LMFDB - Embedded newform 425.2.k.c.86.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(86,425)]

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([8, 0]))

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

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

chi := DirichletCharacter("425.86");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, 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:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.16
Character	$\chi$	$=$	425.86
Dual form			425.2.k.c.341.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.58361 - 1.15056i) q^{2} +(0.0586727 - 0.180576i) q^{3} +(0.565999 - 1.74196i) q^{4} +(0.00528892 + 2.23606i) q^{5} +(-0.114849 - 0.353468i) q^{6} +2.20909 q^{7} +(0.101857 + 0.313482i) q^{8} +(2.39789 + 1.74217i) q^{9} +(2.58110 + 3.53497i) q^{10} +(0.941672 - 0.684165i) q^{11} +(-0.281348 - 0.204412i) q^{12} +(-5.17998 - 3.76347i) q^{13} +(3.49834 - 2.54169i) q^{14} +(0.404089 + 0.130241i) q^{15} +(3.48559 + 2.53243i) q^{16} +(-0.309017 - 0.951057i) q^{17} +5.80178 q^{18} +(-0.0135483 - 0.0416974i) q^{19} +(3.89813 + 1.25639i) q^{20} +(0.129613 - 0.398909i) q^{21} +(0.704069 - 2.16690i) q^{22} +(-2.72097 + 1.97690i) q^{23} +0.0625835 q^{24} +(-4.99994 + 0.0236527i) q^{25} -12.5332 q^{26} +(0.916105 - 0.665589i) q^{27} +(1.25034 - 3.84816i) q^{28} +(2.77078 - 8.52759i) q^{29} +(0.789770 - 0.258679i) q^{30} +(-2.01865 - 6.21277i) q^{31} +7.77430 q^{32} +(-0.0682933 - 0.210185i) q^{33} +(-1.58361 - 1.15056i) q^{34} +(0.0116837 + 4.93966i) q^{35} +(4.39199 - 3.19097i) q^{36} +(4.21902 + 3.06529i) q^{37} +(-0.0694307 - 0.0504443i) q^{38} +(-0.983516 + 0.714566i) q^{39} +(-0.700427 + 0.229415i) q^{40} +(-3.90337 - 2.83596i) q^{41} +(-0.253712 - 0.780844i) q^{42} -6.25163 q^{43} +(-0.658806 - 2.02760i) q^{44} +(-3.88291 + 5.37103i) q^{45} +(-2.03442 + 6.26129i) q^{46} +(-3.11090 + 9.57436i) q^{47} +(0.661805 - 0.480829i) q^{48} -2.11992 q^{49} +(-7.89075 + 5.79019i) q^{50} -0.189869 q^{51} +(-9.48770 + 6.89322i) q^{52} +(-0.454163 + 1.39777i) q^{53} +(0.684953 - 2.10807i) q^{54} +(1.53481 + 2.10202i) q^{55} +(0.225010 + 0.692511i) q^{56} -0.00832447 q^{57} +(-5.42367 - 16.6923i) q^{58} +(5.26601 + 3.82598i) q^{59} +(0.455589 - 0.630193i) q^{60} +(-0.936511 + 0.680415i) q^{61} +(-10.3449 - 7.51603i) q^{62} +(5.29715 + 3.84860i) q^{63} +(5.34028 - 3.87994i) q^{64} +(8.38796 - 11.6027i) q^{65} +(-0.349981 - 0.254276i) q^{66} +(-1.17656 - 3.62107i) q^{67} -1.83161 q^{68} +(0.197334 + 0.607333i) q^{69} +(5.70188 + 7.80906i) q^{70} +(-2.75307 + 8.47307i) q^{71} +(-0.301898 + 0.929146i) q^{72} +(-2.00965 + 1.46010i) q^{73} +10.2081 q^{74} +(-0.289089 + 0.904257i) q^{75} -0.0803038 q^{76} +(2.08024 - 1.51138i) q^{77} +(-0.735355 + 2.26319i) q^{78} +(2.27007 - 6.98657i) q^{79} +(-5.64423 + 7.80739i) q^{80} +(2.68129 + 8.25217i) q^{81} -9.44436 q^{82} +(-3.35409 - 10.3228i) q^{83} +(-0.621524 - 0.451564i) q^{84} +(2.12499 - 0.696011i) q^{85} +(-9.90015 + 7.19288i) q^{86} +(-1.37731 - 1.00067i) q^{87} +(0.310389 + 0.225511i) q^{88} +(3.93080 - 2.85589i) q^{89} +(0.0306852 + 12.9731i) q^{90} +(-11.4430 - 8.31386i) q^{91} +(1.90363 + 5.85877i) q^{92} -1.24032 q^{93} +(6.08942 + 18.7413i) q^{94} +(0.0931664 - 0.0305154i) q^{95} +(0.456139 - 1.40385i) q^{96} +(4.86483 - 14.9724i) q^{97} +(-3.35713 + 2.43909i) q^{98} +3.44995 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 17 q^{6} - 44 q^{7} + 15 q^{8} - 22 q^{9} - 2 q^{10} + 4 q^{11} + 14 q^{12} + 6 q^{13} - 10 q^{14} + 14 q^{15} - 32 q^{16} + 20 q^{17} - 62 q^{18} - 3 q^{19} + 16 q^{21}+ \cdots + 76 q^{99}+O(q^{100}) $ 80 * q + 2 * q^2 + 2 * q^3 - 20 * q^4 - 17 * q^6 - 44 * q^7 + 15 * q^8 - 22 * q^9 - 2 * q^10 + 4 * q^11 + 14 * q^12 + 6 * q^13 - 10 * q^14 + 14 * q^15 - 32 * q^16 + 20 * q^17 - 62 * q^18 - 3 * q^19 + 16 * q^21 + 17 * q^22 - 5 * q^23 + 30 * q^24 - 14 * q^25 + 18 * q^26 + 17 * q^27 + 32 * q^28 + 20 * q^29 - 114 * q^30 - 21 * q^31 - 88 * q^32 - 2 * q^34 - 2 * q^35 + 47 * q^36 + 6 * q^37 + 22 * q^38 - 46 * q^39 + 59 * q^40 - 26 * q^41 - 3 * q^42 - 102 * q^43 - 44 * q^44 + 74 * q^45 + 2 * q^46 + 2 * q^47 + 72 * q^48 + 108 * q^49 + 7 * q^50 + 18 * q^51 + 65 * q^52 - 18 * q^53 - 29 * q^54 - 49 * q^55 - 117 * q^56 + 2 * q^57 + 42 * q^58 + 21 * q^59 + 112 * q^60 + 4 * q^61 + 15 * q^62 + 41 * q^63 - 11 * q^64 + 8 * q^65 - 156 * q^66 + 21 * q^67 - 80 * q^68 - 67 * q^69 + 32 * q^70 - 4 * q^71 + 83 * q^72 - 2 * q^73 + 78 * q^74 - 68 * q^75 + 16 * q^76 + 2 * q^77 - 2 * q^78 - 53 * q^79 - 54 * q^80 - 21 * q^81 - 72 * q^82 - 42 * q^83 - 52 * q^84 + 42 * q^86 - 8 * q^87 + 68 * q^88 - 73 * q^89 + 97 * q^90 - 83 * q^91 + 117 * q^92 - 120 * q^93 + 80 * q^94 + 16 * q^95 + 88 * q^96 + 57 * q^97 + 17 * q^98 + 76 * q^99

Character values

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

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	1.58361	−	1.15056i	1.11978	−	0.813569i	0.135606	−	0.990763i	$-0.456702\pi$
$2$	1.58361	−	1.15056i	1.11978	−	0.813569i	0.984176	+	0.177194i	$0.0567020\pi$
$3$	0.0586727	−	0.180576i	0.0338747	−	0.104256i	−0.932690	−	0.360680i	$-0.882545\pi$
$3$	0.0586727	−	0.180576i	0.0338747	−	0.104256i	0.966564	+	0.256425i	$0.0825446\pi$
$4$	0.565999	−	1.74196i	0.282999	−	0.870982i
$5$	0.00528892	+	2.23606i	0.00236528	+	0.999997i
$5$	0.00528892	+	2.23606i	0.00236528	+	0.999997i
$6$	−0.114849	−	0.353468i	−0.0468868	−	0.144303i
$7$	2.20909			0.834958			0.417479	−	0.908687i	$-0.362914\pi$
$7$	2.20909			0.834958			0.417479	+	0.908687i	$0.362914\pi$
$8$	0.101857	+	0.313482i	0.0360117	+	0.110833i
$9$	2.39789	+	1.74217i	0.799295	+	0.580722i
$10$	2.58110	+	3.53497i	0.816215	+	1.11785i
$11$	0.941672	−	0.684165i	0.283925	−	0.206283i	−0.436703	−	0.899606i	$-0.643854\pi$
$11$	0.941672	−	0.684165i	0.283925	−	0.206283i	0.720627	+	0.693322i	$0.243854\pi$
$12$	−0.281348	−	0.204412i	−0.0812183	−	0.0590085i
$13$	−5.17998	−	3.76347i	−1.43667	−	1.04380i	−0.988726	−	0.149737i	$-0.952157\pi$
$13$	−5.17998	−	3.76347i	−1.43667	−	1.04380i	−0.447942	−	0.894063i	$-0.647843\pi$
$14$	3.49834	−	2.54169i	0.934970	−	0.679296i
$15$	0.404089	+	0.130241i	0.104335	+	0.0336280i
$16$	3.48559	+	2.53243i	0.871397	+	0.633107i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$18$	5.80178			1.36749
$19$	−0.0135483	−	0.0416974i	−0.00310820	−	0.00956605i	0.949490	−	0.313796i	$-0.101601\pi$
$19$	−0.0135483	−	0.0416974i	−0.00310820	−	0.00956605i	−0.952599	+	0.304230i	$0.901601\pi$
$20$	3.89813	+	1.25639i	0.871649	+	0.280938i
$21$	0.129613	−	0.398909i	0.0282839	−	0.0870490i
$22$	0.704069	−	2.16690i	0.150108	−	0.461985i
$23$	−2.72097	+	1.97690i	−0.567362	+	0.412213i	−0.834146	−	0.551544i	$-0.814039\pi$
$23$	−2.72097	+	1.97690i	−0.567362	+	0.412213i	0.266784	+	0.963756i	$0.414039\pi$
$24$	0.0625835			0.0127748
$25$	−4.99994	+	0.0236527i	−0.999989	+	0.00473054i
$26$	−12.5332			−2.45796
$27$	0.916105	−	0.665589i	0.176304	−	0.128093i
$28$	1.25034	−	3.84816i	0.236292	−	0.727233i
$29$	2.77078	−	8.52759i	0.514522	−	1.58353i	−0.269629	−	0.962964i	$-0.586901\pi$
$29$	2.77078	−	8.52759i	0.514522	−	1.58353i	0.784151	−	0.620570i	$-0.213099\pi$
$30$	0.789770	−	0.258679i	0.144192	−	0.0472280i
$31$	−2.01865	−	6.21277i	−0.362560	−	1.11585i	−0.951495	−	0.307665i	$-0.900452\pi$
$31$	−2.01865	−	6.21277i	−0.362560	−	1.11585i	0.588934	−	0.808181i	$-0.299548\pi$
$32$	7.77430			1.37431
$33$	−0.0682933	−	0.210185i	−0.0118883	−	0.0365885i
$34$	−1.58361	−	1.15056i	−0.271587	−	0.197319i
