LMFDB - Embedded newform 260.2.bg.c.23.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(23,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 10]))

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

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

chi := DirichletCharacter("260.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bg (of order $12$, 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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.11
Character	$\chi$	$=$	260.23
Dual form			260.2.bg.c.147.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.932110 - 1.06357i) q^{2} +(-0.450342 - 0.120669i) q^{3} +(-0.262342 + 1.98272i) q^{4} +(-0.808965 - 2.08460i) q^{5} +(0.291429 + 0.591445i) q^{6} +(0.415219 + 1.54962i) q^{7} +(2.35328 - 1.56909i) q^{8} +(-2.40983 - 1.39132i) q^{9} +(-1.46307 + 2.80347i) q^{10} +(-2.40019 - 4.15725i) q^{11} +(0.357396 - 0.861246i) q^{12} +(-1.60047 + 3.23086i) q^{13} +(1.26109 - 1.88603i) q^{14} +(0.112764 + 1.03640i) q^{15} +(-3.86235 - 1.04030i) q^{16} +(0.599908 + 2.23889i) q^{17} +(0.766471 + 3.85987i) q^{18} +(-6.07130 - 3.50527i) q^{19} +(4.34541 - 1.05707i) q^{20} -0.747963i q^{21} +(-2.18427 + 6.42777i) q^{22} +(-3.64269 - 0.976056i) q^{23} +(-1.24912 + 0.422661i) q^{24} +(-3.69115 + 3.37274i) q^{25} +(4.92805 - 1.30931i) q^{26} +(1.90638 + 1.90638i) q^{27} +(-3.18139 + 0.416732i) q^{28} +(-0.166977 + 0.0964041i) q^{29} +(0.997173 - 1.08597i) q^{30} +3.30656 q^{31} +(2.49371 + 5.07754i) q^{32} +(0.579256 + 2.16181i) q^{33} +(1.82202 - 2.72493i) q^{34} +(2.89444 - 2.11915i) q^{35} +(3.39079 - 4.41301i) q^{36} +(1.87924 - 7.01341i) q^{37} +(1.93104 + 9.72452i) q^{38} +(1.11063 - 1.26187i) q^{39} +(-5.17466 - 3.63632i) q^{40} +(-6.13738 + 3.54342i) q^{41} +(-0.795507 + 0.697183i) q^{42} +(-0.137890 - 0.514614i) q^{43} +(8.87233 - 3.66828i) q^{44} +(-0.950876 + 6.14907i) q^{45} +(2.35729 + 4.78403i) q^{46} +(4.81724 - 4.81724i) q^{47} +(1.61385 + 0.934558i) q^{48} +(3.83327 - 2.21314i) q^{49} +(7.02769 + 0.782015i) q^{50} -1.08066i q^{51} +(-5.98603 - 4.02088i) q^{52} +(-6.78706 - 6.78706i) q^{53} +(0.250604 - 3.80451i) q^{54} +(-6.72455 + 8.36651i) q^{55} +(3.40863 + 2.99517i) q^{56} +(2.31119 + 2.31119i) q^{57} +(0.258173 + 0.0877316i) q^{58} +(0.551432 + 0.318370i) q^{59} +(-2.08448 - 0.0483125i) q^{60} +(2.22021 - 3.84551i) q^{61} +(-3.08208 - 3.51675i) q^{62} +(1.15540 - 4.31202i) q^{63} +(3.07589 - 7.38505i) q^{64} +(8.02980 + 0.722701i) q^{65} +(1.75930 - 2.63112i) q^{66} +(12.2192 + 3.27413i) q^{67} +(-4.59647 + 0.602095i) q^{68} +(1.52268 + 0.879118i) q^{69} +(-4.95180 - 1.10315i) q^{70} +(7.79147 - 13.4952i) q^{71} +(-7.85412 + 0.507089i) q^{72} +(4.70372 - 4.70372i) q^{73} +(-9.21087 + 4.53857i) q^{74} +(2.06927 - 1.07348i) q^{75} +(8.54272 - 11.1181i) q^{76} +(5.44554 - 5.44554i) q^{77} +(-2.37730 - 0.00502400i) q^{78} -8.99039 q^{79} +(0.955888 + 8.89305i) q^{80} +(3.54546 + 6.14092i) q^{81} +(9.48937 + 3.22465i) q^{82} +(1.89595 + 1.89595i) q^{83} +(1.48300 + 0.196222i) q^{84} +(4.18189 - 3.06175i) q^{85} +(-0.418797 + 0.626332i) q^{86} +(0.0868297 - 0.0232660i) q^{87} +(-12.1714 - 6.01706i) q^{88} +(5.76138 + 9.97900i) q^{89} +(7.42625 - 4.72029i) q^{90} +(-5.67115 - 1.13861i) q^{91} +(2.89088 - 6.96637i) q^{92} +(-1.48909 - 0.398999i) q^{93} +(-9.61365 - 0.633252i) q^{94} +(-2.39563 + 15.4919i) q^{95} +(-0.510321 - 2.58754i) q^{96} +(-12.9199 + 3.46187i) q^{97} +(-5.92684 - 2.01404i) q^{98} +13.3577i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 6 q^{2} - 12 q^{6} + 12 q^{10} - 12 q^{12} + 4 q^{13} - 12 q^{16} - 24 q^{17} - 42 q^{20} - 12 q^{22} - 24 q^{25} - 36 q^{26} - 6 q^{28} - 36 q^{32} - 12 q^{33} - 76 q^{36} + 48 q^{37} - 16 q^{38}+ \cdots - 162 q^{98}+O(q^{100}) $ 144 * q - 6 * q^2 - 12 * q^6 + 12 * q^10 - 12 * q^12 + 4 * q^13 - 12 * q^16 - 24 * q^17 - 42 * q^20 - 12 * q^22 - 24 * q^25 - 36 * q^26 - 6 * q^28 - 36 * q^32 - 12 * q^33 - 76 * q^36 + 48 * q^37 - 16 * q^38 + 76 * q^40 - 72 * q^41 + 40 * q^42 - 120 * q^45 - 12 * q^46 - 40 * q^48 + 120 * q^50 - 10 * q^52 + 8 * q^53 - 20 * q^56 + 126 * q^58 + 16 * q^61 - 44 * q^62 + 32 * q^65 + 96 * q^66 - 64 * q^68 - 54 * q^72 - 12 * q^76 + 40 * q^77 - 100 * q^78 - 24 * q^80 - 32 * q^81 - 78 * q^82 - 24 * q^85 - 10 * q^88 - 8 * q^90 + 100 * q^92 - 48 * q^93 - 12 * q^97 - 162 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.932110	−	1.06357i	−0.659101	−	0.752054i
$2$	−0.932110	−	1.06357i	−0.659101	−	0.752054i
$3$	−0.450342	−	0.120669i	−0.260005	−	0.0696682i	0.126462	−	0.991972i	$-0.459638\pi$
