LMFDB - Embedded newform 425.2.r.a.69.2

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			69.2
Character	$\chi$	$=$	425.69
Dual form			425.2.r.a.154.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.55039 + 0.828673i) q^{2} +(-0.0154746 - 0.0212989i) q^{3} +(4.19977 - 3.05131i) q^{4} +(2.16953 + 0.541436i) q^{5} +(0.0571160 + 0.0414972i) q^{6} +2.17034i q^{7} +(-5.03006 + 6.92328i) q^{8} +(0.926837 - 2.85251i) q^{9} +(-5.98182 + 0.416954i) q^{10} +(1.91650 + 5.89837i) q^{11} +(-0.129979 - 0.0422328i) q^{12} +(-2.63082 - 0.854806i) q^{13} +(-1.79850 - 5.53522i) q^{14} +(-0.0220405 - 0.0545870i) q^{15} +(3.88315 - 11.9511i) q^{16} +(-0.587785 + 0.809017i) q^{17} +8.04306i q^{18} +(0.467036 + 0.339321i) q^{19} +(10.7636 - 4.34599i) q^{20} +(0.0462259 - 0.0335851i) q^{21} +(-9.77564 - 13.4550i) q^{22} +(6.29681 - 2.04596i) q^{23} +0.225296 q^{24} +(4.41369 + 2.34932i) q^{25} +7.41798 q^{26} +(-0.150213 + 0.0488071i) q^{27} +(6.62238 + 9.11493i) q^{28} +(0.219666 - 0.159597i) q^{29} +(0.101447 + 0.120954i) q^{30} +(-4.64539 - 3.37508i) q^{31} +16.5826i q^{32} +(0.0959719 - 0.132094i) q^{33} +(0.828673 - 2.55039i) q^{34} +(-1.17510 + 4.70861i) q^{35} +(-4.81139 - 14.8079i) q^{36} +(-2.71468 - 0.882054i) q^{37} +(-1.47231 - 0.478382i) q^{38} +(0.0225044 + 0.0692614i) q^{39} +(-14.6614 + 12.2968i) q^{40} +(-3.18738 + 9.80975i) q^{41} +(-0.0900631 + 0.123961i) q^{42} +7.56944i q^{43} +(26.0466 + 18.9240i) q^{44} +(3.55525 - 5.68678i) q^{45} +(-14.3639 + 10.4360i) q^{46} +(4.63968 + 6.38596i) q^{47} +(-0.314636 + 0.102231i) q^{48} +2.28962 q^{49} +(-13.2035 - 2.33418i) q^{50} +0.0263269 q^{51} +(-13.6571 + 4.43747i) q^{52} +(-2.21228 - 3.04494i) q^{53} +(0.342657 - 0.248955i) q^{54} +(0.964303 + 13.8343i) q^{55} +(-15.0259 - 10.9169i) q^{56} -0.0151982i q^{57} +(-0.427981 + 0.589065i) q^{58} +(-2.01108 + 6.18947i) q^{59} +(-0.259127 - 0.162001i) q^{60} +(-1.96408 - 6.04482i) q^{61} +(14.6444 + 4.75826i) q^{62} +(6.19092 + 2.01155i) q^{63} +(-5.97523 - 18.3899i) q^{64} +(-5.24482 - 3.27894i) q^{65} +(-0.135303 + 0.416421i) q^{66} +(-0.241468 + 0.332352i) q^{67} +5.19120i q^{68} +(-0.141017 - 0.102455i) q^{69} +(-0.904933 - 12.9826i) q^{70} +(7.23989 - 5.26009i) q^{71} +(15.0867 + 20.7650i) q^{72} +(11.8579 - 3.85285i) q^{73} +7.65444 q^{74} +(-0.0182621 - 0.130362i) q^{75} +2.99681 q^{76} +(-12.8015 + 4.15945i) q^{77} +(-0.114790 - 0.157995i) q^{78} +(-1.74512 + 1.26790i) q^{79} +(14.8954 - 23.8258i) q^{80} +(-7.27611 - 5.28640i) q^{81} -27.6600i q^{82} +(2.87256 - 3.95373i) q^{83} +(0.0916596 - 0.282099i) q^{84} +(-1.71325 + 1.43694i) q^{85} +(-6.27259 - 19.3050i) q^{86} +(-0.00679847 - 0.00220896i) q^{87} +(-50.4762 - 16.4007i) q^{88} +(5.62243 + 17.3040i) q^{89} +(-4.35480 + 17.4496i) q^{90} +(1.85522 - 5.70978i) q^{91} +(20.2023 - 27.8061i) q^{92} +0.151170i q^{93} +(-17.1249 - 12.4419i) q^{94} +(0.829526 + 0.989036i) q^{95} +(0.353191 - 0.256608i) q^{96} +(-0.271463 - 0.373636i) q^{97} +(-5.83943 + 1.89734i) q^{98} +18.6014 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 $

$2$	−2.55039	+	0.828673i	−1.80340	+	0.585960i	−0.999956	−	0.00942041i	$-0.997001\pi$
$2$	−2.55039	+	0.828673i	−1.80340	+	0.585960i	−0.803444	+	0.595380i	$0.797001\pi$
$3$	−0.0154746	−	0.0212989i	−0.00893424	−	0.0122969i	0.804527	−	0.593917i	$-0.202419\pi$
$3$	−0.0154746	−	0.0212989i	−0.00893424	−	0.0122969i	−0.813461	+	0.581620i	$0.802419\pi$
$4$	4.19977	−	3.05131i	2.09988	−	1.52565i
$5$	2.16953	+	0.541436i	0.970242	+	0.242137i
$5$	2.16953	+	0.541436i	0.970242	+	0.242137i
$6$	0.0571160	+	0.0414972i	0.0233175	+	0.0169412i
$7$			2.17034i			0.820312i	0.912015	+	0.410156i	$0.134526\pi$
$7$			2.17034i			0.820312i	−0.912015	+	0.410156i	$0.865474\pi$
$8$	−5.03006	+	6.92328i	−1.77839	+	2.44775i
$9$	0.926837	−	2.85251i	0.308946	−	0.950837i
$10$	−5.98182	+	0.416954i	−1.89162	+	0.131853i
$11$	1.91650	+	5.89837i	0.577845	+	1.77843i	0.626279	+	0.779599i	$0.284577\pi$
$11$	1.91650	+	5.89837i	0.577845	+	1.77843i	−0.0484334	+	0.998826i	$0.515423\pi$
$12$	−0.129979	−	0.0422328i	−0.0375217	−	0.0121916i
$13$	−2.63082	−	0.854806i	−0.729659	−	0.237080i	−0.0794528	−	0.996839i	$-0.525317\pi$
$13$	−2.63082	−	0.854806i	−0.729659	−	0.237080i	−0.650206	+	0.759758i	$0.725317\pi$
$14$	−1.79850	−	5.53522i	−0.480670	−	1.47935i
$15$	−0.0220405	−	0.0545870i	−0.00569083	−	0.0140943i
$16$	3.88315	−	11.9511i	0.970788	−	2.98778i
$17$	−0.587785	+	0.809017i	−0.142559	+	0.196215i
$17$	−0.587785	+	0.809017i	−0.142559	+	0.196215i
$18$			8.04306i			1.89577i
$19$	0.467036	+	0.339321i	0.107145	+	0.0778456i	0.640068	−	0.768318i	$-0.278906\pi$
$19$	0.467036	+	0.339321i	0.107145	+	0.0778456i	−0.532922	+	0.846164i	$0.678906\pi$
$20$	10.7636	−	4.34599i	2.40681	−	0.971794i
$21$	0.0462259	−	0.0335851i	0.0100873	−	0.00732887i
$22$	−9.77564	−	13.4550i	−2.08417	−	2.86862i
$23$	6.29681	−	2.04596i	1.31298	−	0.426612i	0.432899	−	0.901443i	$-0.357491\pi$
$23$	6.29681	−	2.04596i	1.31298	−	0.426612i	0.880077	+	0.474831i	$0.157491\pi$
$24$	0.225296			0.0459884
$25$	4.41369	+	2.34932i	0.882739	+	0.469864i
$26$	7.41798			1.45479
$27$	−0.150213	+	0.0488071i	−0.0289085	+	0.00939294i
$28$	6.62238	+	9.11493i	1.25151	+	1.72256i
$29$	0.219666	−	0.159597i	0.0407909	−	0.0296363i	−0.567203	−	0.823578i	$-0.691975\pi$
$29$	0.219666	−	0.159597i	0.0407909	−	0.0296363i	0.607994	+	0.793942i	$0.291975\pi$
$30$	0.101447	+	0.120954i	0.0185215	+	0.0220831i
$31$	−4.64539	−	3.37508i	−0.834337	−	0.606181i	0.0864458	−	0.996257i	$-0.472449\pi$
$31$	−4.64539	−	3.37508i	−0.834337	−	0.606181i	−0.920783	+	0.390075i	$0.872449\pi$
$32$			16.5826i			2.93141i
$33$	0.0959719	−	0.132094i	0.0167066	−	0.0229946i
$34$	0.828673	−	2.55039i	0.142116	−	0.437389i
$35$	−1.17510	+	4.70861i	−0.198628	+	0.795901i
$36$	−4.81139	−	14.8079i	−0.801899	−	2.46799i
$37$	−2.71468	−	0.882054i	−0.446291	−	0.145009i	0.0772453	−	0.997012i	$-0.475388\pi$
$37$	−2.71468	−	0.882054i	−0.446291	−	0.145009i	−0.523536	+	0.852003i	$0.675388\pi$
$38$	−1.47231	−	0.478382i	−0.238840	−	0.0776039i
$39$	0.0225044	+	0.0692614i	0.00360359	+	0.0110907i
$40$	−14.6614	+	12.2968i	−2.31816	+	1.94429i
$41$	−3.18738	+	9.80975i	−0.497785	+	1.53203i	0.314785	+	0.949163i	$0.398067\pi$
$41$	−3.18738	+	9.80975i	−0.497785	+	1.53203i	−0.812571	+	0.582863i	$0.801933\pi$
$42$	−0.0900631	+	0.123961i	−0.0138970	+	0.0191276i
$43$			7.56944i			1.15433i	0.816628	+	0.577164i	$0.195841\pi$
$43$			7.56944i			1.15433i	−0.816628	+	0.577164i	$0.804159\pi$
$44$	26.0466	+	18.9240i	3.92667	+	2.85289i
$45$	3.55525	−	5.68678i	0.529985	−	0.847734i
$46$	−14.3639	+	10.4360i	−2.11784	+	1.53870i
$47$	4.63968	+	6.38596i	0.676766	+	0.931489i	0.999889	−	0.0148682i	$-0.00473286\pi$
$47$	4.63968	+	6.38596i	0.676766	+	0.931489i	−0.323123	+	0.946357i	$0.604733\pi$
$48$	−0.314636	+	0.102231i	−0.0454138	+	0.0147558i
$49$	2.28962			0.327088
$50$	−13.2035	−	2.33418i	−1.86725	−	0.330102i
$51$	0.0263269			0.00368650
$52$	−13.6571	+	4.43747i	−1.89390	+	0.615366i
$53$	−2.21228	−	3.04494i	−0.303879	−	0.418254i	0.629581	−	0.776935i	$-0.283227\pi$
$53$	−2.21228	−	3.04494i	−0.303879	−	0.418254i	−0.933460	+	0.358681i	$0.883227\pi$