$35$	0.0116837	+	4.93966i	0.00197491	+	0.834955i
$36$	4.39199	−	3.19097i	0.731999	−	0.531828i
$37$	4.21902	+	3.06529i	0.693602	+	0.503931i	0.877842	−	0.478950i	$-0.158982\pi$
$37$	4.21902	+	3.06529i	0.693602	+	0.503931i	−0.184240	+	0.982881i	$0.558982\pi$
$38$	−0.0694307	−	0.0504443i	−0.0112631	−	0.00818315i
$39$	−0.983516	+	0.714566i	−0.157489	+	0.114422i
$40$	−0.700427	+	0.229415i	−0.110747	+	0.0362738i
$41$	−3.90337	−	2.83596i	−0.609603	−	0.442903i	0.239671	−	0.970854i	$-0.422960\pi$
$41$	−3.90337	−	2.83596i	−0.609603	−	0.442903i	−0.849275	+	0.527951i	$0.822960\pi$
$42$	−0.253712	−	0.780844i	−0.0391485	−	0.120487i
$43$	−6.25163			−0.953365			−0.476683	−	0.879075i	$-0.658161\pi$
$43$	−6.25163			−0.953365			−0.476683	+	0.879075i	$0.658161\pi$
$44$	−0.658806	−	2.02760i	−0.0993187	−	0.305672i
$45$	−3.88291	+	5.37103i	−0.578830	+	0.800667i
$46$	−2.03442	+	6.26129i	−0.299958	+	0.923177i
$47$	−3.11090	+	9.57436i	−0.453771	+	1.39656i	0.418801	+	0.908078i	$0.362450\pi$
$47$	−3.11090	+	9.57436i	−0.453771	+	1.39656i	−0.872572	+	0.488485i	$0.837550\pi$
$48$	0.661805	−	0.480829i	0.0955233	−	0.0694017i
$49$	−2.11992			−0.302846
$50$	−7.89075	+	5.79019i	−1.11592	+	0.818857i
$51$	−0.189869			−0.0265870
$52$	−9.48770	+	6.89322i	−1.31571	+	0.955917i
$53$	−0.454163	+	1.39777i	−0.0623841	+	0.191999i	−0.977391	−	0.211439i	$-0.932185\pi$
$53$	−0.454163	+	1.39777i	−0.0623841	+	0.191999i	0.915007	+	0.403438i	$0.132185\pi$
$54$	0.684953	−	2.10807i	0.0932103	−	0.286872i
$55$	1.53481	+	2.10202i	0.206954	+	0.283436i
$56$	0.225010	+	0.692511i	0.0300683	+	0.0925406i
$57$	−0.00832447			−0.00110260
$58$	−5.42367	−	16.6923i	−0.712163	−	2.19181i
$59$	5.26601	+	3.82598i	0.685577	+	0.498101i	0.875203	−	0.483756i	$-0.160728\pi$
$59$	5.26601	+	3.82598i	0.685577	+	0.498101i	−0.189626	+	0.981856i	$0.560728\pi$
$60$	0.455589	−	0.630193i	0.0588163	−	0.0813576i
$61$	−0.936511	+	0.680415i	−0.119908	+	0.0871182i	−0.646123	−	0.763233i	$-0.723611\pi$
$61$	−0.936511	+	0.680415i	−0.119908	+	0.0871182i	0.526215	+	0.850352i	$0.323611\pi$
$62$	−10.3449	−	7.51603i	−1.31381	−	0.954536i
$63$	5.29715	+	3.84860i	0.667378	+	0.484878i
$64$	5.34028	−	3.87994i	0.667535	−	0.484992i
$65$	8.38796	−	11.6027i	1.04040	−	1.43913i
$66$	−0.349981	−	0.254276i	−0.0430796	−	0.0312992i
$67$	−1.17656	−	3.62107i	−0.143739	−	0.442384i	0.853107	−	0.521735i	$-0.174715\pi$
$67$	−1.17656	−	3.62107i	−0.143739	−	0.442384i	−0.996847	+	0.0793513i	$0.974715\pi$
$68$	−1.83161			−0.222115
$69$	0.197334	+	0.607333i	0.0237563	+	0.0731143i
$70$	5.70188	+	7.80906i	0.681505	+	0.933361i
$71$	−2.75307	+	8.47307i	−0.326729	+	1.00557i	0.643925	+	0.765089i	$0.277305\pi$
$71$	−2.75307	+	8.47307i	−0.326729	+	1.00557i	−0.970654	+	0.240480i	$0.922695\pi$
$72$	−0.301898	+	0.929146i	−0.0355790	+	0.109501i
$73$	−2.00965	+	1.46010i	−0.235212	+	0.170891i	−0.699147	−	0.714977i	$-0.746437\pi$
$73$	−2.00965	+	1.46010i	−0.235212	+	0.170891i	0.463936	+	0.885869i	$0.346437\pi$
$74$	10.2081			1.18667
$75$	−0.289089	+	0.904257i	−0.0333811	+	0.104415i
$76$	−0.0803038			−0.00921148
$77$	2.08024	−	1.51138i	0.237065	−	0.172238i
$78$	−0.735355	+	2.26319i	−0.0832625	+	0.256256i
$79$	2.27007	−	6.98657i	0.255403	−	0.786050i	−0.738347	−	0.674421i	$-0.764393\pi$
$79$	2.27007	−	6.98657i	0.255403	−	0.786050i	0.993750	−	0.111629i	$-0.0356068\pi$
$80$	−5.64423	+	7.80739i	−0.631044	+	0.872892i
$81$	2.68129	+	8.25217i	0.297922	+	0.916908i
$82$	−9.44436			−1.04295
$83$	−3.35409	−	10.3228i	−0.368159	−	1.13308i	−0.947979	−	0.318333i	$-0.896877\pi$
$83$	−3.35409	−	10.3228i	−0.368159	−	1.13308i	0.579819	−	0.814745i	$-0.303123\pi$
$84$	−0.621524	−	0.451564i	−0.0678138	−	0.0492696i
$85$	2.12499	−	0.696011i	0.230487	−	0.0754930i
$86$	−9.90015	+	7.19288i	−1.06756	+	0.775628i
$87$	−1.37731	−	1.00067i	−0.147663	−	0.107283i
$88$	0.310389	+	0.225511i	0.0330876	+	0.0240395i
$89$	3.93080	−	2.85589i	0.416664	−	0.302724i	−0.359630	−	0.933095i	$-0.617097\pi$
$89$	3.93080	−	2.85589i	0.416664	−	0.302724i	0.776294	+	0.630371i	$0.217097\pi$
$90$	0.0306852	+	12.9731i	0.00323450	+	1.36749i
$91$	−11.4430	−	8.31386i	−1.19956	−	0.871529i
$92$	1.90363	+	5.85877i	0.198467	+	0.610819i
$93$	−1.24032			−0.128615
$94$	6.08942	+	18.7413i	0.628076	+	1.93302i
$95$	0.0931664	−	0.0305154i	0.00955867	−	0.00313081i
$96$	0.456139	−	1.40385i	0.0465545	−	0.143280i
$97$	4.86483	−	14.9724i	0.493949	−	1.52022i	−0.324640	−	0.945838i	$-0.605243\pi$
$97$	4.86483	−	14.9724i	0.493949	−	1.52022i	0.818589	−	0.574380i	$-0.194757\pi$
$98$	−3.35713	+	2.43909i	−0.339121	+	0.246386i
$99$	3.44995			0.346733
$100$	−2.78876	+	8.72311i	−0.278876	+	0.872311i
$101$	15.9477			1.58686			0.793428	−	0.608664i	$-0.208294\pi$
$101$	15.9477			1.58686			0.793428	+	0.608664i	$0.208294\pi$
$102$	−0.300678	+	0.218455i	−0.0297716	+	0.0216303i
$103$	−4.69933	+	14.4631i	−0.463039	+	1.42509i	0.398393	+	0.917215i	$0.369568\pi$
$103$	−4.69933	+	14.4631i	−0.463039	+	1.42509i	−0.861432	+	0.507873i	$0.830432\pi$
$104$	0.652168	−	2.00717i	0.0639503	−	0.196819i
$105$	0.892670	+	0.287713i	0.0871157	+	0.0280780i
$106$	0.889002	+	2.73607i	0.0863475	+	0.265750i
$107$	−7.46617			−0.721782			−0.360891	−	0.932608i	$-0.617527\pi$
$107$	−7.46617			−0.721782			−0.360891	+	0.932608i	$0.617527\pi$
$108$	−0.640919	−	1.97255i	−0.0616724	−	0.189808i
$109$	5.89534	+	4.28321i	0.564671	+	0.410257i	0.833165	−	0.553024i	$-0.186526\pi$
$109$	5.89534	+	4.28321i	0.564671	+	0.410257i	−0.268495	+	0.963281i	$0.586526\pi$
$110$	4.84905	+	1.56288i	0.462338	+	0.149015i
$111$	0.801059	−	0.582004i	0.0760332	−	0.0552414i
$112$	7.69998	+	5.59436i	0.727580	+	0.528618i
$113$	−2.71877	−	1.97530i	−0.255760	−	0.185821i	0.452516	−	0.891756i	$-0.350527\pi$
$113$	−2.71877	−	1.97530i	−0.255760	−	0.185821i	−0.708276	+	0.705936i	$0.750527\pi$
$114$	−0.0131827	+	0.00957780i	−0.00123467	+	0.000897043i
$115$	−4.43487	−	6.07381i	−0.413554	−	0.566386i
$116$	−13.2865	−	9.65321i	−1.23362	−	0.896278i
$117$	−5.86440	−	18.0488i	−0.542164	−	1.66861i
$118$	12.7413			1.17294
$119$	−0.682647	−	2.10097i	−0.0625781	−	0.192596i
$120$	0.000330999		0.139941i	3.02160e−5		0.0127748i
$121$	−2.98052	+	9.17310i	−0.270957	+	0.833919i
$122$	−0.700210	+	2.15502i	−0.0633940	+	0.195107i
$123$	−0.741128	+	0.538461i	−0.0668252	+	0.0485514i
$124$	−11.9650			−1.07449
$125$	−0.0793332	−	11.1801i	−0.00709578	−	0.999975i
$126$	12.8167			1.14180
$127$	−3.60863	+	2.62183i	−0.320215	+	0.232649i	−0.736267	−	0.676691i	$-0.763413\pi$
$127$	−3.60863	+	2.62183i	−0.320215	+	0.232649i	0.416052	+	0.909341i	$0.363413\pi$
$128$	−0.811964	+	2.49897i	−0.0717682	+	0.220880i
$129$	−0.366800	+	1.12889i	−0.0322950	+	0.0993936i
$130$	−0.0662869	−	28.0249i	−0.00581375	−	2.45795i
$131$	−5.19802	−	15.9979i	−0.454153	−	1.39774i	−0.872127	−	0.489280i	$-0.837260\pi$
$131$	−5.19802	−	15.9979i	−0.454153	−	1.39774i	0.417974	−	0.908459i	$-0.362740\pi$
$132$	−0.404789			−0.0352324
$133$	−0.0299295	−	0.0921134i	−0.00259521	−	0.00798724i
$134$	−6.02947	−	4.38066i	−0.520866	−	0.378432i
$135$	1.49314	+	2.04495i	0.128509	+	0.176001i
$136$	0.266664	−	0.193743i	0.0228662	−	0.0166133i
$137$	−3.44095	−	2.49999i	−0.293980	−	0.213589i	0.431012	−	0.902346i	$-0.358157\pi$
$137$	−3.44095	−	2.49999i	−0.293980	−	0.213589i	−0.724992	+	0.688757i	$0.758157\pi$
$138$	1.01127	+	0.734733i	0.0860853	+	0.0625447i
$139$	−1.42007	+	1.03174i	−0.120449	+	0.0875114i	−0.646379	−	0.763017i	$-0.723717\pi$
$139$	−1.42007	+	1.03174i	−0.120449	+	0.0875114i	0.525930	+	0.850528i	$0.323717\pi$
