LMFDB - Embedded newform 425.2.r.a.69.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(69,425)]

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([9, 0]))

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

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

chi := DirichletCharacter("425.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.r (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:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			69.14
Character	$\chi$	$=$	425.69
Dual form			425.2.r.a.154.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.07215 + 0.348362i) q^{2} +(0.792633 + 1.09097i) q^{3} +(-0.589886 + 0.428578i) q^{4} +(-1.75044 + 1.39139i) q^{5} +(-1.22987 - 0.893554i) q^{6} +3.55811i q^{7} +(1.80840 - 2.48904i) q^{8} +(0.365112 - 1.12370i) q^{9} +(1.39202 - 2.10156i) q^{10} +(1.50705 + 4.63823i) q^{11} +(-0.935127 - 0.303841i) q^{12} +(0.640501 + 0.208112i) q^{13} +(-1.23951 - 3.81482i) q^{14} +(-2.90541 - 0.806805i) q^{15} +(-0.621148 + 1.91170i) q^{16} +(-0.587785 + 0.809017i) q^{17} +1.33196i q^{18} +(-6.31371 - 4.58718i) q^{19} +(0.436241 - 1.57096i) q^{20} +(-3.88177 + 2.82027i) q^{21} +(-3.23157 - 4.44788i) q^{22} +(-5.87858 + 1.91007i) q^{23} +4.14885 q^{24} +(1.12806 - 4.87109i) q^{25} -0.759211 q^{26} +(5.36284 - 1.74249i) q^{27} +(-1.52493 - 2.09888i) q^{28} +(-0.803048 + 0.583448i) q^{29} +(3.39610 - 0.147121i) q^{30} +(-5.16185 - 3.75031i) q^{31} +3.88724i q^{32} +(-3.86561 + 5.32056i) q^{33} +(0.348362 - 1.07215i) q^{34} +(-4.95072 - 6.22825i) q^{35} +(0.266218 + 0.819334i) q^{36} +(10.5615 + 3.43165i) q^{37} +(8.36724 + 2.71868i) q^{38} +(0.280640 + 0.863721i) q^{39} +(0.297747 + 6.87310i) q^{40} +(-0.930523 + 2.86385i) q^{41} +(3.17936 - 4.37602i) q^{42} -3.95759i q^{43} +(-2.87683 - 2.09014i) q^{44} +(0.924399 + 2.47498i) q^{45} +(5.63732 - 4.09576i) q^{46} +(-4.33980 - 5.97322i) q^{47} +(-2.57794 + 0.837622i) q^{48} -5.66014 q^{49} +(0.487449 + 5.61551i) q^{50} -1.34851 q^{51} +(-0.467015 + 0.151742i) q^{52} +(3.50317 + 4.82171i) q^{53} +(-5.14274 + 3.73642i) q^{54} +(-9.09159 - 6.02204i) q^{55} +(8.85628 + 6.43447i) q^{56} -10.5240i q^{57} +(0.657735 - 0.905295i) q^{58} +(-3.11379 + 9.58328i) q^{59} +(2.05964 - 0.769272i) q^{60} +(2.80258 + 8.62545i) q^{61} +(6.84074 + 2.22269i) q^{62} +(3.99824 + 1.29911i) q^{63} +(-2.59646 - 7.99110i) q^{64} +(-1.41072 + 0.526901i) q^{65} +(2.29103 - 7.05106i) q^{66} +(1.61559 - 2.22366i) q^{67} -0.729140i q^{68} +(-6.74338 - 4.89935i) q^{69} +(7.47760 + 4.95297i) q^{70} +(-7.67294 + 5.57472i) q^{71} +(-2.13667 - 2.94087i) q^{72} +(8.65492 - 2.81215i) q^{73} -12.5190 q^{74} +(6.20833 - 2.63030i) q^{75} +5.69033 q^{76} +(-16.5033 + 5.36226i) q^{77} +(-0.601776 - 0.828273i) q^{78} +(-0.661473 + 0.480589i) q^{79} +(-1.57263 - 4.21056i) q^{80} +(3.28413 + 2.38606i) q^{81} -3.39464i q^{82} +(-4.04620 + 5.56912i) q^{83} +(1.08110 - 3.32728i) q^{84} +(-0.0967771 - 2.23397i) q^{85} +(1.37867 + 4.24312i) q^{86} +(-1.27304 - 0.413637i) q^{87} +(14.2701 + 4.63664i) q^{88} +(0.0168473 + 0.0518505i) q^{89} +(-1.85328 - 2.33152i) q^{90} +(-0.740483 + 2.27897i) q^{91} +(2.64908 - 3.64615i) q^{92} -8.60402i q^{93} +(6.73376 + 4.89236i) q^{94} +(17.4343 - 0.755265i) q^{95} +(-4.24085 + 3.08116i) q^{96} +(8.37450 + 11.5265i) q^{97} +(6.06851 - 1.97178i) q^{98} +5.76222 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) $ 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Character values

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

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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 $

$2$	−1.07215	+	0.348362i	−0.758124	+	0.246329i	−0.662473	−	0.749086i	$-0.730493\pi$
$2$	−1.07215	+	0.348362i	−0.758124	+	0.246329i	−0.0956507	+	0.995415i	$0.530493\pi$
$3$	0.792633	+	1.09097i	0.457627	+	0.629869i	0.974014	−	0.226486i	$-0.0727236\pi$
$3$	0.792633	+	1.09097i	0.457627	+	0.629869i	−0.516388	+	0.856355i	$0.672724\pi$
$4$	−0.589886	+	0.428578i	−0.294943	+	0.214289i
$5$	−1.75044	+	1.39139i	−0.782820	+	0.622249i
$5$	−1.75044	+	1.39139i	−0.782820	+	0.622249i
$6$	−1.22987	−	0.893554i	−0.502093	−	0.364792i
$7$			3.55811i			1.34484i	0.740170	+	0.672419i	$0.234745\pi$
$7$			3.55811i			1.34484i	−0.740170	+	0.672419i	$0.765255\pi$
$8$	1.80840	−	2.48904i	0.639364	−	0.880009i
$9$	0.365112	−	1.12370i	0.121704	−	0.374566i
$10$	1.39202	−	2.10156i	0.440196	−	0.664573i
$11$	1.50705	+	4.63823i	0.454393	+	1.39848i	0.871846	+	0.489781i	$0.162923\pi$
$11$	1.50705	+	4.63823i	0.454393	+	1.39848i	−0.417452	+	0.908699i	$0.637077\pi$
$12$	−0.935127	−	0.303841i	−0.269948	−	0.0877114i
$13$	0.640501	+	0.208112i	0.177643	+	0.0577197i	0.396488	−	0.918040i	$-0.370229\pi$
$13$	0.640501	+	0.208112i	0.177643	+	0.0577197i	−0.218845	+	0.975760i	$0.570229\pi$
$14$	−1.23951	−	3.81482i	−0.331273	−	1.01955i
$15$	−2.90541	−	0.806805i	−0.750175	−	0.208316i
$16$	−0.621148	+	1.91170i	−0.155287	+	0.477924i
$17$	−0.587785	+	0.809017i	−0.142559	+	0.196215i
$17$	−0.587785	+	0.809017i	−0.142559	+	0.196215i
$18$			1.33196i			0.313947i
$19$	−6.31371	−	4.58718i	−1.44846	−	1.05237i	−0.986187	−	0.165635i	$-0.947033\pi$
$19$	−6.31371	−	4.58718i	−1.44846	−	1.05237i	−0.462277	−	0.886736i	$-0.652967\pi$
$20$	0.436241	−	1.57096i	0.0975464	−	0.351278i
$21$	−3.88177	+	2.82027i	−0.847073	+	0.615434i
$22$	−3.23157	−	4.44788i	−0.688973	−	0.948290i
$23$	−5.87858	+	1.91007i	−1.22577	+	0.398277i	−0.849180	−	0.528104i	$-0.822903\pi$
$23$	−5.87858	+	1.91007i	−1.22577	+	0.398277i	−0.376590	+	0.926380i	$0.622903\pi$
$24$	4.14885			0.846881
$25$	1.12806	−	4.87109i	0.225613	−	0.974217i
$26$	−0.759211			−0.148894
$27$	5.36284	−	1.74249i	1.03208	−	0.335343i
$28$	−1.52493	−	2.09888i	−0.288184	−	0.396651i
$29$	−0.803048	+	0.583448i	−0.149122	+	0.108344i	−0.659845	−	0.751402i	$-0.729378\pi$
$29$	−0.803048	+	0.583448i	−0.149122	+	0.108344i	0.510723	+	0.859746i	$0.329378\pi$
$30$	3.39610	−	0.147121i	0.620040	−	0.0268605i
$31$	−5.16185	−	3.75031i	−0.927096	−	0.673575i	0.0181839	−	0.999835i	$-0.494212\pi$
$31$	−5.16185	−	3.75031i	−0.927096	−	0.673575i	−0.945280	+	0.326260i	$0.894212\pi$
$32$			3.88724i			0.687174i
$33$	−3.86561	+	5.32056i	−0.672916	+	0.926190i
$34$	0.348362	−	1.07215i	0.0597437	−	0.183872i
$35$	−4.95072	−	6.22825i	−0.836824	−	1.05277i
$36$	0.266218	+	0.819334i	0.0443696	+	0.136556i
$37$	10.5615	+	3.43165i	1.73630	+	0.564159i	0.994337	−	0.106277i	$-0.0338931\pi$
$37$	10.5615	+	3.43165i	1.73630	+	0.564159i	0.741967	+	0.670436i	$0.233893\pi$
$38$	8.36724	+	2.71868i	1.35735	+	0.441028i
$39$	0.280640	+	0.863721i	0.0449384	+	0.138306i
$40$	0.297747	+	6.87310i	0.0470779	+	1.08673i
$41$	−0.930523	+	2.86385i	−0.145323	+	0.447259i	−0.997052	−	0.0767233i	$-0.975554\pi$
$41$	−0.930523	+	2.86385i	−0.145323	+	0.447259i	0.851729	+	0.523982i	$0.175554\pi$
$42$	3.17936	−	4.37602i	0.490586	−	0.675234i
$43$		−	3.95759i		−	0.603526i	−0.953383	−	0.301763i	$-0.902425\pi$
$43$		−	3.95759i		−	0.603526i	0.953383	−	0.301763i	$-0.0975752\pi$
$44$	−2.87683	−	2.09014i	−0.433699	−	0.315101i
$45$	0.924399	+	2.47498i	0.137801	+	0.368948i
