LMFDB - Embedded newform 425.2.p.a.16.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(16,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("425.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.p (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$42$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			16.9
Character	$\chi$	$=$	425.16
Dual form			425.2.p.a.186.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.46623 - 1.06528i) q^{2} +(-0.575810 + 0.187092i) q^{3} +(0.396985 + 1.22179i) q^{4} +(-0.705078 + 2.12200i) q^{5} +(1.04358 + 0.339079i) q^{6} -1.66418i q^{7} +(-0.400621 + 1.23299i) q^{8} +(-2.13050 + 1.54790i) q^{9} +(3.29433 - 2.36024i) q^{10} +(3.37012 - 4.63857i) q^{11} +(-0.457176 - 0.629248i) q^{12} +(-3.83935 + 2.78945i) q^{13} +(-1.77282 + 2.44008i) q^{14} +(0.00898224 - 1.35378i) q^{15} +(3.97952 - 2.89129i) q^{16} +(3.74605 + 1.72254i) q^{17} +4.77276 q^{18} +(2.15112 - 6.62047i) q^{19} +(-2.87255 - 0.0190592i) q^{20} +(0.311354 + 0.958249i) q^{21} +(-9.88278 + 3.21111i) q^{22} +(2.64857 - 3.64544i) q^{23} -0.784918i q^{24} +(-4.00573 - 2.99234i) q^{25} +8.60095 q^{26} +(2.00477 - 2.75933i) q^{27} +(2.03328 - 0.660654i) q^{28} +(4.86813 - 1.58175i) q^{29} +(-1.45533 + 1.97539i) q^{30} +(-3.69524 - 1.20065i) q^{31} -6.32208 q^{32} +(-1.07271 + 3.30146i) q^{33} +(-3.65760 - 6.51624i) q^{34} +(3.53138 + 1.17337i) q^{35} +(-2.73699 - 1.98854i) q^{36} +(-1.82114 - 2.50659i) q^{37} +(-10.2067 + 7.41561i) q^{38} +(1.68885 - 2.32451i) q^{39} +(-2.33392 - 1.71947i) q^{40} +(-0.846857 - 1.16560i) q^{41} +(0.564288 - 1.73670i) q^{42} -3.58696 q^{43} +(7.00527 + 2.27615i) q^{44} +(-1.78247 - 5.61229i) q^{45} +(-7.76685 + 2.52360i) q^{46} +(-3.96832 - 12.2132i) q^{47} +(-1.75051 + 2.40937i) q^{48} +4.23051 q^{49} +(2.68565 + 8.65471i) q^{50} +(-2.47928 - 0.290997i) q^{51} +(-4.93231 - 3.58353i) q^{52} +(1.40319 + 4.31857i) q^{53} +(-5.87893 + 1.91018i) q^{54} +(7.46684 + 10.4219i) q^{55} +(2.05191 + 0.666705i) q^{56} +4.21459i q^{57} +(-8.82284 - 2.86671i) q^{58} +(4.67053 - 3.39334i) q^{59} +(1.65761 - 0.526456i) q^{60} +(-2.65651 + 3.65638i) q^{61} +(4.13905 + 5.69691i) q^{62} +(2.57598 + 3.54553i) q^{63} +(1.31061 + 0.952216i) q^{64} +(-3.21217 - 10.1139i) q^{65} +(5.08983 - 3.69797i) q^{66} +(0.0828261 - 0.254913i) q^{67} +(-0.617459 + 5.26072i) q^{68} +(-0.843038 + 2.59461i) q^{69} +(-3.92786 - 5.48236i) q^{70} +(5.14108 - 1.67044i) q^{71} +(-1.05501 - 3.24700i) q^{72} +(7.81942 - 10.7625i) q^{73} +5.61528i q^{74} +(2.86638 + 0.973580i) q^{75} +8.94282 q^{76} +(-7.71941 - 5.60848i) q^{77} +(-4.95251 + 1.60917i) q^{78} +(-6.19679 + 2.01346i) q^{79} +(3.32944 + 10.4831i) q^{80} +(1.80322 - 5.54973i) q^{81} +2.61118i q^{82} +(0.520823 - 1.60293i) q^{83} +(-1.04718 + 0.760821i) q^{84} +(-6.29647 + 6.73458i) q^{85} +(5.25932 + 3.82112i) q^{86} +(-2.50718 + 1.82158i) q^{87} +(4.36915 + 6.01362i) q^{88} +(11.0918 + 8.05863i) q^{89} +(-3.36516 + 10.1278i) q^{90} +(4.64215 + 6.38937i) q^{91} +(5.50542 + 1.78882i) q^{92} +2.35238 q^{93} +(-7.19206 + 22.1349i) q^{94} +(12.5319 + 9.23261i) q^{95} +(3.64032 - 1.18281i) q^{96} +(3.20022 - 1.03981i) q^{97} +(-6.20293 - 4.50669i) q^{98} +15.0991i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 8 q^{2} - 44 q^{4} - 4 q^{8} + 28 q^{9} - 18 q^{13} - 10 q^{15} - 28 q^{16} + 2 q^{17} - 60 q^{18} - 8 q^{19} + 32 q^{21} + 6 q^{25} + 52 q^{26} - 54 q^{30} + 44 q^{32} - 24 q^{33} + 26 q^{35} + 34 q^{36}+ \cdots - 36 q^{98}+O(q^{100}) $ 168 * q - 8 * q^2 - 44 * q^4 - 4 * q^8 + 28 * q^9 - 18 * q^13 - 10 * q^15 - 28 * q^16 + 2 * q^17 - 60 * q^18 - 8 * q^19 + 32 * q^21 + 6 * q^25 + 52 * q^26 - 54 * q^30 + 44 * q^32 - 24 * q^33 + 26 * q^35 + 34 * q^36 - 18 * q^38 + 80 * q^42 - 8 * q^43 - 40 * q^47 - 84 * q^49 - 82 * q^50 - 36 * q^51 - 30 * q^52 - 42 * q^53 - 18 * q^55 - 18 * q^59 + 28 * q^60 - 16 * q^64 - 140 * q^66 - 62 * q^67 + 144 * q^68 + 44 * q^69 + 4 * q^70 - 6 * q^72 + 72 * q^76 + 48 * q^77 - 28 * q^81 - 14 * q^83 + 24 * q^84 + 62 * q^85 + 82 * q^86 + 48 * q^87 + 90 * q^89 - 224 * q^93 + 26 * q^94 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$

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 $

$2$	−1.46623	−	1.06528i	−1.03678	−	0.753268i	−0.0671294	−	0.997744i	$-0.521384\pi$
$2$	−1.46623	−	1.06528i	−1.03678	−	0.753268i	−0.969655	+	0.244476i	$0.921384\pi$
$3$	−0.575810	+	0.187092i	−0.332444	+	0.108018i	−0.470483	−	0.882409i	$-0.655920\pi$
$3$	−0.575810	+	0.187092i	−0.332444	+	0.108018i	0.138039	+	0.990427i	$0.455920\pi$
$4$	0.396985	+	1.22179i	0.198493	+	0.610897i
$5$	−0.705078	+	2.12200i	−0.315320	+	0.948985i
$5$	−0.705078	+	2.12200i	−0.315320	+	0.948985i
$6$	1.04358	+	0.339079i	0.426039	+	0.138428i
$7$		−	1.66418i		−	0.629000i	−0.949257	−	0.314500i	$-0.898163\pi$
$7$		−	1.66418i		−	0.629000i	0.949257	−	0.314500i	$-0.101837\pi$
$8$	−0.400621	+	1.23299i	−0.141641	+	0.435926i
$9$	−2.13050	+	1.54790i	−0.710166	+	0.515966i
$10$	3.29433	−	2.36024i	1.04176	−	0.746373i
$11$	3.37012	−	4.63857i	1.01613	−	1.39858i	0.101248	−	0.994861i	$-0.467717\pi$
$11$	3.37012	−	4.63857i	1.01613	−	1.39858i	0.914882	−	0.403721i	$-0.132283\pi$
$12$	−0.457176	−	0.629248i	−0.131975	−	0.181648i
$13$	−3.83935	+	2.78945i	−1.06485	+	0.773655i	−0.974979	−	0.222299i	$-0.928644\pi$
$13$	−3.83935	+	2.78945i	−1.06485	+	0.773655i	−0.0898664	+	0.995954i	$0.528644\pi$
$14$	−1.77282	+	2.44008i	−0.473806	+	0.652138i
$15$	0.00898224	−	1.35378i	0.00231920	−	0.349544i
$16$	3.97952	−	2.89129i	0.994881	−	0.722823i
$17$	3.74605	+	1.72254i	0.908550	+	0.417776i
$17$	3.74605	+	1.72254i	0.908550	+	0.417776i
$18$	4.77276			1.12495
$19$	2.15112	−	6.62047i	0.493501	−	1.51884i	−0.325779	−	0.945446i	$-0.605627\pi$
$19$	2.15112	−	6.62047i	0.493501	−	1.51884i	0.819280	−	0.573394i	$-0.194373\pi$
$20$	−2.87255	−	0.0190592i	−0.642321	−	0.00426176i
$21$	0.311354	+	0.958249i	0.0679430	+	0.209107i
$22$	−9.88278	+	3.21111i	−2.10702	+	0.684611i
$23$	2.64857	−	3.64544i	0.552265	−	0.760127i	−0.438053	−	0.898949i	$-0.644332\pi$
$23$	2.64857	−	3.64544i	0.552265	−	0.760127i	0.990317	+	0.138822i	$0.0443316\pi$
$24$		−	0.784918i		−	0.160221i
$25$	−4.00573	−	2.99234i	−0.801146	−	0.598469i
$26$	8.60095			1.68678
$27$	2.00477	−	2.75933i	0.385818	−	0.531034i
$28$	2.03328	−	0.660654i	0.384254	−	0.124852i
$29$	4.86813	−	1.58175i	0.903990	−	0.293724i	0.180107	−	0.983647i	$-0.442356\pi$
$29$	4.86813	−	1.58175i	0.903990	−	0.293724i	0.723883	+	0.689923i	$0.242356\pi$
$30$	−1.45533	+	1.97539i	−0.265705	+	0.360655i
$31$	−3.69524	−	1.20065i	−0.663684	−	0.215644i	−0.0422458	−	0.999107i	$-0.513451\pi$
$31$	−3.69524	−	1.20065i	−0.663684	−	0.215644i	−0.621438	+	0.783463i	$0.713451\pi$
$32$	−6.32208			−1.11760
$33$	−1.07271	+	3.30146i	−0.186735	+	0.574710i
$34$	−3.65760	−	6.51624i	−0.627273	−	1.11753i
$35$	3.53138	+	1.17337i	0.596912	+	0.198336i
$36$	−2.73699	−	1.98854i	−0.456165	−	0.331423i
$37$	−1.82114	−	2.50659i	−0.299394	−	0.412080i	0.632643	−	0.774444i	$-0.281970\pi$
$37$	−1.82114	−	2.50659i	−0.299394	−	0.412080i	−0.932037	+	0.362363i	$0.881970\pi$
$38$	−10.2067	+	7.41561i	−1.65575	+	1.20297i
$39$	1.68885	−	2.32451i	0.270433	−	0.372219i
$40$	−2.33392	−	1.71947i	−0.369025	−	0.271872i
$41$	−0.846857	−	1.16560i	−0.132257	−	0.182036i	0.737752	−	0.675072i	$-0.235887\pi$