$54$	0.342657	−	0.248955i	0.0466297	−	0.0338784i
$55$	0.964303	+	13.8343i	0.130027	+	1.86542i
$56$	−15.0259	−	10.9169i	−2.00792	−	1.45884i
$57$		−	0.0151982i		−	0.00201305i
$58$	−0.427981	+	0.589065i	−0.0561966	+	0.0773480i
$59$	−2.01108	+	6.18947i	−0.261820	+	0.805800i	0.730589	+	0.682818i	$0.239246\pi$
$59$	−2.01108	+	6.18947i	−0.261820	+	0.805800i	−0.992409	+	0.122982i	$0.960754\pi$
$60$	−0.259127	−	0.162001i	−0.0334531	−	0.0209142i
$61$	−1.96408	−	6.04482i	−0.251475	−	0.773960i	−0.994504	−	0.104701i	$-0.966612\pi$
$61$	−1.96408	−	6.04482i	−0.251475	−	0.773960i	0.743029	−	0.669259i	$-0.233388\pi$
$62$	14.6444	+	4.75826i	1.85984	+	0.604299i
$63$	6.19092	+	2.01155i	0.779983	+	0.253432i
$64$	−5.97523	−	18.3899i	−0.746904	−	2.29873i
$65$	−5.24482	−	3.27894i	−0.650539	−	0.406703i
$66$	−0.135303	+	0.416421i	−0.0166547	+	0.0512579i
$67$	−0.241468	+	0.332352i	−0.0295000	+	0.0406032i	−0.823512	−	0.567299i	$-0.807989\pi$
$67$	−0.241468	+	0.332352i	−0.0295000	+	0.0406032i	0.794012	+	0.607902i	$0.207989\pi$
$68$			5.19120i			0.629525i
$69$	−0.141017	−	0.102455i	−0.0169765	−	0.0123341i
$70$	−0.904933	−	12.9826i	−0.108160	−	1.55172i
$71$	7.23989	−	5.26009i	0.859217	−	0.624258i	−0.0684550	−	0.997654i	$-0.521807\pi$
$71$	7.23989	−	5.26009i	0.859217	−	0.624258i	0.927672	+	0.373397i	$0.121807\pi$
$72$	15.0867	+	20.7650i	1.77798	+	2.44718i
$73$	11.8579	−	3.85285i	1.38786	−	0.450942i	0.482613	−	0.875833i	$-0.339688\pi$
$73$	11.8579	−	3.85285i	1.38786	−	0.450942i	0.905244	+	0.424891i	$0.139688\pi$
$74$	7.65444			0.889810
$75$	−0.0182621	−	0.130362i	−0.00210872	−	0.0150529i
$76$	2.99681			0.343758
$77$	−12.8015	+	4.15945i	−1.45886	+	0.474014i
$78$	−0.114790	−	0.157995i	−0.0129974	−	0.0178894i
$79$	−1.74512	+	1.26790i	−0.196341	+	0.142650i	−0.681612	−	0.731714i	$-0.738721\pi$
$79$	−1.74512	+	1.26790i	−0.196341	+	0.142650i	0.485271	+	0.874364i	$0.338721\pi$
$80$	14.8954	−	23.8258i	1.66535	−	2.66380i
$81$	−7.27611	−	5.28640i	−0.808456	−	0.587378i
$82$		−	27.6600i		−	3.05454i
$83$	2.87256	−	3.95373i	0.315304	−	0.433979i	−0.621722	−	0.783238i	$-0.713567\pi$
$83$	2.87256	−	3.95373i	0.315304	−	0.433979i	0.937026	+	0.349259i	$0.113567\pi$
$84$	0.0916596	−	0.282099i	0.0100009	−	0.0307795i
$85$	−1.71325	+	1.43694i	−0.185828	+	0.155858i
$86$	−6.27259	−	19.3050i	−0.676391	−	2.08172i
$87$	−0.00679847	−	0.00220896i	−0.000728872	−	0.000236825i
$88$	−50.4762	−	16.4007i	−5.38078	−	1.74832i
$89$	5.62243	+	17.3040i	0.595976	+	1.83423i	0.549807	+	0.835292i	$0.314701\pi$
$89$	5.62243	+	17.3040i	0.595976	+	1.83423i	0.0461691	+	0.998934i	$0.485299\pi$
$90$	−4.35480	+	17.4496i	−0.459036	+	1.83935i
$91$	1.85522	−	5.70978i	0.194480	−	0.598548i
$92$	20.2023	−	27.8061i	2.10623	−	2.89898i
$93$			0.151170i			0.0156756i
$94$	−17.1249	−	12.4419i	−1.76629	−	1.28329i
$95$	0.829526	+	0.989036i	0.0851075	+	0.101473i
$96$	0.353191	−	0.256608i	0.0360474	−	0.0261900i
$97$	−0.271463	−	0.373636i	−0.0275628	−	0.0379370i	0.795013	−	0.606592i	$-0.207464\pi$
$97$	−0.271463	−	0.373636i	−0.0275628	−	0.0379370i	−0.822576	+	0.568655i	$0.807464\pi$
$98$	−5.83943	+	1.89734i	−0.589871	+	0.191661i
$99$	18.6014			1.86952
$100$	25.7050	−	3.60096i	2.57050	−	0.360096i
$101$	6.56496			0.653238			0.326619	−	0.945156i	$-0.394091\pi$
$101$	6.56496			0.653238			0.326619	+	0.945156i	$0.394091\pi$
$102$	−0.0671439	+	0.0218164i	−0.00664824	+	0.00216014i
$103$	3.24752	+	4.46983i	0.319988	+	0.440425i	0.938463	−	0.345379i	$-0.112250\pi$
$103$	3.24752	+	4.46983i	0.319988	+	0.440425i	−0.618476	+	0.785804i	$0.712250\pi$
$104$	19.1512	−	13.9142i	1.87793	−	1.36440i
$105$	0.118473	−	0.0478354i	0.0115617	−	0.00466826i
$106$	8.16543	+	5.93253i	0.793096	+	0.576218i
$107$		−	8.90729i		−	0.861100i	−0.902567	−	0.430550i	$-0.858320\pi$
$107$		−	8.90729i		−	0.861100i	0.902567	−	0.430550i	$-0.141680\pi$
$108$	−0.481934	+	0.663325i	−0.0463741	+	0.0638284i
$109$	−0.139793	+	0.430240i	−0.0133898	+	0.0412095i	−0.957528	−	0.288340i	$-0.906897\pi$
$109$	−0.139793	+	0.430240i	−0.0133898	+	0.0412095i	0.944138	+	0.329549i	$0.106897\pi$
$110$	−13.9235	−	34.4839i	−1.32755	−	3.28791i
$111$	0.0232217	+	0.0714692i	0.00220411	+	0.00678355i
$112$	25.9380	+	8.42776i	2.45091	+	0.796349i
$113$	−7.88780	−	2.56290i	−0.742022	−	0.241098i	−0.0864772	−	0.996254i	$-0.527561\pi$
$113$	−7.88780	−	2.56290i	−0.742022	−	0.241098i	−0.655545	+	0.755156i	$0.727561\pi$
$114$	0.0125943	+	0.0387614i	0.00117957	+	0.00363033i
$115$	14.7689	−	1.02944i	1.37720	−	0.0959960i
$116$	0.435567	−	1.34054i	0.0404414	−	0.124466i
$117$	−4.87668	+	6.71218i	−0.450850	+	0.620541i
$118$		−	17.4521i		−	1.60660i
$119$	−1.75584	−	1.27569i	−0.160958	−	0.116943i
$120$	0.488787	+	0.121983i	0.0446199	+	0.0111355i
$121$	−22.2186	+	16.1428i	−2.01988	+	1.46753i
$122$	10.0184	+	13.7891i	0.907019	+	1.24840i
$123$	0.258260	−	0.0839139i	0.0232865	−	0.00756626i
$124$	−29.8080			−2.67683
$125$	8.30362	+	7.48664i	0.742699	+	0.669626i
$126$	−17.4562			−1.55512
$127$	11.2691	−	3.66155i	0.999971	−	0.324910i	0.237117	−	0.971481i	$-0.423797\pi$
$127$	11.2691	−	3.66155i	0.999971	−	0.324910i	0.762854	+	0.646571i	$0.223797\pi$
$128$	10.9844	+	15.1187i	0.970890	+	1.33632i
$129$	0.161221	−	0.117134i	0.0141947	−	0.0103131i
$130$	16.0935	+	4.01636i	1.41149	+	0.352258i
$131$	−7.20229	−	5.23277i	−0.629267	−	0.457189i	0.226879	−	0.973923i	$-0.427148\pi$
$131$	−7.20229	−	5.23277i	−0.629267	−	0.457189i	−0.856146	+	0.516734i	$0.827148\pi$
$132$		−	0.847604i		−	0.0737745i
$133$	−0.736443	+	1.01363i	−0.0638577	+	0.0878926i
$134$	0.340426	−	1.04772i	0.0294084	−	0.0905096i
$135$	−0.352317	+	0.0245578i	−0.0303226	+	0.00211360i
$136$	−2.64446	−	8.13881i	−0.226760	−	0.697897i
$137$	−16.3005	−	5.29635i	−1.39264	−	0.452498i	−0.485840	−	0.874048i	$-0.661486\pi$
$137$	−16.3005	−	5.29635i	−1.39264	−	0.452498i	−0.906805	+	0.421550i	$0.861486\pi$
$138$	0.444550	+	0.144443i	0.0378426	+	0.0122958i
$139$	−5.13295	−	15.7976i	−0.435371	−	1.33993i	−0.892706	−	0.450639i	$-0.851196\pi$
$139$	−5.13295	−	15.7976i	−0.435371	−	1.33993i	0.457335	−	0.889294i	$-0.348804\pi$
$140$	9.43229	+	23.3607i	0.797174	+	1.97434i
$141$	0.0642171	−	0.197640i	0.00540806	−	0.0166443i
$142$	−14.1057	+	19.4148i	−1.18372	+	1.62925i
$143$		−	17.1558i		−	1.43464i
$144$	−30.4916	−	22.1535i	−2.54097	−	1.84612i
$145$	0.562982	−	0.227314i	0.0467531	−	0.0188774i
$146$	−27.0494	+	19.6526i	−2.23863	+	1.62646i
$147$	−0.0354309	−	0.0487664i	−0.00292229	−	0.00402218i
$148$	−14.0925	+	4.57892i	−1.15839	+	0.376385i
$149$	−8.31415			−0.681122			−0.340561	−	0.940222i	$-0.610617\pi$
$149$	−8.31415			−0.681122			−0.340561	+	0.940222i	$0.610617\pi$
$150$	0.154603	+	0.317340i	0.0126232	+	0.0259107i
$151$	17.2152			1.40096			0.700478	−	0.713674i	$-0.252970\pi$
$151$	17.2152			1.40096			0.700478	+	0.713674i	$0.252970\pi$
$152$	−4.69843	+	1.52661i	−0.381093	+	0.123825i
$153$	1.76295	+	2.42649i	0.142526	+	0.196170i
$154$	29.2020	−	21.2165i	2.35316	−	1.70967i
$155$	−8.25092	−	9.83750i	−0.662730	−	0.790167i
$156$	0.305851	+	0.222214i	0.0244877	+	0.0177913i
$157$		−	11.7483i		−	0.937613i	−0.883301	−	0.468806i	$-0.844684\pi$
