LMFDB - Embedded newform 425.2.p.a.16.10

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			16.10
Character	$\chi$	$=$	425.16
Dual form			425.2.p.a.186.10

$q$-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} +(-4.04310 - 0.808311i) 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} +(5.06705 + 5.49221i) 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} +(-4.56593 + 8.00951i) 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	−0.138039	−	0.990427i	$-0.544080\pi$
$3$	0.575810	−	0.187092i	0.332444	−	0.108018i	0.470483	+	0.882409i	$0.344080\pi$
$4$	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	$0.101837\pi$
$7$			1.66418i			0.629000i	−0.949257	+	0.314500i	$0.898163\pi$
$8$	−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	$0.532283\pi$
$11$	−3.37012	+	4.63857i	−1.01613	+	1.39858i	−0.914882	+	0.403721i	$0.867717\pi$
$12$	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
$17$	−4.04310	−	0.808311i	−0.980595	−	0.196044i
$17$	−4.04310	−	0.808311i	−0.980595	−	0.196044i
$18$	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	−0.990317	−	0.138822i	$-0.955668\pi$
$23$	−2.64857	+	3.64544i	−0.552265	+	0.760127i	0.438053	+	0.898949i	$0.355668\pi$
$24$			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	−0.723883	−	0.689923i	$-0.757644\pi$
$29$	−4.86813	+	1.58175i	−0.903990	+	0.293724i	−0.180107	+	0.983647i	$0.557644\pi$
$30$	−1.45533	+	1.97539i	−0.265705	+	0.360655i
$31$	3.69524	+	1.20065i	0.663684	+	0.215644i	0.621438	−	0.783463i	$-0.286549\pi$
$31$	3.69524	+	1.20065i	0.663684	+	0.215644i	0.0422458	+	0.999107i	$0.486549\pi$
$32$	−6.32208			−1.11760
$33$	−1.07271	+	3.30146i	−0.186735	+	0.574710i
$34$	5.06705	+	5.49221i	0.868992	+	0.941907i
$35$	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	0.932037	−	0.362363i	$-0.118030\pi$
$37$	1.82114	+	2.50659i	0.299394	+	0.412080i	−0.632643	+	0.774444i	$0.718030\pi$
$38$	−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	0.870009	−	0.493036i	$-0.164113\pi$
$41$	0.846857	+	1.16560i	0.132257	+	0.182036i	−0.737752	+	0.675072i	$0.764113\pi$
$42$	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	−0.604348	−	0.796720i	$-0.706566\pi$
$61$	2.65651	−	3.65638i	0.340132	−	0.468151i	0.944480	+	0.328569i	$0.106566\pi$
$62$	−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	−0.597755	−	0.801679i	$-0.703940\pi$
$71$	−5.14108	+	1.67044i	−0.610134	+	0.198245i	−0.0123791	+	0.999923i	$0.503940\pi$
$72$	−1.05501	−	3.24700i	−0.124334	−	0.382662i
$73$	−7.81942	+	10.7625i	−0.915193	+	1.25966i	0.0501683	+	0.998741i	$0.484024\pi$
$73$	−7.81942	+	10.7625i	−0.915193	+	1.25966i	−0.965362	+	0.260915i	$0.915976\pi$
$74$		−	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	0.0610863	−	0.998132i	$-0.480543\pi$
$79$	6.19679	−	2.01346i	0.697194	−	0.226532i	0.636107	+	0.771600i	$0.280543\pi$
$80$	−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
$85$	−4.56593	+	8.00951i	−0.495245	+	0.868754i
$86$	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	−0.466941	−	0.884288i	$-0.654644\pi$
$97$	−3.20022	+	1.03981i	−0.324933	+	0.105577i	0.142008	+	0.989865i	$0.454644\pi$
$98$	−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	$0.470763\pi$
$102$	3.94520	+	2.21446i	0.390633	+	0.219265i
$103$	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	$-0.921405\pi$
$107$		−	5.05646i		−	0.488827i	0.969671	−	0.244413i	$-0.0785954\pi$
$108$	−4.16720	−	1.35401i	−0.400989	−	0.130289i