$41$	−0.846857	−	1.16560i	−0.132257	−	0.182036i	−0.870009	+	0.493036i	$0.835887\pi$
$42$	0.564288	−	1.73670i	0.0870715	−	0.267978i
$43$	−3.58696			−0.547006			−0.273503	−	0.961871i	$-0.588182\pi$
$43$	−3.58696			−0.547006			−0.273503	+	0.961871i	$0.588182\pi$
$44$	7.00527	+	2.27615i	1.05608	+	0.343143i
$45$	−1.78247	−	5.61229i	−0.265714	−	0.836631i
$46$	−7.76685	+	2.52360i	−1.14516	+	0.372085i
$47$	−3.96832	−	12.2132i	−0.578840	−	1.78149i	−0.622716	−	0.782448i	$-0.713971\pi$
$47$	−3.96832	−	12.2132i	−0.578840	−	1.78149i	0.0438759	−	0.999037i	$-0.486029\pi$
$48$	−1.75051	+	2.40937i	−0.252664	+	0.347763i
$49$	4.23051			0.604359
$50$	2.68565	+	8.65471i	0.379809	+	1.22396i
$51$	−2.47928	−	0.290997i	−0.347169	−	0.0407478i
$52$	−4.93231	−	3.58353i	−0.683988	−	0.496946i
$53$	1.40319	+	4.31857i	0.192743	+	0.593202i	0.999996	+	0.00299550i	$0.000953498\pi$
$53$	1.40319	+	4.31857i	0.192743	+	0.593202i	−0.807253	+	0.590206i	$0.799047\pi$
$54$	−5.87893	+	1.91018i	−0.800021	+	0.259943i
$55$	7.46684	+	10.4219i	1.00683	+	1.40529i
$56$	2.05191	+	0.666705i	0.274198	+	0.0890922i
$57$			4.21459i			0.558236i
$58$	−8.82284	−	2.86671i	−1.15850	−	0.376418i
$59$	4.67053	−	3.39334i	0.608051	−	0.441775i	−0.240677	−	0.970605i	$-0.577369\pi$
$59$	4.67053	−	3.39334i	0.608051	−	0.441775i	0.848727	+	0.528831i	$0.177369\pi$
$60$	1.65761	−	0.526456i	0.213996	−	0.0679652i
$61$	−2.65651	+	3.65638i	−0.340132	+	0.468151i	−0.944480	−	0.328569i	$-0.893434\pi$
$61$	−2.65651	+	3.65638i	−0.340132	+	0.468151i	0.604348	+	0.796720i	$0.293434\pi$
$62$	4.13905	+	5.69691i	0.525660	+	0.723508i
$63$	2.57598	+	3.54553i	0.324542	+	0.446694i
$64$	1.31061	+	0.952216i	0.163827	+	0.119027i
$65$	−3.21217	−	10.1139i	−0.398420	−	1.25447i
$66$	5.08983	−	3.69797i	0.626514	−	0.455189i
$67$	0.0828261	−	0.254913i	0.0101188	−	0.0311425i	−0.945870	−	0.324547i	$-0.894788\pi$
$67$	0.0828261	−	0.254913i	0.0101188	−	0.0311425i	0.955988	+	0.293404i	$0.0947882\pi$
$68$	−0.617459	+	5.26072i	−0.0748779	+	0.637956i
$69$	−0.843038	+	2.59461i	−0.101490	+	0.312354i
$70$	−3.92786	−	5.48236i	−0.469468	−	0.655267i
$71$	5.14108	−	1.67044i	0.610134	−	0.198245i	0.0123791	−	0.999923i	$-0.496060\pi$
$71$	5.14108	−	1.67044i	0.610134	−	0.198245i	0.597755	+	0.801679i	$0.296060\pi$
$72$	−1.05501	−	3.24700i	−0.124334	−	0.382662i
$73$	7.81942	−	10.7625i	0.915193	−	1.25966i	−0.0501683	−	0.998741i	$-0.515976\pi$
$73$	7.81942	−	10.7625i	0.915193	−	1.25966i	0.965362	−	0.260915i	$-0.0840242\pi$
$74$			5.61528i			0.652763i
$75$	2.86638	+	0.973580i	0.330981	+	0.112419i
$76$	8.94282			1.02581
$77$	−7.71941	−	5.60848i	−0.879708	−	0.639146i
$78$	−4.95251	+	1.60917i	−0.560761	+	0.182202i
$79$	−6.19679	+	2.01346i	−0.697194	+	0.226532i	−0.636107	−	0.771600i	$-0.719457\pi$
$79$	−6.19679	+	2.01346i	−0.697194	+	0.226532i	−0.0610863	+	0.998132i	$0.519457\pi$
$80$	3.32944	+	10.4831i	0.372243	+	1.17205i
$81$	1.80322	−	5.54973i	0.200357	−	0.616636i
$82$			2.61118i			0.288357i
$83$	0.520823	−	1.60293i	0.0571678	−	0.175944i	−0.918395	−	0.395664i	$-0.870514\pi$
$83$	0.520823	−	1.60293i	0.0571678	−	0.175944i	0.975563	+	0.219720i	$0.0705144\pi$
$84$	−1.04718	+	0.760821i	−0.114257	+	0.0830124i
$85$	−6.29647	+	6.73458i	−0.682948	+	0.730467i
$86$	5.25932	+	3.82112i	0.567127	+	0.412042i
$87$	−2.50718	+	1.82158i	−0.268798	+	0.195293i
$88$	4.36915	+	6.01362i	0.465753	+	0.641055i
$89$	11.0918	+	8.05863i	1.17572	+	0.854213i	0.991683	−	0.128705i	$-0.0410821\pi$
$89$	11.0918	+	8.05863i	1.17572	+	0.854213i	0.184041	+	0.982919i	$0.441082\pi$
$90$	−3.36516	+	10.1278i	−0.354719	+	1.06756i
$91$	4.64215	+	6.38937i	0.486629	+	0.669788i
$92$	5.50542	+	1.78882i	0.573980	+	0.186497i
$93$	2.35238			0.243931
$94$	−7.19206	+	22.1349i	−0.741804	+	2.28304i
$95$	12.5319	+	9.23261i	1.28575	+	0.947246i
$96$	3.64032	−	1.18281i	0.371538	−	0.120720i
$97$	3.20022	−	1.03981i	0.324933	−	0.105577i	−0.142008	−	0.989865i	$-0.545356\pi$
$97$	3.20022	−	1.03981i	0.324933	−	0.105577i	0.466941	+	0.884288i	$0.345356\pi$
$98$	−6.20293	−	4.50669i	−0.626590	−	0.455244i
$99$			15.0991i			1.51751i
$100$	2.06581	−	6.08210i	0.206581	−	0.608210i
$101$	1.84357			0.183442			0.0917212	−	0.995785i	$-0.470763\pi$
$101$	1.84357			0.183442			0.0917212	+	0.995785i	$0.470763\pi$
$102$	3.32522	+	3.06781i	0.329245	+	0.303758i
$103$	2.92450	+	9.00069i	0.288160	+	0.886864i	0.985434	+	0.170060i	$0.0543961\pi$
$103$	2.92450	+	9.00069i	0.288160	+	0.886864i	−0.697274	+	0.716805i	$0.745604\pi$
$104$	−1.90123	−	5.85138i	−0.186431	−	0.573775i
$105$	−2.25293	−	0.0149480i	−0.219863	−	0.00145878i
$106$	2.54309	−	7.82683i	0.247007	−	0.760209i
$107$			5.05646i			0.488827i	0.969671	+	0.244413i	$0.0785954\pi$
$107$			5.05646i			0.488827i	−0.969671	+	0.244413i	$0.921405\pi$
$108$	4.16720	+	1.35401i	0.400989	+	0.130289i
$109$	0.992250	+	1.36571i	0.0950403	+	0.130812i	0.853889	−	0.520455i	$-0.174238\pi$
$109$	0.992250	+	1.36571i	0.0950403	+	0.130812i	−0.758849	+	0.651267i	$0.774238\pi$
$110$	0.154165	−	23.2353i	0.0146990	−	2.21540i
$111$	1.51759	+	1.10260i	0.144044	+	0.104654i
$112$	−4.81163	−	6.62264i	−0.454656	−	0.625780i
$113$	3.48151	+	4.79189i	0.327513	+	0.450783i	0.940742	−	0.339122i	$-0.110130\pi$
$113$	3.48151	+	4.79189i	0.327513	+	0.450783i	−0.613229	+	0.789905i	$0.710130\pi$
$114$	4.48972	−	6.17957i	0.420501	−	0.578770i
$115$	5.86817	+	8.19057i	0.547209	+	0.763775i
$116$	3.86515	+	5.31993i	0.358870	+	0.493943i
$117$	3.86195	−	11.8858i	0.357037	−	1.09885i
$118$	−10.4630			−0.963193
$119$	2.86660	−	6.23409i	0.262781	−	0.571478i
$120$	1.66559	+	0.553428i	0.152047	+	0.0505208i
$121$	−6.75946	−	20.8035i	−0.614497	−	1.89123i
$122$	7.79014	−	2.53117i	0.705287	−	0.229161i
$123$	0.705703	+	0.512723i	0.0636311	+	0.0462307i
$124$		−	4.99146i		−	0.448246i
$125$	9.17409	−	6.39031i	0.820556	−	0.571567i
$126$		−	7.94272i		−	0.707593i
$127$	−6.06382	−	4.40562i	−0.538077	−	0.390936i	0.285294	−	0.958440i	$-0.407909\pi$
$127$	−6.06382	−	4.40562i	−0.538077	−	0.390936i	−0.823370	+	0.567505i	$0.807909\pi$
$128$	2.99998	+	9.23298i	0.265163	+	0.816087i
$129$	2.06540	−	0.671090i	0.181849	−	0.0590862i
$130$	−6.06434	+	18.2512i	−0.531877	+	1.60073i
$131$	7.60024	+	2.46947i	0.664036	+	0.215758i	0.621593	−	0.783341i	$-0.286486\pi$
$131$	7.60024	+	2.46947i	0.664036	+	0.215758i	0.0424430	+	0.999099i	$0.486486\pi$
$132$	−4.45955			−0.388154
$133$	−11.0176	−	3.57985i	−0.955350	−	0.310412i
$134$	−0.392996	+	0.285529i	−0.0339497	+	0.0246659i
$135$	4.44177	+	6.19966i	0.382287	+	0.533582i
$136$	−3.62461	+	3.92874i	−0.310808	+	0.336887i
$137$	−7.51075	+	5.45688i	−0.641687	+	0.466213i	−0.860429	−	0.509570i	$-0.829805\pi$
$137$	−7.51075	+	5.45688i	−0.641687	+	0.466213i	0.218743	+	0.975783i	$0.429805\pi$
$138$	4.00008	−	2.90623i	0.340509	−	0.247395i
$139$	7.46292	−	10.2718i	0.632997	−	0.871245i	−0.365221	−	0.930921i	$-0.619007\pi$
$139$	7.46292	−	10.2718i	0.632997	−	0.871245i	0.998218	+	0.0596756i	$0.0190066\pi$
$140$	−0.0317179	+	4.78043i	−0.00268065	+	0.404020i
$141$	4.57000	+	6.29006i	0.384863	+	0.529719i
$142$	−9.31752	−	3.02745i	−0.781909	−	0.254058i
$143$			27.2099i			2.27541i
$144$	−4.00294	+	12.3198i	−0.333579	+	1.02665i
$145$	−0.0759396	+	11.4454i	−0.00630644	+	0.950490i
$146$	−22.9302	+	7.45047i	−1.89772	+	0.616606i
$147$	−2.43597	+	0.791494i	−0.200915	+	0.0652814i