$157$		−	11.7483i		−	0.937613i	0.883301	−	0.468806i	$-0.155316\pi$
$158$	3.40006	−	4.67978i	0.270494	−	0.372303i
$159$	−0.0306198	+	0.0942381i	−0.00242831	+	0.00747357i
$160$	−8.97840	+	35.9764i	−0.709805	+	2.84418i
$161$	4.44043	+	13.6662i	0.349955	+	1.07705i
$162$	22.9376	+	7.45288i	1.80215	+	0.585554i
$163$	−16.7615	−	5.44614i	−1.31286	−	0.426574i	−0.432823	−	0.901479i	$-0.642483\pi$
$163$	−16.7615	−	5.44614i	−1.31286	−	0.426574i	−0.880037	+	0.474904i	$0.842483\pi$
$164$	16.5463	+	50.9244i	1.29205	+	3.97652i
$165$	0.279734	−	0.234619i	0.0217773	−	0.0182651i
$166$	−4.04979	+	12.4640i	−0.314325	+	0.967393i
$167$	−8.76113	+	12.0587i	−0.677957	+	0.933127i	−0.999907	−	0.0136291i	$-0.995662\pi$
$167$	−8.76113	+	12.0587i	−0.677957	+	0.933127i	0.321950	+	0.946757i	$0.395662\pi$
$168$			0.488970i			0.0377249i
$169$	−4.32669	−	3.14353i	−0.332823	−	0.241810i
$170$	3.17870	−	5.08447i	0.243795	−	0.389961i
$171$	1.40078	−	1.01773i	0.107121	−	0.0778276i
$172$	23.0967	+	31.7899i	1.76111	+	2.42396i
$173$	8.03634	−	2.61117i	0.610992	−	0.198523i	0.0128552	−	0.999917i	$-0.495908\pi$
$173$	8.03634	−	2.61117i	0.610992	−	0.198523i	0.598137	+	0.801394i	$0.295908\pi$
$174$	0.0191693			0.00145322
$175$	−5.09882	+	9.57922i	−0.385435	+	0.724121i
$176$	77.9341			5.87451
$177$	0.162950	−	0.0529455i	0.0122480	−	0.00397963i
$178$	−28.6788	−	39.4730i	−2.14957	−	2.95862i
$179$	2.81272	−	2.04356i	0.210233	−	0.152743i	−0.477686	−	0.878530i	$-0.658524\pi$
$179$	2.81272	−	2.04356i	0.210233	−	0.152743i	0.687919	+	0.725788i	$0.258524\pi$
$180$	−2.42090	−	34.7313i	−0.180443	−	2.58872i
$181$	8.62604	+	6.26719i	0.641169	+	0.465836i	0.860251	−	0.509870i	$-0.170306\pi$
$181$	8.62604	+	6.26719i	0.641169	+	0.465836i	−0.219083	+	0.975706i	$0.570306\pi$
$182$			16.0995i			1.19338i
$183$	−0.0983548	+	0.135374i	−0.00727059	+	0.0100071i
$184$	−17.5086	+	53.8859i	−1.29075	+	3.97252i
$185$	−5.41200	−	3.38347i	−0.397898	−	0.248757i
$186$	−0.125270	−	0.385542i	−0.00918525	−	0.0282693i
$187$	−5.89837	−	1.91650i	−0.431332	−	0.140148i
$188$	38.9711	+	12.6625i	2.84226	+	0.923506i
$189$	−0.105928	−	0.326013i	−0.00770514	−	0.0237140i
$190$	−2.93520	−	1.83502i	−0.212942	−	0.133127i
$191$	−0.998004	+	3.07154i	−0.0722130	+	0.222249i	−0.980649	−	0.195776i	$-0.937277\pi$
$191$	−0.998004	+	3.07154i	−0.0722130	+	0.222249i	0.908436	+	0.418025i	$0.137277\pi$
$192$	−0.299220	+	0.411841i	−0.0215944	+	0.0297221i
$193$		−	23.1517i		−	1.66650i	−0.552899	−	0.833249i	$-0.686478\pi$
$193$		−	23.1517i		−	1.66650i	0.552899	−	0.833249i	$-0.313522\pi$
$194$	1.00196	+	0.727965i	0.0719364	+	0.0522648i
$195$	0.0113233	+	0.162449i	0.000810878	+	0.0116332i
$196$	9.61587	−	6.98634i	0.686848	−	0.499024i
$197$	−11.3798	−	15.6629i	−0.810776	−	1.11594i	−0.991203	−	0.132349i	$-0.957748\pi$
$197$	−11.3798	−	15.6629i	−0.810776	−	1.11594i	0.180427	−	0.983588i	$-0.442252\pi$
$198$	−47.4410	+	15.4145i	−3.37148	+	1.09546i
$199$	22.1416			1.56958			0.784790	−	0.619762i	$-0.212771\pi$
$199$	22.1416			1.56958			0.784790	+	0.619762i	$0.212771\pi$
$200$	−38.4661	+	18.7400i	−2.71997	+	1.32512i
$201$	0.0108153			0.000762855
$202$	−16.7432	+	5.44020i	−1.17805	+	0.382771i
$203$	0.346379	+	0.476750i	0.0243110	+	0.0334613i
$204$	0.110567	−	0.0803315i	0.00774123	−	0.00562433i
$205$	−12.2265	+	19.5568i	−0.853933	+	1.36590i
$206$	−11.9865	−	8.70868i	−0.835137	−	0.606762i
$207$		−	19.8580i		−	1.38023i
$208$	−20.4318	+	28.1219i	−1.41669	+	1.94990i
$209$	−1.10637	+	3.40506i	−0.0765292	+	0.235533i
$210$	−0.262511	+	0.220174i	−0.0181150	+	0.0151934i
$211$	−5.18490	−	15.9575i	−0.356943	−	1.09856i	−0.954874	−	0.297010i	$-0.904010\pi$
$211$	−5.18490	−	15.9575i	−0.356943	−	1.09856i	0.597931	−	0.801547i	$-0.295990\pi$
$212$	−18.5821	−	6.03769i	−1.27622	−	0.414670i
$213$	−0.224068	−	0.0728042i	−0.0153529	−	0.00498846i
$214$	7.38122	+	22.7171i	0.504570	+	1.55291i
$215$	−4.09837	+	16.4221i	−0.279506	+	1.11998i
$216$	0.417674	−	1.28547i	0.0284191	−	0.0874651i
$217$	7.32507	−	10.0821i	0.497258	−	0.684417i
$218$		−	1.21312i		−	0.0821630i
$219$	−0.265557	−	0.192938i	−0.0179447	−	0.0130376i
$220$	46.2627	+	55.1586i	3.11903	+	3.71879i
$221$	2.23791	−	1.62594i	0.150538	−	0.109372i
$222$	−0.118449	−	0.163031i	−0.00794978	−	0.0109419i
$223$	16.6282	−	5.40284i	1.11351	−	0.361801i	0.306222	−	0.951960i	$-0.400935\pi$
$223$	16.6282	−	5.40284i	1.11351	−	0.361801i	0.807287	+	0.590159i	$0.200935\pi$
$224$	−35.9899			−2.40467
$225$	10.7922	−	10.4127i	0.719482	−	0.694178i
$226$	22.2408			1.47944
$227$	3.72245	−	1.20950i	0.247067	−	0.0802771i	−0.182865	−	0.983138i	$-0.558537\pi$
$227$	3.72245	−	1.20950i	0.247067	−	0.0802771i	0.429933	+	0.902861i	$0.358537\pi$
$228$	−0.0463744	−	0.0638289i	−0.00307122	−	0.00422717i
$229$	3.97389	−	2.88720i	0.262602	−	0.190791i	−0.448691	−	0.893687i	$-0.648110\pi$
$229$	3.97389	−	2.88720i	0.262602	−	0.190791i	0.711293	+	0.702895i	$0.248110\pi$
$230$	−36.8133	+	14.8640i	−2.42740	+	0.980105i
$231$	0.286689	+	0.208292i	0.0188628	+	0.0137046i
$232$			2.32359i			0.152551i
$233$	7.36756	−	10.1406i	0.482665	−	0.664332i	−0.496349	−	0.868123i	$-0.665326\pi$
$233$	7.36756	−	10.1406i	0.482665	−	0.664332i	0.979014	+	0.203791i	$0.0653264\pi$
$234$	6.87526	−	21.1599i	0.449450	−	1.38326i
$235$	6.60831	+	16.3666i	0.431079	+	1.06764i
$236$	10.4399	+	32.1308i	0.679581	+	2.09153i
$237$	0.0540099	+	0.0175489i	0.00350832	+	0.00113992i
$238$	5.53522	+	1.79850i	0.358795	+	0.116580i
$239$	−8.03530	−	24.7301i	−0.519760	−	1.59966i	−0.774450	−	0.632635i	$-0.781973\pi$
$239$	−8.03530	−	24.7301i	−0.519760	−	1.59966i	0.254689	−	0.967023i	$-0.418027\pi$
$240$	−0.737962	+	0.0514386i	−0.0476353	+	0.00332035i
$241$	−1.42315	+	4.38000i	−0.0916731	+	0.282141i	−0.986372	−	0.164528i	$-0.947390\pi$
$241$	−1.42315	+	4.38000i	−0.0916731	+	0.282141i	0.894699	+	0.446669i	$0.147390\pi$
$242$	43.2891	−	59.5824i	2.78273	−	3.83010i
$243$			0.710607i			0.0455855i
$244$	−26.6933	−	19.3938i	−1.70886	−	1.24156i
$245$	4.96739	+	1.23968i	0.317355	+	0.0792003i
$246$	−0.589128	+	0.428027i	−0.0375614	+	0.0272900i
$247$	−0.938633	−	1.29192i	−0.0597238	−	0.0822028i
$248$	46.7332	−	15.1845i	2.96756	−	0.964219i
$249$	−0.128662			−0.00815361
$250$	−27.3815	−	12.2129i	−1.73176	−	0.772411i
$251$	−4.01531			−0.253444			−0.126722	−	0.991938i	$-0.540446\pi$
$251$	−4.01531			−0.253444			−0.126722	+	0.991938i	$0.540446\pi$
$252$	32.1383	−	10.4424i	2.02452	−	0.657807i
$253$	24.1356	+	33.2198i	1.51739	+	2.08851i
$254$	−25.7064	+	18.6768i	−1.61296	+	1.17189i
$255$	0.0571169	+	0.0142543i	0.00357680	+	0.000892640i
$256$	−9.25617	−	6.72500i	−0.578511	−	0.420313i
$257$			9.13174i			0.569623i	0.958584	+	0.284811i	$0.0919309\pi$
$257$			9.13174i			0.569623i	−0.958584	+	0.284811i	$0.908069\pi$
$258$	−0.314111	+	0.432336i	−0.0195557	+	0.0269161i
$259$	1.91436	−	5.89179i	0.118952	−	0.366098i
$260$	−32.0321	+	2.23275i	−1.98655	+	0.138469i
$261$	−0.251657	−	0.774519i	−0.0155771	−	0.0479415i
$262$	22.7049	+	7.37728i	1.40271	+	0.455770i
$263$	0.297692	+	0.0967261i	0.0183565	+	0.00596438i	0.318181	−	0.948030i	$-0.396928\pi$
$263$	0.297692	+	0.0967261i	0.0183565	+	0.00596438i	−0.299824	+	0.953994i	$0.596928\pi$
