26064 + 2.47414i) q^{13} +(-3.72009 - 0.481232i) q^{14} +(1.90854 + 1.16510i) q^{15} +(-3.48199 - 1.96869i) q^{16} +(-0.901092 + 5.68927i) q^{17} +(-0.798391 + 1.16729i) q^{18} +(-3.66420 + 2.66220i) q^{19} +(-3.66981 + 2.55588i) q^{20} +(-2.14585 - 1.55905i) q^{21} +(4.08067 - 1.45540i) q^{22} +(-3.07781 - 6.04055i) q^{23} +(-1.49412 - 2.40158i) q^{24} +(0.798959 + 4.93575i) q^{25} +(-0.724334 - 3.85959i) q^{26} +(-0.891007 + 0.453990i) q^{27} +(4.58212 - 2.67310i) q^{28} +(-4.48892 + 6.17846i) q^{29} +(-3.14362 + 0.342980i) q^{30} +(1.14385 + 1.57437i) q^{31} +(5.59978 - 0.801520i) q^{32} +(3.02578 + 0.479237i) q^{33} +(-3.90312 - 7.15018i) q^{34} +(-0.475391 - 5.91190i) q^{35} +(-0.113673 - 1.99677i) q^{36} +(-4.87556 - 2.48422i) q^{37} +(1.80534 - 6.14557i) q^{38} +(0.858075 - 2.64088i) q^{39} +(1.90343 - 6.03133i) q^{40} +(-1.46647 - 4.51334i) q^{41} +(3.74957 - 0.106643i) q^{42} +(-0.964168 + 0.964168i) q^{43} +(-3.31381 + 5.15353i) q^{44} +(-2.06731 - 0.852193i) q^{45} +(8.66292 + 4.10806i) q^{46} +(1.87467 + 11.8362i) q^{47} +(3.74709 + 1.39975i) q^{48} +0.0353135i q^{49} +(-5.15661 - 4.83832i) q^{50} -5.76019i q^{51} +(4.14382 + 3.69743i) q^{52} +(1.98116 + 12.5085i) q^{53} +(0.605956 - 1.27782i) q^{54} +(3.58914 + 5.83466i) q^{55} +(-2.82403 + 6.95035i) q^{56} +(3.20263 - 3.20263i) q^{57} +(-0.307052 - 10.7960i) q^{58} +(1.89101 + 5.81992i) q^{59} +(3.22480 - 3.09849i) q^{60} +(2.51370 - 7.73638i) q^{61} +(-2.64052 - 0.775690i) q^{62} +(2.36332 + 1.20417i) q^{63} +(-5.57984 + 5.73283i) q^{64} +(5.73240 - 2.38586i) q^{65} +(-3.80276 + 2.07584i) q^{66} +(-1.31873 - 0.208866i) q^{67} +(10.5454 + 4.63827i) q^{68} +(3.98487 + 5.48470i) q^{69} +(5.63705 + 6.21102i) q^{70} +(7.46718 - 10.2777i) q^{71} +(1.85142 + 2.13828i) q^{72} +(-3.04977 + 1.55394i) q^{73} +(7.60576 - 1.42738i) q^{74} +(-1.56124 - 4.75000i) q^{75} +(3.28432 + 8.44202i) q^{76} +(-3.68898 - 7.24004i) q^{77} +(1.31919 + 3.69876i) q^{78} +(-0.348097 - 0.252907i) q^{79} +(3.07583 + 8.39877i) q^{80} +(0.809017 - 0.587785i) q^{81} +(5.53951 + 3.78884i) q^{82} +(1.82263 - 11.5076i) q^{83} +(-4.10754 + 3.35699i) q^{84} +(9.77992 - 8.38164i) q^{85} +(0.247389 - 1.91240i) q^{86} +(3.46713 - 6.80462i) q^{87} +(-0.738228 - 8.63339i) q^{88} +(2.37328 + 0.771124i) q^{89} +(3.05127 - 0.830528i) q^{90} +(-7.00472 + 2.27597i) q^{91} +(-13.2498 + 2.87881i) q^{92} +(-1.37605 - 1.37605i) q^{93} +(-12.3196 - 11.6382i) q^{94} +(10.0977 + 0.777436i) q^{95} +(-5.40545 + 1.66765i) q^{96} +(-12.2095 + 1.93379i) q^{97} +(-0.0304912 - 0.0395521i) q^{98} -3.06350 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{8}+O(q^{10}) \) 240 * q + 12 * q^8	\( 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) \) 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Introduction

L-functions

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