$140$	8.61133	+	2.77549i	0.727790	+	0.234572i
$141$	1.54637	+	1.12351i	0.130228	+	0.0946163i
$142$	5.38899	+	16.5856i	0.452234	+	1.39183i
$143$	−7.45268			−0.623224
$144$	3.94613	+	12.1449i	0.328844	+	1.01208i
$145$	19.0829	+	6.15054i	1.58475	+	0.510775i
$146$	−1.50257	+	4.62445i	−0.124354	+	0.382722i
$147$	−0.124381	+	0.382806i	−0.0102588	+	0.0315733i
$148$	7.72759	−	5.61442i	0.635204	−	0.461503i
$149$	14.5713			1.19373			0.596864	−	0.802343i	$-0.296413\pi$
$149$	14.5713			1.19373			0.596864	+	0.802343i	$0.296413\pi$
$150$	0.582598	+	1.76461i	0.0475690	+	0.144079i
$151$	−10.2771			−0.836341			−0.418171	−	0.908368i	$-0.637329\pi$
$151$	−10.2771			−0.836341			−0.418171	+	0.908368i	$0.637329\pi$
$152$	0.0116914	−	0.00849431i	0.000948299	−	0.000688980i
$153$	0.915911	−	2.81888i	0.0740470	−	0.227893i
$154$	1.55535	−	4.78688i	0.125334	−	0.385738i
$155$	13.8815	−	4.54669i	1.11499	−	0.365199i
$156$	0.688081	+	2.11769i	0.0550905	+	0.169551i
$157$	−23.5439			−1.87901			−0.939505	−	0.342535i	$-0.888715\pi$
$157$	−23.5439			−1.87901			−0.939505	+	0.342535i	$0.888715\pi$
$158$	−4.44355	−	13.6759i	−0.353510	−	1.08799i
$159$	0.225757	+	0.164022i	0.0179037	+	0.0130078i
$160$	0.0411176	+	17.3838i	0.00325063	+	1.37431i
$161$	−6.01088	+	4.36716i	−0.473724	+	0.344180i
$162$	13.7407	+	9.98324i	1.07957	+	0.784357i
$163$	16.7458	+	12.1666i	1.31164	+	0.952959i	0.999996	+	0.00275920i	$0.000878283\pi$
$163$	16.7458	+	12.1666i	1.31164	+	0.952959i	0.311640	+	0.950200i	$0.399122\pi$
$164$	−7.14945	+	5.19438i	−0.558278	+	0.405613i
$165$	0.469626	−	0.153820i	0.0365603	−	0.0119748i
$166$	−17.1886	−	12.4883i	−1.33410	−	0.969277i
$167$	−4.02663	−	12.3927i	−0.311590	−	0.958976i	−0.977135	−	0.212618i	$-0.931801\pi$
$167$	−4.02663	−	12.3927i	−0.311590	−	0.958976i	0.665545	−	0.746357i	$-0.268199\pi$
$168$	0.138253			0.0106664
$169$	8.65121	+	26.6257i	0.665478	+	2.04813i
$170$	2.56435	−	3.54714i	0.196677	−	0.272053i
$171$	0.0401565	−	0.123589i	0.00307085	−	0.00945109i
$172$	−3.53842	+	10.8901i	−0.269802	+	0.830364i
$173$	−3.35079	+	2.43449i	−0.254756	+	0.185091i	−0.707832	−	0.706381i	$-0.750327\pi$
$173$	−3.35079	+	2.43449i	−0.254756	+	0.185091i	0.453076	+	0.891472i	$0.350327\pi$
$174$	−3.33246			−0.252633
$175$	−11.0453	+	0.0522510i	−0.834948	+	0.00394980i
$176$	5.01488			0.378011
$177$	0.999852	−	0.726435i	0.0751535	−	0.0546022i
$178$	2.93898	−	9.04525i	0.220286	−	0.677970i
$179$	6.27649	−	19.3170i	0.469127	−	1.44382i	−0.384591	−	0.923087i	$-0.625657\pi$
$179$	6.27649	−	19.3170i	0.469127	−	1.44382i	0.853717	−	0.520736i	$-0.174343\pi$
$180$	7.15843	+	9.80389i	0.533558	+	0.730739i
$181$	−0.327726	−	1.00864i	−0.0243596	−	0.0749713i	0.938138	−	0.346263i	$-0.112549\pi$
$181$	−0.327726	−	1.00864i	−0.0243596	−	0.0749713i	−0.962497	+	0.271291i	$0.912549\pi$
$182$	−27.6869			−2.05229
$183$	0.0679190	+	0.209033i	0.00502071	+	0.0154522i
$184$	−0.896873	−	0.651616i	−0.0661184	−	0.0480378i
$185$	−6.83187	+	9.45019i	−0.502289	+	0.694792i
$186$	−1.96418	+	1.42706i	−0.144021	+	0.104637i
$187$	−0.941672	−	0.684165i	−0.0688619	−	0.0500311i
$188$	14.9174	+	10.8381i	1.08797	+	0.790453i
$189$	2.02376	−	1.47035i	0.147207	−	0.106952i
$190$	0.112429	−	0.155518i	0.00815649	−	0.0112825i
$191$	18.0130	+	13.0872i	1.30338	+	0.946959i	0.999983	−	0.00590654i	$-0.00188012\pi$
$191$	18.0130	+	13.0872i	1.30338	+	0.946959i	0.303394	+	0.952865i	$0.401880\pi$
$192$	−0.387295	−	1.19197i	−0.0279506	−	0.0860232i
$193$	11.0215			0.793348			0.396674	−	0.917960i	$-0.370164\pi$
$193$	11.0215			0.793348			0.396674	+	0.917960i	$0.370164\pi$
$194$	−9.52266	−	29.3077i	−0.683687	−	2.10417i
$195$	−1.60302	−	2.19542i	−0.114794	−	0.157218i
$196$	−1.19987	+	3.69282i	−0.0857051	+	0.263773i
$197$	2.23550	−	6.88016i	0.159273	−	0.490191i	−0.839296	−	0.543675i	$-0.817033\pi$
$197$	2.23550	−	6.88016i	0.159273	−	0.490191i	0.998569	+	0.0534838i	$0.0170326\pi$
$198$	5.46338	−	3.96937i	0.388265	−	0.282091i
$199$	−18.2642			−1.29472			−0.647359	−	0.762185i	$-0.724127\pi$
$199$	−18.2642			−1.29472			−0.647359	+	0.762185i	$0.724127\pi$
$200$	−0.516692	−	1.56498i	−0.0365356	−	0.110661i
$201$	−0.722910			−0.0509901
$202$	25.2549	−	18.3488i	1.77693	−	1.29102i
$203$	6.12091	−	18.8382i	0.429604	−	1.32218i
$204$	−0.107465	+	0.330745i	−0.00752409	+	0.0231568i
$205$	6.32074	−	8.74317i	0.441460	−	0.610649i
$206$	9.19871	+	28.3107i	0.640904	+	1.97250i
$207$	−9.96868			−0.692871
$208$	−8.52454	−	26.2358i	−0.591071	−	1.81913i
$209$	−0.0412860	−	0.0299960i	−0.00285581	−	0.00207487i
$210$	1.74467	−	0.571444i	0.120394	−	0.0394334i
$211$	1.90543	−	1.38437i	0.131175	−	0.0953041i	−0.520263	−	0.854006i	$-0.674166\pi$
$211$	1.90543	−	1.38437i	0.131175	−	0.0953041i	0.651438	+	0.758702i	$0.274166\pi$
$212$	2.17781	+	1.58227i	0.149573	+	0.108671i
$213$	1.36850	+	0.994276i	0.0937683	+	0.0681267i
$214$	−11.8235	+	8.59027i	−0.808238	+	0.587219i
$215$	−0.0330644	−	13.9790i	−0.00225497	−	0.953363i
$216$	0.301962	+	0.219388i	0.0205459	+	0.0149275i
$217$	−4.45938	−	13.7246i	−0.302723	−	0.931684i
$218$	14.2640			0.966080
$219$	0.145747	+	0.448563i	0.00984866	+	0.0303111i
$220$	4.53034	−	1.48385i	0.305436	−	0.100041i
$221$	−1.97858	+	6.08943i	−0.133093	+	0.409619i
$222$	0.598936	−	1.84333i	0.0401979	−	0.123716i
$223$	−20.8242	+	15.1297i	−1.39449	+	1.01316i	−0.399135	+	0.916892i	$0.630689\pi$
$223$	−20.8242	+	15.1297i	−1.39449	+	1.01316i	−0.995356	+	0.0962645i	$0.969311\pi$
$224$	17.1741			1.14749
$225$	−12.0305	−	8.65402i	−0.802033	−	0.576934i
$226$	−6.57817			−0.437573
$227$	3.33496	−	2.42299i	0.221349	−	0.160820i	−0.471585	−	0.881821i	$-0.656318\pi$
$227$	3.33496	−	2.42299i	0.221349	−	0.160820i	0.692934	+	0.721001i	$0.256318\pi$
$228$	−0.00471164	+	0.0145009i	−0.000312036	+	0.000960348i
$229$	−4.25135	+	13.0843i	−0.280937	+	0.864635i	0.706650	+	0.707563i	$0.250205\pi$
$229$	−4.25135	+	13.0843i	−0.280937	+	0.864635i	−0.987587	+	0.157072i	$0.949795\pi$
$230$	−14.0114	−	4.51596i	−0.923884	−	0.297774i
$231$	−0.150866	−	0.464318i	−0.00992626	−	0.0305499i
$232$	2.95547			0.194036
$233$	0.447730	+	1.37797i	0.0293318	+	0.0902739i	0.964651	−	0.263532i	$-0.0848874\pi$
$233$	0.447730	+	1.37797i	0.0293318	+	0.0902739i	−0.935319	+	0.353806i	$0.884887\pi$
$234$	−30.0531	−	21.8349i	−1.96463	−	1.42739i
$235$	−21.4253	−	6.90552i	−1.39763	−	0.450466i
$236$	9.64528	−	7.00771i	0.627854	−	0.456163i
$237$	−1.12841	−	0.819841i	−0.0732984	−	0.0532544i
$238$	−3.49834	−	2.54169i	−0.226764	−	0.164753i
$239$	−6.98070	+	5.07177i	−0.451544	+	0.328066i	−0.790205	−	0.612843i	$-0.790026\pi$
$239$	−6.98070	+	5.07177i	−0.451544	+	0.328066i	0.338661	+	0.940908i	$0.390026\pi$
$240$	1.07866	+	1.47729i	0.0696275	+	0.0953588i
$241$	17.1996	+	12.4962i	1.10792	+	0.804953i	0.982335	−	0.187130i	$-0.0599186\pi$
$241$	17.1996	+	12.4962i	1.10792	+	0.804953i	0.125587	+	0.992083i	$0.459919\pi$
$242$	5.83422	+	17.9559i	0.375038	+	1.15425i
$243$	5.04457			0.323609
$244$	0.655195	+	2.01648i	0.0419446	+	0.129092i
$245$	−0.0112121	−	4.74027i	−0.000716314	−	0.302845i
$246$	−0.554126	+	1.70542i	−0.0353298	+	0.108734i
$247$	−0.0867472	+	0.266980i	−0.00551959	+	0.0169876i
$248$	1.74198	−	1.26562i	0.110616	−	0.0803671i
$249$	−2.06085			−0.130601
$250$	−12.9890	−	17.6136i	−0.821494	−	1.11398i
$251$	22.3625			1.41151			0.705754	−	0.708457i	$-0.250608\pi$
$251$	22.3625			1.41151			0.705754	+	0.708457i	$0.250608\pi$
$252$	9.70231	−	7.04914i	0.611188	−	0.444054i
$253$	−1.20974	+	3.72319i	−0.0760555	+	0.234075i
$254$	−2.69810	+	8.30390i	−0.169294	+	0.521033i