$264$	0.431780	+	1.32888i	0.0265742	+	0.0817870i
$265$	−3.15096	−	7.80388i	−0.193562	−	0.479388i
$266$	1.03825	−	3.19541i	0.0636594	−	0.195923i
$267$	0.281553	−	0.387524i	0.0172308	−	0.0237161i
$268$			2.13259i			0.130269i
$269$	−16.3474	−	11.8771i	−0.996719	−	0.724159i	−0.0353367	−	0.999375i	$-0.511250\pi$
$269$	−16.3474	−	11.8771i	−0.996719	−	0.724159i	−0.961382	+	0.275217i	$0.911250\pi$
$270$	0.878196	−	0.354587i	0.0534453	−	0.0215795i
$271$	−13.4484	+	9.77086i	−0.816934	+	0.593538i	−0.915833	−	0.401560i	$-0.868468\pi$
$271$	−13.4484	+	9.77086i	−0.816934	+	0.593538i	0.0988983	+	0.995098i	$0.468468\pi$
$272$	7.38619	+	10.1662i	0.447854	+	0.616418i
$273$	−0.150321	+	0.0488422i	−0.00909783	+	0.00295606i
$274$	45.9616			2.77664
$275$	−5.39832	+	30.5361i	−0.325531	+	1.84139i
$276$	−0.904860			−0.0544662
$277$	−21.7299	+	7.06047i	−1.30562	+	0.424223i	−0.877534	−	0.479514i	$-0.840813\pi$
$277$	−21.7299	+	7.06047i	−1.30562	+	0.424223i	−0.428089	+	0.903737i	$0.640813\pi$
$278$	26.1821	+	36.0365i	1.57030	+	2.16133i
$279$	−13.9330	+	10.1229i	−0.834144	+	0.606041i
$280$	−26.6882	−	31.8202i	−1.59493	−	1.90162i
$281$	−19.2523	−	13.9876i	−1.14850	−	0.834433i	−0.160218	−	0.987082i	$-0.551220\pi$
$281$	−19.2523	−	13.9876i	−1.14850	−	0.834433i	−0.988281	+	0.152648i	$0.951220\pi$
$282$			0.557275i			0.0331852i
$283$	15.9151	−	21.9053i	0.946055	−	1.30213i	−0.00720277	−	0.999974i	$-0.502293\pi$
$283$	15.9151	−	21.9053i	0.946055	−	1.30213i	0.953258	−	0.302159i	$-0.0977073\pi$
$284$	14.3557	−	44.1823i	0.851854	−	2.62174i
$285$	0.00822885	−	0.0329729i	0.000487435	−	0.00195315i
$286$	14.2165	+	43.7540i	0.840641	+	2.58723i
$287$	−21.2905	−	6.91770i	−1.25674	−	0.408339i
$288$	47.3020	+	15.3694i	2.78730	+	0.905648i
$289$	−0.309017	−	0.951057i	−0.0181775	−	0.0559445i
$290$	−1.24746	+	1.04627i	−0.0732532	+	0.0614390i
$291$	−0.00375728	+	0.0115637i	−0.000220256	+	0.000677877i
$292$	38.0440	−	52.3631i	2.22636	−	3.06432i
$293$		−	9.24354i		−	0.540013i	−0.962858	−	0.270007i	$-0.912974\pi$
$293$		−	9.24354i		−	0.540013i	0.962858	−	0.270007i	$-0.0870259\pi$
$294$	0.130774	+	0.0950128i	0.00762689	+	0.00554126i
$295$	−7.71429	+	12.3393i	−0.449143	+	0.718425i
$296$	19.7617	−	14.3577i	1.14863	−	0.834526i
$297$	−0.575765	−	0.792472i	−0.0334093	−	0.0459839i
$298$	21.2043	−	6.88971i	1.22833	−	0.399110i
$299$	−18.3147			−1.05917
$300$	−0.474470	−	0.491765i	−0.0273935	−	0.0283921i
$301$	−16.4283			−0.946910
$302$	−43.9056	+	14.2658i	−2.52649	+	0.820905i
$303$	−0.101590	−	0.139827i	−0.00583619	−	0.00803282i
$304$	5.86883	−	4.26396i	0.336601	−	0.244555i
$305$	−0.988245	−	14.1778i	−0.0565868	−	0.811820i
$306$	−6.50698	−	4.72759i	−0.371979	−	0.270259i
$307$			8.81257i			0.502960i	0.967863	+	0.251480i	$0.0809172\pi$
$307$			8.81257i			0.502960i	−0.967863	+	0.251480i	$0.919083\pi$
$308$	−41.0715	+	56.5300i	−2.34026	+	3.22110i
$309$	0.0449485	−	0.138337i	0.00255703	−	0.00786973i
$310$	29.1951	+	18.2522i	1.65817	+	1.03665i
$311$	1.01537	+	3.12498i	0.0575763	+	0.177202i	0.975709	−	0.219072i	$-0.0703031\pi$
$311$	1.01537	+	3.12498i	0.0575763	+	0.177202i	−0.918132	+	0.396274i	$0.870303\pi$
$312$	−0.592714	−	0.192585i	−0.0335558	−	0.0109030i
$313$	4.75880	+	1.54623i	0.268983	+	0.0873979i	0.440403	−	0.897800i	$-0.354836\pi$
$313$	4.75880	+	1.54623i	0.268983	+	0.0873979i	−0.171420	+	0.985198i	$0.554836\pi$
$314$	9.73546	+	29.9627i	0.549404	+	1.69089i
$315$	12.3422	+	7.71610i	0.695407	+	0.434753i
$316$	−3.46033	+	10.6498i	−0.194659	+	0.599098i
$317$	6.63546	−	9.13293i	0.372685	−	0.512956i	−0.580943	−	0.813944i	$-0.697316\pi$
$317$	6.63546	−	9.13293i	0.372685	−	0.512956i	0.953628	+	0.300988i	$0.0973163\pi$
$318$		−	0.265718i		−	0.0149007i
$319$	1.36235	+	0.989804i	0.0762769	+	0.0554184i
$320$	−3.00649	−	43.1325i	−0.168068	−	2.41118i
$321$	−0.189715	+	0.137836i	−0.0105889	+	0.00769328i
$322$	−22.6497	−	31.1746i	−1.26222	−	1.73729i
$323$	−0.549033	+	0.178392i	−0.0305490	+	0.00992598i
$324$	−46.6884			−2.59380
$325$	−9.60343	−	9.95349i	−0.532702	−	0.552120i
$326$	47.2614			2.61757
$327$	0.0113269	−	0.00368033i	0.000626378	−	0.000203522i
$328$	−51.8830	−	71.4108i	−2.86476	−	3.94300i
$329$	−13.8597	+	10.0697i	−0.764111	+	0.555159i
$330$	−0.519009	+	0.830178i	−0.0285705	+	0.0456998i
$331$	−4.28097	−	3.11031i	−0.235303	−	0.170958i	0.463885	−	0.885895i	$-0.346455\pi$
$331$	−4.28097	−	3.11031i	−0.235303	−	0.170958i	−0.699188	+	0.714938i	$0.746455\pi$
$332$		−	25.3698i		−	1.39235i
$333$	−5.03213	+	6.92614i	−0.275759	+	0.379550i
$334$	12.3516	−	38.0144i	0.675852	−	2.08006i
$335$	−0.703817	+	0.590307i	−0.0384537	+	0.0322519i
$336$	−0.221877	−	0.682867i	−0.0121044	−	0.0372534i
$337$	5.90023	+	1.91710i	0.321406	+	0.104431i	0.465277	−	0.885165i	$-0.345955\pi$
$337$	5.90023	+	1.91710i	0.321406	+	0.104431i	−0.143871	+	0.989597i	$0.545955\pi$
$338$	13.6397	+	4.43181i	0.741903	+	0.241059i
$339$	0.0674733	+	0.207661i	0.00366465	+	0.0112786i
$340$	−2.81070	+	11.2624i	−0.152432	+	0.610792i
$341$	11.0046	−	33.8686i	0.595931	−	1.83409i
$342$	−2.72918	+	3.75640i	−0.147577	+	0.203123i
$343$			20.1616i			1.08863i
$344$	−52.4054	−	38.0747i	−2.82551	−	2.05285i
$345$	−0.250468	−	0.298630i	−0.0134847	−	0.0160777i
$346$	−18.3320	+	13.3190i	−0.985536	+	0.716034i
$347$	6.63483	+	9.13206i	0.356176	+	0.490235i	0.949078	−	0.315040i	$-0.102018\pi$
$347$	6.63483	+	9.13206i	0.356176	+	0.490235i	−0.592902	+	0.805275i	$0.702018\pi$
$348$	−0.0352922	+	0.0114671i	−0.00189186	+	0.000614703i
$349$	1.70507			0.0912701			0.0456351	−	0.998958i	$-0.485469\pi$
$349$	1.70507			0.0912701			0.0456351	+	0.998958i	$0.485469\pi$
$350$	5.06596	−	28.6560i	0.270787	−	1.53173i
$351$	0.436904			0.0233202
$352$	−97.8102	+	31.7805i	−5.21330	+	1.69390i
$353$	−8.78593	−	12.0928i	−0.467628	−	0.643634i	0.508441	−	0.861097i	$-0.330222\pi$
$353$	−8.78593	−	12.0928i	−0.467628	−	0.643634i	−0.976069	+	0.217463i	$0.930222\pi$
$354$	−0.371711	+	0.270064i	−0.0197562	+	0.0143537i
$355$	18.5551	−	7.49197i	0.984804	−	0.397632i
$356$	76.4129	+	55.5172i	4.04988	+	2.94241i
$357$			0.0571384i			0.00302408i
$358$	−5.48010	+	7.54271i	−0.289632	+	0.398644i
$359$	0.751894	−	2.31409i	0.0396835	−	0.122133i	−0.929252	−	0.369446i	$-0.879548\pi$
$359$	0.751894	−	2.31409i	0.0396835	−	0.122133i	0.968936	+	0.247313i	$0.0795475\pi$
$360$	21.4880	+	53.2188i	1.13252	+	2.80488i
$361$	−5.76834	−	17.7531i	−0.303597	−	0.934375i
$362$	−27.1932	−	8.83562i	−1.42924	−	0.464390i
$363$	0.687647	+	0.223430i	0.0360921	+	0.0117270i
$364$	−9.63081	−	29.6406i	−0.504792	−	1.55359i
$365$	27.8120	−	1.93860i	1.45575	−	0.101471i
$366$	0.138663	−	0.426760i	0.00724802	−	0.0223071i
$367$	−12.4195	+	17.0939i	−0.648292	+	0.892297i	−0.999024	−	0.0441790i	$-0.985933\pi$
$367$	−12.4195	+	17.0939i	−0.648292	+	0.892297i	0.350732	+	0.936476i	$0.385933\pi$
$368$		−	83.1986i		−	4.33703i
$369$	25.0282	+	18.1841i	1.30292	+	0.946625i
$370$	16.6065	+	4.14439i	0.863331	+	0.215456i
$371$	6.60855	−	4.80139i	0.343099	−	0.249276i
$372$	0.461265	+	0.634877i	0.0239155	+	0.0329169i
$373$	−1.02412	+	0.332757i	−0.0530270	+	0.0172295i	−0.335410	−	0.942072i	$-0.608875\pi$