$3$	−0.450342	−	0.120669i	−0.260005	−	0.0696682i	−0.386467	+	0.922303i	$0.626305\pi$
$4$	−0.262342	+	1.98272i	−0.131171	+	0.991360i
$5$	−0.808965	−	2.08460i	−0.361780	−	0.932264i
$5$	−0.808965	−	2.08460i	−0.361780	−	0.932264i
$6$	0.291429	+	0.591445i	0.118976	+	0.241456i
$7$	0.415219	+	1.54962i	0.156938	+	0.585701i	0.998932	+	0.0462131i	$0.0147153\pi$
$7$	0.415219	+	1.54962i	0.156938	+	0.585701i	−0.841994	+	0.539488i	$0.818618\pi$
$8$	2.35328	−	1.56909i	0.832011	−	0.554759i
$9$	−2.40983	−	1.39132i	−0.803276	−	0.463772i
$10$	−1.46307	+	2.80347i	−0.462663	+	0.886534i
$11$	−2.40019	−	4.15725i	−0.723684	−	1.25346i	−0.959513	−	0.281663i	$-0.909114\pi$
$11$	−2.40019	−	4.15725i	−0.723684	−	1.25346i	0.235829	−	0.971794i	$-0.424219\pi$
$12$	0.357396	−	0.861246i	0.103171	−	0.248620i
$13$	−1.60047	+	3.23086i	−0.443892	+	0.896080i
$13$	−1.60047	+	3.23086i	−0.443892	+	0.896080i
$14$	1.26109	−	1.88603i	0.337041	−	0.504062i
$15$	0.112764	+	1.03640i	0.0291156	+	0.267598i
$16$	−3.86235	−	1.04030i	−0.965588	−	0.260076i
$17$	0.599908	+	2.23889i	0.145499	+	0.543010i	0.999733	+	0.0231206i	$0.00736018\pi$
$17$	0.599908	+	2.23889i	0.145499	+	0.543010i	−0.854234	+	0.519889i	$0.825973\pi$
$18$	0.766471	+	3.85987i	0.180659	+	0.909780i
$19$	−6.07130	−	3.50527i	−1.39285	−	0.804163i	−0.399222	−	0.916854i	$-0.630720\pi$
$19$	−6.07130	−	3.50527i	−1.39285	−	0.804163i	−0.993630	+	0.112691i	$0.964053\pi$
$20$	4.34541	−	1.05707i	0.971664	−	0.236368i
$21$		−	0.747963i		−	0.163219i
$22$	−2.18427	+	6.42777i	−0.465687	+	1.37040i
$23$	−3.64269	−	0.976056i	−0.759553	−	0.203522i	−0.141802	−	0.989895i	$-0.545290\pi$
$23$	−3.64269	−	0.976056i	−0.759553	−	0.203522i	−0.617751	+	0.786373i	$0.711956\pi$
$24$	−1.24912	+	0.422661i	−0.254976	+	0.0862754i
$25$	−3.69115	+	3.37274i	−0.738231	+	0.674549i
$26$	4.92805	−	1.30931i	0.966471	−	0.256777i
$27$	1.90638	+	1.90638i	0.366883	+	0.366883i
$28$	−3.18139	+	0.416732i	−0.601226	+	0.0787550i
$29$	−0.166977	+	0.0964041i	−0.0310068	+	0.0179018i	−0.515423	−	0.856936i	$-0.672365\pi$
$29$	−0.166977	+	0.0964041i	−0.0310068	+	0.0179018i	0.484416	+	0.874838i	$0.339032\pi$
$30$	0.997173	−	1.08597i	0.182058	−	0.198271i
$31$	3.30656			0.593876			0.296938	−	0.954897i	$-0.404034\pi$
$31$	3.30656			0.593876			0.296938	+	0.954897i	$0.404034\pi$
$32$	2.49371	+	5.07754i	0.440829	+	0.897591i
$33$	0.579256	+	2.16181i	0.100836	+	0.376323i
$34$	1.82202	−	2.72493i	0.312474	−	0.467322i
$35$	2.89444	−	2.11915i	0.489250	−	0.358202i
$36$	3.39079	−	4.41301i	0.565131	−	0.735502i
$37$	1.87924	−	7.01341i	0.308945	−	1.15300i	−0.620552	−	0.784165i	$-0.713091\pi$
$37$	1.87924	−	7.01341i	0.308945	−	1.15300i	0.929496	−	0.368831i	$-0.120242\pi$
$38$	1.93104	+	9.72452i	0.313256	+	1.57752i
$39$	1.11063	−	1.26187i	0.177842	−	0.202060i
$40$	−5.17466	−	3.63632i	−0.818186	−	0.574953i
$41$	−6.13738	+	3.54342i	−0.958498	+	0.553389i	−0.895710	−	0.444638i	$-0.853332\pi$
$41$	−6.13738	+	3.54342i	−0.958498	+	0.553389i	−0.0627875	+	0.998027i	$0.519999\pi$
$42$	−0.795507	+	0.697183i	−0.122749	+	0.107578i
$43$	−0.137890	−	0.514614i	−0.0210281	−	0.0784779i	0.954614	−	0.297844i	$-0.0962676\pi$
$43$	−0.137890	−	0.514614i	−0.0210281	−	0.0784779i	−0.975643	+	0.219366i	$0.929601\pi$
$44$	8.87233	−	3.66828i	1.33755	−	0.553014i
$45$	−0.950876	+	6.14907i	−0.141748	+	0.916649i
$46$	2.35729	+	4.78403i	0.347563	+	0.705367i
$47$	4.81724	−	4.81724i	0.702667	−	0.702667i	−0.262315	−	0.964982i	$-0.584486\pi$
$47$	4.81724	−	4.81724i	0.702667	−	0.702667i	0.964982	+	0.262315i	$0.0844860\pi$
$48$	1.61385	+	0.934558i	0.232939	+	0.134892i
$49$	3.83327	−	2.21314i	0.547610	−	0.316163i
$50$	7.02769	+	0.782015i	0.993866	+	0.110594i
$51$		−	1.08066i		−	0.151322i
$52$	−5.98603	−	4.02088i	−0.830112	−	0.557596i
$53$	−6.78706	−	6.78706i	−0.932275	−	0.932275i	0.0655732	−	0.997848i	$-0.479112\pi$
$53$	−6.78706	−	6.78706i	−0.932275	−	0.932275i	−0.997848	+	0.0655732i	$0.979112\pi$
$54$	0.250604	−	3.80451i	0.0341029	−	0.517729i
$55$	−6.72455	+	8.36651i	−0.906738	+	1.12814i
$56$	3.40863	+	2.99517i	0.455497	+	0.400247i
$57$	2.31119	+	2.31119i	0.306124	+	0.306124i
$58$	0.258173	+	0.0877316i	0.0338998	+	0.0115197i
$59$	0.551432	+	0.318370i	0.0717904	+	0.0414482i	0.535466	−	0.844557i	$-0.320136\pi$
$59$	0.551432	+	0.318370i	0.0717904	+	0.0414482i	−0.463675	+	0.886005i	$0.653470\pi$
$60$	−2.08448	−	0.0483125i	−0.269105	−	0.00623712i
$61$	2.22021	−	3.84551i	0.284268	−	0.492367i	−0.688163	−	0.725556i	$-0.741583\pi$
$61$	2.22021	−	3.84551i	0.284268	−	0.492367i	0.972431	+	0.233189i	$0.0749161\pi$
$62$	−3.08208	−	3.51675i	−0.391425	−	0.446627i
$63$	1.15540	−	4.31202i	0.145567	−	0.543263i