$255$	−0.00100420	−	0.424558i	−6.28855e−5	−	0.0265869i
$256$	5.66899	+	17.4474i	0.354312	+	1.09046i
$257$	19.9478			1.24431			0.622154	−	0.782895i	$-0.286258\pi$
$257$	19.9478			1.24431			0.622154	+	0.782895i	$0.286258\pi$
$258$	0.717993	+	2.20976i	0.0447003	+	0.137573i
$259$	9.32019	+	6.77151i	0.579128	+	0.420761i
$260$	−15.4638	−	21.1786i	−0.959027	−	1.31344i
$261$	21.5005	−	15.6210i	1.33085	−	0.966918i
$262$	−26.6381	−	19.3537i	−1.64571	−	1.19568i
$263$	7.14448	+	5.19077i	0.440547	+	0.320076i	0.785852	−	0.618414i	$-0.212225\pi$
$263$	7.14448	+	5.19077i	0.440547	+	0.320076i	−0.345305	+	0.938491i	$0.612225\pi$
$264$	0.0589332	−	0.0428174i	0.00362709	−	0.00263523i
$265$	−3.12790	−	1.00814i	−0.192146	−	0.0619298i
$266$	−0.153379	−	0.111436i	−0.00940425	−	0.00683258i
$267$	−0.285075	−	0.877371i	−0.0174463	−	0.0536943i
$268$	−6.97370			−0.425987
$269$	7.47045	+	22.9917i	0.455481	+	1.40183i	0.870569	+	0.492046i	$0.163751\pi$
$269$	7.47045	+	22.9917i	0.455481	+	1.40183i	−0.415088	+	0.909781i	$0.636249\pi$
$270$	4.71739	+	1.52045i	0.287091	+	0.0925315i
$271$	−5.11696	+	15.7484i	−0.310833	+	0.956646i	0.666602	+	0.745413i	$0.267748\pi$
$271$	−5.11696	+	15.7484i	−0.310833	+	0.956646i	−0.977436	+	0.211233i	$0.932252\pi$
$272$	1.33138	−	4.09756i	0.0807266	−	0.248451i
$273$	−2.17268	+	1.57854i	−0.131496	+	0.0955377i
$274$	−8.32551			−0.502963
$275$	−4.69212	+	3.44306i	−0.282946	+	0.207624i
$276$	1.16964			0.0704043
$277$	5.10403	−	3.70829i	0.306671	−	0.222810i	−0.423796	−	0.905758i	$-0.639303\pi$
$277$	5.10403	−	3.70829i	0.306671	−	0.222810i	0.730467	+	0.682948i	$0.239303\pi$
$278$	−1.06176	+	3.26776i	−0.0636802	+	0.195987i
$279$	5.98318	−	18.4143i	0.358204	−	1.10244i
$280$	−1.54731	+	0.506800i	−0.0924692	+	0.0302871i
$281$	0.600358	+	1.84771i	0.0358143	+	0.110225i	0.967365	−	0.253385i	$-0.0815440\pi$
$281$	0.600358	+	1.84771i	0.0358143	+	0.110225i	−0.931551	+	0.363610i	$0.881544\pi$
$282$	3.74152			0.222804
$283$	−5.19613	−	15.9920i	−0.308878	−	0.950629i	−0.978202	−	0.207658i	$-0.933416\pi$
$283$	−5.19613	−	15.9920i	−0.308878	−	0.950629i	0.669324	−	0.742971i	$-0.266584\pi$
$284$	13.2016	+	9.59150i	0.783369	+	0.569151i
$285$	−4.40274e−5	−	0.0186140i	−2.60796e−6	−	0.00110260i
$286$	−11.8021	+	8.57475i	−0.697875	+	0.507036i
$287$	−8.62289	−	6.26490i	−0.508993	−	0.369805i
$288$	18.6419	+	13.5441i	1.09848	+	0.798095i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	37.2964	−	12.2159i	2.19012	−	0.717345i
$291$	−2.41822	−	1.75694i	−0.141759	−	0.102994i
$292$	1.40598	+	4.32716i	0.0822786	+	0.253228i
$293$	5.63654			0.329290			0.164645	−	0.986353i	$-0.447352\pi$
$293$	5.63654			0.329290			0.164645	+	0.986353i	$0.447352\pi$
$294$	0.243470	+	0.749324i	0.0141995	+	0.0437015i
$295$	−8.52728	+	11.7954i	−0.496478	+	0.686753i
$296$	−0.531181	+	1.63481i	−0.0308743	+	0.0950212i
$297$	0.407298	−	1.25353i	0.0236338	−	0.0727374i
$298$	23.0753	−	16.7652i	1.33671	−	0.971180i
$299$	21.5346			1.24538
$300$	1.41156	+	1.01539i	0.0814965	+	0.0586237i
$301$	−13.8104			−0.796020
$302$	−16.2750	+	11.8245i	−0.936520	+	0.680421i
$303$	0.935694	−	2.87977i	0.0537542	−	0.165439i
$304$	0.0583719	−	0.179650i	0.00334786	−	0.0103036i
$305$	−1.52640	−	2.09050i	−0.0874016	−	0.119702i
$306$	−1.79285	−	5.51782i	−0.102490	−	0.315433i
$307$	32.6228			1.86188			0.930941	−	0.365169i	$-0.118989\pi$
$307$	32.6228			1.86188			0.930941	+	0.365169i	$0.118989\pi$
$308$	−1.45536	−	4.47914i	−0.0829269	−	0.255223i
$309$	2.33596	+	1.69717i	0.132888	+	0.0965488i
$310$	16.7516	−	23.1716i	0.951426	−	1.31606i
$311$	14.6456	−	10.6407i	0.830478	−	0.603378i	−0.0892165	−	0.996012i	$-0.528436\pi$
$311$	14.6456	−	10.6407i	0.830478	−	0.603378i	0.919695	+	0.392635i	$0.128436\pi$
$312$	−0.324181	−	0.235532i	−0.0183532	−	0.0133343i
$313$	7.55141	+	5.48642i	0.426831	+	0.310111i	0.780380	−	0.625305i	$-0.215025\pi$
$313$	7.55141	+	5.48642i	0.426831	+	0.310111i	−0.353550	+	0.935416i	$0.615025\pi$
$314$	−37.2844	+	27.0887i	−2.10408	+	1.52870i
$315$	−8.57770	+	11.8651i	−0.483298	+	0.668523i
$316$	−10.8855	−	7.90877i	−0.612357	−	0.444903i
$317$	−0.979718	−	3.01526i	−0.0550264	−	0.169354i	0.919766	−	0.392467i	$-0.128378\pi$
$317$	−0.979718	−	3.01526i	−0.0550264	−	0.169354i	−0.974793	+	0.223113i	$0.928378\pi$
$318$	0.546228			0.0306309
$319$	−3.22511	−	9.92587i	−0.180571	−	0.555742i
$320$	8.70403	+	11.9207i	0.486570	+	0.666386i
$321$	−0.438060	+	1.34821i	−0.0244501	+	0.0752498i
$322$	−4.49421	+	13.8318i	−0.250452	+	0.770814i
$323$	−0.0354700	+	0.0257704i	−0.00197360	+	0.00143390i
$324$	15.8926			0.882922
$325$	25.9886	+	18.6946i	1.44159	+	1.03699i
$326$	40.5173			2.24404
$327$	1.11934	−	0.813248i	0.0618997	−	0.0449727i
$328$	0.491440	−	1.51250i	0.0271352	−	0.0835137i
$329$	−6.87225	+	21.1506i	−0.378880	+	1.16607i
$330$	0.566725	−	0.783923i	0.0311972	−	0.0431535i
$331$	−1.53218	−	4.71557i	−0.0842163	−	0.259191i	0.900077	−	0.435730i	$-0.143510\pi$
$331$	−1.53218	−	4.71557i	−0.0842163	−	0.259191i	−0.984294	+	0.176539i	$0.943510\pi$
$332$	−19.8804			−1.09108
$333$	4.77647	+	14.7005i	0.261749	+	0.805580i
$334$	−20.6352	−	14.9923i	−1.12911	−	0.820343i
$335$	8.09071	−	2.65001i	0.442043	−	0.144785i
$336$	1.46199	−	1.06220i	0.0797579	−	0.0579475i
$337$	23.0777	+	16.7669i	1.25712	+	0.913354i	0.998613	−	0.0526546i	$-0.0167682\pi$
$337$	23.0777	+	16.7669i	1.25712	+	0.913354i	0.258511	+	0.966008i	$0.416768\pi$
$338$	44.3346	+	32.2110i	2.41148	+	1.75205i
$339$	−0.516209	+	0.375048i	−0.0280366	+	0.0203698i
$340$	−0.00968724	−	4.09559i	−0.000525364	−	0.222115i
$341$	−6.15146	−	4.46930i	−0.333120	−	0.242026i
$342$	−0.0786044	−	0.241919i	−0.00425044	−	0.0130815i
$343$	−20.1467			−1.08782
$344$	−0.636770	−	1.95978i	−0.0343323	−	0.105664i
$345$	−1.35699	+	0.444464i	−0.0730579	+	0.0239291i
$346$	−2.50531	+	7.71056i	−0.134687	+	0.414523i
$347$	−9.41386	+	28.9729i	−0.505362	+	1.55535i	0.294798	+	0.955560i	$0.404748\pi$
$347$	−9.41386	+	28.9729i	−0.505362	+	1.55535i	−0.800160	+	0.599786i	$0.795252\pi$
$348$	−2.52269	+	1.83284i	−0.135231	+	0.0982508i
$349$	1.79215			0.0959317			0.0479658	−	0.998849i	$-0.484726\pi$
$349$	1.79215			0.0959317			0.0479658	+	0.998849i	$0.484726\pi$
$350$	−17.4314	+	12.7911i	−0.931746	+	0.683711i
$351$	−7.25033			−0.386994
$352$	7.32084	−	5.31890i	0.390202	−	0.283498i
$353$	−2.32019	+	7.14080i	−0.123491	+	0.380067i	−0.993623	−	0.112752i	$-0.964033\pi$
$353$	−2.32019	+	7.14080i	−0.123491	+	0.380067i	0.870132	+	0.492819i	$0.164033\pi$
$354$	0.747568	−	2.30078i	0.0397328	−	0.122285i
$355$	−18.9609	−	6.11122i	−1.00634	−	0.324350i
$356$	−2.75004	−	8.46375i	−0.145752	−	0.448578i
$357$	−0.419437			−0.0221990
$358$	−12.2859	−	37.8121i	−0.649331	−	1.99843i
$359$	−20.0892	−	14.5957i	−1.06027	−	0.770331i	−0.0861314	−	0.996284i	$-0.527450\pi$
$359$	−20.0892	−	14.5957i	−1.06027	−	0.770331i	−0.974138	+	0.225953i	$0.927450\pi$
$360$	−2.07922	−	0.670148i	−0.109585	−	0.0353199i
$361$	15.3698	−	11.1668i	0.808935	−	0.587726i
$362$	−1.67949	−	1.22022i	−0.0882718	−	0.0641332i
$363$	1.48157	+	1.07642i	0.0777621	+	0.0564975i
$364$	−20.9592	+	15.2277i	−1.09856	+	0.798151i
$365$	−3.27550	−	4.48598i	−0.171447	−	0.234807i
$366$	0.348062	+	0.252882i	0.0181935	+	0.0132184i
$367$	−0.997377	−	3.06961i	−0.0520627	−	0.160232i	0.921645	−	0.388035i	$-0.126846\pi$
$367$	−0.997377	−	3.06961i	−0.0520627	−	0.160232i	−0.973707	+	0.227802i	$0.926846\pi$
$368$	−14.4906			−0.755373
$369$	−4.41911	−	13.6006i	−0.230050	−	0.708020i
$370$	0.0539897	+	22.8259i	0.00280679	+	1.18666i