$373$	−1.02412	+	0.332757i	−0.0530270	+	0.0172295i	0.282383	+	0.959302i	$0.408875\pi$
$374$	16.6313			0.859984
$375$	0.0309623	−	0.292711i	0.00159889	−	0.0151155i
$376$	−67.5497			−3.48361
$377$	−0.714326	+	0.232098i	−0.0367896	+	0.0119537i
$378$	0.540316	+	0.743682i	0.0277909	+	0.0382509i
$379$	−5.51323	+	4.00560i	−0.283196	+	0.205754i	−0.720310	−	0.693652i	$-0.756000\pi$
$379$	−5.51323	+	4.00560i	−0.283196	+	0.205754i	0.437114	+	0.899406i	$0.356000\pi$
$380$	6.50167	+	1.62258i	0.333529	+	0.0832367i
$381$	−0.252372	−	0.183359i	−0.0129294	−	0.00939375i
$382$		−	8.66065i		−	0.443117i
$383$	13.2125	−	18.1855i	0.675127	−	0.929233i	−0.324735	−	0.945805i	$-0.605275\pi$
$383$	13.2125	−	18.1855i	0.675127	−	0.929233i	0.999863	+	0.0165718i	$0.00527520\pi$
$384$	0.152033	−	0.467910i	0.00775841	−	0.0238779i
$385$	−30.0252	+	2.09287i	−1.53023	+	0.106662i
$386$	19.1852	+	59.0460i	0.976501	+	3.00536i
$387$	21.5919	+	7.01564i	1.09758	+	0.356625i
$388$	−2.28016	−	0.740869i	−0.115758	−	0.0376119i
$389$	3.46720	+	10.6709i	0.175794	+	0.541038i	0.999669	−	0.0257334i	$-0.00819210\pi$
$389$	3.46720	+	10.6709i	0.175794	+	0.541038i	−0.823875	+	0.566772i	$0.808192\pi$
$390$	−0.163496	−	0.404926i	−0.00827894	−	0.0205042i
$391$	−2.04596	+	6.29681i	−0.103469	+	0.318443i
$392$	−11.5169	+	15.8517i	−0.581692	+	0.800631i
$393$			0.234376i			0.0118227i
$394$	42.0024	+	30.5165i	2.11605	+	1.53740i
$395$	−4.47257	+	1.80588i	−0.225039	+	0.0908637i
$396$	78.1217	−	56.7588i	3.92576	−	2.85224i
$397$	4.87406	+	6.70857i	0.244622	+	0.336693i	0.913619	−	0.406572i	$-0.133276\pi$
$397$	4.87406	+	6.70857i	0.244622	+	0.336693i	−0.668997	+	0.743265i	$0.733276\pi$
$398$	−56.4699	+	18.3482i	−2.83058	+	0.919711i
$399$	0.0329853			0.00165133
$400$	45.2160	−	43.6258i	2.26080	−	2.18129i
$401$	−19.9972			−0.998613			−0.499307	−	0.866425i	$-0.666412\pi$
$401$	−19.9972			−0.998613			−0.499307	+	0.866425i	$0.666412\pi$
$402$	−0.0275833	+	0.00896237i	−0.00137573	+	0.000447002i
$403$	9.33617	+	12.8501i	0.465068	+	0.640111i
$404$	27.5713	−	20.0317i	1.37172	−	0.996616i
$405$	−12.9235	−	15.4085i	−0.642172	−	0.765656i
$406$	−1.27847	−	0.928864i	−0.0634495	−	0.0460988i
$407$		−	17.7027i		−	0.877488i
$408$	−0.132426	+	0.182269i	−0.00655606	+	0.00902364i
$409$	9.40032	−	28.9312i	0.464816	−	1.43056i	−0.394398	−	0.918940i	$-0.629047\pi$
$409$	9.40032	−	28.9312i	0.464816	−	1.43056i	0.859214	−	0.511616i	$-0.170953\pi$
$410$	14.9761	−	60.0091i	0.739618	−	2.96364i
$411$	0.139436	+	0.429141i	0.00687789	+	0.0211680i
$412$	27.2777	+	8.86305i	1.34387	+	0.436651i
$413$	−13.4333	−	4.36473i	−0.661008	−	0.214774i
$414$	16.4558	+	50.6456i	0.808757	+	2.48910i
$415$	8.37278	−	7.02243i	0.411004	−	0.344717i
$416$	14.1749	−	43.6258i	0.694981	−	2.13893i
$417$	−0.257041	+	0.353787i	−0.0125874	+	0.0173250i
$418$		−	9.60105i		−	0.469603i
$419$	−7.20177	−	5.23239i	−0.351830	−	0.255619i	0.397807	−	0.917469i	$-0.369771\pi$
$419$	−7.20177	−	5.23239i	−0.351830	−	0.255619i	−0.749636	+	0.661850i	$0.769771\pi$
$420$	0.351596	−	0.562394i	0.0171561	−	0.0274420i
$421$	26.8247	−	19.4893i	1.30736	−	0.949851i	0.307359	−	0.951594i	$-0.400555\pi$
$421$	26.8247	−	19.4893i	1.30736	−	0.949851i	0.999998	+	0.00174319i	$0.000554874\pi$
$422$	26.4470	+	36.4012i	1.28742	+	1.77198i
$423$	22.5163	−	7.31597i	1.09478	−	0.355715i
$424$	32.2088			1.56420
$425$	−4.49494	+	2.18986i	−0.218037	+	0.106224i
$426$	0.631793			0.0306105
$427$	13.1193	−	4.26273i	0.634888	−	0.206288i
$428$	−27.1789	−	37.4085i	−1.31374	−	1.80821i
$429$	−0.365400	+	0.265478i	−0.0176417	+	0.0128174i
$430$	−3.15611	−	45.2790i	−0.152201	−	2.18355i
$431$	12.7745	+	9.28124i	0.615327	+	0.447061i	0.851286	−	0.524702i	$-0.175823\pi$
$431$	12.7745	+	9.28124i	0.615327	+	0.447061i	−0.235959	+	0.971763i	$0.575823\pi$
$432$			1.98474i			0.0954907i
$433$	10.0675	−	13.8567i	0.483812	−	0.665910i	−0.495420	−	0.868654i	$-0.664986\pi$
$433$	10.0675	−	13.8567i	0.483812	−	0.665910i	0.979232	+	0.202744i	$0.0649858\pi$
$434$	−10.3270	+	31.7834i	−0.495714	+	1.52565i
$435$	−0.0135534	−	0.00847332i	−0.000649838	−	0.000406265i
$436$	0.725695	+	2.23346i	0.0347545	+	0.106963i
$437$	3.63507	+	1.18111i	0.173889	+	0.0565000i
$438$	0.837157	+	0.272009i	0.0400009	+	0.0129971i
$439$	4.31228	+	13.2718i	0.205814	+	0.633430i	0.999679	+	0.0253360i	$0.00806557\pi$
$439$	4.31228	+	13.2718i	0.205814	+	0.633430i	−0.793865	+	0.608094i	$0.791934\pi$
$440$	−100.629	−	62.9114i	−4.79732	−	2.99918i
$441$	2.12210	−	6.53116i	0.101053	−	0.311008i
$442$	−4.36018	+	6.00127i	−0.207393	+	0.285451i
$443$			37.0768i			1.76157i	0.473515	+	0.880786i	$0.342985\pi$
$443$			37.0768i			1.76157i	−0.473515	+	0.880786i	$0.657015\pi$
$444$	0.315601	+	0.229297i	0.0149777	+	0.0108820i
$445$	2.82898	+	40.5858i	0.134106	+	1.92395i
$446$	−37.9314	+	27.5587i	−1.79610	+	1.30494i
$447$	0.128658	+	0.177082i	0.00608531	+	0.00837571i
$448$	39.9123	−	12.9683i	1.88568	−	0.612694i
$449$	0.604564			0.0285311			0.0142656	−	0.999898i	$-0.495459\pi$
$449$	0.604564			0.0285311			0.0142656	+	0.999898i	$0.495459\pi$
$450$	−18.8957	+	35.4996i	−0.890753	+	1.67347i
$451$	−63.9701			−3.01224
$452$	−40.9471	+	13.3045i	−1.92599	+	0.625793i
$453$	−0.266398	−	0.366666i	−0.0125165	−	0.0172275i
$454$	−8.49142	+	6.16938i	−0.398522	+	0.289543i
$455$	7.11643	−	11.3830i	0.333623	−	0.533645i
$456$	0.105221	+	0.0764478i	0.00492744	+	0.00358000i
$457$			34.7122i			1.62377i	0.583819	+	0.811884i	$0.301558\pi$
$457$			34.7122i			1.62377i	−0.583819	+	0.811884i	$0.698442\pi$
$458$	−7.74243	+	10.6565i	−0.361780	+	0.497947i
$459$	0.0488071	−	0.150213i	0.00227812	−	0.00701134i
$460$	58.8846	−	49.3878i	2.74551	−	2.30272i
$461$	1.43678	+	4.42196i	0.0669176	+	0.205951i	0.978924	−	0.204225i	$-0.0654673\pi$
$461$	1.43678	+	4.42196i	0.0669176	+	0.205951i	−0.912006	+	0.410176i	$0.865467\pi$
$462$	−0.903775	−	0.293654i	−0.0420474	−	0.0136620i
$463$	−30.1008	−	9.78033i	−1.39890	−	0.454530i	−0.490066	−	0.871686i	$-0.663027\pi$
$463$	−30.1008	−	9.78033i	−1.39890	−	0.454530i	−0.908835	+	0.417155i	$0.863027\pi$
$464$	−1.05436	−	3.24499i	−0.0489475	−	0.150645i
$465$	−0.0818486	+	0.327967i	−0.00379564	+	0.0152091i
$466$	−10.3870	+	31.9678i	−0.481166	+	1.48088i
$467$	1.65222	−	2.27409i	0.0764558	−	0.105232i	−0.769076	−	0.639157i	$-0.779283\pi$
$467$	1.65222	−	2.27409i	0.0764558	−	0.105232i	0.845532	+	0.533925i	$0.179283\pi$
$468$			43.0699i			1.99091i
$469$	−0.721316	−	0.524067i	−0.0333073	−	0.0241992i
$470$	−30.4163	−	36.2651i	−1.40300	−	1.67279i
$471$	−0.250225	+	0.181799i	−0.0115298	+	0.00837686i
$472$	−32.7356	−	45.0567i	−1.50678	−	2.07390i
$473$	−44.6474	+	14.5068i	−2.05289	+	0.667024i
$474$	−0.152289			−0.00699485
$475$	1.26418	+	2.59488i	0.0580045	+	0.119061i
$476$	−11.2667			−0.516407
$477$	−10.7361	+	3.48838i	−0.491574	+	0.159722i
$478$	40.9863	+	56.4129i	1.87467	+	2.58026i
$479$	−9.76521	+	7.09484i	−0.446184	+	0.324171i	−0.788087	−	0.615564i	$-0.788928\pi$
$479$	−9.76521	+	7.09484i	−0.446184	+	0.324171i	0.341903	+	0.939735i	$0.388928\pi$
$480$	0.905194	−	0.365488i	0.0413163	−	0.0166822i
$481$	6.38786	+	4.64105i	0.291261	+	0.211614i
$482$		−	12.3501i		−	0.562530i