$148$	2.33957	−	3.22014i	0.192311	−	0.264694i
$149$	−13.3763			−1.09583			−0.547913	−	0.836535i	$-0.684577\pi$
$149$	−13.3763			−1.09583			−0.547913	+	0.836535i	$0.684577\pi$
$150$	−3.16565	−	4.48100i	−0.258474	−	0.365872i
$151$	−20.9406			−1.70413			−0.852063	−	0.523440i	$-0.824649\pi$
$151$	−20.9406			−1.70413			−0.852063	+	0.523440i	$0.824649\pi$
$152$	7.30116	+	5.30460i	0.592202	+	0.430260i
$153$	−10.6473	+	2.12864i	−0.860779	+	0.172090i
$154$	5.34386	+	16.4467i	0.430620	+	1.32531i
$155$	5.15321	−	6.99472i	0.413916	−	0.561829i
$156$	3.51052	+	1.14064i	0.281066	+	0.0913240i
$157$	16.6071			1.32539			0.662696	−	0.748888i	$-0.269412\pi$
$157$	16.6071			1.32539			0.662696	+	0.748888i	$0.269412\pi$
$158$	11.2309	+	3.64913i	0.893479	+	0.290309i
$159$	−1.61594	−	2.22415i	−0.128152	−	0.176387i
$160$	4.45756	−	13.4154i	0.352401	−	1.06058i
$161$	−6.06666	−	4.40769i	−0.478120	−	0.347375i
$162$	−8.55596	+	6.21627i	−0.672220	+	0.488396i
$163$	−11.1303	−	15.3196i	−0.871795	−	1.19992i	−0.978627	−	0.205645i	$-0.934071\pi$
$163$	−11.1303	−	15.3196i	−0.871795	−	1.19992i	0.106832	−	0.994277i	$-0.465929\pi$
$164$	1.08793	−	1.49741i	0.0849533	−	0.116928i
$165$	−6.24933	−	4.60407i	−0.486510	−	0.358426i
$166$	−2.47122	+	1.79545i	−0.191804	+	0.139354i
$167$	−6.49280	−	2.10964i	−0.502428	−	0.163249i	0.0468277	−	0.998903i	$-0.485089\pi$
$167$	−6.49280	−	2.10964i	−0.502428	−	0.163249i	−0.549256	+	0.835654i	$0.685089\pi$
$168$	−1.30624			−0.100779
$169$	2.94236	−	9.05566i	0.226336	−	0.696589i
$170$	16.4063	−	3.16696i	1.25831	−	0.242895i
$171$	5.66485	+	17.4346i	0.433202	+	1.33326i
$172$	−1.42397	−	4.38252i	−0.108577	−	0.334164i
$173$	8.44177	−	11.6191i	0.641816	−	0.883383i	−0.356895	−	0.934144i	$-0.616165\pi$
$173$	8.44177	−	11.6191i	0.641816	−	0.883383i	0.998711	+	0.0507610i	$0.0161647\pi$
$174$	5.61661			0.425794
$175$	−4.97979	+	6.66625i	−0.376437	+	0.503921i
$176$		−	28.2033i		−	2.12591i
$177$	−2.05447	+	2.82773i	−0.154423	+	0.212545i
$178$	−7.67840	−	23.6317i	−0.575521	−	1.77127i
$179$	2.47868	+	7.62858i	0.185265	+	0.570187i	0.999953	−	0.00971289i	$-0.00309176\pi$
$179$	2.47868	+	7.62858i	0.185265	+	0.570187i	−0.814688	+	0.579900i	$0.803092\pi$
$180$	6.14946	−	4.40580i	0.458354	−	0.328389i
$181$	−25.0288	−	8.13236i	−1.86038	−	0.604474i	−0.994566	−	0.104104i	$-0.966802\pi$
$181$	−25.0288	−	8.13236i	−1.86038	−	0.604474i	−0.865812	−	0.500369i	$-0.833198\pi$
$182$		−	14.3135i		−	1.06099i
$183$	0.845567	−	2.60239i	0.0625061	−	0.192374i
$184$	3.43371	+	4.72609i	0.253136	+	0.348412i
$185$	6.60301	−	2.09712i	0.485463	−	0.154183i
$186$	−3.44915	−	2.50595i	−0.252904	−	0.183745i
$187$	20.6147	−	11.5712i	1.50750	−	0.846167i
$188$	13.3467	−	9.69696i	0.973409	−	0.707223i
$189$	−4.59202	−	3.33630i	−0.334020	−	0.242680i
$190$	−8.53937	−	26.8872i	−0.619511	−	1.95060i
$191$	−12.0538	+	8.75759i	−0.872182	+	0.633677i	−0.931171	−	0.364582i	$-0.881212\pi$
$191$	−12.0538	+	8.75759i	−0.872182	+	0.633677i	0.0589899	+	0.998259i	$0.481212\pi$
$192$	−0.932815	−	0.303090i	−0.0673201	−	0.0218736i
$193$			11.9941i			0.863354i	0.902028	+	0.431677i	$0.142078\pi$
$193$			11.9941i			0.863354i	−0.902028	+	0.431677i	$0.857922\pi$
$194$	−5.79997	−	1.88453i	−0.416414	−	0.135301i
$195$	3.74182	+	5.22269i	0.267957	+	0.374005i
$196$	1.67945	+	5.16882i	0.119961	+	0.369201i
$197$	−2.31911	+	0.753524i	−0.165230	+	0.0536863i	−0.390464	−	0.920618i	$-0.627685\pi$
$197$	−2.31911	+	0.753524i	−0.165230	+	0.0536863i	0.225234	+	0.974305i	$0.427685\pi$
$198$	16.0848	−	22.1388i	1.14309	−	1.57333i
$199$			8.64410i			0.612764i	0.951909	+	0.306382i	$0.0991185\pi$
$199$			8.64410i			0.612764i	−0.951909	+	0.306382i	$0.900881\pi$
$200$	5.29430	−	3.74021i	0.374363	−	0.264473i
$201$			0.162277i			0.0114462i
$202$	−2.70311	−	1.96393i	−0.190190	−	0.138181i
$203$	−2.63232	−	8.10144i	−0.184752	−	0.568610i
$204$	−0.628699	−	3.14470i	−0.0440177	−	0.220173i
$205$	3.07050	−	0.975190i	0.214453	−	0.0681102i
$206$	5.30027	−	16.3125i	0.369287	−	1.13655i
$207$			11.8663i			0.824766i
$208$	−7.21367	+	22.2014i	−0.500178	+	1.53939i
$209$	−23.4600	−	32.2899i	−1.62276	−	2.23354i
$210$	3.28740	+	2.42192i	0.226852	+	0.167129i
$211$	13.6054	−	18.7262i	0.936631	−	1.28916i	−0.0205850	−	0.999788i	$-0.506553\pi$
$211$	13.6054	−	18.7262i	0.936631	−	1.28916i	0.957216	−	0.289374i	$-0.0934471\pi$
$212$	−4.71936	+	3.42882i	−0.324127	+	0.235492i
$213$	−2.64776	+	1.92371i	−0.181421	+	0.131810i
$214$	5.38656	−	7.41396i	0.368218	−	0.506808i
$215$	2.52908	−	7.61150i	0.172482	−	0.519100i
$216$	2.59906	+	3.57730i	0.176844	+	0.243405i
$217$	−1.99810	+	6.14953i	−0.135640	+	0.417457i
$218$		−	3.05948i		−	0.207214i
$219$	−2.48892	+	7.66010i	−0.168185	+	0.517622i
$220$	−9.76924	+	13.2603i	−0.658642	+	0.894009i
$221$	−19.1873	+	3.83600i	−1.29068	+	0.258038i
$222$	−1.05057	−	3.23333i	−0.0705098	−	0.217007i
$223$	−17.8716	−	12.9845i	−1.19677	−	0.869505i	−0.202807	−	0.979219i	$-0.565007\pi$
$223$	−17.8716	−	12.9845i	−1.19677	−	0.869505i	−0.993963	+	0.109714i	$0.965007\pi$
$224$			10.5211i			0.702969i
$225$	13.1660	+	0.174719i	0.877736	+	0.0116480i
$226$		−	10.7348i		−	0.714070i
$227$	5.08436	−	6.99802i	0.337461	−	0.464475i	−0.606237	−	0.795284i	$-0.707322\pi$
$227$	5.08436	−	6.99802i	0.337461	−	0.464475i	0.943698	+	0.330809i	$0.107322\pi$
$228$	−5.14936	+	1.67313i	−0.341025	+	0.110806i
$229$	2.29625	+	7.06712i	0.151740	+	0.467008i	0.997816	−	0.0660542i	$-0.0210410\pi$
$229$	2.29625	+	7.06712i	0.151740	+	0.467008i	−0.846076	+	0.533063i	$0.821041\pi$
$230$	0.121158	−	18.2606i	0.00798890	−	1.20407i
$231$	5.49421	+	1.78518i	0.361493	+	0.117456i
$232$			6.63603i			0.435676i
$233$	−13.9310	−	4.52646i	−0.912652	−	0.296539i	−0.185203	−	0.982700i	$-0.559294\pi$
$233$	−13.9310	−	4.52646i	−0.912652	−	0.296539i	−0.727449	+	0.686162i	$0.759294\pi$
$234$	−18.3243	+	13.3134i	−1.19790	+	0.870323i
$235$	28.7144	+	0.190518i	1.87312	+	0.0124281i
$236$	6.00009	+	4.35932i	0.390573	+	0.283768i
$237$	3.19147	−	2.31874i	0.207308	−	0.150618i
$238$	−10.8442	+	6.08690i	−0.702924	+	0.394555i
$239$	−13.1264	−	9.53686i	−0.849074	−	0.616888i	0.0758165	−	0.997122i	$-0.475844\pi$
$239$	−13.1264	−	9.53686i	−0.849074	−	0.616888i	−0.924891	+	0.380233i	$0.875844\pi$
$240$	−3.87843	−	5.41337i	−0.250352	−	0.349431i
$241$	6.58377	+	9.06178i	0.424098	+	0.583720i	0.966586	−	0.256343i	$-0.0825177\pi$
$241$	6.58377	+	9.06178i	0.424098	+	0.583720i	−0.542488	+	0.840063i	$0.682518\pi$
$242$	−12.2506	+	37.7035i	−0.787500	+	2.42367i
$243$			13.7651i			0.883032i
$244$	−5.52194	−	1.79419i	−0.353506	−	0.114861i
$245$	−2.98284	+	8.97713i	−0.190567	+	0.573528i
$246$	−0.488531	−	1.50354i	−0.0311476	−	0.0958625i
$247$	10.2086	+	31.4188i	0.649556	+	1.99913i
$248$	2.96078	−	4.07517i	0.188010	−	0.258773i
$249$			1.02042i			0.0646667i
$250$	−20.2589	−	0.403296i	−1.28128	−	0.0255067i
$251$	−12.7255			−0.803228			−0.401614	−	0.915809i	$-0.631551\pi$
$251$	−12.7255			−0.803228			−0.401614	+	0.915809i	$0.631551\pi$
$252$	−3.30928	+	4.55483i	−0.208465	+	0.286928i
$253$	−7.98365	−	24.5712i	−0.501928	−	1.54478i
$254$	4.19775	+	12.9193i	0.263390	+	0.810632i
$255$	2.36558	−	5.05585i	0.148138	−	0.316610i
$256$	6.43827	−	19.8150i	0.402392	−	1.23844i
$257$	2.88442			0.179925			0.0899627	−	0.995945i	$-0.471325\pi$