$371$	−1.00329	+	3.08780i	−0.0520881	+	0.160311i
$372$	−0.702017	+	2.16059i	−0.0363979	+	0.112021i
$373$	−5.09814	+	3.70402i	−0.263972	+	0.191787i	−0.711896	−	0.702285i	$-0.752163\pi$
$373$	−5.09814	+	3.70402i	−0.263972	+	0.191787i	0.447924	+	0.894071i	$0.352163\pi$
$374$	−2.27841			−0.117814
$375$	−2.02350	−	0.641638i	−0.104493	−	0.0331341i
$376$	−3.31826			−0.171126
$377$	−46.4460	+	33.7450i	−2.39209	+	1.73795i
$378$	1.51312	−	4.65691i	0.0778266	−	0.239526i
$379$	−8.43640	+	25.9646i	−0.433349	+	1.33371i	0.461421	+	0.887181i	$0.347340\pi$
$379$	−8.43640	+	25.9646i	−0.433349	+	1.33371i	−0.894769	+	0.446529i	$0.852660\pi$
$380$	−0.000424720	−	0.179564i	−2.17877e−5	−	0.00921145i
$381$	0.261711	+	0.805462i	0.0134078	+	0.0412651i
$382$	43.5833			2.22991
$383$	5.68814	+	17.5063i	0.290650	+	0.894529i	0.984648	+	0.174552i	$0.0558477\pi$
$383$	5.68814	+	17.5063i	0.290650	+	0.894529i	−0.693998	+	0.719977i	$0.744152\pi$
$384$	0.403614	+	0.293242i	0.0205968	+	0.0149645i
$385$	3.39054	+	4.64355i	0.172798	+	0.236657i
$386$	17.4538	−	12.6809i	0.888377	−	0.645443i
$387$	−14.9907	−	10.8914i	−0.762020	−	0.553640i
$388$	−23.3279	−	16.9487i	−1.18430	−	0.860441i
$389$	6.79305	−	4.93544i	0.344421	−	0.250237i	−0.402104	−	0.915594i	$-0.631721\pi$
$389$	6.79305	−	4.93544i	0.344421	−	0.250237i	0.746525	+	0.665357i	$0.231721\pi$
$390$	−5.06452	−	1.63233i	−0.256452	−	0.0826562i
$391$	2.72097	+	1.97690i	0.137606	+	0.0999763i
$392$	−0.215928	−	0.664557i	−0.0109060	−	0.0335652i
$393$	−3.19381			−0.161106
$394$	−4.37588	−	13.4676i	−0.220453	−	0.678486i
$395$	15.6344	+	5.03907i	0.786652	+	0.253543i
$396$	1.95267	−	6.00969i	0.0981252	−	0.301998i
$397$	8.59600	−	26.4558i	0.431421	−	1.32778i	−0.465289	−	0.885159i	$-0.654050\pi$
$397$	8.59600	−	26.4558i	0.431421	−	1.32778i	0.896710	−	0.442619i	$-0.145950\pi$
$398$	−28.9234	+	21.0141i	−1.44980	+	1.05334i
$399$	−0.0183895			−0.000920627
$400$	−17.4876	−	12.5796i	−0.874382	−	0.628978i
$401$	14.0010			0.699177			0.349589	−	0.936903i	$-0.386321\pi$
$401$	14.0010			0.699177			0.349589	+	0.936903i	$0.386321\pi$
$402$	−1.14481	+	0.831751i	−0.0570978	+	0.0414840i
$403$	−12.9250	+	39.7791i	−0.643842	+	1.98154i
$404$	9.02638	−	27.7803i	0.449079	−	1.38212i
$405$	−18.4382	+	6.03918i	−0.916201	+	0.300089i
$406$	−11.9814	−	36.8749i	−0.594626	−	1.83007i
$407$	6.07009			0.300883
$408$	−0.0193394	−	0.0595205i	−0.000957442	−	0.00294670i
$409$	−12.3662	−	8.98454i	−0.611467	−	0.444257i	0.238464	−	0.971151i	$-0.423356\pi$
$409$	−12.3662	−	8.98454i	−0.611467	−	0.444257i	−0.849931	+	0.526895i	$0.823356\pi$
$410$	−0.0499504	−	21.1182i	−0.00246688	−	1.04295i
$411$	−0.653329	+	0.474671i	−0.0322263	+	0.0234138i
$412$	22.5343	+	16.3721i	1.11019	+	0.806597i
$413$	11.6331	+	8.45194i	0.572427	+	0.415893i
$414$	−15.7865	+	11.4696i	−0.775864	+	0.563698i
$415$	23.0648	−	7.55455i	1.13220	−	0.370838i
$416$	−40.2707	−	29.2584i	−1.97443	−	1.43451i
$417$	0.102989	+	0.316967i	0.00504338	+	0.0155219i
$418$	−0.0998931			−0.00488593
$419$	6.38487	+	19.6506i	0.311921	+	0.959996i	0.977003	+	0.213225i	$0.0683967\pi$
$419$	6.38487	+	19.6506i	0.311921	+	0.959996i	−0.665082	+	0.746771i	$0.731603\pi$
$420$	1.00644	−	1.39215i	0.0491091	−	0.0679302i
$421$	−2.43893	+	7.50627i	−0.118866	+	0.365833i	−0.992734	−	0.120331i	$-0.961604\pi$
$421$	−2.43893	+	7.50627i	−0.118866	+	0.365833i	0.873867	+	0.486164i	$0.161604\pi$
$422$	1.42465	−	4.38461i	0.0693507	−	0.213440i
$423$	−24.1397	+	17.5385i	−1.17371	+	0.852752i
$424$	−0.484436			−0.0235263
$425$	1.56756	+	4.74792i	0.0760380	+	0.230308i
$426$	3.31115			0.160426
$427$	−2.06884	+	1.50310i	−0.100118	+	0.0727400i
$428$	−4.22584	+	13.0058i	−0.204264	+	0.628659i
$429$	−0.437268	+	1.34577i	−0.0211115	+	0.0649746i
$430$	−16.1361	−	22.0993i	−0.778151	−	1.06572i
$431$	−2.10878	−	6.49016i	−0.101576	−	0.312620i	0.887335	−	0.461125i	$-0.152554\pi$
$431$	−2.10878	−	6.49016i	−0.101576	−	0.312620i	−0.988912	+	0.148505i	$0.952554\pi$
$432$	4.87872			0.234728
$433$	−7.96295	−	24.5075i	−0.382675	−	1.17775i	−0.938153	−	0.346221i	$-0.887465\pi$
$433$	−7.96295	−	24.5075i	−0.382675	−	1.17775i	0.555478	−	0.831531i	$-0.312535\pi$
$434$	−22.8529	−	16.6036i	−1.09697	−	0.796997i
$435$	2.23028	−	3.08504i	0.106934	−	0.147916i
$436$	10.7980	−	7.84517i	0.517128	−	0.375716i
$437$	0.119296	+	0.0866739i	0.00570672	+	0.00414618i
$438$	0.746904	+	0.542658i	0.0356885	+	0.0259292i
$439$	−24.9943	+	18.1594i	−1.19291	+	0.866702i	−0.993569	−	0.113227i	$-0.963881\pi$
$439$	−24.9943	+	18.1594i	−1.19291	+	0.866702i	−0.199344	+	0.979930i	$0.563881\pi$
$440$	−0.502614	+	0.695241i	−0.0239612	+	0.0331443i
$441$	−5.08332	−	3.69325i	−0.242063	−	0.175869i
$442$	3.87296	+	11.9198i	0.184218	+	0.566965i
$443$	−10.6059			−0.503903			−0.251952	−	0.967740i	$-0.581072\pi$
$443$	−10.6059			−0.503903			−0.251952	+	0.967740i	$0.581072\pi$
$444$	−0.560431	−	1.72483i	−0.0265969	−	0.0818568i
$445$	6.40675	+	8.77441i	0.303709	+	0.415947i
$446$	−15.5698	+	47.9190i	−0.737252	+	2.26903i
$447$	0.854938	−	2.63123i	0.0404372	−	0.124453i
$448$	11.7972	−	8.57114i	0.557363	−	0.404948i
$449$	31.7888			1.50021			0.750103	−	0.661321i	$-0.230004\pi$
$449$	31.7888			1.50021			0.750103	+	0.661321i	$0.230004\pi$
$450$	−29.0086	+	0.137228i	−1.36748	+	0.00646898i
$451$	−5.61595			−0.264445
$452$	−4.97972	+	3.61798i	−0.234226	+	0.170175i
$453$	−0.602987	+	1.85580i	−0.0283308	+	0.0871933i
$454$	2.49348	−	7.67415i	0.117025	−	0.360166i
$455$	18.5298	−	25.6313i	0.868689	−	1.20161i
$456$	−0.000847902	−	0.00260957i	−3.97066e−5	−	0.000122204i
$457$	−3.93548			−0.184094			−0.0920469	−	0.995755i	$-0.529341\pi$
$457$	−3.93548			−0.184094			−0.0920469	+	0.995755i	$0.529341\pi$
$458$	8.32180	+	25.6119i	0.388852	+	1.19676i
$459$	−0.916105	−	0.665589i	−0.0427601	−	0.0310670i
$460$	−13.0905	+	4.28762i	−0.610347	+	0.199911i
$461$	−17.9101	+	13.0124i	−0.834155	+	0.606049i	−0.920732	−	0.390196i	$-0.872407\pi$
$461$	−17.9101	+	13.0124i	−0.834155	+	0.606049i	0.0865770	+	0.996245i	$0.472407\pi$
$462$	−0.773139	−	0.561718i	−0.0359697	−	0.0261335i
$463$	−30.9074	−	22.4555i	−1.43639	−	1.04360i	−0.988782	−	0.149367i	$-0.952276\pi$
$463$	−30.9074	−	22.4555i	−1.43639	−	1.04360i	−0.447607	−	0.894230i	$-0.647724\pi$
$464$	31.2533	−	22.7069i	1.45090	−	1.05414i
$465$	−0.00655993	−	2.77342i	−0.000304210	−	0.128614i
$466$	2.29447	+	1.66703i	0.106289	+	0.0772236i
$467$	−5.44344	−	16.7532i	−0.251893	−	0.775246i	−0.994426	−	0.105437i	$-0.966376\pi$
$467$	−5.44344	−	16.7532i	−0.251893	−	0.775246i	0.742533	−	0.669809i	$-0.233624\pi$
$468$	−34.7596			−1.60676
$469$	−2.59912	−	7.99927i	−0.120016	−	0.369372i
$470$	−41.8745	+	13.7155i	−1.93153	+	0.632647i
$471$	−1.38139	+	4.25147i	−0.0636509	+	0.195897i
$472$	−0.663000	+	2.04050i	−0.0305170	+	0.0939218i
$473$	−5.88699	+	4.27715i	−0.270684	+	0.196663i
$474$	−2.73025			−0.125404
$475$	0.0687271	+	0.208164i	0.00315341	+	0.00955124i
$476$	−4.04619			−0.185457
$477$	−3.52418	+	2.56047i	−0.161361	+	0.117236i
$478$	−5.21932	+	16.0634i	−0.238726	+	0.734724i
$479$	1.12732	−	3.46954i	0.0515086	−	0.158527i	−0.921993	−	0.387205i	$-0.873440\pi$
$479$	1.12732	−	3.46954i	0.0515086	−	0.158527i	0.973502	+	0.228678i	$0.0734404\pi$
$480$	3.14151	+	1.01253i	0.143390	+	0.0462154i
$481$	−10.3183	−	31.7563i	−0.470472	−	1.44796i
$482$	41.6151			1.89552
$483$	0.435930	+	1.34165i	0.0198355	+	0.0610473i
$484$	14.2923	+	10.3839i	0.649648	+	0.471997i
$485$	33.5050	+	10.7989i	1.52138	+	0.490352i