$46$	5.63732	−	4.09576i	0.831178	−	0.603886i
$47$	−4.33980	−	5.97322i	−0.633025	−	0.871284i	0.365194	−	0.930931i	$-0.381003\pi$
$47$	−4.33980	−	5.97322i	−0.633025	−	0.871284i	−0.998220	+	0.0596470i	$0.981003\pi$
$48$	−2.57794	+	0.837622i	−0.372093	+	0.120900i
$49$	−5.66014			−0.808591
$50$	0.487449	+	5.61551i	0.0689357	+	0.794152i
$51$	−1.34851			−0.188829
$52$	−0.467015	+	0.151742i	−0.0647633	+	0.0210429i
$53$	3.50317	+	4.82171i	0.481198	+	0.662312i	0.978735	−	0.205131i	$-0.0657620\pi$
$53$	3.50317	+	4.82171i	0.481198	+	0.662312i	−0.497537	+	0.867443i	$0.665762\pi$
$54$	−5.14274	+	3.73642i	−0.699839	+	0.508463i
$55$	−9.09159	−	6.02204i	−1.22591	−	0.812011i
$56$	8.85628	+	6.43447i	1.18347	+	0.859842i
$57$		−	10.5240i		−	1.39394i
$58$	0.657735	−	0.905295i	0.0863649	−	0.118871i
$59$	−3.11379	+	9.58328i	−0.405382	+	1.24764i	0.515195	+	0.857073i	$0.327720\pi$
$59$	−3.11379	+	9.58328i	−0.405382	+	1.24764i	−0.920576	+	0.390563i	$0.872280\pi$
$60$	2.05964	−	0.769272i	0.265899	−	0.0993125i
$61$	2.80258	+	8.62545i	0.358833	+	1.10438i	0.953753	+	0.300591i	$0.0971837\pi$
$61$	2.80258	+	8.62545i	0.358833	+	1.10438i	−0.594920	+	0.803785i	$0.702816\pi$
$62$	6.84074	+	2.22269i	0.868775	+	0.282282i
$63$	3.99824	+	1.29911i	0.503731	+	0.163672i
$64$	−2.59646	−	7.99110i	−0.324558	−	0.998887i
$65$	−1.41072	+	0.526901i	−0.174979	+	0.0653541i
$66$	2.29103	−	7.05106i	0.282006	−	0.867926i
$67$	1.61559	−	2.22366i	0.197375	−	0.271664i	−0.698845	−	0.715273i	$-0.746302\pi$
$67$	1.61559	−	2.22366i	0.197375	−	0.271664i	0.896220	+	0.443609i	$0.146302\pi$
$68$		−	0.729140i		−	0.0884212i
$69$	−6.74338	−	4.89935i	−0.811807	−	0.589812i
$70$	7.47760	+	4.95297i	0.893744	+	0.591993i
$71$	−7.67294	+	5.57472i	−0.910610	+	0.661597i	−0.941169	−	0.337936i	$-0.890271\pi$
$71$	−7.67294	+	5.57472i	−0.910610	+	0.661597i	0.0305589	+	0.999533i	$0.490271\pi$
$72$	−2.13667	−	2.94087i	−0.251809	−	0.346585i
$73$	8.65492	−	2.81215i	1.01298	−	0.329138i	0.244940	−	0.969538i	$-0.421232\pi$
$73$	8.65492	−	2.81215i	1.01298	−	0.329138i	0.768041	+	0.640400i	$0.221232\pi$
$74$	−12.5190			−1.45530
$75$	6.20833	−	2.63030i	0.716876	−	0.303721i
$76$	5.69033			0.652726
$77$	−16.5033	+	5.36226i	−1.88073	+	0.611086i
$78$	−0.601776	−	0.828273i	−0.0681377	−	0.0937835i
$79$	−0.661473	+	0.480589i	−0.0744216	+	0.0540704i	−0.624374	−	0.781126i	$-0.714646\pi$
$79$	−0.661473	+	0.480589i	−0.0744216	+	0.0540704i	0.549952	+	0.835196i	$0.314646\pi$
$80$	−1.57263	−	4.21056i	−0.175826	−	0.470755i
$81$	3.28413	+	2.38606i	0.364904	+	0.265118i
$82$		−	3.39464i		−	0.374875i
$83$	−4.04620	+	5.56912i	−0.444128	+	0.611290i	−0.971123	−	0.238578i	$-0.923319\pi$
$83$	−4.04620	+	5.56912i	−0.444128	+	0.611290i	0.526995	+	0.849868i	$0.323319\pi$
$84$	1.08110	−	3.32728i	0.117958	−	0.363036i
$85$	−0.0967771	−	2.23397i	−0.0104969	−	0.242308i
$86$	1.37867	+	4.24312i	0.148666	+	0.457548i
$87$	−1.27304	−	0.413637i	−0.136485	−	0.0443465i
$88$	14.2701	+	4.63664i	1.52120	+	0.494267i
$89$	0.0168473	+	0.0518505i	0.00178581	+	0.00549615i	0.951945	−	0.306268i	$-0.0990802\pi$
$89$	0.0168473	+	0.0518505i	0.00178581	+	0.00549615i	−0.950160	+	0.311764i	$0.899080\pi$
$90$	−1.85328	−	2.33152i	−0.195353	−	0.245764i
$91$	−0.740483	+	2.27897i	−0.0776238	+	0.238901i
$92$	2.64908	−	3.64615i	0.276186	−	0.380138i
$93$		−	8.60402i		−	0.892195i
$94$	6.73376	+	4.89236i	0.694534	+	0.504609i
$95$	17.4343	−	0.755265i	1.78872	−	0.0774886i
$96$	−4.24085	+	3.08116i	−0.432830	+	0.314469i
$97$	8.37450	+	11.5265i	0.850302	+	1.17034i	0.983796	+	0.179290i	$0.0573801\pi$
$97$	8.37450	+	11.5265i	0.850302	+	1.17034i	−0.133495	+	0.991050i	$0.542620\pi$
$98$	6.06851	−	1.97178i	0.613012	−	0.199180i
$99$	5.76222			0.579125
$100$	1.42221	+	3.35685i	0.142221	+	0.335685i
$101$	−2.44690			−0.243475			−0.121738	−	0.992562i	$-0.538847\pi$
$101$	−2.44690			−0.243475			−0.121738	+	0.992562i	$0.538847\pi$
$102$	1.44580	−	0.469769i	0.143156	−	0.0465141i
$103$	7.26268	+	9.99623i	0.715613	+	0.984957i	0.999658	+	0.0261464i	$0.00832360\pi$
$103$	7.26268	+	9.99623i	0.715613	+	0.984957i	−0.284045	+	0.958811i	$0.591676\pi$
$104$	1.67628	−	1.21789i	0.164373	−	0.119424i
$105$	2.87070	−	10.3378i	0.280152	−	1.00886i
$106$	−5.43563	−	3.94921i	−0.527955	−	0.383582i
$107$		−	3.69094i		−	0.356817i	−0.983957	−	0.178408i	$-0.942905\pi$
$107$		−	3.69094i		−	0.356817i	0.983957	−	0.178408i	$-0.0570948\pi$
$108$	−2.41667	+	3.32626i	−0.232544	+	0.320070i
$109$	−3.96487	+	12.2026i	−0.379765	+	1.16880i	0.560442	+	0.828194i	$0.310631\pi$
$109$	−3.96487	+	12.2026i	−0.379765	+	1.16880i	−0.940207	+	0.340603i	$0.889369\pi$
$110$	11.8454	+	3.28935i	1.12941	+	0.313627i
$111$	4.62760	+	14.2423i	0.439232	+	1.35182i
$112$	−6.80202	−	2.21011i	−0.642731	−	0.208836i
$113$	1.90795	+	0.619929i	0.179484	+	0.0583180i	0.397380	−	0.917654i	$-0.369919\pi$
$113$	1.90795	+	0.619929i	0.179484	+	0.0583180i	−0.217896	+	0.975972i	$0.569919\pi$
$114$	3.66616	+	11.2833i	0.343367	+	1.05678i
$115$	7.63245	−	11.5229i	0.711729	−	1.07451i
$116$	0.223654	−	0.688336i	0.0207658	−	0.0639104i
$117$	0.467710	−	0.643747i	0.0432398	−	0.0595144i
$118$		−	11.3594i		−	1.04572i
$119$	−2.87857	−	2.09140i	−0.263878	−	0.191719i
$120$	−7.26231	+	5.77267i	−0.662955	+	0.526971i
$121$	−10.3428	+	7.51448i	−0.940254	+	0.683135i
$122$	−6.00956	−	8.27145i	−0.544080	−	0.748862i
$123$	−3.86193	+	1.25482i	−0.348218	+	0.113143i
$124$	4.65220			0.417780
$125$	4.80297	+	10.0961i	0.429591	+	0.903024i
$126$	−4.73928			−0.422208
$127$	14.5944	−	4.74201i	1.29504	−	0.420786i	0.421190	−	0.906972i	$-0.361613\pi$
$127$	14.5944	−	4.74201i	1.29504	−	0.420786i	0.873855	+	0.486187i	$0.161613\pi$
$128$	0.997866	+	1.37344i	0.0881997	+	0.121396i
$129$	4.31759	−	3.13691i	0.380143	−	0.276190i
$130$	1.32895	−	1.05636i	0.116557	−	0.0926488i
$131$	3.00442	+	2.18284i	0.262497	+	0.190716i	0.711247	−	0.702942i	$-0.248131\pi$
$131$	3.00442	+	2.18284i	0.262497	+	0.190716i	−0.448750	+	0.893657i	$0.648131\pi$
$132$		−	4.79524i		−	0.417372i
$133$	16.3217	−	22.4649i	1.41527	−	1.94795i
$134$	−0.957509	+	2.94691i	−0.0827162	+	0.254574i
$135$	−6.96283	+	10.5119i	−0.599265	+	0.904722i
$136$	0.950730	+	2.92604i	0.0815244	+	0.250906i
$137$	8.68920	+	2.82329i	0.742368	+	0.241210i	0.655694	−	0.755027i	$-0.272376\pi$
$137$	8.68920	+	2.82329i	0.742368	+	0.241210i	0.0866741	+	0.996237i	$0.472376\pi$
$138$	8.93666	+	2.90370i	0.760739	+	0.247179i
$139$	−4.64047	−	14.2819i	−0.393599	−	1.21137i	−0.930047	−	0.367440i	$-0.880234\pi$
$139$	−4.64047	−	14.2819i	−0.393599	−	1.21137i	0.536448	−	0.843933i	$-0.319766\pi$
$140$	5.58965	+	1.55219i	0.472412	+	0.131184i
$141$	3.07671	−	9.46915i	0.259106	−	0.797446i
$142$	6.28451	−	8.64989i	0.527385	−	0.725883i
$143$			3.28443i			0.274658i
$144$	1.92138	+	1.39597i	0.160115	+	0.116331i
$145$	0.593880	−	2.13864i	0.0493191	−	0.177605i
$146$	−8.29972	+	6.03010i	−0.686889	+	0.499054i
$147$	−4.48641	−	6.17502i	−0.370033	−	0.509307i
$148$	−7.70083	+	2.50215i	−0.633004	+	0.205675i
$149$	4.44346			0.364023			0.182011	−	0.983296i	$-0.441739\pi$
$149$	4.44346			0.364023			0.182011	+	0.983296i	$0.441739\pi$
$150$	−5.73995	+	4.98282i	−0.468665	+	0.406846i