$483$	0.222362	−	0.306055i	0.0101178	−	0.0139260i
$484$	−44.0565	+	135.592i	−2.00257	+	6.16326i
$485$	−0.386645	−	0.957593i	−0.0175567	−	0.0434821i
$486$	−0.588861	−	1.81233i	−0.0267113	−	0.0822088i
$487$	−2.59084	−	0.841815i	−0.117402	−	0.0381463i	0.249727	−	0.968316i	$-0.419659\pi$
$487$	−2.59084	−	0.841815i	−0.117402	−	0.0381463i	−0.367129	+	0.930170i	$0.619659\pi$
$488$	51.7294	+	16.8079i	2.34168	+	0.760858i
$489$	0.143380	+	0.441278i	0.00648386	+	0.0199553i
$490$	−13.6961	+	0.954666i	−0.618726	+	0.0431274i
$491$	−2.37266	+	7.30230i	−0.107077	+	0.329548i	−0.990212	−	0.139570i	$-0.955428\pi$
$491$	−2.37266	+	7.30230i	−0.107077	+	0.329548i	0.883136	+	0.469118i	$0.155428\pi$
$492$	0.828586	−	1.14045i	0.0373555	−	0.0514155i
$493$			0.271522i			0.0122287i
$494$	3.46446	+	2.51708i	0.155873	+	0.113249i
$495$	40.3563	+	10.0715i	1.81388	+	0.452680i
$496$	−58.3747	+	42.4117i	−2.62110	+	1.90434i
$497$	11.4162	+	15.7130i	0.512086	+	0.704826i
$498$	0.328138	−	0.106618i	0.0147042	−	0.00477769i
$499$	12.4428			0.557015			0.278507	−	0.960434i	$-0.410160\pi$
$499$	12.4428			0.557015			0.278507	+	0.960434i	$0.410160\pi$
$500$	57.7174	+	6.10523i	2.58120	+	0.273034i
$501$	0.392411			0.0175316
$502$	10.2406	−	3.32738i	0.457061	−	0.148508i
$503$	11.4219	+	15.7209i	0.509279	+	0.700962i	0.983797	−	0.179284i	$-0.0573779\pi$
$503$	11.4219	+	15.7209i	0.509279	+	0.700962i	−0.474519	+	0.880245i	$0.657378\pi$
$504$	−45.0672	+	32.7433i	−2.00745	+	1.45850i
$505$	14.2429	+	3.55450i	0.633799	+	0.158173i
$506$	−89.0837	−	64.7231i	−3.96025	−	2.87729i
$507$			0.140799i			0.00625308i
$508$	36.1551	−	49.7632i	1.60412	−	2.20788i
$509$	−6.02411	+	18.5403i	−0.267014	+	0.821784i	0.724209	+	0.689581i	$0.242205\pi$
$509$	−6.02411	+	18.5403i	−0.267014	+	0.821784i	−0.991223	+	0.132204i	$0.957795\pi$
$510$	−0.157483	+	0.0109771i	−0.00697345	+	0.000486075i
$511$	8.36201	+	25.7356i	0.369913	+	1.13848i
$512$	−6.36647	−	2.06859i	−0.281361	−	0.0914197i
$513$	−0.0867160	−	0.0281757i	−0.00382861	−	0.00124399i
$514$	−7.56723	−	23.2895i	−0.333776	−	1.02726i
$515$	4.62546	+	11.4557i	0.203822	+	0.504800i
$516$	0.319679	−	0.983869i	0.0140731	−	0.0433124i
$517$	−28.7749	+	39.6052i	−1.26552	+	1.74183i
$518$			16.6127i			0.729922i
$519$	−0.179974	−	0.130759i	−0.00789998	−	0.00573967i
$520$	49.0828	−	19.8181i	2.15242	−	0.869079i
$521$	3.20337	−	2.32739i	0.140342	−	0.101965i	−0.515399	−	0.856950i	$-0.672356\pi$
$521$	3.20337	−	2.32739i	0.140342	−	0.101965i	0.655741	+	0.754986i	$0.272356\pi$
$522$	1.28365	+	1.76679i	0.0561836	+	0.0773301i
$523$	−12.7441	+	4.14080i	−0.557260	+	0.181065i	−0.574088	−	0.818794i	$-0.694643\pi$
$523$	−12.7441	+	4.14080i	−0.557260	+	0.181065i	0.0168282	+	0.999858i	$0.494643\pi$
$524$	−46.2147			−2.01890
$525$	0.282929	−	0.0396349i	0.0123480	−	0.00172981i
$526$	−0.839386			−0.0365990
$527$	5.46099	−	1.77438i	0.237884	−	0.0772933i
$528$	−1.20600	−	1.65991i	−0.0524843	−	0.0722384i
$529$	16.8565	−	12.2469i	0.732890	−	0.532476i
$530$	14.5030	+	17.2918i	0.629971	+	0.751109i
$531$	15.7916	+	11.4733i	0.685296	+	0.497897i
$532$			6.50411i			0.281989i
$533$	16.7709	−	23.0831i	0.726427	−	0.999840i
$534$	−0.396939	+	1.22165i	−0.0171772	+	0.0528661i
$535$	4.82272	−	19.3246i	0.208504	−	0.835475i
$536$	−1.08637	−	3.34350i	−0.0469239	−	0.144417i
$537$	−0.0870512	−	0.0282847i	−0.00375654	−	0.00122057i
$538$	51.5345	+	16.7446i	2.22181	+	0.721910i
$539$	4.38805	+	13.5050i	0.189007	+	0.581702i
$540$	−1.40472	+	1.17816i	−0.0604493	+	0.0507001i
$541$	11.0869	−	34.1219i	0.476661	−	1.46701i	−0.367043	−	0.930204i	$-0.619630\pi$
$541$	11.0869	−	34.1219i	0.476661	−	1.46701i	0.843704	−	0.536809i	$-0.180370\pi$
$542$	26.2019	−	36.0639i	1.12547	−	1.54908i
$543$		−	0.280707i		−	0.0120463i
$544$	−13.4156	−	9.74700i	−0.575189	−	0.417899i
$545$	−0.536233	+	0.857727i	−0.0229697	+	0.0367410i
$546$	0.342903	−	0.249133i	0.0146749	−	0.0106619i
$547$	−2.93391	−	4.03818i	−0.125445	−	0.172660i	0.741675	−	0.670759i	$-0.234032\pi$
$547$	−2.93391	−	4.03818i	−0.125445	−	0.172660i	−0.867120	+	0.498099i	$0.834032\pi$
$548$	−84.6191	+	27.4944i	−3.61475	+	1.17450i
$549$	−19.0633			−0.813601
$550$	−11.5366	−	82.3524i	−0.491921	−	3.51152i
$551$	0.156746			0.00667761
$552$	1.41865	−	0.460947i	0.0603817	−	0.0196192i
$553$	−2.75178	−	3.78750i	−0.117018	−	0.161061i
$554$	49.5689	−	36.0139i	2.10598	−	1.53009i
$555$	0.0116842	+	0.167627i	0.000495968	+	0.00711539i
$556$	−69.7605	−	50.6840i	−2.95850	−	2.14948i
$557$			34.0368i			1.44219i	0.692838	+	0.721093i	$0.256360\pi$
$557$			34.0368i			1.44219i	−0.692838	+	0.721093i	$0.743640\pi$
$558$	27.1460	−	37.3632i	1.14918	−	1.58171i
$559$	6.47040	−	19.9138i	0.273669	−	0.842266i
$560$	51.7101	+	32.3280i	2.18515	+	1.36611i
$561$	0.0504554	+	0.155286i	0.00213023	+	0.00655617i
$562$	60.6922	+	19.7201i	2.56015	+	0.831842i
$563$	−4.67712	−	1.51969i	−0.197117	−	0.0640472i	0.208795	−	0.977959i	$-0.433046\pi$
$563$	−4.67712	−	1.51969i	−0.197117	−	0.0640472i	−0.405912	+	0.913912i	$0.633046\pi$
$564$	−0.333364	−	1.02599i	−0.0140372	−	0.0432019i
$565$	−15.7252	−	9.83102i	−0.661562	−	0.413594i
$566$	−22.4375	+	69.0554i	−0.943117	+	2.90262i
$567$	11.4733	−	15.7916i	0.481833	−	0.663186i
$568$			76.5823i			3.21332i
$569$	29.5759	+	21.4882i	1.23989	+	0.900831i	0.997591	−	0.0693714i	$-0.0220993\pi$
$569$	29.5759	+	21.4882i	1.23989	+	0.900831i	0.242296	+	0.970202i	$0.422099\pi$
$570$	0.00633695	+	0.0909128i	0.000265426	+	0.00380792i
$571$	14.1225	−	10.2606i	0.591010	−	0.429394i	−0.251667	−	0.967814i	$-0.580979\pi$
$571$	14.1225	−	10.2606i	0.591010	−	0.429394i	0.842676	+	0.538420i	$0.180979\pi$
$572$	−52.3476	−	72.0503i	−2.18876	−	3.01258i
$573$	0.0808641	−	0.0262743i	0.00337815	−	0.00109763i
$574$	60.0316			2.50567
$575$	32.5988	+	5.76298i	1.35946	+	0.240333i
$576$	−57.9954			−2.41647
$577$	−5.90064	+	1.91723i	−0.245647	+	0.0798155i	−0.429253	−	0.903184i	$-0.641223\pi$
$577$	−5.90064	+	1.91723i	−0.245647	+	0.0798155i	0.183606	+	0.983000i	$0.441223\pi$
$578$	1.57623	+	2.16949i	0.0655625	+	0.0902390i
$579$	−0.493106	+	0.358263i	−0.0204928	+	0.0148889i
$580$	1.67079	−	2.67250i	0.0693757	−	0.110970i
$581$	8.58095	+	6.23443i	0.355998	+	0.258648i
$582$		−	0.0326056i		−	0.00135154i
$583$	13.7203	−	18.8844i	0.568239	−	0.782113i
$584$	−32.9714	+	101.475i	−1.36436	+	4.19908i
$585$	−14.2143	+	11.9218i	−0.587689	+	0.492908i
$586$	7.65986	+	23.5746i	0.316426	+	0.973859i
$587$	−19.9337	−	6.47684i	−0.822751	−	0.267328i	−0.132762	−	0.991148i	$-0.542385\pi$
$587$	−19.9337	−	6.47684i	−0.822751	−	0.267328i	−0.689989	+	0.723820i	$0.742385\pi$
$588$	−0.297603	−	0.0966970i	−0.0122729	−	0.00398772i
$589$	−1.02433	−	3.15256i	−0.0422067	−	0.129899i
$590$	9.44919	−	37.8628i	0.389017	−	1.55879i
$591$	−0.157506	+	0.484754i	−0.00647894	+	0.0199401i
$592$	−21.0830	+	29.0183i	−0.866508	+	1.19265i
$593$		−	24.8380i		−	1.01997i	−0.860183	−	0.509986i	$-0.829650\pi$
$593$		−	24.8380i		−	1.01997i	0.860183	−	0.509986i	$-0.170350\pi$
$594$	2.12513	+	1.54399i	0.0871950	+	0.0633509i
$595$	−3.11864	−	3.71833i	−0.127852	−	0.152437i
$596$	−34.9175	+	25.3691i	−1.43028	+	1.03916i
$597$	−0.342632	−	0.471593i	−0.0140230	−	0.0193010i