$109$	−0.992250	−	1.36571i	−0.0950403	−	0.130812i	0.758849	−	0.651267i	$-0.225762\pi$
$109$	−0.992250	−	1.36571i	−0.0950403	−	0.130812i	−0.853889	+	0.520455i	$0.825762\pi$
$110$	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	0.613229	−	0.789905i	$-0.289870\pi$
$113$	−3.48151	−	4.79189i	−0.327513	−	0.450783i	−0.940742	+	0.339122i	$0.889870\pi$
$114$	−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
$119$	1.34517	−	6.72843i	0.123312	−	0.616794i
$120$	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	−0.0424430	−	0.999099i	$-0.513514\pi$
$131$	−7.60024	−	2.46947i	−0.664036	−	0.215758i	−0.621593	+	0.783341i	$0.713514\pi$
$132$	−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
$136$	2.61639	−	4.66126i	0.224353	−	0.399699i
$137$	−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	−0.998218	−	0.0596756i	$-0.980993\pi$
$139$	−7.46292	+	10.2718i	−0.632997	+	0.871245i	0.365221	+	0.930921i	$0.380993\pi$
$140$	−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
$153$	9.86499	−	4.53619i	0.797537	−	0.366730i
$154$	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	$0.0659294\pi$
$163$	11.1303	+	15.3196i	0.871795	+	1.19992i	−0.106832	+	0.994277i	$0.534071\pi$
$164$	−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	0.549256	−	0.835654i	$-0.314911\pi$
$167$	6.49280	+	2.10964i	0.502428	+	0.163249i	−0.0468277	+	0.998903i	$0.514911\pi$
$168$	−1.30624			−0.100779
$169$	2.94236	−	9.05566i	0.226336	−	0.696589i
$170$	15.2271	−	6.87982i	1.16787	−	0.527658i
$171$	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	−0.998711	−	0.0507610i	$-0.983835\pi$
$173$	−8.44177	+	11.6191i	−0.641816	+	0.883383i	0.356895	+	0.934144i	$0.383835\pi$
$174$	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	$0.0331976\pi$
$181$	25.0288	+	8.13236i	1.86038	+	0.604474i	0.865812	+	0.500369i	$0.166802\pi$
$182$			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
$187$	17.3751	−	16.0301i	1.27060	−	1.17224i
$188$	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	$-0.857922\pi$
$193$		−	11.9941i		−	0.863354i	0.902028	−	0.431677i	$-0.142078\pi$
$194$	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	−0.225234	−	0.974305i	$-0.572315\pi$
$197$	2.31911	−	0.753524i	0.165230	−	0.0536863i	0.390464	+	0.920618i	$0.372315\pi$
$198$	−16.0848	+	22.1388i	−1.14309	+	1.57333i
$199$		−	8.64410i		−	0.612764i	−0.951909	−	0.306382i	$-0.900881\pi$
$199$		−	8.64410i		−	0.612764i	0.951909	−	0.306382i	$-0.0991185\pi$
$200$	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
$204$	−1.33978	−	2.91365i	−0.0938032	−	0.203996i
$205$	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	$0.493447\pi$
$211$	−13.6054	+	18.7262i	−0.936631	+	1.28916i	−0.957216	+	0.289374i	$0.906553\pi$
$212$	−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
$221$	17.7776	−	8.17464i	1.19585	−	0.549886i
$222$	−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	−0.943698	−	0.330809i	$-0.892678\pi$
$227$	−5.08436	+	6.99802i	−0.337461	+	0.464475i	0.606237	+	0.795284i	$0.292678\pi$
$228$	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	0.727449	−	0.686162i	$-0.240706\pi$
$233$	13.9310	+	4.52646i	0.912652	+	0.296539i	0.185203	+	0.982700i	$0.440706\pi$
$234$	−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
$238$	−9.14002	+	8.43247i	−0.592459	+	0.546596i
$239$	−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	0.542488	−	0.840063i	$-0.317482\pi$
$241$	−6.58377	−	9.06178i	−0.424098	−	0.583720i	−0.966586	+	0.256343i	$0.917482\pi$