$257$	2.88442			0.179925			0.0899627	+	0.995945i	$0.471325\pi$
$258$	−3.74327	−	1.21626i	−0.233046	−	0.0757211i
$259$	−4.17141	+	3.03070i	−0.259199	+	0.188319i
$260$	11.0819	−	7.93966i	0.687270	−	0.492397i
$261$	−7.92316	+	10.9053i	−0.490431	+	0.675021i
$262$	−8.51305	−	11.7172i	−0.525938	−	0.723892i
$263$	10.3363	−	7.50973i	0.637361	−	0.463070i	−0.221582	−	0.975142i	$-0.571122\pi$
$263$	10.3363	−	7.50973i	0.637361	−	0.463070i	0.858942	+	0.512072i	$0.171122\pi$
$264$	−3.64090	−	2.64527i	−0.224082	−	0.162805i
$265$	−10.1533	−	0.0673668i	−0.623715	−	0.00413831i
$266$	12.3409	+	16.9858i	0.756669	+	1.04147i
$267$	−7.89444	−	2.56506i	−0.483132	−	0.156979i
$268$	0.344332			0.0210334
$269$	19.2277	+	6.24747i	1.17234	+	0.380915i	0.829514	−	0.558486i	$-0.188618\pi$
$269$	19.2277	+	6.24747i	1.17234	+	0.380915i	0.342821	+	0.939401i	$0.388618\pi$
$270$	0.0917074	−	13.8219i	0.00558113	−	0.841174i
$271$	1.06862	+	3.28888i	0.0649141	+	0.199785i	0.978253	−	0.207415i	$-0.0665051\pi$
$271$	1.06862	+	3.28888i	0.0649141	+	0.199785i	−0.913339	+	0.407200i	$0.866505\pi$
$272$	19.8878	−	3.97605i	1.20588	−	0.241084i
$273$	−3.86839	−	2.81055i	−0.234126	−	0.170102i
$274$	16.8256			1.01647
$275$	−27.3800	+	8.49632i	−1.65108	+	0.512347i
$276$	−3.50475			−0.210961
$277$	18.6837	−	25.7159i	1.12260	−	1.54512i	0.321175	−	0.947020i	$-0.395922\pi$
$277$	18.6837	−	25.7159i	1.12260	−	1.54512i	0.801421	−	0.598101i	$-0.204078\pi$
$278$	−21.8848	+	7.11080i	−1.31256	+	0.426477i
$279$	9.73118	−	3.16185i	0.582591	−	0.189295i
$280$	−2.86150	+	3.88406i	−0.171007	+	0.232117i
$281$	−8.21939	+	25.2967i	−0.490327	+	1.50907i	0.333786	+	0.942649i	$0.391674\pi$
$281$	−8.21939	+	25.2967i	−0.490327	+	1.50907i	−0.824114	+	0.566424i	$0.808326\pi$
$282$		−	14.0910i		−	0.839110i
$283$	−14.0674	−	4.57077i	−0.836220	−	0.271704i	−0.140557	−	0.990073i	$-0.544889\pi$
$283$	−14.0674	−	4.57077i	−0.836220	−	0.271704i	−0.695663	+	0.718368i	$0.744889\pi$
$284$	4.08187	+	5.61821i	0.242214	+	0.333379i
$285$	−8.94333	−	2.97161i	−0.529757	−	0.176023i
$286$	28.9862	−	39.8961i	1.71399	−	2.35911i
$287$	−1.93976	+	1.40932i	−0.114501	+	0.0831896i
$288$	13.4692	−	9.78594i	0.793679	−	0.576642i
$289$	11.0657	+	12.9054i	0.650926	+	0.759141i
$290$	12.3039	−	16.7008i	0.722512	−	0.980703i
$291$	−1.64818	+	1.19747i	−0.0966178	+	0.0701970i
$292$	16.2538	+	5.28117i	0.951179	+	0.309057i
$293$	12.5555			0.733503			0.366751	−	0.930319i	$-0.380470\pi$
$293$	12.5555			0.733503			0.366751	+	0.930319i	$0.380470\pi$
$294$	4.41487	+	1.43448i	0.257480	+	0.0836604i
$295$	3.90756	+	12.3034i	0.227507	+	0.716332i
$296$	3.82018	−	1.24125i	0.222043	−	0.0721462i
$297$	−6.04304	−	18.5986i	−0.350653	−	1.07920i
$298$	19.6127	+	14.2495i	1.13614	+	0.825451i
$299$			21.3842i			1.23668i
$300$	−0.0516038	+	3.88863i	−0.00297935	+	0.224510i
$301$			5.96933i			0.344067i
$302$	30.7039	+	22.3077i	1.76681	+	1.28366i
$303$	−1.06155	+	0.344918i	−0.0609843	+	0.0198150i
$304$	−10.5813	−	32.5658i	−0.606878	−	1.86778i
$305$	−5.88577	−	8.21514i	−0.337018	−	0.470397i
$306$	17.8790	+	8.22124i	1.02207	+	0.469977i
$307$	10.9995			0.627773			0.313886	−	0.949461i	$-0.398369\pi$
$307$	10.9995			0.627773			0.313886	+	0.949461i	$0.398369\pi$
$308$	3.78792	−	11.6580i	0.215837	−	0.664277i
$309$	−3.36791	−	4.63553i	−0.191594	−	0.263706i
$310$	−15.0072	+	4.76628i	−0.852350	+	0.270706i
$311$	−15.8179	+	21.7715i	−0.896951	+	1.23455i	0.0744800	+	0.997223i	$0.476270\pi$
$311$	−15.8179	+	21.7715i	−0.896951	+	1.23455i	−0.971431	+	0.237324i	$0.923730\pi$
$312$	2.18949	+	3.01358i	0.123956	+	0.170610i
$313$	9.97421	+	13.7283i	0.563776	+	0.775971i	0.991800	−	0.127796i	$-0.0407904\pi$
$313$	9.97421	+	13.7283i	0.563776	+	0.775971i	−0.428025	+	0.903767i	$0.640790\pi$
$314$	−24.3499	−	17.6913i	−1.37415	−	0.998376i
$315$	−9.33986	+	2.96634i	−0.526241	+	0.167134i
$316$	−4.92007	−	6.77190i	−0.276776	−	0.380949i
$317$	0.940404	+	0.305556i	0.0528183	+	0.0171617i	0.335307	−	0.942109i	$-0.391160\pi$
$317$	0.940404	+	0.305556i	0.0528183	+	0.0171617i	−0.282489	+	0.959271i	$0.591160\pi$
$318$			4.98256i			0.279408i
$319$	9.06912	−	27.9119i	0.507773	−	1.56277i
$320$	−2.94468	+	2.10973i	−0.164613	+	0.117937i
$321$	−0.946023	−	2.91156i	−0.0528019	−	0.162507i
$322$	4.19972	+	12.9254i	0.234041	+	0.720305i
$323$	19.4622	−	21.0952i	1.08291	−	1.17377i
$324$	7.49647			0.416471
$325$	23.7264	+	0.314860i	1.31611	+	0.0174653i
$326$			34.3191i			1.90076i
$327$	−0.826861	−	0.600750i	−0.0457255	−	0.0332215i
$328$	1.77644	−	0.577199i	0.0980873	−	0.0318705i
$329$	−20.3250	+	6.60400i	−1.12055	+	0.364090i
$330$	4.25836	+	13.4079i	0.234415	+	0.738083i
$331$	−0.401373	+	1.23530i	−0.0220614	+	0.0678982i	−0.961481	−	0.274871i	$-0.911365\pi$
$331$	−0.401373	+	1.23530i	−0.0220614	+	0.0678982i	0.939420	+	0.342769i	$0.111365\pi$
$332$	2.16521			0.118831
$333$	7.75988	+	2.52134i	0.425239	+	0.138168i
$334$	7.27262	+	10.0099i	0.397940	+	0.547717i
$335$	0.482525	+	0.355490i	0.0263631	+	0.0194225i
$336$	4.00962	+	2.91316i	0.218743	+	0.158926i
$337$	−6.83893	−	9.41298i	−0.372540	−	0.512757i	0.581049	−	0.813869i	$-0.302642\pi$
$337$	−6.83893	−	9.41298i	−0.372540	−	0.512757i	−0.953589	+	0.301111i	$0.902642\pi$
$338$	−13.9610	+	10.1433i	−0.759380	+	0.551722i
$339$	−2.90121	−	2.10785i	−0.157572	−	0.114483i
$340$	−10.7279	−	5.01946i	−0.581801	−	0.272219i
$341$	−18.0227	+	13.0943i	−0.975985	+	0.709094i
$342$	10.2668	−	31.5979i	0.555164	−	1.70862i
$343$		−	18.6896i		−	1.00914i
$344$	1.43701	−	4.42267i	0.0774785	−	0.238454i
$345$	−4.91133	−	3.61832i	−0.264417	−	0.194804i
$346$	−24.7552	+	8.04346i	−1.33085	+	0.432419i
$347$	−23.1318	+	7.51599i	−1.24178	+	0.403479i	−0.854969	−	0.518679i	$-0.826424\pi$
$347$	−23.1318	+	7.51599i	−1.24178	+	0.403479i	−0.386813	+	0.922158i	$0.626424\pi$
$348$	−3.22091	−	2.34013i	−0.172659	−	0.125444i
$349$	19.3235			1.03436			0.517181	−	0.855876i	$-0.326981\pi$
$349$	19.3235			1.03436			0.517181	+	0.855876i	$0.326981\pi$
$350$	14.4030	−	4.46941i	0.769872	−	0.238900i
$351$			16.1863i			0.863959i
$352$	−21.3062	+	29.3255i	−1.13562	+	1.56305i
$353$	9.81265	+	30.2002i	0.522275	+	1.60740i	0.769643	+	0.638475i	$0.220434\pi$
$353$	9.81265	+	30.2002i	0.522275	+	1.60740i	−0.247368	+	0.968922i	$0.579566\pi$
$354$	6.02467	−	1.95753i	0.320207	−	0.104042i
$355$	−0.0801974	+	12.0871i	−0.00425644	+	0.641519i
$356$	−5.44273	+	16.7510i	−0.288464	+	0.887801i
$357$	−0.484271	+	4.12597i	−0.0256303	+	0.218369i
$358$	4.49227	−	13.8258i	0.237424	−	0.730715i
$359$	−6.72998	+	4.88962i	−0.355195	+	0.258064i	−0.751045	−	0.660251i	$-0.770450\pi$
$359$	−6.72998	+	4.88962i	−0.355195	+	0.258064i	0.395850	+	0.918315i	$0.370450\pi$
$360$	7.63398	+	0.0506509i	0.402346	+	0.00266954i
$361$	−23.8320	−	17.3149i	−1.25431	−	0.911312i
$362$	28.0349	+	38.5867i	1.47348	+	2.02807i
$363$	7.78432	+	10.7142i	0.408571	+	0.562350i
$364$	−5.96363	+	8.20823i	−0.312579	+	0.430228i
$365$	17.3247	+	24.1812i	0.906816	+	1.26570i
$366$	−4.01208	+	2.91494i	−0.209715	+	0.152367i
$367$	13.9319	+	4.52674i	0.727238	+	0.236294i	0.649158	−	0.760653i	$-0.275121\pi$
$367$	13.9319	+	4.52674i	0.727238	+	0.236294i	0.0780792	+	0.996947i	$0.475121\pi$
$368$		−	22.1649i		−	1.15543i
$369$	3.60846	+	1.17246i	0.187849	+	0.0610357i
$370$	−11.9156	−	3.95920i	−0.619462	−	0.205829i
$371$	7.18687	−	2.33516i	0.373124	−	0.121235i