$486$	7.98863	−	5.80408i	0.362372	−	0.263278i
$487$	−0.104378	−	0.0758349i	−0.00472981	−	0.00343641i	0.585418	−	0.810732i	$-0.300930\pi$
$487$	−0.104378	−	0.0758349i	−0.00472981	−	0.00343641i	−0.590148	+	0.807295i	$0.700930\pi$
$488$	−0.308688	−	0.224275i	−0.0139736	−	0.0101524i
$489$	3.17951	−	2.31005i	0.143783	−	0.104464i
$490$	−5.47172	−	7.49384i	−0.247187	−	0.338537i
$491$	−20.1702	−	14.6545i	−0.910269	−	0.661349i	0.0308138	−	0.999525i	$-0.490190\pi$
$491$	−20.1702	−	14.6545i	−0.910269	−	0.661349i	−0.941083	+	0.338176i	$0.890190\pi$
$492$	0.518502	+	1.59579i	0.0233759	+	0.0719436i
$493$	−8.96644			−0.403828
$494$	0.169803	+	0.522601i	0.00763981	+	0.0235129i
$495$	0.0182465	+	7.71430i	0.000820120	+	0.346732i
$496$	8.69721	−	26.7672i	0.390516	−	1.20188i
$497$	−6.08178	+	18.7178i	−0.272805	+	0.839608i
$498$	−3.26358	+	2.37113i	−0.146245	+	0.106253i
$499$	11.6035			0.519442			0.259721	−	0.965684i	$-0.416369\pi$
$499$	11.6035			0.519442			0.259721	+	0.965684i	$0.416369\pi$
$500$	−19.5202	−	6.18970i	−0.872969	−	0.276812i
$501$	−2.47408			−0.110534
$502$	35.4135	−	25.7294i	1.58058	−	1.14836i
$503$	−12.0671	+	37.1389i	−0.538048	+	1.65594i	0.198923	+	0.980015i	$0.436256\pi$
$503$	−12.0671	+	37.1389i	−0.538048	+	1.65594i	−0.736971	+	0.675925i	$0.763744\pi$
$504$	−0.666919	+	2.05257i	−0.0297069	+	0.0914286i
$505$	0.0843461	+	35.6600i	0.00375335	+	1.58685i
$506$	2.36800	+	7.28795i	0.105270	+	0.323989i
$507$	5.31555			0.236072
$508$	2.52465	+	7.77006i	0.112013	+	0.344741i
$509$	16.7079	+	12.1390i	0.740563	+	0.538050i	0.892887	−	0.450280i	$-0.148676\pi$
$509$	16.7079	+	12.1390i	0.740563	+	0.538050i	−0.152325	+	0.988331i	$0.548676\pi$
$510$	−0.490070	−	0.671180i	−0.0217007	−	0.0297203i
$511$	−4.43950	+	3.22549i	−0.196392	+	0.142687i
$512$	24.8002	+	18.0184i	1.09602	+	0.796308i
$513$	−0.0401650	−	0.0291816i	−0.00177333	−	0.00128840i
$514$	31.5895	−	22.9511i	1.39335	−	1.01233i
$515$	−32.3651	−	10.4315i	−1.42618	−	0.459667i
$516$	1.75889	+	1.27791i	0.0774307	+	0.0562567i
$517$	3.62099	+	11.1443i	0.159251	+	0.490124i
$518$	22.5506			0.990816
$519$	0.243011	+	0.747910i	0.0106670	+	0.0328296i
$520$	4.49159	+	1.44767i	0.196969	+	0.0634846i
$521$	8.94522	−	27.5306i	0.391897	−	1.20614i	−0.539454	−	0.842015i	$-0.681369\pi$
$521$	8.94522	−	27.5306i	0.391897	−	1.20614i	0.931352	−	0.364121i	$-0.118631\pi$
$522$	16.0755	−	49.4753i	0.703605	−	2.16547i
$523$	−21.7399	+	15.7949i	−0.950618	+	0.690664i	−0.950953	−	0.309336i	$-0.899893\pi$
$523$	−21.7399	+	15.7949i	−0.950618	+	0.690664i	0.000335282		1.00000i	$0.499893\pi$
$524$	−30.8098			−1.34593
$525$	−0.638624	+	1.99759i	−0.0278718	+	0.0871818i
$526$	17.2864			0.753721
$527$	−5.28490	+	3.83970i	−0.230214	+	0.167260i
$528$	0.294236	−	0.905567i	0.0128050	−	0.0394097i
$529$	−3.61184	+	11.1161i	−0.157036	+	0.483308i
$530$	−6.11331	+	2.00233i	−0.265545	+	0.0869758i
$531$	5.96180	+	18.3485i	0.258720	+	0.796259i
$532$	−0.177398			−0.00769119
$533$	9.54628	+	29.3804i	0.413495	+	1.27261i
$534$	−1.46092	−	1.06142i	−0.0632200	−	0.0459321i
$535$	−0.0394880	−	16.6948i	−0.00170721	−	0.721780i
$536$	1.01530	−	0.737659i	0.0438543	−	0.0318620i
$537$	−3.11994	−	2.26677i	−0.134635	−	0.0978182i
$538$	38.2836	+	27.8146i	1.65052	+	1.19917i
$539$	−1.99627	+	1.45037i	−0.0859853	+	0.0624720i
$540$	4.40734	−	1.44357i	0.189662	−	0.0621212i
$541$	2.59964	+	1.88875i	0.111767	+	0.0812035i	0.642265	−	0.766483i	$-0.277995\pi$
$541$	2.59964	+	1.88875i	0.111767	+	0.0812035i	−0.530498	+	0.847686i	$0.677995\pi$
$542$	10.0162	+	30.8267i	0.430232	+	1.32412i
$543$	−0.201364			−0.00864135
$544$	−2.40239	−	7.39379i	−0.103002	−	0.317006i
$545$	−9.54635	+	13.2050i	−0.408921	+	0.565639i
$546$	−1.62447	+	4.99959i	−0.0695207	+	0.213963i
$547$	−6.41166	+	19.7330i	−0.274143	+	0.843724i	0.715302	+	0.698815i	$0.246289\pi$
$547$	−6.41166	+	19.7330i	−0.274143	+	0.843724i	−0.989445	+	0.144909i	$0.953711\pi$
$548$	−6.30247	+	4.57902i	−0.269228	+	0.195606i
$549$	−3.43104			−0.146433
$550$	−3.46905	+	10.8510i	−0.147921	+	0.462690i
$551$	−0.393118			−0.0167474
$552$	−0.170288	+	0.123722i	−0.00724795	+	0.00526594i
$553$	5.01480	−	15.4340i	0.213251	−	0.656319i
$554$	3.81617	−	11.7450i	0.162134	−	0.498996i
$555$	1.30563	+	1.78814i	0.0554210	+	0.0759023i
$556$	0.993502	+	3.05769i	0.0421339	+	0.129675i
$557$	6.97504			0.295542			0.147771	−	0.989022i	$-0.452790\pi$
$557$	6.97504			0.295542			0.147771	+	0.989022i	$0.452790\pi$
$558$	−11.7118	−	36.0451i	−0.495799	−	1.52591i
$559$	32.3833	+	23.5279i	1.36967	+	0.995123i
$560$	−12.4686	+	17.2472i	−0.526895	+	0.728828i
$561$	−0.178794	+	0.129902i	−0.00754869	+	0.00548445i
$562$	3.07663	+	2.23531i	0.129780	+	0.0942907i
$563$	16.3086	+	11.8489i	0.687324	+	0.499370i	0.875779	−	0.482712i	$-0.160348\pi$
$563$	16.3086	+	11.8489i	0.687324	+	0.499370i	−0.188456	+	0.982082i	$0.560348\pi$
$564$	2.83235	−	2.05783i	0.119264	−	0.0866501i
$565$	4.40251	−	6.08978i	0.185215	−	0.256199i
$566$	−26.6285	−	19.3467i	−1.11928	−	0.813203i
$567$	5.92322	+	18.2298i	0.248752	+	0.765580i
$568$	−2.93658			−0.123216
$569$	−7.98088	−	24.5626i	−0.334576	−	1.02972i	−0.966931	−	0.255040i	$-0.917911\pi$
$569$	−7.98088	−	24.5626i	−0.334576	−	1.02972i	0.632355	−	0.774679i	$-0.282089\pi$
$570$	−0.0214863	−	0.0294267i	−0.000899961	−	0.00123255i
$571$	5.33889	−	16.4314i	0.223426	−	0.687633i	−0.775022	−	0.631934i	$-0.782261\pi$
$571$	5.33889	−	16.4314i	0.223426	−	0.687633i	0.998448	−	0.0556990i	$-0.0177387\pi$
$572$	−4.21820	+	12.9823i	−0.176372	+	0.542817i
$573$	3.42011	−	2.48486i	0.142877	−	0.103806i
$574$	−20.8634			−0.870823
$575$	13.5580	−	9.94876i	0.565406	−	0.414892i
$576$	19.5649			0.815203
$577$	−9.37776	+	6.81334i	−0.390401	+	0.283643i	−0.765620	−	0.643293i	$-0.777568\pi$
$577$	−9.37776	+	6.81334i	−0.390401	+	0.283643i	0.375219	+	0.926936i	$0.377568\pi$
$578$	−0.604885	+	1.86165i	−0.0251599	+	0.0774342i
$579$	0.646664	−	1.99023i	0.0268744	−	0.0827110i
$580$	21.5149	−	29.7605i	0.893358	−	1.23574i
$581$	−7.40949	−	22.8041i	−0.307398	−	0.946072i
$582$	−5.85099			−0.242531
$583$	0.528633	+	1.62696i	0.0218937	+	0.0673820i
$584$	−0.662411	−	0.481270i	−0.0274107	−	0.0199151i
$585$	40.3271	−	13.2086i	1.66732	−	0.546109i
$586$	8.92608	−	6.48518i	0.368733	−	0.267900i
$587$	14.7545	+	10.7198i	0.608983	+	0.442452i	0.849056	−	0.528303i	$-0.177171\pi$
$587$	14.7545	+	10.7198i	0.608983	+	0.442452i	−0.240073	+	0.970755i	$0.577171\pi$
$588$	0.596436	+	0.433336i	0.0245966	+	0.0178705i
$589$	−0.231707	+	0.168345i	−0.00954733	+	0.00693654i
$590$	0.0673879	+	28.4904i	0.00277432	+	1.17293i
$591$	−1.11123	−	0.807354i	−0.0457098	−	0.0332101i
$592$	6.94312	+	21.3687i	0.285360	+	0.878249i
$593$	38.7818			1.59258			0.796288	−	0.604917i	$-0.206794\pi$
$593$	38.7818			1.59258			0.796288	+	0.604917i	$0.206794\pi$
$594$	−0.797265	−	2.45373i	−0.0327122	−	0.100678i
$595$	4.69429	−	1.53755i	0.192447	−	0.0630335i
$596$	8.24734	−	25.3827i	0.337824	−	1.03972i
$597$	−1.07161	+	3.29808i	−0.0438582	+	0.134982i
$598$	34.1024	−	24.7769i	1.39455	−	1.01320i
$599$	−20.5456			−0.839470			−0.419735	−	0.907647i	$-0.637877\pi$
$599$	−20.5456			−0.839470			−0.419735	+	0.907647i	$0.637877\pi$
$600$	−0.312914	+	0.00148027i	−0.0127747	+	6.04318e-5i
$601$	−30.1229			−1.22874			−0.614369	−	0.789019i	$-0.710589\pi$
$601$	−30.1229			−1.22874			−0.614369	+	0.789019i	$0.710589\pi$
$602$	−21.8703	+	15.8897i	−0.891368	+	0.647617i
$603$	3.48726	−	10.7327i	0.142012	−	0.437068i
$604$	−5.81684	+	17.9024i	−0.236684	+	0.728439i
$605$	−20.5274	−	6.61612i	−0.834557	−	0.268983i