$64$	3.07589	−	7.38505i	0.384486	−	0.923131i
$65$	8.02980	+	0.722701i	0.995974	+	0.0896400i
$66$	1.75930	−	2.63112i	0.216555	−	0.323869i
$67$	12.2192	+	3.27413i	1.49282	+	0.399999i	0.910687	−	0.413097i	$-0.135553\pi$
$67$	12.2192	+	3.27413i	1.49282	+	0.399999i	0.582130	+	0.813096i	$0.302220\pi$
$68$	−4.59647	+	0.602095i	−0.557404	+	0.0730147i
$69$	1.52268	+	0.879118i	0.183309	+	0.105833i
$70$	−4.95180	−	1.10315i	−0.591853	−	0.131851i
$71$	7.79147	−	13.4952i	0.924678	−	1.60159i	0.132599	−	0.991170i	$-0.457668\pi$
$71$	7.79147	−	13.4952i	0.924678	−	1.60159i	0.792079	−	0.610419i	$-0.208999\pi$
$72$	−7.85412	+	0.507089i	−0.925616	+	0.0597611i
$73$	4.70372	−	4.70372i	0.550529	−	0.550529i	−0.376065	−	0.926593i	$-0.622723\pi$
$73$	4.70372	−	4.70372i	0.550529	−	0.550529i	0.926593	+	0.376065i	$0.122723\pi$
$74$	−9.21087	+	4.53857i	−1.07074	+	0.527599i
$75$	2.06927	−	1.07348i	0.238938	−	0.123955i
$76$	8.54272	−	11.1181i	0.979917	−	1.27533i
$77$	5.44554	−	5.44554i	0.620577	−	0.620577i
$78$	−2.37730	−	0.00502400i	−0.269177	−	0.000568856i
$79$	−8.99039			−1.01150			−0.505749	−	0.862681i	$-0.668784\pi$
$79$	−8.99039			−1.01150			−0.505749	+	0.862681i	$0.668784\pi$
$80$	0.955888	+	8.89305i	0.106872	+	0.994273i
$81$	3.54546	+	6.14092i	0.393940	+	0.682325i
$82$	9.48937	+	3.22465i	1.04793	+	0.356103i
$83$	1.89595	+	1.89595i	0.208107	+	0.208107i	0.803462	−	0.595355i	$-0.202989\pi$
$83$	1.89595	+	1.89595i	0.208107	+	0.208107i	−0.595355	+	0.803462i	$0.702989\pi$
$84$	1.48300	+	0.196222i	0.161809	+	0.0214096i
$85$	4.18189	−	3.06175i	0.453590	−	0.332094i
$86$	−0.418797	+	0.626332i	−0.0451600	+	0.0675391i
$87$	0.0868297	−	0.0232660i	0.00930912	−	0.00249437i
$88$	−12.1714	−	6.01706i	−1.29748	−	0.641421i
$89$	5.76138	+	9.97900i	0.610705	+	1.05777i	0.991122	+	0.132957i	$0.0424471\pi$
$89$	5.76138	+	9.97900i	0.610705	+	1.05777i	−0.380417	+	0.924815i	$0.624220\pi$
$90$	7.42625	−	4.72029i	0.782796	−	0.497562i
$91$	−5.67115	−	1.13861i	−0.594498	−	0.119359i
$92$	2.89088	−	6.96637i	0.301395	−	0.726294i
$93$	−1.48909	−	0.398999i	−0.154411	−	0.0413743i
$94$	−9.61365	−	0.633252i	−0.991572	−	0.0653150i
$95$	−2.39563	+	15.4919i	−0.245786	+	1.58943i
$96$	−0.510321	−	2.58754i	−0.0520844	−	0.264090i
$97$	−12.9199	+	3.46187i	−1.31182	+	0.351500i	−0.845906	−	0.533332i	$-0.820940\pi$
$97$	−12.9199	+	3.46187i	−1.31182	+	0.351500i	−0.465910	+	0.884832i	$0.654273\pi$
$98$	−5.92684	−	2.01404i	−0.598702	−	0.203449i
$99$			13.3577i			1.34250i
$100$	−5.71886	−	8.20333i	−0.571886	−	0.820333i
$101$	−3.46540	−	6.00225i	−0.344820	−	0.597246i	0.640501	−	0.767957i	$-0.278727\pi$
$101$	−3.46540	−	6.00225i	−0.344820	−	0.597246i	−0.985321	+	0.170711i	$0.945393\pi$
$102$	−1.14935	+	1.00729i	−0.113802	+	0.0997366i
$103$	0.448935	−	0.448935i	0.0442349	−	0.0442349i	−0.684643	−	0.728878i	$-0.740042\pi$
$103$	0.448935	−	0.448935i	0.0442349	−	0.0442349i	0.728878	+	0.684643i	$0.240042\pi$
$104$	1.30316	+	10.1144i	0.127785	+	0.991802i
$105$	−1.55921	+	0.605075i	−0.152163	+	0.0590493i
$106$	−0.892196	+	13.5448i	−0.0866577	+	1.31558i
$107$	−3.21016	+	11.9805i	−0.310338	+	1.15820i	0.617915	+	0.786245i	$0.287978\pi$
$107$	−3.21016	+	11.9805i	−0.310338	+	1.15820i	−0.928253	+	0.371951i	$0.878689\pi$
$108$	−4.27994	+	3.27969i	−0.411837	+	0.315589i
$109$	−4.26295			−0.408317			−0.204158	−	0.978938i	$-0.565446\pi$
$109$	−4.26295			−0.408317			−0.204158	+	0.978938i	$0.565446\pi$
$110$	15.1663	−	0.646508i	1.44605	−	0.0616421i
$111$	−1.69260	+	2.93167i	−0.160654	+	0.278262i
$112$	0.00834912	−	6.41713i	0.000788918	−	0.606361i
$113$	−2.01671	+	0.540375i	−0.189716	+	0.0508342i	−0.352426	−	0.935840i	$-0.614643\pi$
$113$	−2.01671	+	0.540375i	−0.189716	+	0.0508342i	0.162710	+	0.986674i	$0.447976\pi$
$114$	0.303818	−	4.61238i	0.0284552	−	0.431989i
$115$	0.912117	+	8.38316i	0.0850553	+	0.781734i
$116$	−0.147337	−	0.356359i	−0.0136799	−	0.0330871i
$117$	8.35202	−	5.55907i	0.772145	−	0.513936i
$118$	−0.175389	−	0.883240i	−0.0161458	−	0.0813088i
$119$	−3.22033	+	1.85926i	−0.295207	+	0.170438i
$120$	1.89158	+	2.26201i	0.172677	+	0.206492i
$121$	−6.02181	+	10.4301i	−0.547437	+	0.948189i
$122$	−6.15942	+	1.22310i	−0.557648	+	0.110735i
$123$	3.19150	−	0.855160i	0.287768	−	0.0771072i
$124$	−0.867451	+	6.55599i	−0.0778994	+	0.588745i
$125$	10.0168	+	4.96616i	0.895934	+	0.444187i
$126$	−5.66307	+	2.79043i	−0.504506	+	0.248591i
$127$	−5.31632	+	19.8408i	−0.471747	+	1.76058i	0.161742	+	0.986833i	$0.448289\pi$
$127$	−5.31632	+	19.8408i	−0.471747	+	1.76058i	−0.633489	+	0.773751i	$0.718378\pi$
$128$	−10.7215	+	3.61227i	−0.947660	+	0.319283i