$151$	0.138640			0.0112824			0.00564120	−	0.999984i	$-0.498204\pi$
$151$	0.138640			0.0112824			0.00564120	+	0.999984i	$0.498204\pi$
$152$	−22.8354	+	7.41966i	−1.85219	+	0.601814i
$153$	0.694484	+	0.955876i	0.0561457	+	0.0772780i
$154$	15.8260	−	11.4983i	1.27530	−	0.926558i
$155$	14.2536	−	0.617477i	1.14488	−	0.0495969i
$156$	−0.535717	−	0.389221i	−0.0428917	−	0.0311626i
$157$			1.13360i			0.0904709i	0.998976	+	0.0452354i	$0.0144038\pi$
$157$			1.13360i			0.0904709i	−0.998976	+	0.0452354i	$0.985596\pi$
$158$	0.541779	−	0.745695i	0.0431016	−	0.0593243i
$159$	−2.48358	+	7.64369i	−0.196961	+	0.606184i
$160$	−5.40867	−	6.80438i	−0.427593	−	0.537933i
$161$	−6.79623	−	20.9166i	−0.535618	−	1.64846i
$162$	−4.35229	−	1.41415i	−0.341948	−	0.111106i
$163$	−18.7139	−	6.08052i	−1.46579	−	0.476263i	−0.535955	−	0.844247i	$-0.680048\pi$
$163$	−18.7139	−	6.08052i	−1.46579	−	0.476263i	−0.929832	+	0.367984i	$0.880048\pi$
$164$	−0.678481	−	2.08815i	−0.0529805	−	0.163057i
$165$	−0.636461	−	14.6919i	−0.0495484	−	1.14376i
$166$	2.39806	−	7.38047i	0.186125	−	0.572835i
$167$	−12.5608	+	17.2885i	−0.971984	+	1.33782i	−0.0309458	+	0.999521i	$0.509852\pi$
$167$	−12.5608	+	17.2885i	−0.971984	+	1.33782i	−0.941038	+	0.338300i	$0.890148\pi$
$168$			14.7621i			1.13892i
$169$	−10.1503	−	7.37462i	−0.780791	−	0.567278i
$170$	0.881992	+	2.36144i	0.0676457	+	0.181114i
$171$	−7.45982	+	5.41988i	−0.570467	+	0.414468i
$172$	1.69613	+	2.33453i	0.129329	+	0.178006i
$173$	0.872463	−	0.283480i	0.0663321	−	0.0215526i	−0.275663	−	0.961254i	$-0.588897\pi$
$173$	0.872463	−	0.283480i	0.0663321	−	0.0215526i	0.341995	+	0.939702i	$0.388897\pi$
$174$	1.50899			0.114396
$175$	17.3319	+	4.01378i	1.31016	+	0.303413i
$176$	−9.80299			−0.738928
$177$	−12.9231	+	4.19898i	−0.971361	+	0.315614i
$178$	−0.0361256	−	0.0497226i	−0.00270773	−	0.00372686i
$179$	19.5512	−	14.2047i	1.46132	−	1.06171i	0.478306	−	0.878193i	$-0.341251\pi$
$179$	19.5512	−	14.2047i	1.46132	−	1.06171i	0.983016	−	0.183519i	$-0.0587489\pi$
$180$	−1.60601	−	1.06378i	−0.119705	−	0.0792895i
$181$	−9.56926	−	6.95248i	−0.711278	−	0.516773i	0.172308	−	0.985043i	$-0.444878\pi$
$181$	−9.56926	−	6.95248i	−0.711278	−	0.516773i	−0.883586	+	0.468270i	$0.844878\pi$
$182$		−	2.70136i		−	0.200238i
$183$	−7.18865	+	9.89433i	−0.531400	+	0.731410i
$184$	−5.87656	+	18.0862i	−0.433226	+	1.33333i
$185$	−23.2620	+	8.68832i	−1.71026	+	0.638778i
$186$	2.99732	+	9.22479i	0.219774	+	0.676395i
$187$	−4.63823	−	1.50705i	−0.339181	−	0.110207i
$188$	5.11998	+	1.66358i	0.373413	+	0.121329i
$189$	6.19997	+	19.0816i	0.450982	+	1.38798i
$190$	−18.4291	+	6.88321i	−1.33699	+	0.499361i
$191$	−4.78954	+	14.7407i	−0.346559	+	1.06660i	0.614185	+	0.789162i	$0.289485\pi$
$191$	−4.78954	+	14.7407i	−0.346559	+	1.06660i	−0.960744	+	0.277437i	$0.910515\pi$
$192$	6.65997	−	9.16666i	0.480642	−	0.661547i
$193$			25.7916i			1.85652i	0.371928	+	0.928262i	$0.378697\pi$
$193$			25.7916i			1.85652i	−0.371928	+	0.928262i	$0.621303\pi$
$194$	−12.9941	−	9.44078i	−0.932923	−	0.677808i
$195$	−1.69302	−	1.12141i	−0.121239	−	0.0803058i
$196$	3.33884	−	2.42581i	0.238489	−	0.173272i
$197$	5.94040	+	8.17625i	0.423236	+	0.582534i	0.966384	−	0.257103i	$-0.0827679\pi$
$197$	5.94040	+	8.17625i	0.423236	+	0.582534i	−0.543148	+	0.839637i	$0.682768\pi$
$198$	−6.17796	+	2.00734i	−0.439049	+	0.142656i
$199$	−18.7019			−1.32574			−0.662870	−	0.748735i	$-0.730662\pi$
$199$	−18.7019			−1.32574			−0.662870	+	0.748735i	$0.730662\pi$
$200$	−10.0844	−	11.6166i	−0.713071	−	0.821421i
$201$	3.70651			0.261437
$202$	2.62344	−	0.852407i	0.184584	−	0.0599751i
$203$	−2.07597	−	2.85733i	−0.145705	−	0.200545i
$204$	0.795466	−	0.577940i	0.0556938	−	0.0404639i
$205$	−2.35592	−	6.30772i	−0.164544	−	0.440550i
$206$	−11.2690	−	8.18740i	−0.785148	−	0.570443i
$207$			7.30315i			0.507604i
$208$	−0.795692	+	1.09518i	−0.0551713	+	0.0759368i
$209$	11.7613	−	36.1976i	0.813546	−	2.50384i
$210$	0.523473	+	12.0837i	0.0361230	+	0.833853i
$211$	−1.58849	−	4.88886i	−0.109356	−	0.336563i	0.881372	−	0.472423i	$-0.156620\pi$
$211$	−1.58849	−	4.88886i	−0.109356	−	0.336563i	−0.990728	+	0.135860i	$0.956620\pi$
$212$	−4.13295	−	1.34288i	−0.283852	−	0.0922292i
$213$	−12.1636	−	3.95221i	−0.833439	−	0.270801i
$214$	1.28579	+	3.95724i	0.0878945	+	0.270511i
$215$	5.50655	+	6.92751i	0.375544	+	0.472452i
$216$	5.36099	−	16.4994i	0.364769	−	1.12265i
$217$	13.3440	−	18.3664i	0.905850	−	1.24679i
$218$		−	14.4642i		−	0.979641i
$219$	9.92813	+	7.21321i	0.670881	+	0.487424i
$220$	7.94392	−	0.344135i	0.535579	−	0.0232016i
$221$	−0.544843	+	0.395852i	−0.0366501	+	0.0266279i
$222$	−9.92296	−	13.6578i	−0.665985	−	0.916650i
$223$	−5.14990	+	1.67330i	−0.344863	+	0.112053i	−0.476327	−	0.879268i	$-0.658032\pi$
$223$	−5.14990	+	1.67330i	−0.344863	+	0.112053i	0.131464	+	0.991321i	$0.458032\pi$
$224$	−13.8312			−0.924138
$225$	−5.06177	−	3.04610i	−0.337451	−	0.203073i
$226$	−2.26156			−0.150437
$227$	−19.3030	+	6.27192i	−1.28118	+	0.416282i	−0.868997	−	0.494818i	$-0.835235\pi$
$227$	−19.3030	+	6.27192i	−1.28118	+	0.416282i	−0.412187	+	0.911099i	$0.635235\pi$
$228$	4.51034	+	6.20796i	0.298705	+	0.411132i
$229$	13.4545	−	9.77530i	0.889101	−	0.645970i	−0.0465423	−	0.998916i	$-0.514820\pi$
$229$	13.4545	−	9.77530i	0.889101	−	0.645970i	0.935644	+	0.352947i	$0.114820\pi$
$230$	−4.16899	+	15.0131i	−0.274895	+	0.989933i
$231$	−18.9311	−	13.7543i	−1.24558	−	0.904964i
$232$			3.05392i			0.200500i
$233$	−0.753026	+	1.03645i	−0.0493324	+	0.0679002i	−0.832971	−	0.553317i	$-0.813362\pi$
$233$	−0.753026	+	1.03645i	−0.0493324	+	0.0679002i	0.783638	+	0.621218i	$0.213362\pi$
$234$	−0.277197	+	0.853125i	−0.0181209	+	0.0557705i
$235$	15.9076	+	4.41740i	1.03770	+	0.288159i
$236$	−2.27039	−	6.98755i	−0.147790	−	0.454851i
$237$	−1.04861	−	0.340714i	−0.0681146	−	0.0221318i
$238$	3.81482	+	1.23951i	0.247278	+	0.0803456i
$239$	7.53529	+	23.1912i	0.487418	+	1.50012i	0.828449	+	0.560065i	$0.189224\pi$
$239$	7.53529	+	23.1912i	0.487418	+	1.50012i	−0.341031	+	0.940052i	$0.610776\pi$
$240$	3.34706	−	5.05312i	0.216052	−	0.326178i
$241$	2.64859	−	8.15153i	0.170611	−	0.525086i	−0.828795	−	0.559552i	$-0.810973\pi$
$241$	2.64859	−	8.15153i	0.170611	−	0.525086i	0.999406	+	0.0344662i	$0.0109731\pi$
$242$	8.47126	−	11.6597i	0.544553	−	0.749513i
$243$		−	11.4423i		−	0.734025i
$244$	−5.34988	−	3.88691i	−0.342491	−	0.248834i
$245$	9.90772	−	7.87546i	0.632981	−	0.503145i
$246$	3.70343	−	2.69070i	0.236122	−	0.171553i
$247$	−3.08929	−	4.25205i	−0.196567	−	0.270551i
$248$	−18.6693	+	6.06604i	−1.18550	+	0.385194i
$249$	−9.28286			−0.588278
$250$	−8.66661	−	9.15136i	−0.548125	−	0.578783i
$251$	9.99354			0.630787			0.315393	−	0.948961i	$-0.397864\pi$
$251$	9.99354			0.630787			0.315393	+	0.948961i	$0.397864\pi$
$252$	−2.91528	+	0.947232i	−0.183645	+	0.0596700i
$253$	−17.7187	−	24.3877i	−1.11396	−	1.53324i
$254$	−13.9955	+	10.1683i	−0.878153	+	0.638015i
$255$	2.36048	−	1.87630i	0.147819	−	0.117499i
$256$	12.0469	+	8.75262i	0.752934	+	0.547039i
$257$		−	8.50072i		−	0.530260i	−0.964213	−	0.265130i	$-0.914585\pi$
$257$		−	8.50072i		−	0.530260i	0.964213	−	0.265130i	$-0.0854149\pi$