$606$	−1.83157	−	5.63701i	−0.0744026	−	0.228988i
$607$	−3.36579			−0.136613			−0.0683066	−	0.997664i	$-0.521760\pi$
$607$	−3.36579			−0.136613			−0.0683066	+	0.997664i	$0.521760\pi$
$608$	−0.105329	−	0.324168i	−0.00427164	−	0.0131468i
$609$	−3.04260	−	2.21058i	−0.123292	−	0.0895772i
$610$	−4.82247	−	1.55431i	−0.195256	−	0.0629324i
$611$	52.1472	−	37.8872i	2.10965	−	1.53275i
$612$	−4.39199	−	3.19097i	−0.177536	−	0.128987i
$613$	−20.6581	−	15.0090i	−0.834372	−	0.606207i	0.0864211	−	0.996259i	$-0.472457\pi$
$613$	−20.6581	−	15.0090i	−0.834372	−	0.606207i	−0.920793	+	0.390052i	$0.872457\pi$
$614$	51.6618	−	37.5345i	2.08490	−	1.51477i
$615$	−1.20795	−	1.65436i	−0.0487093	−	0.0667102i
$616$	0.685677	+	0.498174i	0.0276267	+	0.0200720i
$617$	−7.51360	−	23.1245i	−0.302486	−	0.930956i	−0.980603	−	0.196003i	$-0.937204\pi$
$617$	−7.51360	−	23.1245i	−0.302486	−	0.930956i	0.678117	−	0.734954i	$-0.262796\pi$
$618$	5.65195			0.227355
$619$	0.120572	+	0.371082i	0.00484619	+	0.0149150i	0.953450	−	0.301550i	$-0.0975040\pi$
$619$	0.120572	+	0.371082i	0.00484619	+	0.0149150i	−0.948604	+	0.316465i	$0.897504\pi$
$620$	−0.0632818	−	26.7544i	−0.00254146	−	1.07448i
$621$	−1.17689	+	3.62210i	−0.0472271	+	0.145350i
$622$	10.9502	−	33.7014i	0.439065	−	1.35130i
$623$	8.68350	−	6.30893i	0.347897	−	0.252762i
$624$	−5.23772			−0.209677
$625$	24.9989	−	0.236524i	0.999955	−	0.00946097i
$626$	18.2709			0.730254
$627$	−0.00783892	+	0.00569531i	−0.000313056	+	0.000227449i
$628$	−13.3258	+	41.0127i	−0.531759	+	1.63659i
$629$	1.61152	−	4.95975i	0.0642555	−	0.197758i
$630$	0.0677863	+	28.6589i	0.00270067	+	1.14180i
$631$	−3.85948	−	11.8783i	−0.153644	−	0.472866i	0.844377	−	0.535749i	$-0.179971\pi$
$631$	−3.85948	−	11.8783i	−0.153644	−	0.472866i	−0.998021	+	0.0628825i	$0.979971\pi$
$632$	2.42139			0.0963175
$633$	−0.138188	−	0.425299i	−0.00549248	−	0.0169041i
$634$	−5.02073	−	3.64777i	−0.199399	−	0.144872i
$635$	−5.88165	−	8.05526i	−0.233406	−	0.319663i
$636$	0.413499	−	0.300424i	0.0163963	−	0.0119126i
$637$	10.9811	+	7.97826i	0.435088	+	0.316110i
$638$	−16.5276	−	12.0080i	−0.654335	−	0.475402i
$639$	−21.3630	+	15.5212i	−0.845109	+	0.614008i
$640$	−5.59214	−	1.80239i	−0.221049	−	0.0712455i
$641$	−15.3586	−	11.1587i	−0.606630	−	0.440742i	0.241596	−	0.970377i	$-0.422329\pi$
$641$	−15.3586	−	11.1587i	−0.606630	−	0.440742i	−0.848226	+	0.529635i	$0.822329\pi$
$642$	0.857481	+	2.63905i	0.0338421	+	0.104155i
$643$	−31.4802			−1.24146			−0.620729	−	0.784025i	$-0.713163\pi$
$643$	−31.4802			−1.24146			−0.620729	+	0.784025i	$0.713163\pi$
$644$	4.20529	+	12.9425i	0.165712	+	0.510008i
$645$	−2.52622	−	0.814217i	−0.0994698	−	0.0320598i
$646$	−0.0265201	+	0.0816206i	−0.00104342	+	0.00321132i
$647$	−4.50280	+	13.8582i	−0.177023	+	0.544822i	−0.999720	−	0.0236586i	$-0.992469\pi$
$647$	−4.50280	+	13.8582i	−0.177023	+	0.544822i	0.822697	+	0.568480i	$0.192469\pi$
$648$	−2.31380	+	1.68108i	−0.0908947	+	0.0660389i
$649$	7.57646			0.297402
$650$	62.6651	−	0.296443i	2.45793	−	0.0116275i
$651$	−2.73997			−0.107388
$652$	30.6719	−	22.2844i	1.20120	−	0.872725i
$653$	6.05031	−	18.6209i	0.236767	−	0.728694i	−0.760115	−	0.649788i	$-0.774857\pi$
$653$	6.05031	−	18.6209i	0.236767	−	0.728694i	0.996882	−	0.0789054i	$-0.0251425\pi$
$654$	0.836908	−	2.57574i	0.0327257	−	0.100719i
$655$	35.7447	−	11.7077i	1.39666	−	0.457458i
$656$	−6.42366	−	19.7700i	−0.250802	−	0.771889i
$657$	−7.36265			−0.287244
$658$	13.4521	+	41.4013i	0.524417	+	1.61399i
$659$	−13.2870	−	9.65359i	−0.517589	−	0.376050i	0.298106	−	0.954533i	$-0.403645\pi$
$659$	−13.2870	−	9.65359i	−0.517589	−	0.376050i	−0.815695	+	0.578482i	$0.803645\pi$
$660$	−0.00214090	−	0.905133i	−8.33343e−5	−	0.0352323i
$661$	−24.6531	+	17.9115i	−0.958895	+	0.696678i	−0.952894	−	0.303304i	$-0.901910\pi$
$661$	−24.6531	+	17.9115i	−0.958895	+	0.696678i	−0.00600104	+	0.999982i	$0.501910\pi$
$662$	−7.85192	−	5.70475i	−0.305174	−	0.221722i
$663$	0.983516	+	0.714566i	0.0381966	+	0.0277515i
$664$	2.89439	−	2.10290i	0.112324	−	0.0816082i
$665$	0.205813	−	0.0674113i	0.00798108	−	0.00261410i
$666$	24.4778	+	17.7842i	0.948496	+	0.689123i
$667$	9.31900	+	28.6809i	0.360833	+	1.11053i
$668$	−23.8667			−0.923431
$669$	1.51024	+	4.64805i	0.0583893	+	0.179704i
$670$	9.76354	−	13.5054i	0.377199	−	0.521760i
$671$	−0.416370	+	1.28146i	−0.0160738	+	0.0494700i
$672$	1.00765	−	3.10123i	0.0388710	−	0.119633i
$673$	37.5146	−	27.2560i	1.44608	−	1.05064i	0.459356	−	0.888252i	$-0.348080\pi$
$673$	37.5146	−	27.2560i	1.44608	−	1.05064i	0.986727	−	0.162388i	$-0.0519197\pi$
$674$	55.8375			2.15078
$675$	−4.56473	+	3.34958i	−0.175697	+	0.128925i
$676$	51.2776			1.97222
$677$	29.4592	−	21.4034i	1.13221	−	0.822598i	0.146195	−	0.989256i	$-0.453297\pi$
$677$	29.4592	−	21.4034i	1.13221	−	0.822598i	0.986015	+	0.166658i	$0.0532974\pi$
$678$	−0.385959	+	1.18786i	−0.0148227	+	0.0456194i
$679$	10.7468	−	33.0754i	0.412426	−	1.26932i
$680$	0.434631	+	0.595252i	0.0166673	+	0.0228269i
$681$	−0.241863	−	0.744378i	−0.00926821	−	0.0285246i
$682$	−14.8837			−0.569927
$683$	−14.3276	−	44.0959i	−0.548231	−	1.68728i	−0.713182	−	0.700979i	$-0.752746\pi$
$683$	−14.3276	−	44.0959i	−0.548231	−	1.68728i	0.164951	−	0.986302i	$-0.447254\pi$
$684$	−0.192559	−	0.139903i	−0.00736269	−	0.00534931i
$685$	5.57194	−	7.70739i	0.212893	−	0.294484i
$686$	−31.9046	+	23.1800i	−1.21812	+	0.885017i
$687$	2.11327	+	1.53538i	0.0806264	+	0.0585785i
$688$	−21.7906	−	15.8318i	−0.830760	−	0.603582i
$689$	7.61303	−	5.53119i	0.290033	−	0.210722i
$690$	−1.63756	+	2.26516i	−0.0623409	+	0.0862330i
$691$	24.5348	+	17.8256i	0.933348	+	0.678117i	0.946810	−	0.321792i	$-0.104285\pi$
$691$	24.5348	+	17.8256i	0.933348	+	0.678117i	−0.0134621	+	0.999909i	$0.504285\pi$
$692$	2.34425	+	7.21487i	0.0891152	+	0.274268i
$693$	7.62125			0.289507
$694$	18.4272	+	56.7130i	0.699485	+	2.15279i
$695$	−2.31456	−	3.16992i	−0.0877961	−	0.120242i
$696$	0.173405	−	0.533687i	0.00657292	−	0.0202294i
$697$	−1.49095	+	4.58868i	−0.0564739	+	0.173809i
$698$	2.83807	−	2.06198i	0.107423	−	0.0780470i
$699$	0.275098			0.0104052
$700$	−6.16062	+	19.2701i	−0.232850	+	0.728343i
$701$	0.433045			0.0163559			0.00817793	−	0.999967i	$-0.497397\pi$
$701$	0.433045			0.0163559			0.00817793	+	0.999967i	$0.497397\pi$
$702$	−11.4817	+	8.34194i	−0.433349	+	0.314846i
$703$	0.0706543	−	0.217452i	0.00266478	−	0.00820135i
$704$	2.37427	−	7.30726i	0.0894837	−	0.275403i
$705$	−2.50405	+	3.46373i	−0.0943080	+	0.130452i
$706$	4.54165	+	13.9778i	0.170927	+	0.526060i
$707$	35.2299			1.32496
$708$	−0.699509	−	2.15287i	−0.0262892	−	0.0809097i
$709$	−27.8044	−	20.2011i	−1.04422	−	0.758667i	−0.0731118	−	0.997324i	$-0.523293\pi$
$709$	−27.8044	−	20.2011i	−1.04422	−	0.758667i	−0.971104	+	0.238657i	$0.923293\pi$
$710$	−37.0580	+	12.1378i	−1.39076	+	0.455525i
$711$	17.6151	−	12.7981i	0.660619	−	0.479968i
$712$	1.29565	+	0.941345i	0.0485565	+	0.0352784i
$713$	17.7747	+	12.9141i	0.665669	+	0.483637i
$714$	−0.664225	+	0.482588i	−0.0248580	+	0.0180604i
$715$	−0.0394166	−	16.6646i	−0.00147410	−	0.623222i
$716$	−30.0971	−	21.8668i	−1.12478	−	0.817202i
$717$	0.506264	+	1.55812i	0.0189068	+	0.0581891i
$718$	−48.6067			−1.81399
$719$	6.65199	+	20.4727i	0.248078	+	0.763504i	0.995115	+	0.0987222i	$0.0314755\pi$
$719$	6.65199	+	20.4727i	0.248078	+	0.763504i	−0.747037	+	0.664782i	$0.768524\pi$
$720$	−27.1360	+	8.88803i	−1.01130	+	0.331237i
$721$	−10.3812	+	31.9502i	−0.386618	+	1.18989i
$722$	11.4917	−	35.3677i	0.427675	−	1.31625i