$242$	−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
$255$	−1.13059	+	5.46620i	−0.0708004	+	0.342307i
$256$	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	−0.342821	−	0.939401i	$-0.611382\pi$
$269$	−19.2277	−	6.24747i	−1.17234	−	0.380915i	−0.829514	+	0.558486i	$0.811382\pi$
$270$	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	$0.866505\pi$
$272$	−18.4267	+	8.47309i	−1.11728	+	0.513756i
$273$	−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	$0.604078\pi$
$277$	−18.6837	+	25.7159i	−1.12260	+	1.54512i	−0.801421	+	0.598101i	$0.795922\pi$
$278$	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	0.695663	−	0.718368i	$-0.255111\pi$
$283$	14.0674	+	4.57077i	0.836220	+	0.271704i	0.140557	+	0.990073i	$0.455111\pi$
$284$	−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
$289$	15.6933	+	6.53616i	0.923133	+	0.384480i
$290$	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
$306$	−19.2967	−	3.85787i	−1.10312	−	0.220540i
$307$	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	$-0.523730\pi$
$311$	15.8179	−	21.7715i	0.896951	−	1.23455i	0.971431	−	0.237324i	$-0.0762703\pi$
$312$	−2.18949	−	3.01358i	−0.123956	−	0.170610i
$313$	−9.97421	−	13.7283i	−0.563776	−	0.775971i	0.428025	−	0.903767i	$-0.359210\pi$
$313$	−9.97421	−	13.7283i	−0.563776	−	0.775971i	−0.991800	+	0.127796i	$0.959210\pi$
$314$	−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	0.282489	−	0.959271i	$-0.408840\pi$
$317$	−0.940404	−	0.305556i	−0.0528183	−	0.0171617i	−0.335307	+	0.942109i	$0.608840\pi$
$318$		−	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
$323$	−14.0486	+	25.0284i	−0.781684	+	1.39262i
$324$	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	0.953589	−	0.301111i	$-0.0973575\pi$
$337$	6.83893	+	9.41298i	0.372540	+	0.512757i	−0.581049	+	0.813869i	$0.697358\pi$
$338$	−13.9610	+	10.1433i	−0.759380	+	0.551722i
$339$	−2.90121	−	2.10785i	−0.157572	−	0.114483i
$340$	−11.5986	−	2.39897i	−0.629022	−	0.130102i
$341$	−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	0.386813	−	0.922158i	$-0.373576\pi$
$347$	23.1318	−	7.51599i	1.24178	−	0.403479i	0.854969	+	0.518679i	$0.173576\pi$
$348$	−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	−0.0780792	−	0.996947i	$-0.524879\pi$
$367$	−13.9319	−	4.52674i	−0.727238	−	0.236294i	−0.649158	+	0.760653i	$0.724879\pi$
$368$			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	0.0883713	−	0.996088i	$-0.471834\pi$
$379$	14.5104	−	4.71473i	0.745351	−	0.242179i	0.656980	+	0.753908i	$0.271834\pi$
$380$	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
$391$	13.6551	−	12.5980i	0.690567	−	0.637109i
$392$	−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	−0.693090	−	0.720851i	$-0.743751\pi$
$397$	−16.5397	+	5.37408i	−0.830105	+	0.269717i	−0.137015	+	0.990569i	$0.543751\pi$
$398$	−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	$0.351115\pi$
$401$			35.7483i			1.78518i	−0.450866	+	0.892592i	$0.648885\pi$
$402$	−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
$408$	0.634458	−	3.17350i	0.0314104	−	0.157112i
$409$	−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	0.122469	−	0.992472i	$-0.460919\pi$
$419$	−7.40610	−	2.40639i	−0.361812	−	0.117560i	−0.484281	+	0.874913i	$0.660919\pi$
$420$	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
$425$	13.7768	+	15.3362i	0.668274	+	0.743915i
$426$	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	0.505388	−	0.862892i	$-0.331349\pi$
$431$	8.45078	+	2.74582i	0.407060	+	0.132262i	−0.0983282	+	0.995154i	$0.531349\pi$