$129$			0.248392i			0.0218697i
$130$	−6.71602	−	9.21385i	−0.589034	−	0.808108i
$131$		−	20.7668i		−	1.81441i	−0.420691	−	0.907204i	$-0.638212\pi$
$131$		−	20.7668i		−	1.81441i	0.420691	−	0.907204i	$-0.361788\pi$
$132$	−4.43823	+	0.581367i	−0.386298	+	0.0506015i
$133$	2.91091	−	10.8636i	0.252408	−	0.941998i
$134$	−7.90741	−	16.0478i	−0.683096	−	1.38632i
$135$	2.43185	−	5.51624i	0.209301	−	0.474762i
$136$	4.92478	+	4.32742i	0.422296	+	0.371074i
$137$	−6.46071	+	1.73114i	−0.551976	+	0.147901i	−0.524017	−	0.851708i	$-0.675567\pi$
$137$	−6.46071	+	1.73114i	−0.551976	+	0.147901i	−0.0279584	+	0.999609i	$0.508901\pi$
$138$	−0.484303	−	2.43890i	−0.0412266	−	0.207613i
$139$	1.31963	−	2.28566i	0.111929	−	0.193868i	−0.804619	−	0.593792i	$-0.797630\pi$
$139$	1.31963	−	2.28566i	0.111929	−	0.193868i	0.916548	+	0.399924i	$0.130964\pi$
$140$	3.44235	+	6.29481i	0.290932	+	0.532009i
$141$	−2.75070	+	1.58812i	−0.231651	+	0.133744i
$142$	−21.6156	+	4.29229i	−1.81394	+	0.360201i
$143$	17.2729	−	1.10111i	1.44444	−	0.0920798i
$144$	7.86022	+	7.88070i	0.655018	+	0.656725i
$145$	0.336043	+	0.270093i	0.0279068	+	0.0224300i
$146$	−9.38710	−	0.618330i	−0.776882	−	0.0511733i
$147$	−1.99334	+	0.534114i	−0.164408	+	0.0440530i
$148$	13.4126	+	5.56591i	1.10251	+	0.457515i
$149$	3.56464	−	6.17414i	0.292027	−	0.505805i	−0.682262	−	0.731108i	$-0.739004\pi$
$149$	3.56464	−	6.17414i	0.292027	−	0.505805i	0.974289	+	0.225302i	$0.0723370\pi$
$150$	−3.07050	−	1.20020i	−0.250705	−	0.0979957i
$151$	−8.04195			−0.654445			−0.327222	−	0.944947i	$-0.606113\pi$
$151$	−8.04195			−0.654445			−0.327222	+	0.944947i	$0.606113\pi$
$152$	−19.7876	+	1.27756i	−1.60498	+	0.103623i
$153$	1.66932	−	6.23000i	0.134957	−	0.503665i
$154$	−10.8675	−	0.715846i	−0.875731	−	0.0576845i
$155$	−2.67489	−	6.89288i	−0.214853	−	0.553649i
$156$	2.21056	+	2.53310i	0.176987	+	0.202810i
$157$	6.06353	−	6.06353i	0.483922	−	0.483922i	−0.422460	−	0.906382i	$-0.638833\pi$
$157$	6.06353	−	6.06353i	0.483922	−	0.483922i	0.906382	+	0.422460i	$0.138833\pi$
$158$	8.38003	+	9.56187i	0.666680	+	0.760702i
$159$	2.23751	+	3.87549i	0.177446	+	0.307346i
$160$	8.56734	−	9.30595i	0.677308	−	0.735700i
$161$		−	6.05005i		−	0.476811i
$162$	3.22651	−	9.49485i	0.253499	−	0.745986i
$163$	−11.6529	+	3.12238i	−0.912723	+	0.244563i	−0.684472	−	0.729039i	$-0.739967\pi$
$163$	−11.6529	+	3.12238i	−0.912723	+	0.244563i	−0.228251	+	0.973602i	$0.573301\pi$
$164$	−5.41551	−	13.0983i	−0.422880	−	1.02280i
$165$	4.03793	−	2.95635i	0.314352	−	0.230151i
$166$	0.249232	−	3.78369i	0.0193442	−	0.293671i
$167$	1.58671	+	0.425159i	0.122784	+	0.0328998i	0.319688	−	0.947523i	$-0.396422\pi$
$167$	1.58671	+	0.425159i	0.122784	+	0.0328998i	−0.196904	+	0.980423i	$0.563089\pi$
$168$	−1.17362	−	1.76017i	−0.0905470	−	0.135800i
$169$	−7.87697	−	10.3418i	−0.605920	−	0.795525i
$170$	−7.15436	−	1.59382i	−0.548714	−	0.122241i
$171$	9.75386	+	16.8942i	0.745897	+	1.29193i
$172$	1.05651	−	0.138393i	0.0805581	−	0.0105524i
$173$	−9.41180	+	2.52188i	−0.715566	+	0.191735i	−0.598192	−	0.801353i	$-0.704114\pi$
$173$	−9.41180	+	2.52188i	−0.715566	+	0.191735i	−0.117373	+	0.993088i	$0.537447\pi$
$174$	−0.105680	−	0.0706627i	−0.00801156	−	0.00535692i
$175$	−6.75910	−	4.31945i	−0.510940	−	0.326520i
$176$	4.94558	+	18.5537i	0.372787	+	1.39854i
$177$	−0.209916	−	0.209916i	−0.0157782	−	0.0157782i
$178$	5.24308	−	15.4291i	0.392985	−	1.15646i
$179$	2.36542	+	4.09703i	0.176800	+	0.306226i	0.940783	−	0.339010i	$-0.110092\pi$
$179$	2.36542	+	4.09703i	0.176800	+	0.306226i	−0.763983	+	0.645237i	$0.776759\pi$
$180$	−11.9424	−	3.49848i	−0.890135	−	0.260761i
$181$	20.1729			1.49944			0.749720	−	0.661755i	$-0.230188\pi$
$181$	20.1729			1.49944			0.749720	+	0.661755i	$0.230188\pi$
$182$	4.07515	+	7.09295i	0.302071	+	0.525764i
$183$	−1.46389	+	1.46389i	−0.108214	+	0.108214i
$184$	−10.1038	+	3.41879i	−0.744862	+	0.252036i
$185$	−16.1404	+	1.75613i	−1.18667	+	0.129113i
$186$	0.963629	+	1.95565i	0.0706567	+	0.143395i
$187$	7.86772	−	7.86772i	0.575345	−	0.575345i
$188$	8.28747	+	10.8150i	0.604426	+	0.788765i
$189$	−2.16260	+	3.74573i	−0.157306	+	0.272461i
$190$	18.7096	−	11.8922i	1.35734	−	0.862754i
$191$	−3.81826	−	2.20448i	−0.276280	−	0.159510i	0.355458	−	0.934692i	$-0.384325\pi$
$191$	−3.81826	−	2.20448i	−0.276280	−	0.159510i	−0.631738	+	0.775182i	$0.717658\pi$
$192$	−2.27635	+	2.95464i	−0.164281	+	0.213232i
$193$	5.89392	+	1.57927i	0.424254	+	0.113679i	0.464628	−	0.885506i	$-0.346188\pi$
$193$	5.89392	+	1.57927i	0.424254	+	0.113679i	−0.0403737	+	0.999185i	$0.512855\pi$
$194$	15.7247	+	10.5143i	1.12897	+	0.754882i