$598$	46.7096	−	15.1769i	1.91010	−	0.620628i
$599$	12.9951			0.530966			0.265483	−	0.964116i	$-0.414469\pi$
$599$	12.9951			0.530966			0.265483	+	0.964116i	$0.414469\pi$
$600$	0.994389	+	0.529293i	0.0405958	+	0.0216083i
$601$	9.44016			0.385072			0.192536	−	0.981290i	$-0.438329\pi$
$601$	9.44016			0.385072			0.192536	+	0.981290i	$0.438329\pi$
$602$	41.8985	−	13.6137i	1.70766	−	0.554851i
$603$	0.724235	+	0.996824i	0.0294931	+	0.0405938i
$604$	72.3000	−	52.5290i	2.94185	−	2.13738i
$605$	−56.9442	+	22.9922i	−2.31511	+	0.934767i
$606$	0.374965	+	0.272428i	0.0152319	+	0.0110666i
$607$			12.7661i			0.518160i	0.965856	+	0.259080i	$0.0834193\pi$
$607$			12.7661i			0.518160i	−0.965856	+	0.259080i	$0.916581\pi$
$608$	−5.62682	+	7.74466i	−0.228198	+	0.314087i
$609$	0.00479419	−	0.0147550i	0.000194270	−	0.000597902i
$610$	14.2692	+	35.3401i	0.577742	+	1.43088i
$611$	−6.74740	−	20.7664i	−0.272970	−	0.840117i
$612$	14.8079	+	4.81139i	0.598576	+	0.194489i
$613$	−20.9278	−	6.79986i	−0.845266	−	0.274644i	−0.145804	−	0.989313i	$-0.546577\pi$
$613$	−20.9278	−	6.79986i	−0.845266	−	0.274644i	−0.699462	+	0.714670i	$0.746577\pi$
$614$	−7.30273	−	22.4755i	−0.294714	−	0.907037i
$615$	0.605737	−	0.0422220i	0.0244257	−	0.00170256i
$616$	35.5951	−	109.551i	1.43417	−	4.41392i
$617$	7.75580	−	10.6749i	0.312237	−	0.429757i	−0.623840	−	0.781552i	$-0.714428\pi$
$617$	7.75580	−	10.6749i	0.312237	−	0.429757i	0.936077	+	0.351795i	$0.114428\pi$
$618$			0.390062i			0.0156906i
$619$	−33.0713	−	24.0277i	−1.32925	−	0.965756i	−0.999767	−	0.0215944i	$-0.993126\pi$
$619$	−33.0713	−	24.0277i	−1.32925	−	0.965756i	−0.329482	−	0.944162i	$-0.606874\pi$
$620$	−64.6692	−	16.1391i	−2.59718	−	0.648162i
$621$	−0.846005	+	0.614658i	−0.0339490	+	0.0246654i
$622$	−5.17918	−	7.12853i	−0.207666	−	0.285828i
$623$	−37.5557	+	12.2026i	−1.50464	+	0.488886i
$624$	0.915138			0.0366349
$625$	13.9614	+	20.7384i	0.558456	+	0.829534i
$626$	−13.4181			−0.536296
$627$	0.0896446	−	0.0291273i	0.00358006	−	0.00116323i
$628$	−35.8476	−	49.3399i	−1.43047	−	1.96888i
$629$	2.30925	−	1.67777i	0.0920757	−	0.0668969i
$630$	−37.8717	−	9.45141i	−1.50884	−	0.376553i
$631$	7.94981	+	5.77587i	0.316477	+	0.229934i	0.734671	−	0.678424i	$-0.237337\pi$
$631$	7.94981	+	5.77587i	0.316477	+	0.229934i	−0.418194	+	0.908358i	$0.637337\pi$
$632$		−	18.4596i		−	0.734283i
$633$	−0.259643	+	0.357368i	−0.0103199	+	0.0142041i
$634$	−9.35482	+	28.7912i	−0.371527	+	1.14344i
$635$	26.4311	−	1.84234i	1.04889	−	0.0731112i
$636$	0.158954	+	0.489209i	0.00630292	+	0.0193984i
$637$	−6.02358	−	1.95718i	−0.238663	−	0.0775462i
$638$	−4.29475	−	1.39545i	−0.170031	−	0.0552463i
$639$	−8.29426	−	25.5271i	−0.328116	−	1.00984i
$640$	15.6451	+	38.7477i	0.618426	+	1.53164i
$641$	15.0851	−	46.4271i	0.595825	−	1.83376i	0.0452465	−	0.998976i	$-0.485593\pi$
$641$	15.0851	−	46.4271i	0.595825	−	1.83376i	0.550578	−	0.834784i	$-0.314407\pi$
$642$	0.369628	−	0.508749i	0.0145880	−	0.0200787i
$643$		−	2.11575i		−	0.0834371i	−0.999129	−	0.0417185i	$-0.986717\pi$
$643$		−	2.11575i		−	0.0834371i	0.999129	−	0.0417185i	$-0.0132833\pi$
$644$	60.3486	+	43.8459i	2.37807	+	1.72777i
$645$	0.413193	−	0.166834i	0.0162695	−	0.00656909i
$646$	1.25242	−	0.909938i	0.0492759	−	0.0358010i
$647$	15.4107	+	21.2109i	0.605855	+	0.833888i	0.996228	−	0.0867685i	$-0.0276541\pi$
$647$	15.4107	+	21.2109i	0.605855	+	0.833888i	−0.390373	+	0.920657i	$0.627654\pi$
$648$	73.1985	−	23.7836i	2.87551	−	0.934309i
$649$	−40.3620			−1.58435
$650$	32.7407	+	17.4272i	1.28420	+	0.683551i
$651$	−0.328090			−0.0128589
$652$	−87.0122	+	28.2720i	−3.40766	+	1.10722i
$653$	7.78049	+	10.7089i	0.304474	+	0.419072i	0.933648	−	0.358192i	$-0.116607\pi$
$653$	7.78049	+	10.7089i	0.304474	+	0.419072i	−0.629174	+	0.777265i	$0.716607\pi$
$654$	−0.0258382	+	0.0187725i	−0.00101035	+	0.000734065i
$655$	−12.7924	−	15.2522i	−0.499839	−	0.595953i
$656$	104.860	+	76.1855i	4.09411	+	2.97454i
$657$		−	37.3956i		−	1.45894i
$658$	27.0033	−	37.1668i	1.05270	−	1.44891i
$659$	−4.27919	+	13.1700i	−0.166694	+	0.513030i	−0.999157	−	0.0410499i	$-0.986930\pi$
$659$	−4.27919	+	13.1700i	−0.166694	+	0.513030i	0.832464	+	0.554080i	$0.186930\pi$
$660$	0.458923	−	1.83890i	0.0178636	−	0.0715791i
$661$	−6.76210	−	20.8116i	−0.263015	−	0.809478i	−0.992144	−	0.125101i	$-0.960074\pi$
$661$	−6.76210	−	20.8116i	−0.263015	−	0.809478i	0.729129	−	0.684377i	$-0.239926\pi$
$662$	13.4956	+	4.38498i	0.524520	+	0.170427i
$663$	−0.0692614	−	0.0225044i	−0.00268989	−	0.000873998i
$664$	12.9237	+	39.7750i	0.501536	+	1.54357i
$665$	−2.14655	+	1.80035i	−0.0832395	+	0.0698147i
$666$	7.09441	−	21.8344i	0.274903	−	0.846064i
$667$	1.05667	−	1.45438i	0.0409143	−	0.0563137i
$668$			77.3765i			2.99379i
$669$	−0.372390	−	0.270557i	−0.0143974	−	0.0104603i
$670$	1.30584	−	2.08875i	0.0504490	−	0.0806954i
$671$	31.8904	−	23.1697i	1.23112	−	0.894458i
$672$	0.556928	+	0.766545i	0.0214839	+	0.0295701i
$673$	21.1100	−	6.85905i	0.813730	−	0.264397i	0.127553	−	0.991832i	$-0.459288\pi$
$673$	21.1100	−	6.85905i	0.813730	−	0.264397i	0.686177	+	0.727435i	$0.259288\pi$
$674$	−16.6366			−0.640816
$675$	−0.777657	−	0.137478i	−0.0299320	−	0.00529154i
$676$	−27.7630			−1.06781
$677$	−14.8400	+	4.82179i	−0.570346	+	0.185317i	−0.579971	−	0.814637i	$-0.696936\pi$
$677$	−14.8400	+	4.82179i	−0.570346	+	0.185317i	0.00962517	+	0.999954i	$0.496936\pi$
$678$	−0.344167	−	0.473705i	−0.0132176	−	0.0181925i
$679$	0.810918	−	0.589166i	0.0311202	−	0.0226101i
$680$	−1.33058	−	19.0892i	−0.0510256	−	0.732036i
$681$	−0.0833642	−	0.0605676i	−0.00319452	−	0.00232096i
$682$			95.4973i			3.65678i
$683$	−1.00833	+	1.38785i	−0.0385829	+	0.0531048i	−0.827873	−	0.560916i	$-0.810449\pi$
$683$	−1.00833	+	1.38785i	−0.0385829	+	0.0531048i	0.789290	+	0.614021i	$0.210449\pi$
$684$	2.77756	−	8.54844i	0.106203	−	0.326858i
$685$	−32.4967	−	20.3162i	−1.24164	−	0.776244i
$686$	−16.7074	−	51.4201i	−0.637892	−	1.96323i
$687$	−0.122988	−	0.0399613i	−0.00469230	−	0.00152462i
$688$	90.4632	+	29.3933i	3.44888	+	1.12061i
$689$	3.21727	+	9.90175i	0.122568	+	0.377227i
$690$	0.886257	+	0.554069i	0.0337392	+	0.0210930i
$691$	−5.70281	+	17.5514i	−0.216945	+	0.667688i	0.782065	+	0.623197i	$0.214167\pi$
$691$	−5.70281	+	17.5514i	−0.216945	+	0.667688i	−0.999010	+	0.0444911i	$0.985833\pi$
$692$	25.7833	−	35.4877i	0.980134	−	1.34904i
$693$			40.3715i			1.53359i
$694$	−24.4889	−	17.7922i	−0.929587	−	0.675384i
$695$	−2.58269	−	37.0525i	−0.0979670	−	1.40548i
$696$	0.0494899	−	0.0359565i	0.00187591	−	0.00136293i
$697$	−6.06276	−	8.34467i	−0.229643	−	0.316077i
$698$	−4.34859	+	1.41294i	−0.164597	+	0.0534807i
$699$	−0.329993			−0.0124815
$700$	7.81531	+	55.7886i	0.295391	+	2.10861i
$701$	−2.86228			−0.108107			−0.0540534	−	0.998538i	$-0.517214\pi$
$701$	−2.86228			−0.108107			−0.0540534	+	0.998538i	$0.517214\pi$
$702$	−1.11428	+	0.362050i	−0.0420556	+	0.0136647i
$703$	−0.968554	−	1.33310i	−0.0365297	−	0.0502788i
$704$	97.0188	−	70.4883i	3.65653	−	2.65663i
$705$	0.246330	−	0.394016i	0.00927733	−	0.0148395i
$706$	32.4285	+	23.5607i	1.22046	+	0.886719i
$707$			14.2482i			0.535859i