$432$			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	−0.346089	−	0.938202i	$-0.612491\pi$
$439$	13.6848	−	18.8355i	0.653141	−	0.898971i	0.999230	+	0.0392303i	$0.0124906\pi$
$440$	−15.8415	+	5.03125i	−0.755213	+	0.239856i
$441$	−9.01310	+	6.54840i	−0.429195	+	0.311829i
$442$	−34.7745	−	6.95224i	−1.65405	−	0.330684i
$443$	−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	$0.0280228\pi$
$449$			3.72609i			0.175845i	−0.996127	+	0.0879225i	$0.971977\pi$
$450$	−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
$459$	10.3359	−	9.53576i	0.482438	−	0.445091i
$460$	−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	−0.683846	−	0.729627i	$-0.739694\pi$
$479$	−17.6889	+	5.74746i	−0.808224	+	0.262608i	−0.124379	+	0.992235i	$0.539694\pi$
$480$	−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	$-0.945463\pi$
$487$	−18.6038	−	25.6059i	−0.843017	−	1.16031i	0.142342	−	0.989818i	$-0.454537\pi$
$488$	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	$0.230863\pi$
$499$			29.6359i			1.32668i	−0.748316	+	0.663342i	$0.769137\pi$
$500$	−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	0.463781	−	0.885950i	$-0.346492\pi$
$503$	30.4957	−	9.90865i	1.35974	−	0.441805i	0.895955	+	0.444145i	$0.146492\pi$
$504$	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	$0.00622567\pi$
$510$	7.48076	−	6.81034i	0.331254	−	0.301567i
$511$	−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	−0.689106	−	0.724661i	$-0.741997\pi$
$521$	−18.7319	+	6.08637i	−0.820660	+	0.266648i	−0.131554	+	0.991309i	$0.541997\pi$
$522$	−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
$527$	−13.9697	−	7.84126i	−0.608529	−	0.341571i
$528$	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	0.818512	−	0.574490i	$-0.194799\pi$
$541$	0.446716	+	0.614852i	0.0192058	+	0.0264345i	−0.799306	+	0.600924i	$0.794799\pi$
$542$	1.93673	−	5.96065i	0.0831898	−	0.256032i
$543$	15.9333			0.683765
$544$	25.5608	+	5.11021i	1.09591	+	0.219098i
$545$	−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	−0.821378	−	0.570384i	$-0.806794\pi$
$547$	−26.9108	+	8.74385i	−1.15062	+	0.373860i	−0.329245	+	0.944244i	$0.606794\pi$
$548$	−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
$561$	7.00567	−	12.4810i	0.295780	−	0.526949i
$562$	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	0.0256746	−	0.999670i	$-0.491827\pi$
$571$	15.1507	−	4.92276i	0.634037	−	0.206011i	0.608363	+	0.793659i	$0.291827\pi$
$572$	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	$0.890693\pi$
$578$	−16.0472	−	26.3013i	−0.667474	−	1.09399i
$579$	−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
$595$	−13.3293	−	7.59852i	−0.546446	−	0.311509i
$596$	−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	$0.379754\pi$
$601$			45.5735i			1.85898i	−0.368843	+	0.929492i	$0.620246\pi$
$602$	−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	$-0.792899\pi$
$607$		−	29.8450i		−	1.21137i	0.795705	−	0.605685i	$-0.207101\pi$
$608$	−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
$612$	9.45855	+	10.2522i	0.382339	+	0.414420i
$613$	−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	−0.289540	−	0.957166i	$-0.593502\pi$
$617$	−26.9854	−	8.76808i	−1.08639	−	0.352990i	−0.796851	+	0.604176i	$0.793502\pi$
$618$		−	10.3846i		−	0.417728i
$619$	−29.0381	−	9.43504i	−1.16714	−	0.379226i	−0.339564	−	0.940583i	$-0.610280\pi$
$619$	−29.0381	−	9.43504i	−1.16714	−	0.379226i	−0.827574	+	0.561357i	$0.810280\pi$