$195$	−3.52895	−	1.29441i	−0.252713	−	0.0926946i
$196$	3.38240	+	8.18089i	0.241600	+	0.584350i
$197$	2.62740	−	9.80560i	0.187195	−	0.698620i	−0.806955	−	0.590613i	$-0.798886\pi$
$197$	2.62740	−	9.80560i	0.187195	−	0.698620i	0.994150	−	0.108008i	$-0.0344472\pi$
$198$	14.2068	−	12.4508i	1.00963	−	0.884841i
$199$	2.12844	−	3.68657i	0.150881	−	0.261334i	−0.780670	−	0.624943i	$-0.785122\pi$
$199$	2.12844	−	3.68657i	0.150881	−	0.261334i	0.931552	+	0.363609i	$0.118456\pi$
$200$	−3.39418	+	13.7288i	−0.240005	+	0.970772i
$201$	−5.10775	−	2.94896i	−0.360273	−	0.208004i
$202$	−3.15365	+	9.28043i	−0.221890	+	0.652969i
$203$	−0.218722	−	0.218722i	−0.0153512	−	0.0153512i
$204$	2.14264	+	0.283502i	0.150015	+	0.0198491i
$205$	12.3516	+	9.92751i	0.862670	+	0.693368i
$206$	−0.895928	−	0.0590149i	−0.0624223	−	0.00411176i
$207$	7.42026	+	7.42026i	0.515744	+	0.515744i
$208$	9.54267	−	10.8138i	0.661665	−	0.749799i
$209$			33.6532i			2.32784i
$210$	2.09689	+	1.09432i	0.144699	+	0.0755153i
$211$	−10.0854	+	5.82279i	−0.694305	+	0.400857i	−0.805223	−	0.592972i	$-0.797954\pi$
$211$	−10.0854	+	5.82279i	−0.694305	+	0.400857i	0.110918	+	0.993830i	$0.464621\pi$
$212$	15.2374	−	11.6763i	1.04651	−	0.801932i
$213$	−5.13728	+	5.13728i	−0.352001	+	0.352001i
$214$	15.7342	−	7.75290i	1.07557	−	0.529977i
$215$	−0.961218	+	0.703751i	−0.0655545	+	0.0479955i
$216$	7.47754	+	1.49496i	0.508782	+	0.101719i
$217$	1.37295	+	5.12391i	0.0932018	+	0.347834i
$218$	3.97354	+	4.53393i	0.269122	+	0.307076i
$219$	−2.68588	+	1.55069i	−0.181495	+	0.104786i
$220$	−14.8243	−	15.5278i	−0.999455	−	1.04688i
$221$	−8.19368	−	1.64506i	−0.551167	−	0.110659i
$222$	4.69571	−	0.932447i	0.315155	−	0.0625817i
$223$	3.46231	−	12.9215i	0.231854	−	0.865290i	−0.747688	−	0.664050i	$-0.768836\pi$
$223$	3.46231	−	12.9215i	0.231854	−	0.865290i	0.979542	−	0.201240i	$-0.0644970\pi$
$224$	−6.83281	+	5.97259i	−0.456537	+	0.399060i
$225$	13.5876	−	2.99218i	0.905840	−	0.199478i
$226$	2.45452	+	1.64121i	0.163272	+	0.109172i
$227$	−6.77457	−	25.2830i	−0.449644	−	1.67809i	−0.703375	−	0.710819i	$-0.748324\pi$
$227$	−6.77457	−	25.2830i	−0.449644	−	1.67809i	0.253731	−	0.967275i	$-0.418342\pi$
$228$	−5.18876	+	3.97611i	−0.343634	+	0.263324i
$229$	2.91316			0.192507			0.0962536	−	0.995357i	$-0.469314\pi$
$229$	2.91316			0.192507			0.0962536	+	0.995357i	$0.469314\pi$
$230$	8.06585	−	8.78412i	0.531846	−	0.579208i
$231$	−3.10947	+	1.79525i	−0.204588	+	0.118119i
$232$	−0.241677	+	0.488869i	−0.0158669	+	0.0320958i
$233$	−10.5307	−	10.5307i	−0.689891	−	0.689891i	0.272317	−	0.962208i	$-0.412210\pi$
$233$	−10.5307	−	10.5307i	−0.689891	−	0.689891i	−0.962208	+	0.272317i	$0.912210\pi$
$234$	−13.6974	−	3.70126i	−0.895429	−	0.241959i
$235$	−13.9390	−	6.14507i	−0.909282	−	0.400860i
$236$	−0.775901	+	1.00981i	−0.0505069	+	0.0657333i
$237$	4.04875	+	1.08486i	0.262995	+	0.0704693i
$238$	4.97914	+	1.69200i	0.322750	+	0.109676i
$239$		−	26.6105i		−	1.72129i	−0.509207	−	0.860644i	$-0.670061\pi$
$239$		−	26.6105i		−	1.72129i	0.509207	−	0.860644i	$-0.329939\pi$
$240$	0.642637	−	4.12026i	0.0414820	−	0.265962i
$241$	−19.5311	−	11.2763i	−1.25811	−	0.726368i	−0.285401	−	0.958408i	$-0.592127\pi$
$241$	−19.5311	−	11.2763i	−1.25811	−	0.726368i	−0.972706	+	0.232040i	$0.925460\pi$
$242$	16.7061	−	3.31739i	1.07391	−	0.213250i
$243$	−2.94900	−	11.0058i	−0.189179	−	0.706025i
$244$	7.04211	+	5.41088i	0.450825	+	0.346396i
$245$	−7.71450	−	6.20050i	−0.492861	−	0.396135i
$246$	−3.88435	−	2.59727i	−0.247657	−	0.165596i
$247$	21.0420	−	14.0055i	1.33887	−	0.891146i
$248$	7.78128	−	5.18831i	0.494112	−	0.329458i
$249$	−0.625043	−	1.08261i	−0.0396105	−	0.0686074i
$250$	−4.05496	−	15.2826i	−0.256458	−	0.966555i
$251$	3.53371	+	2.04019i	0.223046	+	0.128776i	0.607360	−	0.794427i	$-0.292229\pi$
$251$	3.53371	+	2.04019i	0.223046	+	0.128776i	−0.384314	+	0.923202i	$0.625562\pi$
$252$	8.24641	+	3.42206i	0.519475	+	0.215570i
$253$	4.68543	+	17.4863i	0.294571	+	1.09935i
$254$	26.0574	−	12.8395i	1.63498	−	0.805624i
$255$	−2.25274	+	0.874212i	−0.141072	+	0.0547453i
$256$	13.8355	+	8.03603i	0.864721	+	0.502252i
$257$	−1.15209	−	0.308702i	−0.0718656	−	0.0192563i	0.222707	−	0.974885i	$-0.428511\pi$
$257$	−1.15209	−	0.308702i	−0.0718656	−	0.0192563i	−0.294573	+	0.955629i	$0.595177\pi$
$258$	0.264181	−	0.231528i	0.0164472	−	0.0144143i
$259$	11.6484			0.723796
$260$	−3.53947	+	15.7312i	−0.219509	+	0.975611i
$261$	0.536514			0.0332094
$262$	−22.0869	+	19.3570i	−1.36453	+	1.19588i
$263$	−2.93769	−	0.787152i	−0.181146	−	0.0485378i	0.167106	−	0.985939i	$-0.446558\pi$
$263$	−2.93769	−	0.787152i	−0.181146	−	0.0485378i	−0.348252	+	0.937401i	$0.613224\pi$