$372$	0.933862	+	2.87413i	0.0484185	+	0.149017i
$373$	−9.33952	−	6.78556i	−0.483582	−	0.351343i	0.319129	−	0.947711i	$-0.396610\pi$
$373$	−9.33952	−	6.78556i	−0.483582	−	0.351343i	−0.802711	+	0.596368i	$0.796610\pi$
$374$	−42.5526	−	4.99447i	−2.20034	−	0.258258i
$375$	−4.08695	+	5.39600i	−0.211049	+	0.278648i
$376$	16.6486			0.858584
$377$	−14.2783	+	19.6523i	−0.735368	+	1.01215i
$378$	3.17888	+	9.78359i	0.163504	+	0.503213i
$379$	−14.5104	+	4.71473i	−0.745351	+	0.242179i	−0.656980	−	0.753908i	$-0.728166\pi$
$379$	−14.5104	+	4.71473i	−0.745351	+	0.242179i	−0.0883713	+	0.996088i	$0.528166\pi$
$380$	−6.30538	+	18.9766i	−0.323459	+	0.973480i
$381$	4.31586	+	1.40231i	0.221108	+	0.0718424i
$382$	27.0030			1.38159
$383$	3.43885	−	10.5837i	0.175717	−	0.540802i	−0.823948	−	0.566665i	$-0.808233\pi$
$383$	3.43885	−	10.5837i	0.175717	−	0.540802i	0.999665	+	0.0258630i	$0.00823338\pi$
$384$	−3.45483	−	4.75516i	−0.176303	−	0.242661i
$385$	17.3440	−	12.4261i	0.883930	−	0.633295i
$386$	12.7771	−	17.5862i	0.650337	−	0.895112i
$387$	7.64200	−	5.55224i	0.388465	−	0.282236i
$388$	2.54088	+	3.49722i	0.128994	+	0.177545i
$389$	14.3707	+	10.4410i	0.728626	+	0.529378i	0.889128	−	0.457658i	$-0.151312\pi$
$389$	14.3707	+	10.4410i	0.728626	+	0.529378i	−0.160503	+	0.987035i	$0.551312\pi$
$390$	0.0772558	−	11.6438i	0.00391200	−	0.589606i
$391$	16.2011	−	9.09375i	0.819323	−	0.459890i
$392$	−1.69483	+	5.21616i	−0.0856021	+	0.263456i
$393$	−4.83830			−0.244060
$394$	4.20307	+	1.36566i	0.211748	+	0.0688010i
$395$	0.0966658	−	14.5692i	0.00486379	−	0.733057i
$396$	−18.4480	+	5.99411i	−0.927045	+	0.301215i
$397$	16.5397	−	5.37408i	0.830105	−	0.269717i	0.137015	−	0.990569i	$-0.456249\pi$
$397$	16.5397	−	5.37408i	0.830105	−	0.269717i	0.693090	+	0.720851i	$0.256249\pi$
$398$	9.20841	−	12.6743i	0.461576	−	0.635304i
$399$	7.01382			0.351130
$400$	−24.5926	−	0.326356i	−1.22963	−	0.0163178i
$401$		−	35.7483i		−	1.78518i	−0.450866	−	0.892592i	$-0.648885\pi$
$401$		−	35.7483i		−	1.78518i	0.450866	−	0.892592i	$-0.351115\pi$
$402$	0.172871	−	0.237937i	0.00862202	−	0.0118672i
$403$	17.5365	−	5.69795i	0.873555	−	0.283835i
$404$	0.731871	+	2.25247i	0.0364120	+	0.112064i
$405$	10.5051	+	7.73940i	0.522002	+	0.384574i
$406$	−4.77072	+	14.6828i	−0.236767	+	0.728694i
$407$	−17.7645			−0.880552
$408$	1.35205	−	2.94034i	0.0669364	−	0.145569i
$409$	−11.6728	+	8.48075i	−0.577181	+	0.419346i	−0.837707	−	0.546121i	$-0.816104\pi$
$409$	−11.6728	+	8.48075i	−0.577181	+	0.419346i	0.260526	+	0.965467i	$0.416104\pi$
$410$	−5.54092	−	1.84109i	−0.273647	−	0.0909248i
$411$	3.30382	−	4.54732i	0.162966	−	0.224303i
$412$	−9.83601	+	7.14628i	−0.484585	+	0.352072i
$413$	−5.64712	−	7.77259i	−0.277876	−	0.382464i
$414$	12.6410	−	17.3988i	0.621270	−	0.855105i
$415$	3.03419	+	2.23537i	0.148942	+	0.109730i
$416$	24.2727	−	17.6352i	1.19007	−	0.864635i
$417$	−2.37545	+	7.31087i	−0.116326	+	0.358015i
$418$			72.3361i			3.53807i
$419$	7.40610	+	2.40639i	0.361812	+	0.117560i	0.484281	−	0.874913i	$-0.339081\pi$
$419$	7.40610	+	2.40639i	0.361812	+	0.117560i	−0.122469	+	0.992472i	$0.539081\pi$
$420$	−0.876116	−	2.75855i	−0.0427501	−	0.134604i
$421$	3.88971	+	11.9713i	0.189573	+	0.583445i	0.999997	−	0.00239844i	$-0.000763448\pi$
$421$	3.88971	+	11.9713i	0.189573	+	0.583445i	−0.810424	+	0.585843i	$0.800763\pi$
$422$	−39.8973	+	12.9634i	−1.94217	+	0.631049i
$423$	27.3594	+	19.8777i	1.33026	+	0.966489i
$424$	−5.88689			−0.285893
$425$	−9.85124	−	18.1095i	−0.477855	−	0.878438i
$426$	5.93153			0.287383
$427$	6.08486	+	4.42091i	0.294467	+	0.213943i
$428$	−6.17796	+	2.00734i	−0.298623	+	0.0970285i
$429$	−5.09075	−	15.6677i	−0.245784	−	0.756445i
$430$	−11.8166	+	8.46607i	−0.569848	+	0.408270i
$431$	−8.45078	−	2.74582i	−0.407060	−	0.132262i	0.0983282	−	0.995154i	$-0.468651\pi$
$431$	−8.45078	−	2.74582i	−0.407060	−	0.132262i	−0.505388	+	0.862892i	$0.668651\pi$
$432$		−	16.7772i		−	0.807194i
$433$	0.691471	−	2.12813i	0.0332300	−	0.102271i	−0.933066	−	0.359706i	$-0.882877\pi$
$433$	0.691471	−	2.12813i	0.0332300	−	0.102271i	0.966296	+	0.257434i	$0.0828771\pi$
$434$	9.48067	−	6.88811i	0.455087	−	0.330640i
$435$	−2.09762	−	6.60459i	−0.100573	−	0.316666i
$436$	−1.27471	+	1.75449i	−0.0610477	+	0.0840250i
$437$	−18.4371	−	25.3766i	−0.881968	−	1.21393i
$438$	11.8095	−	8.58011i	0.564280	−	0.409973i
$439$	−13.6848	+	18.8355i	−0.653141	+	0.898971i	−0.999230	−	0.0392303i	$-0.987509\pi$
$439$	−13.6848	+	18.8355i	−0.653141	+	0.898971i	0.346089	+	0.938202i	$0.387509\pi$
$440$	−15.8415	+	5.03125i	−0.755213	+	0.239856i
$441$	−9.01310	+	6.54840i	−0.429195	+	0.311829i
$442$	32.2196	+	14.8154i	1.53253	+	0.704699i
$443$	−24.7538			−1.17609			−0.588043	−	0.808830i	$-0.700101\pi$
$443$	−24.7538			−1.17609			−0.588043	+	0.808830i	$0.700101\pi$
$444$	−0.744684	+	2.29190i	−0.0353411	+	0.108769i
$445$	−24.9209	+	17.8547i	−1.18137	+	0.846394i
$446$	12.3718	+	38.0766i	0.585823	+	1.80298i
$447$	7.70218	−	2.50259i	0.364300	−	0.118368i
$448$	1.58466	−	2.18109i	0.0748680	−	0.103047i
$449$		−	3.72609i		−	0.175845i	−0.996127	−	0.0879225i	$-0.971977\pi$
$449$		−	3.72609i		−	0.175845i	0.996127	−	0.0879225i	$-0.0280228\pi$
$450$	−19.1184	−	14.2817i	−0.901249	−	0.673247i
$451$	−8.26073			−0.388983
$452$	−4.47260	+	6.15600i	−0.210373	+	0.289554i
$453$	12.0578	−	3.91782i	0.566526	−	0.184075i
$454$	−14.9097	+	4.84446i	−0.699748	+	0.227362i
$455$	−16.8313	+	5.34562i	−0.789063	+	0.250606i
$456$	−5.19653	−	1.68845i	−0.243350	−	0.0790691i
$457$	−24.8196			−1.16101			−0.580506	−	0.814256i	$-0.697145\pi$
$457$	−24.8196			−1.16101			−0.580506	+	0.814256i	$0.697145\pi$
$458$	4.16164	−	12.8082i	0.194461	−	0.598488i
$459$	12.2630	−	6.88330i	0.572389	−	0.321285i
$460$	−7.67762	+	10.4212i	−0.357971	+	0.485892i
$461$	7.73568	+	5.62030i	0.360286	+	0.261763i	0.753172	−	0.657824i	$-0.228523\pi$
$461$	7.73568	+	5.62030i	0.360286	+	0.261763i	−0.392885	+	0.919588i	$0.628523\pi$
$462$	−6.15409	−	8.47037i	−0.286314	−	0.394077i
$463$	28.9075	−	21.0026i	1.34345	−	0.976072i	0.344138	−	0.938919i	$-0.388171\pi$
$463$	28.9075	−	21.0026i	1.34345	−	0.976072i	0.999310	−	0.0371523i	$-0.0118287\pi$
$464$	14.7995	−	20.3698i	0.687052	−	0.945646i
$465$	−1.65861	+	4.99175i	−0.0769164	+	0.231487i
$466$	15.6042	+	21.4773i	0.722850	+	0.994918i
$467$	2.19220	−	6.74689i	0.101443	−	0.312209i	−0.887436	−	0.460930i	$-0.847516\pi$
$467$	2.19220	−	6.74689i	0.101443	−	0.312209i	0.988879	+	0.148721i	$0.0475158\pi$
$468$	16.0552			0.742152
$469$	−0.424220	−	0.137837i	−0.0195887	−	0.00636474i
$470$	−41.8992	−	30.8683i	−1.93266	−	1.42385i
$471$	−9.56254	+	3.10706i	−0.440618	+	0.143166i
$472$	2.31282	+	7.11814i	0.106456	+	0.327639i
$473$	−12.0885	+	16.6384i	−0.555829	+	0.765032i
$474$	−7.14956			−0.328390
$475$	−28.4275	+	20.0829i	−1.30434	+	0.921468i
$476$	8.75477	+	1.02756i	0.401274	+	0.0470982i
$477$	−9.67420	−	7.02872i	−0.442951	−	0.321823i
$478$	9.08689	+	27.9666i	0.415625	+	1.27916i
$479$	17.6889	−	5.74746i	0.808224	−	0.262608i	0.124379	−	0.992235i	$-0.460306\pi$
$479$	17.6889	−	5.74746i	0.808224	−	0.262608i	0.683846	+	0.729627i	$0.260306\pi$
$480$	−0.0567865	+	8.55871i	−0.00259194	+	0.390650i
$481$	13.9840	+	4.54368i	0.637616	+	0.207174i
$482$		−	20.3003i		−	0.924652i
$483$	4.31788	+	1.40297i	0.196471	+	0.0638372i