$723$	3.26566	−	2.37264i	0.121451	−	0.0882396i
$724$	−1.94250			−0.0721924
$725$	−13.6521	+	42.7030i	−0.507025	+	1.58595i
$726$	3.58471			0.133041
$727$	3.28659	−	2.38785i	0.121893	−	0.0885604i	−0.525168	−	0.850998i	$-0.675998\pi$
$727$	3.28659	−	2.38785i	0.121893	−	0.0885604i	0.647061	+	0.762438i	$0.275998\pi$
$728$	1.44070	−	4.43401i	0.0533958	−	0.164335i
$729$	−7.74790	+	23.8456i	−0.286959	+	0.883170i
$730$	−10.3485	−	3.33539i	−0.383015	−	0.123448i
$731$	1.93186	+	5.94566i	0.0714525	+	0.219908i
$732$	0.402570			0.0148794
$733$	−14.6774	−	45.1724i	−0.542122	−	1.66848i	−0.727736	−	0.685858i	$-0.759427\pi$
$733$	−14.6774	−	45.1724i	−0.542122	−	1.66848i	0.185613	−	0.982623i	$-0.440573\pi$
$734$	−5.11123	−	3.71353i	−0.188659	−	0.137069i
$735$	−0.856637	−	0.276100i	−0.0315975	−	0.0101841i
$736$	−21.1537	+	15.3690i	−0.779734	+	0.566510i
$737$	−3.58534	−	2.60490i	−0.132068	−	0.0959527i
$738$	−22.6465	−	16.4536i	−0.833629	−	0.605667i
$739$	−5.37874	+	3.90788i	−0.197860	+	0.143754i	−0.682304	−	0.731068i	$-0.739022\pi$
$739$	−5.37874	+	3.90788i	−0.197860	+	0.143754i	0.484444	+	0.874822i	$0.339022\pi$
$740$	12.5951	+	17.2497i	0.463004	+	0.634111i
$741$	0.0431206	+	0.0313289i	0.00158407	+	0.00115090i
$742$	1.96389	+	6.04422i	0.0720965	+	0.221890i
$743$	16.6415			0.610516			0.305258	−	0.952270i	$-0.401257\pi$
$743$	16.6415			0.610516			0.305258	+	0.952270i	$0.401257\pi$
$744$	−0.126334	−	0.388817i	−0.00463164	−	0.0142547i
$745$	0.0770665	+	32.5823i	0.00282350	+	1.19372i
$746$	−3.81177	+	11.7314i	−0.139559	+	0.429518i
$747$	9.94136	−	30.5964i	0.363735	−	1.11946i
$748$	−1.72478	+	1.25312i	−0.0630640	+	0.0458187i
$749$	−16.4934			−0.602657
$750$	−3.94269	+	1.31206i	−0.143967	+	0.0479096i
$751$	5.06441			0.184803			0.0924015	−	0.995722i	$-0.470546\pi$
$751$	5.06441			0.184803			0.0924015	+	0.995722i	$0.470546\pi$
$752$	−35.0897	+	25.4941i	−1.27959	+	0.929676i
$753$	1.31207	−	4.03813i	0.0478144	−	0.147158i
$754$	−34.7267	+	106.878i	−1.26467	+	3.89226i
$755$	−0.0543549	−	22.9803i	−0.00197818	−	0.836339i
$756$	−1.41585	−	4.35753i	−0.0514939	−	0.158482i
$757$	−13.9677			−0.507665			−0.253833	−	0.967248i	$-0.581691\pi$
$757$	−13.9677			−0.507665			−0.253833	+	0.967248i	$0.581691\pi$
$758$	16.5138	+	50.8243i	0.599809	+	1.84602i
$759$	0.601340	+	0.436899i	0.0218273	+	0.0158584i
$760$	0.0190556	+	0.0260978i	0.000691221	+	0.000946667i
$761$	0.150673	−	0.109470i	0.00546188	−	0.00396829i	−0.585051	−	0.810997i	$-0.698926\pi$
$761$	0.150673	−	0.109470i	0.00546188	−	0.00396829i	0.590513	+	0.807028i	$0.298926\pi$
$762$	1.34118	+	0.974425i	0.0485858	+	0.0352997i
$763$	13.0233	+	9.46200i	0.471476	+	0.342547i
$764$	32.9928	−	23.9707i	1.19364	−	0.867229i
$765$	6.30804	+	2.03312i	0.228068	+	0.0735078i
$766$	29.1498	+	21.1786i	1.05323	+	0.765213i
$767$	−12.8788	−	39.6370i	−0.465028	−	1.43121i
$768$	3.48319			0.125689
$769$	−11.6782	−	35.9418i	−0.421127	−	1.29609i	−0.906655	−	0.421874i	$-0.861373\pi$
$769$	−11.6782	−	35.9418i	−0.421127	−	1.29609i	0.485528	−	0.874221i	$-0.338627\pi$
$770$	10.7120	+	3.45254i	0.386033	+	0.124421i
$771$	1.17039	−

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.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.58361 - 1.15056i) q^{2} +(0.0586727 - 0.180576i) q^{3} +(0.565999 - 1.74196i) q^{4} +(0.00528892 + 2.23606i) q^{5} +(-0.114849 - 0.353468i) q^{6} +2.20909 q^{7} +(0.101857 + 0.313482i) q^{8} +(2.39789 + 1.74217i) q^{9} +(2.58110 + 3.53497i) q^{10} +(0.941672 - 0.684165i) q^{11} +(-0.281348 - 0.204412i) q^{12} +(-5.17998 - 3.76347i) q^{13} +(3.49834 - 2.54169i) q^{14} +(0.404089 + 0.130241i) q^{15} +(3.48559 + 2.53243i) q^{16} +(-0.309017 - 0.951057i) q^{17} +5.80178 q^{18} +(-0.0135483 - 0.0416974i) q^{19} +(3.89813 + 1.25639i) q^{20} +(0.129613 - 0.398909i) q^{21} +(0.704069 - 2.16690i) q^{22} +(-2.72097 + 1.97690i) q^{23} +0.0625835 q^{24} +(-4.99994 + 0.0236527i) q^{25} -12.5332 q^{26} +(0.916105 - 0.665589i) q^{27} +(1.25034 - 3.84816i) q^{28} +(2.77078 - 8.52759i) q^{29} +(0.789770 - 0.258679i) q^{30} +(-2.01865 - 6.21277i) q^{31} +7.77430 q^{32} +(-0.0682933 - 0.210185i) q^{33} +(-1.58361 - 1.15056i) q^{34} +(0.0116837 + 4.93966i) q^{35} +(4.39199 - 3.19097i) q^{36} +(4.21902 + 3.06529i) q^{37} +(-0.0694307 - 0.0504443i) q^{38} +(-0.983516 + 0.714566i) q^{39} +(-0.700427 + 0.229415i) q^{40} +(-3.90337 - 2.83596i) q^{41} +(-0.253712 - 0.780844i) q^{42} -6.25163 q^{43} +(-0.658806 - 2.02760i) q^{44} +(-3.88291 + 5.37103i) q^{45} +(-2.03442 + 6.26129i) q^{46} +(-3.11090 + 9.57436i) q^{47} +(0.661805 - 0.480829i) q^{48} -2.11992 q^{49} +(-7.89075 + 5.79019i) q^{50} -0.189869 q^{51} +(-9.48770 + 6.89322i) q^{52} +(-0.454163 + 1.39777i) q^{53} +(0.684953 - 2.10807i) q^{54} +(1.53481 + 2.10202i) q^{55} +(0.225010 + 0.692511i) q^{56} -0.00832447 q^{57} +(-5.42367 - 16.6923i) q^{58} +(5.26601 + 3.82598i) q^{59} +(0.455589 - 0.630193i) q^{60} +(-0.936511 + 0.680415i) q^{61} +(-10.3449 - 7.51603i) q^{62} +(5.29715 + 3.84860i) q^{63} +(5.34028 - 3.87994i) q^{64} +(8.38796 - 11.6027i) q^{65} +(-0.349981 - 0.254276i) q^{66} +(-1.17656 - 3.62107i) q^{67} -1.83161 q^{68} +(0.197334 + 0.607333i) q^{69} +(5.70188 + 7.80906i) q^{70} +(-2.75307 + 8.47307i) q^{71} +(-0.301898 + 0.929146i) q^{72} +(-2.00965 + 1.46010i) q^{73} +10.2081 q^{74} +(-0.289089 + 0.904257i) q^{75} -0.0803038 q^{76} +(2.08024 - 1.51138i) q^{77} +(-0.735355 + 2.26319i) q^{78} +(2.27007 - 6.98657i) q^{79} +(-5.64423 + 7.80739i) q^{80} +(2.68129 + 8.25217i) q^{81} -9.44436 q^{82} +(-3.35409 - 10.3228i) q^{83} +(-0.621524 - 0.451564i) q^{84} +(2.12499 - 0.696011i) q^{85} +(-9.90015 + 7.19288i) q^{86} +(-1.37731 - 1.00067i) q^{87} +(0.310389 + 0.225511i) q^{88} +(3.93080 - 2.85589i) q^{89} +(0.0306852 + 12.9731i) q^{90} +(-11.4430 - 8.31386i) q^{91} +(1.90363 + 5.85877i) q^{92} -1.24032 q^{93} +(6.08942 + 18.7413i) q^{94} +(0.0931664 - 0.0305154i) q^{95} +(0.456139 - 1.40385i) q^{96} +(4.86483 - 14.9724i) q^{97} +(-3.35713 + 2.43909i) q^{98} +3.44995 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 17 q^{6} - 44 q^{7} + 15 q^{8} - 22 q^{9} - 2 q^{10} + 4 q^{11} + 14 q^{12} + 6 q^{13} - 10 q^{14} + 14 q^{15} - 32 q^{16} + 20 q^{17} - 62 q^{18} - 3 q^{19} + 16 q^{21}+ \cdots + 76 q^{99}+O(q^{100}) \) 80 * q + 2 * q^2 + 2 * q^3 - 20 * q^4 - 17 * q^6 - 44 * q^7 + 15 * q^8 - 22 * q^9 - 2 * q^10 + 4 * q^11 + 14 * q^12 + 6 * q^13 - 10 * q^14 + 14 * q^15 - 32 * q^16 + 20 * q^17 - 62 * q^18 - 3 * q^19 + 16 * q^21 + 17 * q^22 - 5 * q^23 + 30 * q^24 - 14 * q^25 + 18 * q^26 + 17 * q^27 + 32 * q^28 + 20 * q^29 - 114 * q^30 - 21 * q^31 - 88 * q^32 - 2 * q^34 - 2 * q^35 + 47 * q^36 + 6 * q^37 + 22 * q^38 - 46 * q^39 + 59 * q^40 - 26 * q^41 - 3 * q^42 - 102 * q^43 - 44 * q^44 + 74 * q^45 + 2 * q^46 + 2 * q^47 + 72 * q^48 + 108 * q^49 + 7 * q^50 + 18 * q^51 + 65 * q^52 - 18 * q^53 - 29 * q^54 - 49 * q^55 - 117 * q^56 + 2 * q^57 + 42 * q^58 + 21 * q^59 + 112 * q^60 + 4 * q^61 + 15 * q^62 + 41 * q^63 - 11 * q^64 + 8 * q^65 - 156 * q^66 + 21 * q^67 - 80 * q^68 - 67 * q^69 + 32 * q^70 - 4 * q^71 + 83 * q^72 - 2 * q^73 + 78 * q^74 - 68 * q^75 + 16 * q^76 + 2 * q^77 - 2 * q^78 - 53 * q^79 - 54 * q^80 - 21 * q^81 - 72 * q^82 - 42 * q^83 - 52 * q^84 + 42 * q^86 - 8 * q^87 + 68 * q^88 - 73 * q^89 + 97 * q^90 - 83 * q^91 + 117 * q^92 - 120 * q^93 + 80 * q^94 + 16 * q^95 + 88 * q^96 + 57 * q^97 + 17 * q^98 + 76 * q^99

Introduction

L-functions

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