$264$	4.75524	+	4.17845i	0.292665	+	0.257166i
$265$	−8.65785	+	19.6388i	−0.531847	+	1.20640i
$266$	−14.2675	+	7.03018i	−0.874796	+	0.431048i
$267$	−1.39044	−	5.18918i	−0.0850934	−	0.317573i
$268$	−9.69731	+	23.3684i	−0.592357	+	1.42745i
$269$	−16.8423	−	9.72390i	−1.02689	−	0.592876i	−0.110799	−	0.993843i	$-0.535341\pi$
$269$	−16.8423	−	9.72390i	−1.02689	−	0.592876i	−0.916093	+	0.400966i	$0.868674\pi$
$270$	−8.13364	+	2.55531i	−0.494997	+	0.155511i
$271$	0.794611	+	1.37631i	0.0482692	+	0.0836047i	0.889151	−	0.457615i	$-0.151296\pi$
$271$	0.794611	+	1.37631i	0.0482692	+	0.0836047i	−0.840881	+	0.541220i	$0.817963\pi$
$272$	0.0120628	−	9.27146i	0.000731415	−	0.562165i
$273$	2.41657	+	1.19709i	0.146257	+	0.0724515i
$274$	7.86327	+	5.25777i	0.475038	+	0.317634i
$275$	22.8808	+	7.24982i	1.37976	+	0.437181i
$276$	−2.14251	+	2.78841i	−0.128964	+	0.167843i
$277$	5.30017	+	19.7805i	0.318456	+	1.18850i	0.920728	+	0.390205i	$0.127596\pi$
$277$	5.30017	+	19.7805i	0.318456	+	1.18850i	−0.602272	+	0.798291i	$0.705738\pi$
$278$	−3.66099	+	0.726979i	−0.219572	+	0.0436013i
$279$	−7.96825	−	4.60047i	−0.477047	−	0.275423i
$280$	3.48629	−	9.52862i	0.208346	−	0.569444i
$281$			17.6174i			1.05096i	0.850805	+	0.525482i	$0.176115\pi$
$281$			17.6174i			1.05096i	−0.850805	+	0.525482i	$0.823885\pi$
$282$	4.25302	+	1.44525i	0.253264	+	0.0860633i
$283$	6.08062	+	1.62930i	0.361456	+	0.0968517i	0.434976	−	0.900442i	$-0.356757\pi$
$283$	6.08062	+	1.62930i	0.361456	+	0.0968517i	−0.0735206	+	0.997294i	$0.523423\pi$
$284$	24.7132	+	18.9887i	1.46646	+	1.12677i
$285$	2.94824	−	6.68758i	0.174639	−	0.396138i
$286$	−17.2714	−	17.3445i	−1.02128	−	1.02560i
$287$	−8.03930	−	8.03930i	−0.474545	−	0.474545i
$288$	1.05505	−	15.7055i	0.0621694	−	0.925458i
$289$	10.0697	−	5.81375i	0.592335	−	0.341985i
$290$	−0.0259671	−	0.609160i	−0.00152484	−	0.0357711i
$291$	6.23611			0.365567
$292$	8.09217	+	10.5601i	0.473559	+	0.617986i
$293$	4.06647	+	15.1763i	0.237565	+	0.886606i	0.976976	+	0.213351i	$0.0684378\pi$
$293$	4.06647	+	15.1763i	0.237565	+	0.886606i	−0.739410	+	0.673255i	$0.764896\pi$
$294$	2.42608	+	1.62219i	0.141492	+	0.0946083i
$295$	0.217585	−	1.40707i	0.0126683	−	0.0819227i
$296$	−6.58232	−	19.4532i	−0.382590	−	1.13070i
$297$	3.34962	−	12.5010i	0.194365	−	0.725379i
$298$	−9.88924	+	1.96375i	−0.572868	+	0.113757i
$299$	8.98353	−	10.2069i	0.519531	−	0.590279i
$300$	1.58556	+	4.38440i	0.0915421	+	0.253133i
$301$	0.740201	−	0.427355i	0.0426645	−	0.0246323i
$302$	7.49598	+	8.55314i	0.431345	+	0.492178i
$303$	0.836332	+	3.12123i	0.0480460	+	0.179310i
$304$	19.8030	+	19.8546i	1.13578	+	1.13874i
$305$	−9.81243	−	1.51737i	−0.561858	−	0.0868844i
$306$	−8.18200	+	4.03161i	−0.467734	+	0.230472i
$307$	−9.45961	+	9.45961i	−0.539888	+	0.539888i	−0.923496	−	0.383608i	$-0.874681\pi$
$307$	−9.45961	+	9.45961i	−0.539888	+	0.539888i	0.383608	+	0.923496i	$0.374681\pi$
$308$	9.36839	+	12.2256i	0.533814	+	0.696617i
$309$	−0.256347	+	0.148002i	−0.0145831	+	0.00841953i
$310$	−4.83773	+	9.26984i	−0.274765	+	0.526492i
$311$			24.4740i			1.38779i	0.720074	+	0.693897i	$0.244108\pi$
$311$			24.4740i			1.38779i	−0.720074	+	0.693897i	$0.755892\pi$
$312$	0.633628	−	4.71221i	0.0358721	−	0.266776i
$313$	2.53045	+	2.53045i	0.143029	+	0.143029i	0.774996	−	0.631966i	$-0.217752\pi$
$313$	2.53045	+	2.53045i	0.143029	+	0.143029i	−0.631966	+	0.774996i	$0.717752\pi$
$314$	−12.1008	−	0.797083i	−0.682889	−	0.0449820i
$315$	−9.92353	+	1.07971i	−0.559127	+	0.0608350i
$316$	2.35856	−	17.8254i	0.132679	−	1.00276i
$317$	−15.9400	−	15.9400i	−0.895281	−	0.895281i	0.0997331	−	0.995014i	$-0.468201\pi$
$317$	−15.9400	−	15.9400i	−0.895281	−	0.895281i	−0.995014	+	0.0997331i	$0.968201\pi$
$318$	2.03623	−	5.99212i	0.114186	−	0.336022i
$319$	0.801552	+	0.462776i	0.0448783	+	0.0259105i
$320$	−17.8832	−	0.437764i	−0.999701	−	0.0244718i
$321$	2.89134	−	5.00794i	0.161379	−	0.279516i
$322$	−6.43463	+	5.63932i	−0.358588	+	0.314267i
$323$	4.20568	−	15.6958i	0.234010	−	0.873337i
$324$	−13.1059	+	5.41864i	−0.728103	+	0.301035i
$325$	−4.98928	−	17.3236i	−0.276755	−	0.960940i
$326$	14.1826	+	9.48319i	0.785502	+	0.525225i
$327$	1.91979	+	0.514405i	0.106164	+	0.0284467i
$328$	−8.88304	+	17.9688i	−0.490484	+	0.992161i
$329$	9.46510	+	5.46468i	0.521828	+	0.301277i
$330$	−6.90806	−	1.53896i	−0.380276	−	0.0847167i
$331$	−11.3848	+	19.7191i	−0.625766	+	1.08386i	0.362626	+	0.931935i	$0.381880\pi$
$331$	−11.3848	+	19.7191i	−0.625766	+	1.08386i	−0.988392	+	0.151924i	$0.951453\pi$
$332$	−4.25651	+	3.26174i	−0.233607	+	0.179011i
$333$	−14.2865	+	14.2865i	−0.782895	+	0.782895i