$484$	22.7342	−	16.5173i	1.03337	−	0.750789i
$485$	−0.0499213	+	7.52401i	−0.00226681	+	0.341648i
$486$	14.6637	−	20.1829i	0.665160	−	0.915515i
$487$	18.6038	+	25.6059i	0.843017	+	1.16031i	0.985359	+	0.170495i	$0.0545367\pi$
$487$	18.6038	+	25.6059i	0.843017	+	1.16031i	−0.142342	+	0.989818i	$0.545463\pi$
$488$	−3.44401	−	4.74027i	−0.155903	−	0.214582i
$489$	9.27512	+	6.73877i	0.419435	+	0.304738i
$490$	13.9367	−	9.98502i	0.629597	−	0.451077i
$491$	16.7622	−	12.1785i	0.756468	−	0.549606i	−0.141357	−	0.989959i	$-0.545147\pi$
$491$	16.7622	−	12.1785i	0.756468	−	0.549606i	0.897825	+	0.440352i	$0.145147\pi$
$492$	−0.346289	+	1.06577i	−0.0156119	+	0.0480485i
$493$	20.9609	+	2.46021i	0.944031	+	0.110802i
$494$	18.5017	−	56.9423i	0.832430	−	2.56196i
$495$	−32.0402	−	10.6460i	−1.44010	−	0.478503i
$496$	−18.1767	+	5.90598i	−0.816159	+	0.265186i
$497$	−2.77991	−	8.55567i	−0.124696	−	0.383774i
$498$	1.08704	−	1.49618i	0.0487114	−	0.0670454i
$499$		−	29.6359i		−	1.32668i	−0.748316	−	0.663342i	$-0.769137\pi$
$499$		−	29.6359i		−	1.32668i	0.748316	−	0.663342i	$-0.230863\pi$
$500$	11.4496	+	8.67199i	0.512043	+	0.387823i
$501$	4.13332			0.184663
$502$	18.6586	+	13.5563i	0.832775	+	0.605046i
$503$	−30.4957	+	9.90865i	−1.35974	+	0.441805i	−0.895955	−	0.444145i	$-0.853508\pi$
$503$	−30.4957	+	9.90865i	−1.35974	+	0.441805i	−0.463781	+	0.885950i	$0.653508\pi$
$504$	−5.40358	+	1.75573i	−0.240694	+	0.0782064i
$505$	−1.29986	+	3.91206i	−0.0578431	+	0.174084i
$506$	−14.4693	+	44.5319i	−0.643239	+	1.97969i
$507$			5.76483i			0.256025i
$508$	2.97552	−	9.15770i	0.132017	−	0.406307i
$509$	29.1075	−	21.1478i	1.29017	−	0.937361i	0.290358	−	0.956918i	$-0.406226\pi$
$509$	29.1075	−	21.1478i	1.29017	−	0.937361i	0.999809	+	0.0195573i	$0.00622567\pi$
$510$	−8.85440	+	4.89305i	−0.392080	+	0.216668i
$511$	−17.9107	−	13.0129i	−0.792324	−	0.575657i
$512$	−14.8405	+	10.7822i	−0.655862	+	0.476512i
$513$	−13.9556	−	19.2082i	−0.616153	−	0.848062i
$514$	−4.22924	−	3.07273i	−0.186544	−	0.135532i
$515$	−21.1614	−	0.140405i	−0.932484	−	0.00618697i
$516$	1.63987	+	2.25709i	0.0721912	+	0.0993626i
$517$	−70.0258	−	22.7528i	−3.07973	−	1.00067i
$518$	9.34482			0.410588
$519$	−2.68701	+	8.26977i	−0.117947	+	0.363003i
$520$	13.7571	+	0.0912777i	0.603290	+	0.00400279i
$521$	18.7319	−	6.08637i	0.820660	−	0.266648i	0.131554	−	0.991309i	$-0.458003\pi$
$521$	18.7319	−	6.08637i	0.820660	−	0.266648i	0.689106	+	0.724661i	$0.258003\pi$
$522$	23.2344	−	7.54932i	1.01694	−	0.330425i
$523$	−3.56450	−	2.58976i	−0.155865	−	0.113242i	0.507119	−	0.861876i	$-0.330710\pi$
$523$	−3.56450	−	2.58976i	−0.155865	−	0.113242i	−0.662984	+	0.748633i	$0.730710\pi$
$524$			10.2663i			0.448484i
$525$	1.62021	−	4.77017i	0.0707118	−	0.208187i
$526$	−23.1553			−1.00962
$527$	−11.7744	−	10.8629i	−0.512899	−	0.473195i
$528$	5.27661	+	16.2397i	0.229635	+	0.706744i
$529$	0.833060	+	2.56390i	0.0362200	+	0.111474i
$530$	14.8154	+	10.9150i	0.643541	+	0.474115i
$531$	−4.69801	+	14.4590i	−0.203876	+	0.627467i
$532$		−	14.8824i		−	0.645235i
$533$	6.50277	+	2.11288i	0.281666	+	0.0915189i
$534$	8.84260	+	12.1708i	0.382657	+	0.526682i
$535$	−10.7298	−	3.56520i	−0.463889	−	0.154137i
$536$	0.281122	+	0.204247i	0.0121426	+	0.00882212i
$537$	−2.85449	−	3.92887i	−0.123180	−	0.169543i
$538$	−21.5370	−	29.6432i	−0.928528	−	1.27801i
$539$	14.2573	−	19.6235i	0.614107	−	0.845246i
$540$	−5.81139	+	7.88810i	−0.250083	+	0.339450i
$541$	−0.446716	−	0.614852i	−0.0192058	−	0.0264345i	0.799306	−	0.600924i	$-0.205201\pi$
$541$	−0.446716	−	0.614852i	−0.0192058	−	0.0264345i	−0.818512	+	0.574490i	$0.805201\pi$
$542$	1.93673	−	5.96065i	0.0831898	−	0.256032i
$543$	15.9333			0.683765
$544$	−23.6828	−	10.8900i	−1.01539	−	0.466905i
$545$	−3.59765	+	1.14261i	−0.154107	+	0.0489442i
$546$	2.67794	+	8.24185i	0.114605	+	0.352719i
$547$	26.9108	−	8.74385i	1.15062	−	0.373860i	0.329245	−	0.944244i	$-0.393206\pi$
$547$	26.9108	−	8.74385i	1.15062	−	0.373860i	0.821378	+	0.570384i	$0.193206\pi$
$548$	−9.64884	−	7.01029i	−0.412178	−	0.299465i
$549$		−	11.9019i		−	0.507961i
$550$	49.1965	+	16.7098i	2.09775	+	0.712509i
$551$		−	35.6319i		−	1.51797i
$552$	−2.86137	−	2.07891i	−0.121788	−	0.0884843i
$553$	3.35076	+	10.3126i	0.142489	+	0.438535i
$554$	−54.7895	+	17.8022i	−2.32778	+	0.756342i
$555$	−3.40972	+	2.44291i	−0.144735	+	0.103696i
$556$	15.5127	+	5.04039i	0.657886	+	0.213760i
$557$	−27.9438			−1.18402			−0.592009	−	0.805931i	$-0.701665\pi$
$557$	−27.9438			−1.18402			−0.592009	+	0.805931i	$0.701665\pi$
$558$	−17.6365	−	5.73043i	−0.746611	−	0.242589i
$559$	13.7716	−	10.0056i	0.582476	−	0.423194i
$560$	17.4458	−	5.54078i	0.737218	−	0.234141i
$561$	−9.70529	+	10.5196i	−0.409758	+	0.444139i
$562$	38.9996	−	28.3349i	1.64510	−	1.19524i
$563$	16.5852	−	12.0498i	0.698981	−	0.507839i	−0.180619	−	0.983553i	$-0.557810\pi$
$563$	16.5852	−	12.0498i	0.698981	−	0.507839i	0.879600	+	0.475714i	$0.157810\pi$
$564$	−5.87094	+	8.08066i	−0.247211	+	0.340257i
$565$	−12.6231	+	4.00910i	−0.531058	+	0.168664i
$566$	15.7569	+	21.6876i	0.662314	+	0.911597i
$567$	−9.23573	−	3.00087i	−0.387864	−	0.126025i
$568$			7.00810i			0.294053i
$569$	7.33069	−	22.5615i	0.307318	−	0.945829i	−0.671483	−	0.741020i	$-0.734343\pi$
$569$	7.33069	−	22.5615i	0.307318	−	0.945829i	0.978802	−	0.204809i	$-0.0656574\pi$
$570$	9.94743	+	13.8843i	0.416652	+	0.581547i
$571$	−15.1507	+	4.92276i	−0.634037	+	0.206011i	−0.608363	−	0.793659i	$-0.708173\pi$
$571$	−15.1507	+	4.92276i	−0.634037	+	0.206011i	−0.0256746	+	0.999670i	$0.508173\pi$
$572$	−33.2449	+	10.8019i	−1.39004	+	0.451652i
$573$	5.30221	−	7.29787i	0.221503	−	0.304873i
$574$	4.34547			0.181377
$575$	−21.5179	+	6.67724i	−0.897357	+	0.278460i
$576$	−4.26619			−0.177758
$577$	−21.9162	−	15.9230i	−0.912381	−	0.662884i	0.0292346	−	0.999573i	$-0.490693\pi$
$577$	−21.9162	−	15.9230i	−0.912381	−	0.662884i	−0.941616	+	0.336689i	$0.890693\pi$
$578$	−2.47709	−	30.7105i	−0.103033	−	1.27739i
$579$	−2.24400	−	6.90631i	−0.0932574	−	0.287017i
$580$	−14.0141	+	4.45088i	−0.581904	+	0.184813i
$581$	−2.66756	−	0.866742i	−0.110669	−	0.0359585i
$582$	3.69226			0.153049
$583$	24.7609	+	8.04531i	1.02549	+	0.333203i
$584$	10.1374	+	13.9529i	0.419488	+	0.577376i
$585$	22.4987	+	16.5755i	0.930209	+	0.685312i
$586$	−18.4094	−	13.3752i	−0.760484	−	0.552524i
$587$	9.85468	−	7.15984i	0.406746	−	0.295518i	−0.365537	−	0.930797i	$-0.619115\pi$
$587$	9.85468	−	7.15984i	0.406746	−	0.295518i	0.772283	+	0.635278i	$0.219115\pi$
$588$	−1.93409	−	2.66204i	−0.0797604	−	0.109781i
$589$	−15.8978	+	21.8814i	−0.655057	+	0.901609i
$590$	7.37719	−	22.2023i	0.303714	−	0.914056i
$591$	1.19439	−	0.867772i	0.0491305	−	0.0356954i
$592$	−14.4946	−	4.70957i	−0.595723	−	0.193562i
$593$	3.32867			0.136692			0.0683460	−	0.997662i	$-0.478228\pi$
$593$	3.32867			0.136692			0.0683460	+	0.997662i	$0.478228\pi$
$594$	−10.9522	+	33.7074i	−0.449374	+	1.38303i
$595$	11.2075	+	10.4784i	0.459464	+	0.429574i
$596$	−5.31018	−	16.3430i	−0.217513	−	0.669437i
$597$	−1.61724	−	4.97736i	−0.0661893	−	0.203710i
$598$	22.7802	−	31.3543i	0.931552	−	1.28217i
$599$	10.5541			0.431229			0.215614	−	0.976479i	$-0.430825\pi$
$599$	10.5541			0.431229			0.215614	+	0.976479i	$0.430825\pi$
$600$	−2.34874	+	3.14417i	−0.0958871	+	0.128360i
$601$		−	45.5735i		−	1.85898i	−0.368843	−	0.929492i	$-0.620246\pi$