$258$	−3.53632	+	4.86733i	−0.220162	+	0.303026i
$259$	−12.2102	+	37.5790i	−0.758703	+	2.33505i
$260$	0.606348	−	0.915416i	0.0376041	−	0.0567717i
$261$	0.362418	+	1.11541i	0.0224331	+	0.0690420i
$262$	−3.98161	−	1.29370i	−0.245984	−	0.0799252i
$263$	8.15048	+	2.64825i	0.502580	+	0.163298i	0.549325	−	0.835609i	$-0.314885\pi$
$263$	8.15048	+	2.64825i	0.502580	+	0.163298i	−0.0467449	+	0.998907i	$0.514885\pi$
$264$	6.25254	+	19.2433i	0.384817	+	1.18435i
$265$	−12.8410	−	3.56581i	−0.788814	−	0.219046i
$266$	−9.67336	+	29.7715i	−0.593112	+	1.82541i
$267$	−0.0432135	+	0.0594782i	−0.00264462	+	0.00364001i
$268$			2.00411i			0.122421i
$269$	7.30953	+	5.31069i	0.445670	+	0.323798i	0.787884	−	0.615824i	$-0.211177\pi$
$269$	7.30953	+	5.31069i	0.445670	+	0.323798i	−0.342214	+	0.939622i	$0.611177\pi$
$270$	3.80323	−	13.6959i	0.231457	−	0.833508i
$271$	25.6771	−	18.6555i	1.55977	−	1.13324i	0.623573	−	0.781765i	$-0.285680\pi$
$271$	25.6771	−	18.6555i	1.55977	−	1.13324i	0.936197	−	0.351475i	$-0.114320\pi$
$272$	−1.18149	−	1.62619i	−0.0716385	−	0.0986020i
$273$	−3.07321	+	0.998547i	−0.185999	+	0.0604348i
$274$	−10.2996			−0.622224
$275$	24.2933	−	2.10876i	1.46494	−	0.127163i
$276$	6.07758			0.365827
$277$	11.7311	−	3.81166i	0.704852	−	0.229020i	0.0654085	−	0.997859i	$-0.479165\pi$
$277$	11.7311	−	3.81166i	0.704852	−	0.229020i	0.639443	+	0.768838i	$0.279165\pi$
$278$	9.95054	+	13.6957i	0.596794	+	0.821416i
$279$	−6.09887	+	4.43109i	−0.365130	+	0.265282i
$280$	−24.4552	+	1.05942i	−1.46148	+	0.0633122i
$281$	8.72798	+	6.34125i	0.520668	+	0.378287i	0.816855	−	0.576842i	$-0.195715\pi$
$281$	8.72798	+	6.34125i	0.520668	+	0.378287i	−0.296188	+	0.955130i	$0.595715\pi$
$282$			11.2241i			0.668388i
$283$	−7.06201	+	9.72002i	−0.419793	+	0.577795i	−0.965573	−	0.260133i	$-0.916233\pi$
$283$	−7.06201	+	9.72002i	−0.419793	+	0.577795i	0.545780	+	0.837929i	$0.316233\pi$
$284$	2.13696	−	6.57690i	0.126805	−	0.390267i
$285$	14.6430	+	18.4216i	0.867375	+	1.09120i
$286$	−1.14417	−	3.52140i	−0.0676563	−	0.208225i
$287$	−10.1899	−	3.31090i	−0.601491	−	0.195436i
$288$	4.36809	+	1.41928i	0.257392	+	0.0836319i
$289$	−0.309017	−	0.951057i	−0.0181775	−	0.0559445i
$290$	0.108294	+	2.49983i	0.00635925	+	0.146795i
$291$	−5.93712	+	18.2726i	−0.348040	+	1.07116i
$292$	−3.90019	+	5.36816i	−0.228242	+	0.314148i
$293$			1.66631i			0.0973470i	0.998815	+	0.0486735i	$0.0154994\pi$
$293$			1.66631i			0.0973470i	−0.998815	+	0.0486735i	$0.984501\pi$
$294$	6.96125	+	5.05764i	0.405988	+	0.294968i
$295$	−7.88357	−	21.1074i	−0.458999	−	1.22892i
$296$	27.6409	−	20.0823i	1.60660	−	1.16726i
$297$	16.1642	+	22.2481i	0.937940	+	1.29096i
$298$	−4.76405	+	1.54794i	−0.275974	+	0.0896695i
$299$	−4.16275			−0.240738
$300$	−2.53492	+	4.21233i	−0.146354	+	0.243199i
$301$	14.0815			0.811646
$302$	−0.148643	+	0.0482971i	−0.00855345	+	0.00277919i
$303$	−1.93949	−	2.66948i	−0.111421	−	0.153358i
$304$	12.6910	−	9.22057i	0.727881	−	0.528836i
$305$	−16.9071	−	11.1988i	−0.968098	−	0.641243i
$306$	−1.07758	−	0.782909i	−0.0616013	−	0.0447559i
$307$		−	12.8925i		−	0.735811i	−0.929863	−	0.367906i	$-0.880075\pi$
$307$		−	12.8925i		−	0.735811i	0.929863	−	0.367906i	$-0.119925\pi$
$308$	7.43695	−	10.2361i	0.423759	−	0.583255i
$309$	−5.14890	+	15.8467i	−0.292910	+	0.901486i
$310$	−15.0669	+	5.62746i	−0.855744	+	0.319618i
$311$	−1.84025	−	5.66369i	−0.104351	−	0.321159i	0.885227	−	0.465160i	$-0.154003\pi$
$311$	−1.84025	−	5.66369i	−0.104351	−	0.321159i	−0.989578	+	0.144001i	$0.954003\pi$
$312$	2.65735	+	0.863424i	0.150443	+	0.0488818i
$313$	−15.1972	−	4.93787i	−0.858997	−	0.279105i	−0.153787	−	0.988104i	$-0.549147\pi$
$313$	−15.1972	−	4.93787i	−0.858997	−	0.279105i	−0.705209	+	0.708999i	$0.749147\pi$
$314$	−0.394902	−	1.21538i	−0.0222856	−	0.0685881i
$315$	−8.80625	+	3.28911i	−0.496176	+	0.185320i
$316$	0.184225	−	0.566985i	0.0103635	−	0.0318954i
$317$	10.2220	−	14.0693i	0.574122	−	0.790212i	−0.418913	−	0.908026i	$-0.637589\pi$
$317$	10.2220	−	14.0693i	0.574122	−	0.790212i	0.993036	+	0.117815i	$0.0375889\pi$
$318$		−	9.06036i		−	0.508080i
$319$	−3.91640	−	2.84543i	−0.219276	−	0.159314i
$320$	15.6637	+	10.3752i	0.875627	+	0.579993i
$321$	4.02669	−	2.92556i	0.224748	−	0.163289i
$322$	14.5731	+	20.0582i	0.812129	+	1.11780i
$323$	7.42221	−	2.41162i	0.412983	−	0.134186i
$324$	−2.95988			−0.164438
$325$	1.73626	−	2.88517i	0.0963101	−	0.160041i
$326$	22.1823			1.22857
$327$	−16.4553	+	5.34665i	−0.909980	+	0.295670i
$328$	5.44550	+	7.49509i	0.300678	+	0.413847i
$329$	21.2534	−	15.4415i	1.17174	−	0.851317i
$330$	5.80048	+	15.5302i	0.319306	+	0.854908i
$331$	1.19224	+	0.866213i	0.0655314	+	0.0476114i	0.620069	−	0.784548i	$-0.287105\pi$
$331$	1.19224	+	0.866213i	0.0655314	+	0.0476114i	−0.554537	+	0.832159i	$0.687105\pi$
$332$		−	5.01926i		−	0.275467i
$333$	7.71228	−	10.6150i	0.422630	−	0.581701i
$334$	7.44440	−	22.9115i	0.407340	−	1.25366i
$335$	0.266001	+	6.14030i	0.0145332	+	0.335480i
$336$	−2.98035	−	9.17258i	−0.162591	−	0.500405i
$337$	3.55471	+	1.15500i	0.193637	+	0.0629166i	0.404230	−	0.914657i	$-0.367539\pi$
$337$	3.55471	+	1.15500i	0.193637	+	0.0629166i	−0.210593	+	0.977574i	$0.567539\pi$
$338$	13.4517	+	4.37071i	0.731674	+	0.237735i
$339$	0.835979	+	2.57288i	0.0454042	+	0.139740i
$340$	1.01452	+	1.27631i	0.0550200	+	0.0692178i
$341$	9.61560	−	29.5938i	0.520714	−	1.60259i
$342$	6.10996	−	8.40964i	0.330389	−	0.454741i
$343$			4.76737i			0.257414i
$344$	−9.85060	−	7.15688i	−0.531109	−	0.385873i
$345$	18.6208	−	0.806663i	1.00251	−	0.0434293i
$346$	−0.836656	+	0.607866i	−0.0449789	+	0.0326791i
$347$	4.95599	+	6.82134i	0.266052	+	0.366189i	0.921052	−	0.389440i	$-0.127331\pi$
$347$	4.95599	+	6.82134i	0.266052	+	0.366189i	−0.655000	+	0.755629i	$0.727331\pi$
$348$	0.928227	−	0.301599i	0.0497582	−	0.0161674i
$349$	5.91569			0.316660			0.158330	−	0.987386i	$-0.449389\pi$
$349$	5.91569			0.316660			0.158330	+	0.987386i	$0.449389\pi$
$350$	−19.9806	+	1.73440i	−1.06801	+	0.0927074i
$351$	3.79754			0.202698
$352$	−18.0299	+	5.85828i	−0.960999	+	0.312247i
$353$	10.8612	+	14.9492i	0.578083	+	0.795663i	0.993484	−	0.113976i	$-0.0363586\pi$
$353$	10.8612	+	14.9492i	0.578083	+	0.795663i	−0.415401	+	0.909639i	$0.636359\pi$
$354$	12.3927	−	9.00386i	0.658667	−	0.478550i
$355$	5.67439	−	20.4342i	0.301166	−	1.08454i
$356$	−0.0321600	−	0.0233656i	−0.00170447	−	0.00123837i
$357$		−	4.79814i		−	0.253944i
$358$	−16.0134	+	22.0405i	−0.846332	+	1.16488i
$359$	−2.85756	+	8.79468i	−0.150816	+	0.464165i	−0.997713	−	0.0675923i	$-0.978468\pi$
$359$	−2.85756	+	8.79468i	−0.150816	+	0.464165i	0.846897	+	0.531758i	$0.178468\pi$
$360$	7.83201	+	2.17487i	0.412783	+	0.114626i
$361$	12.9494	+	39.8541i	0.681547	+	2.09759i
$362$	12.6817	+	4.12052i	0.666533	+	0.216570i
$363$	−16.3961	−	5.32741i	−0.860571	−	0.279616i
$364$	−0.539916	−	1.66169i	−0.0282993	−	0.0870962i
$365$	−11.2371	+	16.9649i	−0.588176	+	0.887982i
$366$	4.26049	−	13.1125i	0.222700	−	0.685399i
$367$	−9.30662	+	12.8095i	−0.485802	+	0.668648i	−0.979607	−	0.200924i	$-0.935606\pi$
$367$	−9.30662	+	12.8095i	−0.485802	+	0.668648i	0.493805	+	0.869573i	$0.335606\pi$
$368$		−	12.4245i		−	0.647672i