$334$	−1.02681	−	2.08387i	−0.0561844	−	0.114024i
$335$	−3.05965	−	28.1209i	−0.167167	−	1.53641i
$336$	−0.778107	+	2.88890i	−0.0424492	+	0.157602i
$337$	−8.35062	+	8.35062i	−0.454887	+	0.454887i	−0.896973	−	0.442086i	$-0.854239\pi$
$337$	−8.35062	+	8.35062i	−0.454887	+	0.454887i	0.442086	+	0.896973i	$0.354239\pi$
$338$	−3.65701	+	18.0174i	−0.198915	+	0.980017i
$339$	0.973415			0.0528687
$340$	4.97351	+	9.09474i	0.269726	+	0.493232i
$341$	−7.93637	−	13.7462i	−0.429779	−	0.744399i
$342$	8.87640	−	26.1211i	0.479981	−	1.41247i
$343$	12.9620	+	12.9620i	0.699880	+	0.699880i
$344$	−1.13197	−	0.994670i	−0.0610319	−	0.0536290i
$345$	0.600822	−	3.88536i	0.0323472	−	0.209181i
$346$	11.4550	+	7.65939i	0.615826	+	0.411771i
$347$	−14.4802	+	3.87996i	−0.777338	+	0.208287i	−0.625611	−	0.780135i	$-0.715150\pi$
$347$	−14.4802	+	3.87996i	−0.777338	+	0.208287i	−0.151727	+	0.988422i	$0.548484\pi$
$348$	0.0233508	+	0.178263i	0.00125173	+	0.00955588i
$349$	−10.1314	−	17.5481i	−0.542321	−	0.939327i	−0.998770	−	0.0495780i	$-0.984212\pi$
$349$	−10.1314	−	17.5481i	−0.542321	−	0.939327i	0.456449	−	0.889749i	$-0.349121\pi$
$350$	1.70621	+	11.2149i	0.0912006	+	0.599464i
$351$	−9.21036	+	3.10814i	−0.491613	+	0.165900i
$352$	15.1232	−	22.5540i	0.806071	−	1.20213i
$353$	10.5398	+	2.82413i	0.560976	+	0.150313i	0.528155	−	0.849148i	$-0.322884\pi$
$353$	10.5398	+	2.82413i	0.560976	+	0.150313i	0.0328214	+	0.999461i	$0.489551\pi$
$354$	−0.0275946	+	0.418924i	−0.00146664	+	0.0222656i
$355$	−34.4352	−	5.32498i	−1.82763	−	0.282621i
$356$	−21.2970	+	8.80528i	−1.12874	+	0.466679i
$357$	1.67460	−	0.448709i	0.0886295	−	0.0237482i
$358$	2.15263	−	6.33466i	0.113770	−	0.334797i
$359$			21.5827i			1.13909i	0.821959	+	0.569547i	$0.192881\pi$
$359$			21.5827i			1.13909i	−0.821959	+	0.569547i	$0.807119\pi$
$360$	7.41078	+	15.9625i	0.390583	+	0.841298i
$361$	15.0738	+	26.1086i	0.793357	+	1.37413i
$362$	−18.8034	−	21.4552i	−0.988283	−	1.12766i
$363$	3.97046	−	3.97046i	0.208395	−	0.208395i
$364$	3.74532	−	10.9456i	0.196308	−	0.573705i
$365$	−13.6105	−	6.00025i	−0.712408	−	0.314068i
$366$	2.92144	+	0.192436i	0.152706	+	0.0100588i
$367$	2.25237	−	8.40595i	0.117573	−	0.438787i	−0.881894	−	0.471448i	$-0.843731\pi$
$367$	2.25237	−	8.40595i	0.117573	−	0.438787i	0.999466	+	0.0326610i	$0.0103982\pi$
$368$	13.0540	+	7.55937i	0.680485	+	0.394059i
$369$	19.7201			1.02658
$370$	16.9124	+	15.5295i	0.879234	+	0.807339i
$371$	7.69924	−	13.3355i	0.399724	−	0.692343i
$372$	1.18175	−	2.84776i	0.0612711	−	0.147650i
$373$	20.1012	−	5.38609i	1.04080	−	0.278881i	0.302354	−	0.953196i	$-0.402227\pi$
$373$	20.1012	−	5.38609i	1.04080	−	0.278881i	0.738444	+	0.674315i	$0.235561\pi$
$374$	−15.7014	−	1.03425i	−0.811901	−	0.0534800i
$375$	−3.91175	−	3.44519i	−0.202002	−	0.177909i
$376$	3.77763	−	18.8950i	0.194816	−	0.974437i
$377$	−0.0442265	−	0.693772i	−0.00227778	−	0.0357311i
$378$	5.99960	−	1.19137i	0.308586	−	0.0612773i
$379$	−0.00181279	+	0.00104661i	−9.31166e−5	+	5.37609e-5i	−0.500047	−	0.865999i	$-0.666684\pi$
$379$	−0.00181279	+	0.00104661i	−9.31166e−5	+	5.37609e-5i	0.499953	+	0.866052i	$0.333350\pi$
$380$	−30.0876	−	8.81404i	−1.54346	−	0.452151i
$381$	4.78833	−	8.29363i	0.245313	−	0.424895i
$382$	1.21444	+	6.11579i	0.0621360	+	0.312911i
$383$	3.73551	−	1.00093i	0.190876	−	0.0511450i	−0.162115	−	0.986772i	$-0.551831\pi$
$383$	3.73551	−	1.00093i	0.190876	−	0.0511450i	0.352990	+	0.935627i	$0.385165\pi$
$384$	5.26425	−	0.333002i	0.268640	−	0.0169934i
$385$	−15.7571	−	6.94655i	−0.803054	−	0.354029i
$386$	−3.81413	−	7.74063i	−0.194134	−	0.393988i
$387$	−0.383698	+	1.43198i	−0.0195045	+	0.0727917i
$388$	−3.47449	−	26.5247i	−0.176391	−	1.34659i
$389$		−	6.23999i		−	0.316380i	−0.987409	−	0.158190i	$-0.949434\pi$
$389$		−	6.23999i		−	0.316380i	0.987409	−	0.158190i	$-0.0505658\pi$
$390$	1.91268	+	4.95980i	0.0968524	+	0.251149i
$391$		−	8.74112i		−	0.442057i
$392$	5.54814	−	11.2229i	0.280224	−	0.566842i
$393$	−2.50591	+	9.35219i	−0.126407	+	0.471756i
$394$	−12.8779	+	6.34549i	−0.648781	+	0.319681i
$395$	7.27291	+	18.7414i	0.365940	+	0.942983i
$396$	−26.4845	−	3.50428i	−1.33090	−	0.176097i
$397$	−1.11636	+	0.299127i	−0.0560283	+	0.0150128i	−0.286724	−	0.958013i	$-0.592566\pi$
$397$	−1.11636	+	0.299127i	−0.0560283	+	0.0150128i	0.230696	+	0.973026i	$0.425900\pi$
$398$	−5.90485	+	1.17255i	−0.295983	+	0.0587746i
$399$	−2.62181	+	4.54110i	−0.131255	+	0.227340i
$400$	17.7652	−	9.18681i	0.888260	−	0.459340i
$401$	−5.24184	+	3.02638i	−0.261765	+	0.151130i	−0.625139	−	0.780513i	$-0.714958\pi$
$401$	−5.24184	+	3.02638i	−0.261765	+	0.151130i	0.363374	+	0.931643i	$0.381625\pi$