$601$		−	45.5735i		−	1.85898i	0.368843	−	0.929492i	$-0.379754\pi$
$602$	6.35902	−	8.75244i	0.259174	−	0.356723i
$603$	0.218118	+	0.671297i	0.00888244	+	0.0273373i
$604$	−8.31312	−	25.5852i	−0.338256	−	1.04105i
$605$	48.9108	+	0.324520i	1.98851	+	0.0131936i
$606$	1.92391	+	0.625117i	0.0781536	+	0.0253936i
$607$			29.8450i			1.21137i	0.795705	+	0.605685i	$0.207101\pi$
$607$			29.8450i			1.21137i	−0.795705	+	0.605685i	$0.792899\pi$
$608$	−13.5996	+	41.8552i	−0.551535	+	1.69745i
$609$	3.03143	+	4.17240i	0.122840	+	0.169074i
$610$	−0.121521	+	18.3153i	−0.00492024	+	0.741566i
$611$	49.3041	+	35.8215i	1.99463	+	1.44918i
$612$	−6.82756	−	12.1637i	−0.275988	−	0.491689i
$613$	−12.5906	+	9.14761i	−0.508530	+	0.369468i	−0.812266	−	0.583288i	$-0.801766\pi$
$613$	−12.5906	+	9.14761i	−0.508530	+	0.369468i	0.303736	+	0.952756i	$0.401766\pi$
$614$	−16.1278	−	11.7175i	−0.650865	−	0.472881i
$615$	−1.58557	+	1.13599i	−0.0639364	+	0.0458075i
$616$	10.0077	−	7.27105i	0.403223	−	0.292959i
$617$	26.9854	+	8.76808i	1.08639	+	0.352990i	0.796851	−	0.604176i	$-0.206498\pi$
$617$	26.9854	+	8.76808i	1.08639	+	0.352990i	0.289540	+	0.957166i	$0.406498\pi$
$618$			10.3846i			0.417728i
$619$	29.0381	+	9.43504i	1.16714	+	0.379226i	0.827574	−	0.561357i	$-0.189720\pi$
$619$	29.0381	+	9.43504i	1.16714	+	0.379226i	0.339564	+	0.940583i	$0.389720\pi$
$620$	10.5919	+	3.51937i	0.425379	+	0.141341i
$621$	−4.74921	−	14.6166i	−0.190579	−	0.586542i
$622$	46.3855	−	15.0716i	1.85989	−	0.604315i
$623$	13.4110	−	18.4587i	0.537300	−	0.739530i
$624$		−	14.1334i		−	0.565789i
$625$	7.09177	+	23.9730i	0.283671	+	0.958922i
$626$		−	30.7543i		−	1.22919i
$627$	19.5497	+	14.2037i	0.780739	+	0.567240i
$628$	6.59278	+	20.2905i	0.263081	+	0.809679i
$629$	−2.50440	−	12.5268i	−0.0998570	−	0.499475i
$630$	16.8544	+	5.60023i	0.671496	+	0.223119i
$631$	−4.04302	+	12.4431i	−0.160950	+	0.495353i	−0.998715	−	0.0506778i	$-0.983862\pi$
$631$	−4.04302	+	12.4431i	−0.160950	+	0.495353i	0.837765	+	0.546031i	$0.183862\pi$
$632$		−	8.44720i		−	0.336011i
$633$	−4.33058	+	13.3282i	−0.172125	+	0.529747i
$634$	−1.05335	−	1.44981i	−0.0418339	−	0.0575794i
$635$	13.6242	−	9.76109i	0.540659	−	0.387357i
$636$	2.07595	−	2.85730i	0.0823168	−	0.113299i
$637$	−16.2424	+	11.8008i	−0.643549	+	0.467565i
$638$	−43.0315	+	31.2642i	−1.70363	+	1.23776i
$639$	−8.36740	+	11.5167i	−0.331009	+	0.455595i
$640$	−21.7075	−	0.144028i	−0.858066	−	0.00569322i
$641$	18.6554	+	25.6770i	0.736846	+	1.01418i	0.998794	+	0.0490995i	$0.0156351\pi$
$641$	18.6554	+	25.6770i	0.736846	+	1.01418i	−0.261948	+	0.965082i	$0.584365\pi$
$642$	−1.71454	+	5.27681i	−0.0676675	+	0.208259i
$643$		−	21.1373i		−	0.833574i	−0.909004	−	0.416787i	$-0.863156\pi$
$643$		−	21.1373i		−	0.833574i	0.909004	−	0.416787i	$-0.136844\pi$
$644$	2.97691	−	9.16200i	0.117307	−	0.361033i
$645$	−0.0322189	+	4.85595i	−0.00126862	+	0.191203i
$646$	−51.0085	+	10.1978i	−2.00690	+	0.401227i
$647$	−4.40644	−	13.5616i	−0.173235	−	0.533163i	0.826313	−	0.563211i	$-0.190434\pi$
$647$	−4.40644	−	13.5616i	−0.173235	−	0.533163i	−0.999548	+	0.0300479i	$0.990434\pi$
$648$	6.12033	+	4.44668i	0.240429	+	0.174682i
$649$		−	33.1005i		−	1.29931i
$650$	−34.4531	−	25.7370i	−1.35136	−	1.00949i
$651$		−	3.91479i		−	0.153433i
$652$	14.2988	−	19.6806i	0.559985	−	0.770753i
$653$	−42.7164	+	13.8794i	−1.67162	+	0.543143i	−0.983257	−	0.182222i	$-0.941671\pi$
$653$	−42.7164	+	13.8794i	−1.67162	+	0.543143i	−0.688364	+	0.725365i	$0.741671\pi$
$654$	0.572405	+	1.76168i	0.0223828	+	0.0688871i
$655$	−10.5990	+	14.3865i	−0.414135	+	0.562127i
$656$	−6.74018	−	2.19002i	−0.263160	−	0.0855058i
$657$			35.0331i			1.36677i
$658$	36.8364	+	11.9689i	1.43603	+	0.466595i
$659$	−13.9137	+	10.1089i	−0.542001	+	0.393787i	−0.824828	−	0.565384i	$-0.808728\pi$
$659$	−13.9137	+	10.1089i	−0.542001	+	0.393787i	0.282827	+	0.959171i	$0.408728\pi$
$660$	3.14433	−	9.46315i	0.122393	−	0.368353i
$661$	−18.0231	−	13.0946i	−0.701018	−	0.509319i	0.179246	−	0.983804i	$-0.442634\pi$
$661$	−18.0231	−	13.0946i	−0.701018	−	0.509319i	−0.880263	+	0.474485i	$0.842634\pi$
$662$	1.90445	−	1.38366i	0.0740185	−	0.0537776i
$663$	10.3306	−	5.79860i	0.401206	−	0.225199i
$664$	1.76774	+	1.28434i	0.0686015	+	0.0498419i
$665$	15.3647	−	20.8553i	0.595818	−	0.808734i
$666$	−8.69187	−	11.9633i	−0.336803	−	0.463570i
$667$	7.12740	−	21.9359i	0.275974	−	0.849361i
$668$		−	8.77037i		−	0.339336i
$669$	12.7199	+	4.13295i	0.491781	+	0.159789i
$670$	−0.328798	−	1.03526i	−0.0127026	−	0.0399954i
$671$	8.00760	+	24.6449i	0.309130	+	0.951404i
$672$	−1.96841	−	6.05813i	−0.0759329	−	0.233698i
$673$	−22.9687	+	31.6137i	−0.885379	+	1.21862i	0.0895233	+	0.995985i	$0.471466\pi$
$673$	−22.9687	+	31.6137i	−0.885379	+	1.21862i	−0.974902	+	0.222634i	$0.928534\pi$
$674$			21.0870i			0.812242i
$675$	−16.2874	+	5.05418i	−0.626904	+	0.194535i
$676$	12.2322			0.470471
$677$	5.41856	−	7.45800i	0.208252	−	0.286634i	−0.692095	−	0.721806i	$-0.743312\pi$
$677$	5.41856	−	7.45800i	0.208252	−	0.286634i	0.900348	+	0.435172i	$0.143312\pi$
$678$	2.00840	+	6.18121i	0.0771321	+	0.237388i
$679$	−1.73044	−	5.32574i	−0.0664081	−	0.204383i
$680$	−5.78114	−	10.4615i	−0.221697	−	0.401179i
$681$	−1.61835	+	4.98077i	−0.0620153	+	0.190863i
$682$	40.3746			1.54602
$683$	21.1232	+	6.86334i	0.808257	+	0.262618i	0.683859	−	0.729614i	$-0.260300\pi$
$683$	21.1232	+	6.86334i	0.808257	+	0.262618i	0.124397	+	0.992232i	$0.460300\pi$
$684$	−19.0526	+	13.8426i	−0.728496	+	0.529284i
$685$	−6.28381	−	19.7853i	−0.240092	−	0.755958i
$686$	−19.9097	+	27.4033i	−0.760154	+	1.04626i
$687$	−2.64440	−	3.63971i	−0.100890	−	0.138863i
$688$	−14.2744	+	10.3709i	−0.544205	+	0.395388i
$689$	−17.4338	−	12.6664i	−0.664175	−	0.482551i
$690$	3.34664	+	10.5373i	0.127404	+	0.401147i
$691$	26.6357	+	36.6609i	1.01327	+	1.39465i	0.916816	+	0.399309i	$0.130750\pi$
$691$	26.6357	+	36.6609i	1.01327	+	1.39465i	0.0964534	+	0.995337i	$0.469250\pi$
$692$	17.5474	+	5.70150i	0.667052	+	0.216738i
$693$	25.1275			0.954516
$694$	41.9233	+	13.6217i	1.59139	+	0.517073i
$695$	16.5348	+	23.0787i	0.627202	+	0.875426i
$696$	−1.24155	−	3.82109i	−0.0470607	−	0.144838i
$697$	−1.16458	−	5.82513i	−0.0441117	−	0.220643i
$698$	−28.3327	−	20.5849i	−1.07241	−	0.779152i
$699$	8.86848			0.335437
$700$	−10.1217	−	3.43788i	−0.382564	−	0.129940i
$701$	44.8843			1.69526			0.847628	−	0.530592i	$-0.178030\pi$
$701$	44.8843			1.69526			0.847628	+	0.530592i	$0.178030\pi$
$702$	17.2429	−	23.7329i	0.650793	−	0.895739i
$703$	−20.5123	+	6.66484i	−0.773635	+	0.251369i
$704$	8.83384	−	2.87029i	0.332938	−	0.108178i
$705$	−16.5697	+	5.26253i	−0.624051	+	0.198199i
$706$	17.7841	−	54.7339i	0.669314	−	2.05994i
$707$		−	3.06803i		−	0.115385i
$708$	−4.27050	−	1.38757i	−0.160495	−	0.0521481i
$709$	−6.20126	−	8.53530i	−0.232893	−	0.320550i	0.676535	−	0.736410i	$-0.263481\pi$
$709$	−6.20126	−	8.53530i	−0.232893	−	0.320550i	−0.909429	+	0.415860i	$0.863481\pi$
$710$	12.9938	−	17.6372i	0.487649	−	0.661911i
$711$	10.0856	−	13.8817i	0.378241	−	0.520603i
$712$	−14.3798	+	10.4475i	−0.538905	+	0.391537i
$713$	−14.1640	+	10.2907i	−0.530446	+	0.385392i
$714$	5.10537	−	5.53375i	0.191064	−	0.207095i
$715$	−57.7393	−	19.1851i	−2.15933	−	0.717482i
$716$	−8.33656	+	6.05686i	−0.311552	+	0.226356i
$717$	9.34256	+	3.03558i	0.348904	+	0.113366i