$369$	2.87837	+	2.09126i	0.149842	+	0.108866i
$370$	21.9137	−	17.4188i	1.13924	−	0.905560i
$371$	−17.1562	+	12.4647i	−0.890703	+	0.647134i
$372$	3.68749	+	5.07539i	0.191187	+	0.263147i
$373$	−6.53606	+	2.12369i	−0.338424	+	0.109961i	−0.473299	−	0.880902i	$-0.656937\pi$
$373$	−6.53606	+	2.12369i	−0.338424	+	0.109961i	0.134875	+	0.990863i	$0.456937\pi$
$374$	5.49788			0.284288
$375$	−7.20751	+	13.2424i	−0.372194	+	0.683834i
$376$	−22.7157			−1.17147
$377$	−0.635775	+	0.206576i	−0.0327441	+	0.0106392i
$378$	−13.2946	−	18.2984i	−0.683800	−	0.941170i
$379$	14.0383	−	10.1994i	0.721098	−	0.523908i	−0.165637	−	0.986187i	$-0.552968\pi$
$379$	14.0383	−	10.1994i	0.721098	−	0.523908i	0.886735	+	0.462278i	$0.152968\pi$
$380$	−9.96057	+	7.91748i	−0.510967	+	0.406158i
$381$	16.7414	+	12.1633i	0.857687	+	0.623146i
$382$		−	17.4727i		−	0.893982i
$383$	17.6945	−	24.3543i	0.904145	−	1.24445i	−0.0649822	−	0.997886i	$-0.520699\pi$
$383$	17.6945	−	24.3543i	0.904145	−	1.24445i	0.969127	−	0.246562i	$-0.0793009\pi$
$384$	−0.707439	+	2.17727i	−0.0361014	+	0.111109i
$385$	21.4271	−	32.3489i	1.09202	−	1.64865i
$386$	−8.98484	−	27.6525i	−0.457316	−	1.40747i
$387$	−4.44714	−	1.44496i	−0.226061	−	0.0734516i
$388$	−9.88001	−	3.21021i	−0.501581	−	0.162974i
$389$	3.62141	+	11.1455i	0.183613	+	0.565102i	0.999922	−	0.0125137i	$-0.00398334\pi$
$389$	3.62141	+	11.1455i	0.183613	+	0.565102i	−0.816309	+	0.577615i	$0.803983\pi$
$390$	2.20582	+	0.612536i	0.111696	+	0.0310170i
$391$	1.91007	−	5.87858i	0.0965963	−	0.297293i
$392$	−10.2358	+	14.0883i	−0.516984	+	0.711568i
$393$			5.00791i			0.252616i
$394$	−9.21729	−	6.69675i	−0.464360	−	0.337378i
$395$	0.489182	−	1.76161i	0.0246134	−	0.0886361i
$396$	−3.39906	+	2.46956i	−0.170809	+	0.124100i
$397$	13.4643	+	18.5321i	0.675756	+	0.930098i	0.999873	−	0.0159185i	$-0.00506724\pi$
$397$	13.4643	+	18.5321i	0.675756	+	0.930098i	−0.324117	+	0.946017i	$0.605067\pi$
$398$	20.0512	−	6.51502i	1.00507	−	0.326569i
$399$	37.4455			1.87462
$400$	8.61134	+	5.18218i	0.430567	+	0.259109i
$401$	9.45401			0.472111			0.236055	−	0.971740i	$-0.424145\pi$
$401$	9.45401			0.472111			0.236055	+	0.971740i	$0.424145\pi$
$402$	−3.97393	+	1.29121i	−0.198202	+	0.0643996i
$403$	−2.52569	−	3.47632i	−0.125814	−	0.173168i
$404$	1.44339	−	1.04869i	0.0718114	−	0.0521740i
$405$	−9.06861	+	0.392858i	−0.450623	+	0.0195213i
$406$	3.22114	+	2.34029i	0.159862	+	0.116147i
$407$			54.1585i			2.68454i
$408$	−2.43863	+	3.35649i	−0.120730	+	0.166171i
$409$	6.32646	−	19.4708i	0.312823	−	0.962771i	−0.663818	−	0.747894i	$-0.731065\pi$
$409$	6.32646	−	19.4708i	0.312823	−	0.962771i	0.976641	−	0.214877i	$-0.0689350\pi$
$410$	4.72327	+	5.94210i	0.233266	+	0.293460i
$411$	3.80723	+	11.7174i	0.187797	+	0.577979i
$412$	−8.56832	−	2.78401i	−0.422131	−	0.137159i
$413$	−34.0983	−	11.0792i	−1.67787	−	0.545173i
$414$	−2.54414	−	7.83007i	−0.125038	−	0.384827i
$415$	−0.666195	−	15.3782i	−0.0327022	−	0.754888i
$416$	−0.808980	+	2.48979i	−0.0396635	+	0.122072i
$417$	11.9029	−	16.3829i	0.582885	−	0.802273i
$418$			42.9064i			2.09862i
$419$	−1.30701	−	0.949595i	−0.0638514	−	0.0463907i	0.555402	−	0.831582i	$-0.312565\pi$
$419$	−1.30701	−	0.949595i	−0.0638514	−	0.0463907i	−0.619253	+	0.785191i	$0.712565\pi$
$420$	2.73715	+	7.32843i	0.133559	+	0.357591i
$421$	−15.3130	+	11.1255i	−0.746308	+	0.542224i	−0.894680	−	0.446707i	$-0.852597\pi$
$421$	−15.3130	+	11.1255i	−0.746308	+	0.542224i	0.148372	+	0.988932i	$0.452597\pi$
$422$	3.40619	+	4.68822i	0.165811	+	0.228219i
$423$	−8.29662	+	2.69574i	−0.403396	+	0.131071i
$424$	18.3366			0.890502
$425$	3.27773	+	3.77578i	0.158993	+	0.183152i
$426$	14.4180			0.698556
$427$	−30.6903	+	9.97188i	−1.48521	+	0.482573i
$428$	1.58186	+	2.17724i	0.0764619	+	0.105241i
$429$	−3.58320	+	2.60335i	−0.172998	+	0.125691i
$430$	−8.31713	−	5.50905i	−0.401087	−	0.265670i
$431$	−17.0722	−	12.4037i	−0.822338	−	0.597464i	0.0950432	−	0.995473i	$-0.469701\pi$
$431$	−17.0722	−	12.4037i	−0.822338	−	0.597464i	−0.917381	+	0.398010i	$0.869701\pi$
$432$			11.3345i			0.545329i
$433$	−3.49181	+	4.80606i	−0.167806	+	0.230965i	−0.884635	−	0.466284i	$-0.845593\pi$
$433$	−3.49181	+	4.80606i	−0.167806	+	0.230965i	0.716830	+	0.697248i	$0.245593\pi$
$434$	−7.90858	+	24.3401i	−0.379624	+	1.16836i
$435$	2.80391	−	1.04726i	0.134437	−	0.0502120i
$436$	−2.89094	−	8.89740i	−0.138451	−	0.426108i
$437$	45.8775	+	14.9065i	2.19462	+	0.713075i
$438$	−13.1573	−	4.27505i	−0.628678	−	0.204270i
$439$	−1.79560	−	5.52630i	−0.0856995	−	0.263756i	0.899019	−	0.437910i	$-0.144281\pi$
$439$	−1.79560	−	5.52630i	−0.0856995	−	0.263756i	−0.984718	+	0.174154i	$0.944281\pi$
$440$	−31.4303	+	11.7391i	−1.49838	+	0.559642i
$441$	−2.06658	+	6.36029i	−0.0984088	+	0.302871i
$442$	0.446253	−	0.614215i	0.0212261	−	0.0292152i
$443$		−	24.3470i		−	1.15676i	−0.815766	−	0.578382i	$-0.803684\pi$
$443$		−	24.3470i		−	1.15676i	0.815766	−	0.578382i	$-0.196316\pi$
$444$	−8.83369	−	6.41805i	−0.419228	−	0.304587i
$445$	−0.101634	−	0.0673200i	−0.00481793	−	0.00319128i
$446$	4.93854	−	3.58806i	0.233847	−	0.169900i
$447$	3.52203	+	4.84766i	0.166587	+	0.229287i
$448$	28.4332	−	9.23850i	1.34334	−	0.436478i
$449$	−36.5614			−1.72544			−0.862720	−	0.505681i	$-0.831241\pi$
$449$	−36.5614			−1.72544			−0.862720	+	0.505681i	$0.831241\pi$
$450$	6.48811	+	1.50254i	0.305853	+	0.0708305i
$451$	−14.6856			−0.691516
$452$	−1.39116	+	0.452015i	−0.0654346	+	0.0212610i
$453$	0.109891	+	0.151252i	0.00516313	+	0.00710643i
$454$	18.5108	−	13.4489i	0.868754	−	0.631186i
$455$	−1.87477	−	5.01950i	−0.0878907	−	0.235318i
$456$	−26.1946	−	19.0315i	−1.22668	−	0.891233i
$457$			28.2090i			1.31956i	0.751458	+	0.659781i	$0.229351\pi$
$457$			28.2090i			1.31956i	−0.751458	+	0.659781i	$0.770649\pi$
$458$	−11.0199	+	15.1676i	−0.514928	+	0.708737i
$459$	−1.74249	+	5.36284i	−0.0813325	+	0.250316i
$460$	0.436164	+	10.0683i	0.0203362	+	0.469436i
$461$	−12.1843	−	37.4994i	−0.567479	−	1.74652i	−0.660468	−	0.750855i	$-0.729642\pi$
$461$	−12.1843	−	37.4994i	−0.567479	−	1.74652i	0.0929884	−	0.995667i	$-0.470358\pi$
$462$	25.0885	+	8.15173i	1.16722	+	0.379253i
$463$	−0.904110	−	0.293763i	−0.0420176	−	0.0136523i	0.287933	−	0.957651i	$-0.407032\pi$
$463$	−0.904110	−	0.293763i	−0.0420176	−	0.0136523i	−0.329950	+	0.943998i	$0.607032\pi$
$464$	−0.616564	−	1.89759i	−0.0286233	−	0.0880934i
$465$	11.9716	+	15.0608i	0.555167	+	0.698428i
$466$	0.446296	−	1.37356i	0.0206743	−	0.0636288i
$467$	8.30915	−	11.4366i	0.384502	−	0.529221i	−0.572269	−	0.820066i	$-0.693936\pi$
$467$	8.30915	−	11.4366i	0.384502	−	0.529221i	0.956770	+	0.290845i	$0.0939365\pi$
$468$			0.580187i			0.0268192i
$469$	7.91204	+	5.74843i	0.365344	+	0.265438i
$470$	−18.5942	+	0.805513i	−0.857687	+	0.0371555i
$471$	−1.23671	+	0.898526i	−0.0569848	+	0.0414019i
$472$	18.2222	+	25.0807i	0.838745	+	1.15443i
$473$	18.3562	−	5.96429i	0.844019	−	0.274238i
$474$	1.24296			0.0570910
$475$	−29.4668	+	25.5800i	−1.35203	+	1.17369i
$476$	2.59436			0.118912
$477$	6.69720	−	2.17605i	0.306644	−	0.0996346i
$478$	−16.1579	−	22.2395i	−0.739046	−	1.01721i
$479$	−11.9199	+	8.66029i	−0.544633	+	0.395699i	−0.825803	−	0.563959i	$-0.809278\pi$