$708$	0.522797	−	0.719568i	0.0196479	−	0.0270430i
$709$	10.2822	−	31.6455i	0.386158	−	1.18847i	−0.549479	−	0.835508i	$-0.685174\pi$
$709$	10.2822	−	31.6455i	0.386158	−	1.18847i	0.935637	−	0.352964i	$-0.114826\pi$
$710$	−41.1145	+	34.4836i	−1.54300	+	1.29415i
$711$	1.99927	+	6.15311i	0.0749783	+	0.230760i
$712$	−148.082	−	48.1147i	−5.54961	−	1.80318i
$713$	−36.1564	−	11.7479i	−1.35407	−	0.439964i
$714$	−0.0473490	−	0.145725i	−0.00177199	−	0.00545363i
$715$	9.28876	−	37.2199i	0.347380	−	1.39195i
$716$	5.57723	−	17.1650i	0.208431	−	0.641485i
$717$	−0.402382	+	0.553831i	−0.0150272	+	0.0206832i
$718$			6.52492i			0.243508i
$719$	−15.2686	−	11.0933i	−0.569424	−	0.413710i	0.265472	−	0.964119i	$-0.414472\pi$
$719$	−15.2686	−	11.0933i	−0.569424	−	0.413710i	−0.834896	+	0.550408i	$0.814472\pi$
$720$	−54.1577	−	64.5718i	−2.01834	−	2.40645i
$721$	−9.70105	+	7.04822i	−0.361286	+	0.262490i
$722$	29.4231	+	40.4974i	1.09501	+	1.50716i
$723$	0.115312	−	0.0374671i	0.00428850	−	0.00139342i
$724$	55.3505			2.05709
$725$	1.34448	−	0.188346i	0.0499328	−	0.00699498i
$726$	−1.93892			−0.0719601
$727$	41.1862	−	13.3822i	1.52751	−	0.496318i	0.579613	−	0.814892i	$-0.303204\pi$
$727$	41.1862	−	13.3822i	1.52751	−	0.496318i	0.947898	+	0.318573i	$0.103204\pi$
$728$	30.1986	+	41.5647i	1.11923	+	1.54049i
$729$	−21.8132	+	15.8482i	−0.807896	+	0.586971i
$730$	−69.3251	+	27.9913i	−2.56584	+	1.03600i
$731$	−6.12381	−	4.44921i	−0.226497	−	0.164560i
$732$			0.868649i			0.0321062i
$733$	−2.11428	+	2.91006i	−0.0780928	+	0.107486i	−0.846276	−	0.532744i	$-0.821161\pi$
$733$	−2.11428	+	2.91006i	−0.0780928	+	0.107486i	0.768184	+	0.640230i	$0.221161\pi$
$734$	17.5093	−	53.8880i	0.646279	−	1.98904i
$735$	−0.0504643	−	0.124984i	−0.00186140	−	0.00461009i
$736$	33.9273	+	104.417i	1.25058	+	3.84888i
$737$	−2.42310	−	0.787314i	−0.0892562	−	0.0290011i
$738$	−78.9004	−	25.6363i	−2.90437	−	0.943686i
$739$	−14.8011	−	45.5530i	−0.544467	−	1.67570i	−0.722255	−	0.691627i	$-0.756894\pi$
$739$	−14.8011	−	45.5530i	−0.544467	−	1.67570i	0.177788	−	0.984069i	$-0.443106\pi$
$740$	−33.0531	+	2.30392i	−1.21506	+	0.0846939i
$741$	−0.0129915	+	0.0399837i	−0.000477255	+	0.00146884i
$742$	−12.8756	+	17.7218i	−0.472679	+	0.650586i
$743$			41.1245i			1.50871i	0.656467	+	0.754355i	$0.272050\pi$
$743$			41.1245i			1.50871i	−0.656467	+	0.754355i	$0.727950\pi$
$744$	−1.04659	−	0.760392i	−0.0383699	−	0.0278773i
$745$	−18.0378	−	4.50158i	−0.660853	−	0.164925i
$746$	2.33617	−	1.69732i	0.0855331	−	0.0621434i
$747$	−8.61568	−	11.8585i	−0.315231	−	0.433878i
$748$	−30.6196	+	9.94891i	−1.11956	+	0.363768i
$749$	19.3318			0.706370
$750$	0.163595	+	0.772185i	0.00597365	+	0.0281962i
$751$	−15.8581			−0.578669			−0.289335	−	0.957228i	$-0.593434\pi$
$751$	−15.8581			−0.578669			−0.289335	+	0.957228i	$0.593434\pi$
$752$	94.3359	−	30.6516i	3.44008	−	1.11775i
$753$	0.0621352	+	0.0855217i	0.00226433	+	0.00311658i
$754$	1.62948	−	1.18388i	0.0593420	−	0.0431145i
$755$	37.3489	+	9.32095i	1.35927	+	0.339224i
$756$	−1.43964	−	1.04596i	−0.0523592	−	0.0380412i
$757$			11.1123i			0.403884i	0.979397	+	0.201942i	$0.0647252\pi$
$757$			11.1123i			0.403884i	−0.979397	+	0.201942i	$0.935275\pi$
$758$	10.7416	−	14.7845i	0.390151	−	0.536997i
$759$	0.334058	−	1.02813i	0.0121255	−	0.0373186i
$760$	−11.0199	+	0.768130i	−0.399735	+	0.0278630i
$761$	11.3237	+	34.8508i	0.410484	+	1.26334i	0.916228	+	0.400657i	$0.131218\pi$
$761$	11.3237	+	34.8508i	0.410484	+	1.26334i	−0.505744	+	0.862684i	$0.668782\pi$
$762$	0.795591	+	0.258503i	0.0288212	+	0.00936458i
$763$	−0.933767	−	0.303399i	−0.0338046	−	0.0109838i
$764$	5.18084	+	15.9450i	0.187436	+	0.576869i
$765$	2.51098	+	6.21886i	0.0907845	+	0.224843i
$766$	−18.6273	+	57.3289i	−0.673031	+	2.07138i
$767$	10.5816	−	14.5643i	0.382079	−	0.525886i
$768$			0.301213i			0.0108691i
$769$	−16.5533	−	12.0266i	−0.596926	−	0.433692i	0.247861	−	0.968796i	$-0.420272\pi$
$769$	−16.5533	−	12.0266i	−0.596926	−	0.433692i	−0.844786	+	0.535104i	$0.820272\pi$
$770$	74.8418	−	30.2187i	2.69711	−	1.08901i
$771$	0.194496 <

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+(-2.55039 + 0.828673i) q^{2} +(-0.0154746 - 0.0212989i) q^{3} +(4.19977 - 3.05131i) q^{4} +(2.16953 + 0.541436i) q^{5} +(0.0571160 + 0.0414972i) q^{6} +2.17034i q^{7} +(-5.03006 + 6.92328i) q^{8} +(0.926837 - 2.85251i) q^{9} +(-5.98182 + 0.416954i) q^{10} +(1.91650 + 5.89837i) q^{11} +(-0.129979 - 0.0422328i) q^{12} +(-2.63082 - 0.854806i) q^{13} +(-1.79850 - 5.53522i) q^{14} +(-0.0220405 - 0.0545870i) q^{15} +(3.88315 - 11.9511i) q^{16} +(-0.587785 + 0.809017i) q^{17} +8.04306i q^{18} +(0.467036 + 0.339321i) q^{19} +(10.7636 - 4.34599i) q^{20} +(0.0462259 - 0.0335851i) q^{21} +(-9.77564 - 13.4550i) q^{22} +(6.29681 - 2.04596i) q^{23} +0.225296 q^{24} +(4.41369 + 2.34932i) q^{25} +7.41798 q^{26} +(-0.150213 + 0.0488071i) q^{27} +(6.62238 + 9.11493i) q^{28} +(0.219666 - 0.159597i) q^{29} +(0.101447 + 0.120954i) q^{30} +(-4.64539 - 3.37508i) q^{31} +16.5826i q^{32} +(0.0959719 - 0.132094i) q^{33} +(0.828673 - 2.55039i) q^{34} +(-1.17510 + 4.70861i) q^{35} +(-4.81139 - 14.8079i) q^{36} +(-2.71468 - 0.882054i) q^{37} +(-1.47231 - 0.478382i) q^{38} +(0.0225044 + 0.0692614i) q^{39} +(-14.6614 + 12.2968i) q^{40} +(-3.18738 + 9.80975i) q^{41} +(-0.0900631 + 0.123961i) q^{42} +7.56944i q^{43} +(26.0466 + 18.9240i) q^{44} +(3.55525 - 5.68678i) q^{45} +(-14.3639 + 10.4360i) q^{46} +(4.63968 + 6.38596i) q^{47} +(-0.314636 + 0.102231i) q^{48} +2.28962 q^{49} +(-13.2035 - 2.33418i) q^{50} +0.0263269 q^{51} +(-13.6571 + 4.43747i) q^{52} +(-2.21228 - 3.04494i) q^{53} +(0.342657 - 0.248955i) q^{54} +(0.964303 + 13.8343i) q^{55} +(-15.0259 - 10.9169i) q^{56} -0.0151982i q^{57} +(-0.427981 + 0.589065i) q^{58} +(-2.01108 + 6.18947i) q^{59} +(-0.259127 - 0.162001i) q^{60} +(-1.96408 - 6.04482i) q^{61} +(14.6444 + 4.75826i) q^{62} +(6.19092 + 2.01155i) q^{63} +(-5.97523 - 18.3899i) q^{64} +(-5.24482 - 3.27894i) q^{65} +(-0.135303 + 0.416421i) q^{66} +(-0.241468 + 0.332352i) q^{67} +5.19120i q^{68} +(-0.141017 - 0.102455i) q^{69} +(-0.904933 - 12.9826i) q^{70} +(7.23989 - 5.26009i) q^{71} +(15.0867 + 20.7650i) q^{72} +(11.8579 - 3.85285i) q^{73} +7.65444 q^{74} +(-0.0182621 - 0.130362i) q^{75} +2.99681 q^{76} +(-12.8015 + 4.15945i) q^{77} +(-0.114790 - 0.157995i) q^{78} +(-1.74512 + 1.26790i) q^{79} +(14.8954 - 23.8258i) q^{80} +(-7.27611 - 5.28640i) q^{81} -27.6600i q^{82} +(2.87256 - 3.95373i) q^{83} +(0.0916596 - 0.282099i) q^{84} +(-1.71325 + 1.43694i) q^{85} +(-6.27259 - 19.3050i) q^{86} +(-0.00679847 - 0.00220896i) q^{87} +(-50.4762 - 16.4007i) q^{88} +(5.62243 + 17.3040i) q^{89} +(-4.35480 + 17.4496i) q^{90} +(1.85522 - 5.70978i) q^{91} +(20.2023 - 27.8061i) q^{92} +0.151170i q^{93} +(-17.1249 - 12.4419i) q^{94} +(0.829526 + 0.989036i) q^{95} +(0.353191 - 0.256608i) q^{96} +(-0.271463 - 0.373636i) q^{97} +(-5.83943 + 1.89734i) q^{98} +18.6014 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

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Representations

Groups

Database

Properties

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