$718$	15.0766			0.562652
$719$	−33.5503	−	10.9012i	−1.25122	−	0.406544i	−0.392859	−	0.919599i	$-0.628514\pi$
$719$	−33.5503	−	10.9012i	−1.25122	−	0.406544i	−0.858356	+	0.513054i	$0.828514\pi$
$720$	−23.3202	−	17.1806i	−0.869091	−	0.640284i
$721$	14.9787	−	4.86689i	0.557838	−	0.181252i
$722$	16.4980	+	50.7755i	0.613991	+	1.88967i
$723$	−5.48638	−	3.98609i	−0.204041	−	0.148244i
$724$		−	33.8085i		−	1.25648i
$725$	−24.2336	−	8.23105i	−0.900013	−	0.305694i
$726$		−	24.0020i		−	0.890799i
$727$	22.3985	+	16.2735i	0.830715	+	0.603549i	0.919761	−	0.392478i	$-0.128382\pi$
$727$	22.3985	+	16.2735i	0.830715	+	0.603549i	−0.0890469	+	0.996027i	$0.528382\pi$
$728$	−9.73774	+	3.16398i	−0.360905	+	0.117265i
$729$	2.83430	+	8.72309i	0.104974	+	0.323077i
$730$	0.357696	−	53.9110i	0.0132389	−	1.99533i
$731$	−13.4369	−	6.17866i	−0.496982	−	0.228526i
$732$	3.51526			0.129928
$733$	1.55108	−	4.77374i	0.0572905	−	0.176322i	−0.918316	−	0.395847i	$-0.870451\pi$
$733$	1.55108	−	4.77374i	0.0572905	−	0.176322i	0.975607	+	0.219525i	$0.0704509\pi$
$734$	−15.6051	−	21.4786i	−0.575996	−	0.792791i
$735$	0.0379995	−	5.72718i	0.00140163	−	0.211250i
$736$	−16.7445	+	23.0468i	−0.617209	+	0.849516i
$737$	−0.903297	−	1.24328i	−0.0332734	−	0.0457969i
$738$	−4.04185	−	5.56312i	−0.148782	−	0.204781i
$739$	0.294051	+	0.213640i	0.0108168	+	0.00785889i	0.593181	−	0.805069i	$-0.297872\pi$
$739$	0.294051	+	0.213640i	0.0108168	+	0.00785889i	−0.582364	+	0.812928i	$0.697872\pi$
$740$	5.18355	+	7.23500i	0.190551	+	0.265964i
$741$	−11.7564	−	16.1813i	−0.431882	−	0.594434i
$742$	−13.0252	−	4.23216i	−0.478172	−	0.155367i
$743$			9.51616i			0.349114i	0.984647	+	0.174557i	$0.0558494\pi$
$743$			9.51616i			0.349114i	−0.984647	+	0.174557i	$0.944151\pi$
$744$	−0.942416	+	2.90046i	−0.0345506	+	0.106336i
$745$	9.43130	−	28.3844i	0.345536	−	1.03992i
$746$	6.46540	+	19.8985i	0.236715	+	0.728534i
$747$	1.37156	+	4.22122i	0.0501826	+	0.154446i
$748$	22.3213	+	20.5934i	0.816149	+	0.752969i
$749$	8.41485			0.307472
$750$	11.7407	−	3.55805i	0.428710	−	0.129921i
$751$			37.9812i			1.38595i	0.720960	+	0.692977i	$0.243701\pi$
$751$			37.9812i			1.38595i	−0.720960	+	0.692977i	$0.756299\pi$
$752$	−51.1041	−	37.1293i	−1.86358	−	1.35397i
$753$	7.32748	−	2.38084i	0.267028	−	0.0867627i
$754$	41.8706	−	13.6046i	1.52484	−	0.495449i
$755$	14.7648	−	44.4360i	0.537345	−	1.61719i
$756$	2.25331	−	6.93496i	0.0819519	−	0.252222i
$757$	9.72243			0.353368			0.176684	−	0.984268i	$-0.443463\pi$
$757$	9.72243			0.353368			0.176684	+	0.984268i	$0.443463\pi$
$758$	26.2982	+	8.54481i	0.955194	+	0.310361i
$759$	9.19413	+	12.6546i	0.333726	+	0.459334i
$760$	−16.4042	+	11.7529i	−0.595044	+	0.426322i
$761$	32.1216	+	23.3377i	1.16441	+	0.845992i	0.990329	−	0.138740i	$-0.0443053\pi$
$761$	32.1216	+	23.3377i	1.16441	+	0.845992i	0.174079	+	0.984732i	$0.444305\pi$
$762$	−4.83421	−	6.65372i	−0.175125	−	0.241039i
$763$	2.27279	−	1.65128i	0.0822806	−	0.0597803i
$764$	−15.4852	−	11.2506i	−0.560233	−	0.407033i
$765$	2.99018	−	24.0943i	0.108110	−	0.871131i
$766$	−16.3168	+	11.8548i	−0.589550	+	0.428333i
$767$	−8.46625	+	26.0564i	−0.305699	+	0.940844i
$768$			12.6142i			0.455176i
$769$	−12.8779	+	39.6340i	−0.464388	+	1.42924i	0.395363	+	0.918525i	$0.370619\pi$
$769$	−12.8779	+	39.6340i	−0.464388	+	1.42924i	−0.859751	+	0.510714i	$0.829381\pi$
$770$	−38.6677	−	0.256557i	−1.39349	−	0.00924569i
$771$	−1.66088	+	0.539652i	−0.0598151	+	0.0194351i
$772$	−14.6543	+

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.46623 - 1.06528i) q^{2} +(-0.575810 + 0.187092i) q^{3} +(0.396985 + 1.22179i) q^{4} +(-0.705078 + 2.12200i) q^{5} +(1.04358 + 0.339079i) q^{6} -1.66418i q^{7} +(-0.400621 + 1.23299i) q^{8} +(-2.13050 + 1.54790i) q^{9} +(3.29433 - 2.36024i) q^{10} +(3.37012 - 4.63857i) q^{11} +(-0.457176 - 0.629248i) q^{12} +(-3.83935 + 2.78945i) q^{13} +(-1.77282 + 2.44008i) q^{14} +(0.00898224 - 1.35378i) q^{15} +(3.97952 - 2.89129i) q^{16} +(3.74605 + 1.72254i) q^{17} +4.77276 q^{18} +(2.15112 - 6.62047i) q^{19} +(-2.87255 - 0.0190592i) q^{20} +(0.311354 + 0.958249i) q^{21} +(-9.88278 + 3.21111i) q^{22} +(2.64857 - 3.64544i) q^{23} -0.784918i q^{24} +(-4.00573 - 2.99234i) q^{25} +8.60095 q^{26} +(2.00477 - 2.75933i) q^{27} +(2.03328 - 0.660654i) q^{28} +(4.86813 - 1.58175i) q^{29} +(-1.45533 + 1.97539i) q^{30} +(-3.69524 - 1.20065i) q^{31} -6.32208 q^{32} +(-1.07271 + 3.30146i) q^{33} +(-3.65760 - 6.51624i) q^{34} +(3.53138 + 1.17337i) q^{35} +(-2.73699 - 1.98854i) q^{36} +(-1.82114 - 2.50659i) q^{37} +(-10.2067 + 7.41561i) q^{38} +(1.68885 - 2.32451i) q^{39} +(-2.33392 - 1.71947i) q^{40} +(-0.846857 - 1.16560i) q^{41} +(0.564288 - 1.73670i) q^{42} -3.58696 q^{43} +(7.00527 + 2.27615i) q^{44} +(-1.78247 - 5.61229i) q^{45} +(-7.76685 + 2.52360i) q^{46} +(-3.96832 - 12.2132i) q^{47} +(-1.75051 + 2.40937i) q^{48} +4.23051 q^{49} +(2.68565 + 8.65471i) q^{50} +(-2.47928 - 0.290997i) q^{51} +(-4.93231 - 3.58353i) q^{52} +(1.40319 + 4.31857i) q^{53} +(-5.87893 + 1.91018i) q^{54} +(7.46684 + 10.4219i) q^{55} +(2.05191 + 0.666705i) q^{56} +4.21459i q^{57} +(-8.82284 - 2.86671i) q^{58} +(4.67053 - 3.39334i) q^{59} +(1.65761 - 0.526456i) q^{60} +(-2.65651 + 3.65638i) q^{61} +(4.13905 + 5.69691i) q^{62} +(2.57598 + 3.54553i) q^{63} +(1.31061 + 0.952216i) q^{64} +(-3.21217 - 10.1139i) q^{65} +(5.08983 - 3.69797i) q^{66} +(0.0828261 - 0.254913i) q^{67} +(-0.617459 + 5.26072i) q^{68} +(-0.843038 + 2.59461i) q^{69} +(-3.92786 - 5.48236i) q^{70} +(5.14108 - 1.67044i) q^{71} +(-1.05501 - 3.24700i) q^{72} +(7.81942 - 10.7625i) q^{73} +5.61528i q^{74} +(2.86638 + 0.973580i) q^{75} +8.94282 q^{76} +(-7.71941 - 5.60848i) q^{77} +(-4.95251 + 1.60917i) q^{78} +(-6.19679 + 2.01346i) q^{79} +(3.32944 + 10.4831i) q^{80} +(1.80322 - 5.54973i) q^{81} +2.61118i q^{82} +(0.520823 - 1.60293i) q^{83} +(-1.04718 + 0.760821i) q^{84} +(-6.29647 + 6.73458i) q^{85} +(5.25932 + 3.82112i) q^{86} +(-2.50718 + 1.82158i) q^{87} +(4.36915 + 6.01362i) q^{88} +(11.0918 + 8.05863i) q^{89} +(-3.36516 + 10.1278i) q^{90} +(4.64215 + 6.38937i) q^{91} +(5.50542 + 1.78882i) q^{92} +2.35238 q^{93} +(-7.19206 + 22.1349i) q^{94} +(12.5319 + 9.23261i) q^{95} +(3.64032 - 1.18281i) q^{96} +(3.20022 - 1.03981i) q^{97} +(-6.20293 - 4.50669i) q^{98} +15.0991i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 8 q^{2} - 44 q^{4} - 4 q^{8} + 28 q^{9} - 18 q^{13} - 10 q^{15} - 28 q^{16} + 2 q^{17} - 60 q^{18} - 8 q^{19} + 32 q^{21} + 6 q^{25} + 52 q^{26} - 54 q^{30} + 44 q^{32} - 24 q^{33} + 26 q^{35} + 34 q^{36}+ \cdots - 36 q^{98}+O(q^{100}) \) 168 * q - 8 * q^2 - 44 * q^4 - 4 * q^8 + 28 * q^9 - 18 * q^13 - 10 * q^15 - 28 * q^16 + 2 * q^17 - 60 * q^18 - 8 * q^19 + 32 * q^21 + 6 * q^25 + 52 * q^26 - 54 * q^30 + 44 * q^32 - 24 * q^33 + 26 * q^35 + 34 * q^36 - 18 * q^38 + 80 * q^42 - 8 * q^43 - 40 * q^47 - 84 * q^49 - 82 * q^50 - 36 * q^51 - 30 * q^52 - 42 * q^53 - 18 * q^55 - 18 * q^59 + 28 * q^60 - 16 * q^64 - 140 * q^66 - 62 * q^67 + 144 * q^68 + 44 * q^69 + 4 * q^70 - 6 * q^72 + 72 * q^76 + 48 * q^77 - 28 * q^81 - 14 * q^83 + 24 * q^84 + 62 * q^85 + 82 * q^86 + 48 * q^87 + 90 * q^89 - 224 * q^93 + 26 * q^94 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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