$479$	−11.9199	+	8.66029i	−0.544633	+	0.395699i	0.281170	+	0.959658i	$0.409278\pi$
$480$	3.13625	−	11.2941i	0.143150	−	0.515501i
$481$	6.05050	+	4.39595i	0.275879	+	0.200438i
$482$			9.66232i			0.440107i
$483$	17.4324	−	23.9937i	0.793203	−	1.09175i
$484$	2.88054	−	8.86538i	0.130933	−	0.402972i
$485$	−30.6969	−	8.52424i	−1.39388	−	0.387066i
$486$	3.98607	+	12.2679i	0.180812	+	0.556482i
$487$	27.5806	+	8.96149i	1.24980	+	0.406084i	0.857849	−	0.513903i	$-0.171801\pi$
$487$	27.5806	+	8.96149i	1.24980	+	0.406084i	0.391950	+	0.919987i	$0.371801\pi$
$488$	26.5373	+	8.62248i	1.20129	+	0.390321i
$489$	−8.19963	−	25.2359i	−0.370800	−	1.14120i
$490$	−7.87904	+	11.8951i	−0.355939	+	0.537368i
$491$	0.954784	−	2.93852i	0.0430888	−	0.132614i	−0.927198	−	0.374572i	$-0.877790\pi$
$491$	0.954784	−	2.93852i	0.0430888	−	0.132614i	0.970287	+	0.241958i	$0.0777897\pi$
$492$	1.74031	−	2.39534i	0.0784594	−	0.107990i
$493$		−	0.992621i		−	0.0447054i
$494$	4.79344	+	3.48264i	0.215667	+	0.156691i
$495$	−10.0864	+	8.01750i	−0.453350	+	0.360360i
$496$	10.3757	−	7.53840i	0.465883	−	0.338484i
$497$	−19.8354	−	27.3012i	−0.889741	−	1.22462i
$498$	9.95261	−	3.23380i	0.445987	−	0.144910i
$499$	28.7291			1.28609			0.643045	−	0.765828i	$-0.277671\pi$
$499$	28.7291			1.28609			0.643045	+	0.765828i	$0.277671\pi$
$500$	−7.16018	−	3.89711i	−0.320213	−	0.174284i
$501$	−28.8172			−1.28746
$502$	−10.7146	+	3.48137i	−0.478215	+	0.155381i
$503$	10.0047	+	13.7702i	0.446086	+	0.613985i	0.971551	−	0.236830i	$-0.0761086\pi$
$503$	10.0047	+	13.7702i	0.446086	+	0.613985i	−0.525465	+	0.850815i	$0.676109\pi$
$504$	10.4639	−	7.60250i	0.466101	−	0.338642i
$505$	4.28314	−	3.40459i	0.190597	−	0.151502i
$506$	27.4928	+	19.9747i	1.22220	+	0.887983i
$507$		−	16.9190i		−	0.751398i
$508$	−6.57673	+	9.05209i	−0.291795	+	0.401621i
$509$	1.84477	−	5.67761i	0.0817678	−	0.251655i	−0.901812	−	0.432128i	$-0.857763\pi$
$509$	1.84477	−	5.67761i	0.0817678	−	0.251655i	0.983580	+	0.180473i	$0.0577628\pi$
$510$	−1.87715	+	2.83398i	−0.0831217	+	0.125491i
$511$	10.0059	+	30.7951i	0.442637	+	1.36230i
$512$	−19.1944	−	6.23663i	−0.848279	−	0.275623i
$513$	−41.8525	−	13.5987i	−1.84783	−	0.600398i
$514$	2.96133	+	9.11404i	0.130619	+	0.402003i
$515$	−26.6215	−	7.39254i	−1.17308	−	0.325754i
$516$	−1.20248	+	3.70085i	−0.0529361	+	0.162921i
$517$	21.1649	−	29.1310i	0.930831	−	1.28118i
$518$		−	44.5439i		−	1.95715i
$519$	1.00081	+	0.727131i	0.0439307	+	0.0319175i
$520$	−1.23966	+	4.46419i	−0.0543628	+	0.195768i
$521$	20.7511	−	15.0765i	0.909122	−	0.660515i	−0.0316710	−	0.999498i	$-0.510083\pi$
$521$	20.7511	−	15.0765i	0.909122	−	0.660515i	0.940793	+	0.338983i	$0.110083\pi$
$522$	−0.777132	−	1.06963i	−0.0340142	−	0.0468165i
$523$	10.4001	−	3.37919i	0.454763	−	0.147762i	−0.0726736	−	0.997356i	$-0.523153\pi$
$523$	10.4001	−	3.37919i	0.454763	−	0.147762i	0.527437	+	0.849594i	$0.323153\pi$
$524$	−2.70778			−0.118290
$525$	9.35890	+	22.0899i	0.408456	+	0.964082i
$526$	−9.66109			−0.421243
$527$	6.06812	−	1.97165i	0.264332	−	0.0858865i
$528$	−7.77017	−	10.6947i	−0.338153	−	0.465428i
$529$	12.3020	−	8.93793i	0.534870	−	0.388606i
$530$	15.0096	−	0.650226i	0.651976	−	0.0282440i
$531$	9.63184	+	6.99794i	0.417986	+	0.303685i
$532$			20.2468i			0.877811i
$533$	−1.19200	+	1.64065i	−0.0516314	+	0.0710645i
$534$	0.0256113	−	0.0788235i	0.00110831	−	0.00341103i
$535$	5.13554	+	6.46077i	0.222029	+	0.279323i
$536$	−2.61318	−	8.04253i	−0.112872	−	0.347384i
$537$	30.9938	+	10.0705i	1.33748	+	0.434574i
$538$	−9.68695	−	3.14748i	−0.417634	−	0.135698i
$539$	−8.53013	−	26.2530i	−0.367419	−	1.13080i
$540$	−0.397898	−	9.18495i	−0.0171228	−	0.395257i
$541$	12.3935	−	38.1432i	0.532837	−	1.63990i	−0.215440	−	0.976517i	$-0.569119\pi$
$541$	12.3935	−	38.1432i	0.532837	−	1.63990i	0.748277	−	0.663387i	$-0.230881\pi$
$542$	−21.0308	+	28.9464i	−0.903349	+	1.24335i
$543$		−	15.9505i		−	0.684501i
$544$	−3.14485	−	2.28486i	−0.134834	−	0.0979628i
$545$	−10.0383	−	26.8766i	−0.429995	−	1.15127i
$546$	2.94709	−	2.14118i	0.126124	−	0.0916342i
$547$	−11.3469	−	15.6177i	−0.485160	−	0.667765i	0.494327	−	0.869276i	$-0.335415\pi$
$547$	−11.3469	−	15.6177i	−0.485160	−	0.667765i	−0.979486	+	0.201511i	$0.935415\pi$
$548$	−6.33564	+	2.05857i	−0.270645	+	0.0879379i
$549$	10.7157			0.457333
$550$	−25.3114	+	10.7238i	−1.07928	+	0.457263i
$551$	7.74659			0.330016
$552$	−24.3894	+	7.92459i	−1.03808	+	0.337293i
$553$	−1.70999	−	2.35359i	−0.0727160	−	0.100085i
$554$	−11.2496	+	8.17333i	−0.477951	+	0.347251i
$555$	−27.9169	−	18.4914i	−1.18501	−	0.784918i
$556$	8.85824	+	6.43589i	0.375673	+	0.272943i
$557$			1.65627i			0.0701785i	0.999384	+	0.0350892i	$0.0111715\pi$
$557$			1.65627i			0.0701785i	−0.999384	+	0.0350892i	$0.988828\pi$
$558$	4.99527	−	6.87541i	0.211467	−	0.291059i
$559$	0.823620	−	2.53484i	0.0348354	−	0.107212i
$560$	14.9816	−	5.59561i	0.633090	−	0.236458i
$561$	−2.03227	−	6.25469i	−0.0858026	−	0.264073i
$562$	−11.5668	−	3.75827i	−0.487914	−	0.158533i
$563$	19.6348	+	6.37973i	0.827508	+	0.268874i	0.691995	−	0.721902i	$-0.256732\pi$
$563$	19.6348	+	6.37973i	0.827508	+	0.268874i	0.135513	+	0.990776i	$0.456732\pi$
$564$	2.24335	+	6.90433i	0.0944622	+	0.290725i
$565$	−4.20231	+	1.56955i	−0.176792	+	0.0660315i
$566$	4.18544	−	12.8815i	0.175927	−	0.541448i
$567$	−8.48987	+	11.6853i	−0.356541	+	0.490736i
$568$			29.1796i			1.22435i
$569$	−10.3231	−	7.50015i	−0.432766	−	0.314423i	0.349988	−	0.936754i	$-0.386186\pi$
$569$	−10.3231	−	7.50015i	−0.432766	−	0.314423i	−0.782754	+	0.622332i	$0.786186\pi$
$570$	−22.1168	−	14.6496i	−0.926373	−	0.613605i
$571$	20.7268	−	15.0589i	0.867389	−	0.630195i	−0.0624959	−	0.998045i	$-0.519906\pi$
$571$	20.7268	−	15.0589i	0.867389	−	0.630195i	0.929885	+	0.367850i	$0.119906\pi$
$572$	−1.40763	−	1.93744i	−0.0588561	−	0.0810084i
$573$	−19.8779	+	6.45873i	−0.830413	+	0.269817i
$574$	12.0785			0.504147
$575$	2.67268	+	30.7898i	0.111458	+	1.28402i
$576$	−9.92759			−0.413650
$577$	20.6239	−	6.70113i	0.858586	−	0.278971i	0.153548	−	0.988141i	$-0.450930\pi$
$577$	20.6239	−	6.70113i	0.858586	−	0.278971i	0.705038	+	0.709170i	$0.250930\pi$
$578$	0.662625	+	0.912025i	0.0275616	+	0.0379352i
$579$	−28.1378	+	20.4433i	−1.16937	+	0.849595i
$580$	0.566252	+	1.51608i	0.0235123	+	0.0629518i
$581$	−19.8155	−	14.3968i	−0.822086	−	0.597281i
$582$		−	21.6592i		−	0.897803i
$583$	−17.0847	+	23.5151i	−0.707577	+	0.973896i
$584$	8.65194	−	26.6279i	0.358020	−	1.10187i
$585$	0.0770070	+	1.77761i	0.00318385	+	0.0734949i
$586$	−0.580480	−	1.78654i	−0.0239794	−	0.0738011i
$587$	5.50323	+	1.78811i	0.227143	+	0.0738032i	0.420377	−	0.907349i	$-0.361898\pi$
$587$	5.50323	+	1.78811i	0.227143	+	0.0738032i	−0.193234	+	0.981153i	$0.561898\pi$
$588$	5.29295	+	1.71978i	0.218277	+	0.0709226i
$589$	15.3871	+	47.3567i	0.634015	+	1.95130i
$590$	15.8054	+	19.8840i	0.650698	+	0.818610i
$591$	−4.21146	+	12.9615i	−0.173236	+	0.533166i
$592$	−13.1205	+	18.0589i	−0.539250	+	0.742214i
$593$			1.07460i			0.0441287i	0.999757	+	0.0220644i	$0.00702387\pi$
$593$			1.07460i			0.0441287i	−0.999757	+	0.0220644i	$0.992976\pi$
$594$	−25.0808	−	18.2222i	−1.02908	−	0.747668i