$620$	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
$629$	−5.33695	−	11.6064i	−0.212798	−	0.462778i
$630$	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	$-0.984365\pi$
$641$	−18.6554	−	25.6770i	−0.736846	−	1.01418i	0.261948	−	0.965082i	$-0.415635\pi$
$642$	−1.71454	+	5.27681i	−0.0676675	+	0.208259i
$643$			21.1373i			0.833574i	0.909004	+	0.416787i	$0.136844\pi$
$643$			21.1373i			0.833574i	−0.909004	+	0.416787i	$0.863156\pi$
$644$	2.97691	−	9.16200i	0.117307	−	0.361033i
$645$	−0.0322189	+	4.85595i	−0.00126862	+	0.191203i
$646$	47.2609	−	21.7318i	1.85945	−	0.855028i
$647$	−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	0.688364	−	0.725365i	$-0.258329\pi$
$653$	42.7164	−	13.8794i	1.67162	−	0.543143i	0.983257	+	0.182222i	$0.0583290\pi$
$654$	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
$663$	8.70712	−	8.03308i	0.338156	−	0.311979i
$664$	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	$-0.528534\pi$
$673$	22.9687	−	31.6137i	0.885379	−	1.21862i	0.974902	−	0.222634i	$-0.0714656\pi$
$674$		−	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	−0.900348	−	0.435172i	$-0.856688\pi$
$677$	−5.41856	+	7.45800i	−0.208252	+	0.286634i	0.692095	+	0.721806i	$0.256688\pi$
$678$	2.00840	+	6.18121i	0.0771321	+	0.237388i
$679$	−1.73044	−	5.32574i	−0.0664081	−	0.204383i
$680$	−8.04641	−	8.83851i	−0.308566	−	0.338941i
$681$	−1.61835	+	4.98077i	−0.0620153	+	0.190863i
$682$	40.3746			1.54602
$683$	−21.1232	−	6.86334i	−0.808257	−	0.262618i	−0.124397	−	0.992232i	$-0.539700\pi$
$683$	−21.1232	−	6.86334i	−0.808257	−	0.262618i	−0.683859	+	0.729614i	$0.739700\pi$
$684$	−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	$-0.869250\pi$
$691$	−26.6357	−	36.6609i	−1.01327	−	1.39465i	−0.0964534	−	0.995337i	$-0.530750\pi$
$692$	−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
$697$	−2.48176	−	5.39716i	−0.0940034	−	0.204432i
$698$	−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	0.909429	−	0.415860i	$-0.136519\pi$
$709$	6.20126	+	8.53530i	0.232893	+	0.320550i	−0.676535	+	0.736410i	$0.736519\pi$
$710$	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
$714$	−3.68526	+	6.56552i	−0.137917	+	0.245708i
$715$	−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	0.858356	−	0.513054i	$-0.171486\pi$
$719$	33.5503	+	10.9012i	1.25122	+	0.406544i	0.392859	+	0.919599i	$0.371486\pi$
$720$	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
$731$	14.5024	+	2.89938i	0.536391	+	0.107237i
$732$	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	$-0.944151\pi$
$743$		−	9.51616i		−	0.349114i	0.984647	−	0.174557i	$-0.0558494\pi$
$744$	−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
$748$	26.4832	+	14.8651i	0.968320	+	0.543523i
$749$	8.41485			0.307472
$750$	11.7407	−	3.55805i	0.428710	−	0.129921i
$751$		−	37.9812i		−	1.38595i	−0.720960	−	0.692977i	$-0.756299\pi$
$751$		−	37.9812i		−	1.38595i	0.720960	−	0.692977i	$-0.243701\pi$
$752$	−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
$765$	−2.67020	−	24.1318i	−0.0965413	−	0.872488i
$766$	−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

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} +(-4.04310 - 0.808311i) 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} +(5.06705 + 5.49221i) 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} +(-4.56593 + 8.00951i) 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

Fields

Representations

Groups

Database

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