$595$	7.94872	−	0.344343i	0.325866	−	0.0141167i
$596$	−2.62114	+	1.90437i	−0.107366	+	0.0780060i
$597$	−14.8237	−	20.4031i	−0.606694	−	0.835043i
$598$	4.46309	−	1.45014i	0.182509	−	0.0593008i
$599$	35.6765			1.45770			0.728850	−	0.684673i	$-0.240055\pi$
$599$	35.6765			1.45770			0.728850	+	0.684673i	$0.240055\pi$
$600$	4.68017	−	20.2094i	0.191067	−	0.825046i
$601$	−39.1336			−1.59629			−0.798147	−	0.602462i	$-0.794186\pi$
$601$	−39.1336			−1.59629			−0.798147	+	0.602462i	$0.794186\pi$
$602$	−15.0975	+	4.90547i	−0.615328	+	0.199932i
$603$	−1.90886	−	2.62732i	−0.0777348	−	0.106993i
$604$	−0.0817821	+	0.0594182i	−0.00332767	+	0.00241769i
$605$	7.64884	−	27.5445i	0.310970	−	1.11984i
$606$	3.00937	+	2.18644i	0.122247	+	0.0888179i
$607$			33.2152i			1.34816i	0.738657	+	0.674081i	$0.235460\pi$
$607$			33.2152i			1.34816i	−0.738657	+	0.674081i	$0.764540\pi$
$608$	17.8315	−	24.5429i	0.723162	−	0.995347i
$609$	1.47177	−	4.52963i	0.0596389	−	0.183550i
$610$	22.0282	+	6.11702i	0.891895	+	0.247671i
$611$	−1.53655	−	4.72902i	−0.0621622	−	0.191316i
$612$	−0.819334	−	0.266218i	−0.0331196	−	0.0107612i
$613$	15.6706	+	5.09167i	0.632928	+	0.205651i	0.607872	−	0.794035i	$-0.292024\pi$
$613$	15.6706	+	5.09167i	0.632928	+	0.205651i	0.0250562	+	0.999686i	$0.492024\pi$
$614$	4.49125	+	13.8226i	0.181252	+	0.557836i
$615$	5.01413	−	7.56993i	0.202189	−	0.305249i
$616$	−16.4977	+	50.7746i	−0.664710	+	2.04577i
$617$	14.7049	−	20.2396i	0.591997	−	0.814814i	−0.402949	−	0.915222i	$-0.632015\pi$
$617$	14.7049	−	20.2396i	0.591997	−	0.814814i	0.994946	+	0.100408i	$0.0320149\pi$
$618$		−	18.7837i		−	0.755590i
$619$	7.73044	+	5.61649i	0.310713	+	0.225746i	0.732202	−	0.681087i	$-0.238493\pi$
$619$	7.73044	+	5.61649i	0.310713	+	0.225746i	−0.421490	+	0.906833i	$0.638493\pi$
$620$	−8.14339	+	6.47303i	−0.327047	+	0.259963i
$621$	−28.1976	+	20.4868i	−1.13153	+	0.822106i
$622$	3.94604	+	5.43125i	0.158222	+	0.217773i
$623$	−0.184490	+	0.0599444i	−0.00739143	+	0.00240162i
$624$	−1.82549			−0.0730781
$625$	−22.4549	−	10.9898i	−0.898198	−	0.439592i
$626$	18.0138			0.719978
$627$	48.8127	−	15.8602i	1.94939	−	0.633395i
$628$	−0.485834	−	0.668693i	−0.0193869	−	0.0266838i
$629$	−8.98417	+	6.52738i	−0.358222	+	0.260264i
$630$	8.29581	−	6.59418i	0.330513	−	0.262719i
$631$	38.1243	+	27.6989i	1.51770	+	1.10268i	0.962611	+	0.270887i	$0.0873170\pi$
$631$	38.1243	+	27.6989i	1.51770	+	1.10268i	0.555092	+	0.831789i	$0.312683\pi$
$632$			2.51553i			0.100062i
$633$	4.07449	−	5.60806i	0.161947	−	0.222900i
$634$	−6.05824	+	18.6454i	−0.240604	+	0.740502i
$635$	−18.9486	+	28.6071i	−0.751953	+	1.13524i
$636$	−1.81088	−	5.57332i	−0.0718061	−	0.220996i
$637$	−3.62533	−	1.17794i	−0.143641	−	0.0466717i
$638$	5.19021	+	1.68640i	0.205482	+	0.0667653i
$639$	3.46282	+	10.6575i	0.136987	+	0.421603i
$640$	−3.65770	−	1.01571i	−0.144583	−	0.0401494i
$641$	8.83633	−	27.1954i	0.349014	−	1.07415i	−0.610386	−	0.792104i	$-0.708986\pi$
$641$	8.83633	−	27.1954i	0.349014	−	1.07415i	0.959400	−	0.282050i	$-0.0910144\pi$
$642$	−3.29806	+	4.53939i	−0.130164	+	0.179155i
$643$		−	9.63291i		−	0.379885i	−0.981795	−	0.189942i	$-0.939170\pi$
$643$		−	9.63291i		−	0.379885i	0.981795	−	0.189942i	$-0.0608301\pi$
$644$	12.9734	+	9.42573i	0.511224	+	0.371426i
$645$	−3.19300	+	11.4984i	−0.125724	+	0.452750i
$646$	−7.11760	+	5.17124i	−0.280038	+	0.203460i
$647$	−20.9357	−	28.8156i	−0.823068	−	1.13286i	−0.989174	−	0.146749i	$-0.953119\pi$
$647$	−20.9357	−	28.8156i	−0.823068	−	1.13286i	0.166105	−	0.986108i	$-0.446881\pi$
$648$	11.8780	−	3.85940i	0.466613	−	0.151612i
$649$	−49.1421			−1.92900
$650$	−0.856439	+	3.69818i	−0.0335923	+	0.145055i
$651$	30.6140			1.19986
$652$	13.6451	−	4.43355i	0.534382	−	0.173631i
$653$	4.16438	+	5.73177i	0.162965	+	0.224302i	0.882688	−	0.469959i	$-0.155731\pi$
$653$	4.16438	+	5.73177i	0.162965	+	0.224302i	−0.719723	+	0.694261i	$0.755731\pi$
$654$	15.7800	−	11.4648i	0.617045	−	0.448310i
$655$	−8.29623	+	0.359398i	−0.324161	+	0.0140428i
$656$	−4.89683	−	3.55775i	−0.191189	−	0.138907i
$657$		−	10.7523i		−	0.419486i
$658$	−17.4076	+	23.9595i	−0.678617	+	0.934037i
$659$	−14.8822	+	45.8026i	−0.579727	+	1.78422i	0.0397584	+	0.999209i	$0.487341\pi$
$659$	−14.8822	+	45.8026i	−0.579727	+	1.78422i	−0.619486	+	0.785008i	$0.712659\pi$
$660$	6.67205	+	8.39377i	0.259709	+	0.326727i
$661$	−1.37723	−	4.23868i	−0.0535680	−	0.164865i	0.920693	−	0.390287i	$-0.127624\pi$
$661$	−1.37723	−	4.23868i	−0.0535680	−	0.164865i	−0.974261	+	0.225421i	$0.927624\pi$
$662$	−1.58001	−	0.513378i	−0.0614090	−	0.0199530i
$663$	−0.863721	−	0.280640i	−0.0335441	−	0.0108992i
$664$	6.54464	+	20.1423i	0.253981	+	0.781674i
$665$	2.68732	+	62.0332i	0.104210	+	2.40554i
$666$	−4.57083	+	14.0676i	−0.177116	+	0.545107i
$667$	3.60636	−	4.96372i	0.139639	−	0.192196i
$668$		−	15.5815i		−	0.602867i
$669$	−5.90750	−	4.29205i	−0.228397	−	0.165940i
$670$	−2.42424	−	6.49065i	−0.0936566	−	0.250756i
$671$	−35.7832	+	25.9980i	−1.38139	+	1.00364i
$672$	−10.9631	−	15.0894i	−0.422911	−	0.582086i
$673$	−47.2763	+	15.3610i	−1.82237	+	0.592123i	−0.822645	+	0.568556i	$0.807502\pi$
$673$	−47.2763	+	15.3610i	−1.82237	+	0.592123i	−0.999722	+	0.0235669i	$0.992498\pi$
$674$	−4.21354			−0.162299
$675$	−2.43820	−	28.0885i	−0.0938462	−	1.08113i
$676$	9.14811			0.351851
$677$	25.9813	−	8.44182i	0.998541	−	0.324446i	0.236258	−	0.971690i	$-0.424079\pi$
$677$	25.9813	−	8.44182i	0.998541	−	0.324446i	0.762282	+	0.647245i	$0.224079\pi$
$678$	−1.79259	−	2.46729i	−0.0688440	−	0.0947556i
$679$	−41.0126	+	29.7974i	−1.57392	+	1.14352i
$680$	−5.73546	−	3.79902i	−0.219945	−	0.145686i
$681$	−22.1426	−	16.0876i	−0.848507	−	0.616476i
$682$			35.0787i			1.34323i
$683$	16.8895	−	23.2464i	0.646258	−	0.889497i	−0.352672	−	0.935747i	$-0.614727\pi$
$683$	16.8895	−	23.2464i	0.646258	−	0.889497i	0.998930	+	0.0462495i	$0.0147269\pi$
$684$	2.07761	−	6.39422i	0.0794394	−	0.244489i
$685$	−19.1382	+	7.14807i	−0.731233	+	0.273114i
$686$	−1.66077	−	5.11133i	−0.0634086	−	0.195152i
$687$	21.3290	+	6.93022i	0.813753	+	0.264404i
$688$	7.56570	+	2.45825i	0.288440	+	0.0937197i
$689$	1.24034	+	3.81736i	0.0472530	+	0.145430i
$690$	−19.6832	+	7.35164i	−0.749328	+	0.279872i
$691$	13.9338	−	42.8838i	0.530067	−	1.63138i	−0.224006	−	0.974588i	$-0.571914\pi$
$691$	13.9338	−	42.8838i	0.530067	−	1.63138i	0.754073	−	0.656790i	$-0.228086\pi$
$692$	−0.393161	+	0.541139i	−0.0149457	+	0.0205710i
$693$			20.5026i			0.778830i
$694$	−7.68986	−	5.58701i	−0.291903	−	0.212080i
$695$	27.9945	+	18.5429i	1.06189	+	0.703370i
$696$	−3.33173	+	2.42064i	−0.126289	+	0.0917542i
$697$	−1.76996	−	2.43614i	−0.0670420	−	0.0922754i
$698$	−6.34250	+	2.06080i	−0.240067	+	0.0780026i
$699$	−1.72761			−0.0653441
$700$	−11.9440	+	5.06037i	−0.451442	+	0.191264i
$701$	−11.5662			−0.436850			−0.218425	−	0.975854i	$-0.570092\pi$
$701$	−11.5662			−0.436850			−0.218425	+	0.975854i	$0.570092\pi$
$702$	−4.07153	+	1.32292i	−0.153670	+	0.0499304i
$703$	−50.9408	−	70.1140i	−1.92127	−	2.64440i
$704$	33.1515	−	24.0860i	1.24945	−	0.907776i
$705$	7.78969	+	20.8561i	0.293377	+	0.785485i
$706$	−16.8525	−	12.2441i	−0.634254	−	0.460812i
$707$		−	8.70632i		−	0.327435i
$708$	5.82359	−	8.01548i	0.218864	−	0.301240i
$709$	2.40100	−	7.38953i	0.0901715	−	0.277519i	−0.895794	−	0.444470i	$-0.853392\pi$
$709$	2.40100	−	7.38953i	0.0901715	−	0.277519i	0.985965	+	0.166951i	$0.0533920\pi$
$710$	1.03473	+	23.8853i	0.0388326	+	0.896400i
$711$	0.298525	+	0.918766i	0.0111956	+	0.0344564i
$712$	0.159525	+	0.0518327i	0.00597844	+	0.00194251i
$713$	37.5077	+	12.1870i	1.40468	+	0.456407i
$714$	1.67149	+	5.14432i	0.0625540	+	0.192521i
$715$	−4.56992	−	5.74919i	−0.170905	−	0.215007i
$716$	−5.44513	+	16.7584i	−0.203494	+	0.626290i
$717$	−19.3281	+	26.6029i	−0.721822	+	0.993503i
$718$		−	10.4247i		−	0.389045i
$719$	−35.1060	−	25.5060i	−1.30923	−	0.951214i	−1.00000		0.000227888i	$-0.999927\pi$
$719$	−35.1060	−	25.5060i	−1.30923	−	0.951214i	−0.309234	−	0.950986i	$-0.600073\pi$
$720$	−5.30559	+	0.229842i	−0.197728	+	0.00856569i
$721$	−35.5677	+	25.8414i	−1.32461	+	0.962385i
$722$	−27.7674	−	38.2185i	−1.03339	−	1.42235i
$723$	10.9924	−	3.57165i	0.408812	−	0.132831i
$724$	8.62445			0.320525
$725$	1.93614	+	4.56988i	0.0719063	+	0.169721i
$726$	19.4349			0.721297
$727$	−14.8240	+	4.81660i	−0.549790	+	0.178638i	−0.570722	−	0.821143i	$-0.693337\pi$
$727$	−14.8240	+	4.81660i	−0.549790	+	0.178638i	0.0209319	+	0.999781i	$0.493337\pi$
$728$	4.33338	+	5.96438i	0.160606	+	0.221055i
$729$	22.3356	−	16.2277i	0.827243	−	0.601027i
$730$	6.13792	−	22.1035i	0.227174	−	0.818086i
$731$	3.20176	+	2.32621i	0.118421	+	0.0860380i
$732$		−	8.91743i		−	0.329598i
$733$	6.90993	−	9.51070i	0.255224	−	0.351286i	−0.662108	−	0.749408i	$-0.730338\pi$
$733$	6.90993	−	9.51070i	0.255224	−	0.351286i	0.917332	+	0.398122i	$0.130338\pi$
$734$	5.51575	−	16.9757i	0.203590	−	0.626586i
$735$	16.4450	+	4.56663i	0.606585	+	0.168443i
$736$	−7.42490	−	22.8515i	−0.273685	−	0.842317i
$737$	12.7486	+	4.14229i	0.469602	+	0.152583i
$738$	−3.81455	−	1.23942i	−0.140416	−	0.0456238i
$739$	11.9035	+	36.6351i	0.437876	+	1.34764i	0.890111	+	0.455744i	$0.150627\pi$
$739$	11.9035	+	36.6351i	0.437876	+	1.34764i	−0.452236	+	0.891899i	$0.649373\pi$
$740$	9.99835	−	15.0947i	0.367547	−	0.554893i
$741$	2.19016	−	6.74063i	0.0804576	−	0.247623i
$742$	14.0517	−	19.3406i	0.515855	−	0.710014i
$743$		−	17.6301i		−	0.646786i	−0.946265	−	0.323393i	$-0.895176\pi$
$743$		−	17.6301i		−	0.646786i	0.946265	−	0.323393i	$-0.104824\pi$
$744$	−21.4158	−	15.5595i	−0.785140	−	0.570438i
$745$	−7.77800	+	6.18259i	−0.284964	+	0.226513i
$746$	6.26781	−	4.55383i	0.229481	−	0.166728i
$747$	4.78070	+	6.58006i	0.174917	+	0.240752i
$748$	3.38192	−	1.09885i	0.123655	−	0.0401780i
$749$	13.1328			0.479861
$750$	3.11438	−	16.7086i	0.113721	−	0.610113i
$751$	33.0325			1.20537			0.602686	−	0.797979i	$-0.294097\pi$
$751$	33.0325			1.20537			0.602686	+	0.797979i	$0.294097\pi$
$752$	14.1146	−	4.58613i	0.514708	−	0.167239i
$753$	7.92121	+	10.9026i	0.288665	+	0.397313i
$754$	0.609683	−	0.442960i	0.0222033	−	0.0161317i
$755$	−0.242681	+	0.192903i	−0.00883208	+	0.00702045i
$756$	−11.8352	−	8.59878i	−0.430442	−	0.312735i
$757$		−	7.20049i		−	0.261706i	−0.991402	−	0.130853i	$-0.958228\pi$
$757$		−	7.20049i		−	0.261706i	0.991402	−	0.130853i	$-0.0417717\pi$
$758$	−11.4980	+	15.8257i	−0.417628	+	0.574815i
$759$	12.5617	−	38.6609i	0.455961	−	1.40330i
$760$	29.6482	−	44.7606i	1.07545	−	1.62364i
$761$	2.49077	+	7.66580i	0.0902903	+	0.277885i	0.985998	−	0.166759i	$-0.0533302\pi$
$761$	2.49077	+	7.66580i	0.0902903	+	0.277885i	−0.895707	+	0.444644i	$0.853330\pi$
$762$	−22.1865	−	7.20883i	−0.803732	−	0.261148i
$763$	−43.4182	−	14.1074i	−1.57184	−	0.510723i
$764$	−3.49225	−	10.7480i	−0.126345	−	0.388850i
$765$	−2.54565	−	0.706902i	−0.0920381	−	0.0255581i
$766$	−10.4870	+	32.2756i	−0.378910	+	1.16616i
$767$	−3.98878	+	5.49008i	−0.144026	+	0.198235i
$768$			20.0804i			0.724590i
$769$	−2.70288	−	1.96376i	−0.0974684	−	0.0708149i	0.537984	−	0.842955i	$-0.319186\pi$
$769$	−2.70288	−	1.96376i	−0.0974684	−	0.0708149i	−0.635452	+	0.772140i	$0.719186\pi$
$770$	−11.7039	+	42.1472i	−0.421778	+	1.51888i
$771$	9.27399	−	6.73795i	0.333995	−	0.242661i

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.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07215 + 0.348362i) q^{2} +(0.792633 + 1.09097i) q^{3} +(-0.589886 + 0.428578i) q^{4} +(-1.75044 + 1.39139i) q^{5} +(-1.22987 - 0.893554i) q^{6} +3.55811i q^{7} +(1.80840 - 2.48904i) q^{8} +(0.365112 - 1.12370i) q^{9} +(1.39202 - 2.10156i) q^{10} +(1.50705 + 4.63823i) q^{11} +(-0.935127 - 0.303841i) q^{12} +(0.640501 + 0.208112i) q^{13} +(-1.23951 - 3.81482i) q^{14} +(-2.90541 - 0.806805i) q^{15} +(-0.621148 + 1.91170i) q^{16} +(-0.587785 + 0.809017i) q^{17} +1.33196i q^{18} +(-6.31371 - 4.58718i) q^{19} +(0.436241 - 1.57096i) q^{20} +(-3.88177 + 2.82027i) q^{21} +(-3.23157 - 4.44788i) q^{22} +(-5.87858 + 1.91007i) q^{23} +4.14885 q^{24} +(1.12806 - 4.87109i) q^{25} -0.759211 q^{26} +(5.36284 - 1.74249i) q^{27} +(-1.52493 - 2.09888i) q^{28} +(-0.803048 + 0.583448i) q^{29} +(3.39610 - 0.147121i) q^{30} +(-5.16185 - 3.75031i) q^{31} +3.88724i q^{32} +(-3.86561 + 5.32056i) q^{33} +(0.348362 - 1.07215i) q^{34} +(-4.95072 - 6.22825i) q^{35} +(0.266218 + 0.819334i) q^{36} +(10.5615 + 3.43165i) q^{37} +(8.36724 + 2.71868i) q^{38} +(0.280640 + 0.863721i) q^{39} +(0.297747 + 6.87310i) q^{40} +(-0.930523 + 2.86385i) q^{41} +(3.17936 - 4.37602i) q^{42} -3.95759i q^{43} +(-2.87683 - 2.09014i) q^{44} +(0.924399 + 2.47498i) q^{45} +(5.63732 - 4.09576i) q^{46} +(-4.33980 - 5.97322i) q^{47} +(-2.57794 + 0.837622i) q^{48} -5.66014 q^{49} +(0.487449 + 5.61551i) q^{50} -1.34851 q^{51} +(-0.467015 + 0.151742i) q^{52} +(3.50317 + 4.82171i) q^{53} +(-5.14274 + 3.73642i) q^{54} +(-9.09159 - 6.02204i) q^{55} +(8.85628 + 6.43447i) q^{56} -10.5240i q^{57} +(0.657735 - 0.905295i) q^{58} +(-3.11379 + 9.58328i) q^{59} +(2.05964 - 0.769272i) q^{60} +(2.80258 + 8.62545i) q^{61} +(6.84074 + 2.22269i) q^{62} +(3.99824 + 1.29911i) q^{63} +(-2.59646 - 7.99110i) q^{64} +(-1.41072 + 0.526901i) q^{65} +(2.29103 - 7.05106i) q^{66} +(1.61559 - 2.22366i) q^{67} -0.729140i q^{68} +(-6.74338 - 4.89935i) q^{69} +(7.47760 + 4.95297i) q^{70} +(-7.67294 + 5.57472i) q^{71} +(-2.13667 - 2.94087i) q^{72} +(8.65492 - 2.81215i) q^{73} -12.5190 q^{74} +(6.20833 - 2.63030i) q^{75} +5.69033 q^{76} +(-16.5033 + 5.36226i) q^{77} +(-0.601776 - 0.828273i) q^{78} +(-0.661473 + 0.480589i) q^{79} +(-1.57263 - 4.21056i) q^{80} +(3.28413 + 2.38606i) q^{81} -3.39464i q^{82} +(-4.04620 + 5.56912i) q^{83} +(1.08110 - 3.32728i) q^{84} +(-0.0967771 - 2.23397i) q^{85} +(1.37867 + 4.24312i) q^{86} +(-1.27304 - 0.413637i) q^{87} +(14.2701 + 4.63664i) q^{88} +(0.0168473 + 0.0518505i) q^{89} +(-1.85328 - 2.33152i) q^{90} +(-0.740483 + 2.27897i) q^{91} +(2.64908 - 3.64615i) q^{92} -8.60402i q^{93} +(6.73376 + 4.89236i) q^{94} +(17.4343 - 0.755265i) q^{95} +(-4.24085 + 3.08116i) q^{96} +(8.37450 + 11.5265i) q^{97} +(6.06851 - 1.97178i) q^{98} +5.76222 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) \) 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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