$402$	1.62457	+	8.18118i	0.0810263	+	0.408040i
$403$	−5.29207	+	10.6831i	−0.263617	+	0.532161i
$404$	12.8099	−	5.29627i	0.637316	−	0.263499i
$405$	9.93324	−	12.3587i	0.493587	−	0.614108i
$406$	−0.0287521	+	0.436497i	−0.00142694	+	0.0216630i
$407$	−33.6670	+	9.02104i	−1.66881	+	0.447156i
$408$	−1.69565	−	2.54309i	−0.0839472	−	0.125902i
$409$	−3.46601	+	6.00331i	−0.171383	+	0.296845i	−0.938904	−	0.344180i	$-0.888157\pi$
$409$	−3.46601	+	6.00331i	−0.171383	+	0.296845i	0.767520	+	0.641025i	$0.221490\pi$
$410$	−0.954445	−	22.3902i	−0.0471367	−	1.10577i
$411$	3.11843			0.153821
$412$	0.772337	+	1.00789i	0.0380503	+	0.0496550i
$413$	−0.264386	+	0.986702i	−0.0130096	+	0.0485525i
$414$	0.975433	−	14.8084i	0.0479399	−	0.727794i
$415$	2.41854	−	5.48605i	0.118722	−	0.269300i
$416$	−20.3960	−	0.0696399i	−0.999994	−	0.00341438i
$417$	−0.870093	+	0.870093i	−0.0426087	+	0.0426087i
$418$	35.7924	−	31.3685i	1.75066	−	1.53428i
$419$	4.27814	+	7.40996i	0.209001	+	0.362000i	0.951400	−	0.307958i	$-0.0996455\pi$
$419$	4.27814	+	7.40996i	0.209001	+	0.362000i	−0.742399	+	0.669958i	$0.766312\pi$
$420$	−0.790649	−	3.25021i	−0.0385797	−	0.158594i
$421$		−	32.7224i		−	1.59479i	−0.603458	−	0.797395i	$-0.706211\pi$
$421$		−	32.7224i		−	1.59479i	0.603458	−	0.797395i	$-0.293789\pi$
$422$	15.5936	+	5.29896i	0.759083	+	0.257949i
$423$	−18.3110	+	4.90643i	−0.890313	+	0.238559i
$424$	−26.6214	−	5.32234i	−1.29285	−	0.258476i
$425$	−9.76554	−	6.24074i	−0.473698	−	0.302720i
$426$	10.2523	+	0.675323i	0.496728	+	0.0327195i
$427$	6.88094	+	1.84374i	0.332992	+	0.0892250i
$428$	−22.9117	−	9.50782i	−1.10748	−	0.459578i
$429$	−7.91161	−	1.58843i	−0.381976	−	0.0766900i
$430$	1.64445	+	0.366345i	0.0793023	+	0.0176667i
$431$	−3.81867	−	6.61413i	−0.183939	−	0.318591i	0.759280	−	0.650765i	$-0.225552\pi$
$431$	−3.81867	−	6.61413i	−0.183939	−	0.318591i	−0.943218	+	0.332173i	$0.892218\pi$
$432$	−5.37990	−	9.34632i	−0.258841	−	0.449675i
$433$	4.96669	−	1.33082i	0.238684	−	0.0639551i	−0.137494	−	0.990503i	$-0.543905\pi$
$433$	4.96669	−	1.33082i	0.238684	−	0.0639551i	0.376178	+	0.926547i	$0.377238\pi$
$434$	4.16988	−	6.23627i	0.200160	−	0.299350i
$435$	−0.118742	−	0.162184i	−0.00569327	−	0.00777614i
$436$	1.11835	−	8.45224i	0.0535594	−	0.404789i
$437$	18.6945	+	18.6945i	0.894280	+	0.894280i
$438$	4.15279	+	1.41119i	0.198428	+	0.0674293i
$439$	18.5626	+	32.1513i	0.885943	+	1.53450i	0.844629	+	0.535351i	$0.179821\pi$
$439$	18.5626	+	32.1513i	0.885943	+	1.53450i	0.0413131	+	0.999146i	$0.486846\pi$
$440$	−2.69693	+	30.2402i	−0.128571	+	1.44165i
$441$	−12.3167			−0.586509
$442$	5.88778	+	10.2479i	0.280053	+	0.487442i
$443$	−21.7235	+	21.7235i	−1.03211	+	1.03211i	−0.0326454	+	0.999467i	$0.510393\pi$
$443$	−21.7235	+	21.7235i	−1.03211	+	1.03211i	−0.999467	+	0.0326454i	$0.989607\pi$
$444$	−5.36863	−	4.12505i	−0.254784	−	0.195766i
$445$	16.1415	−	20.0828i	0.765181	−	0.952018i
$446$	−16.9701	+	8.36189i	−0.803560	+	0.395947i
$447$	−2.35034	+	2.35034i	−0.111167	+	0.111167i
$448$	12.7212	+	1.70004i	0.601019	+	0.0803192i
$449$	9.86545	−	17.0875i	0.465579	−	0.806407i	−0.533648	−	0.845707i	$-0.679179\pi$
$449$	9.86545	−	17.0875i	0.465579	−	0.806407i	0.999227	+	0.0392995i	$0.0125126\pi$
$450$	−15.8475	−	11.6623i	−0.747059	−	0.549764i
$451$	29.4617	+	17.0097i	1.38730	+	0.800957i
$452$	−0.542345	−	4.14033i	−0.0255098	−	0.194745i
$453$	3.62163	+	0.970413i	0.170159	+	0.0455940i
$454$	−20.5755	+	30.7718i	−0.965657	+	1.44419i
$455$	2.21422	+	12.7432i	0.103804	+	0.597411i
$456$	9.06535	+	1.81241i	0.424524	+	0.0848737i
$457$	2.29446	−	8.56304i	0.107330	−	0.400562i	−0.891269	−	0.453475i	$-0.850184\pi$
$457$	2.29446	−	8.56304i	0.107330	−	0.400562i	0.998599	+	0.0529133i	$0.0168507\pi$
$458$	−2.71539	−	3.09834i	−0.126882	−	0.144776i
$459$	−3.12452	+	5.41182i	−0.145840	+	0.252602i
$460$	−16.8607	−	0.390786i	−0.786136	−	0.0182205i
$461$	−7.47079	−	4.31326i	−0.347949	−	0.200889i	0.315832	−	0.948815i	$-0.397716\pi$
$461$	−7.47079	−	4.31326i	−0.347949	−	0.200889i	−0.663782	+	0.747926i	$0.731050\pi$
$462$	4.80773	+	1.63375i	0.223676	+	0.0760089i
$463$	5.04631	+	5.04631i	0.234522	+	0.234522i	0.814577	−	0.580055i	$-0.196969\pi$
$463$	5.04631	+	5.04631i	0.234522	+	0.234522i	−0.580055	+	0.814577i	$0.696969\pi$
$464$	0.745213	−	0.198640i	0.0345957	−	0.00922165i
$465$	0.372862	+	3.42693i	0.0172910	+	0.158920i
$466$	−1.38432	+	21.0159i	−0.0641274	+	0.973543i
$467$	−0.417525	−	0.417525i	−0.0193208	−	0.0193208i	0.697380	−	0.716701i	$-0.254349\pi$
$467$	−0.417525	−	0.417525i	−0.0193208	−	0.0193208i	−0.716701	+	0.697380i	$0.754349\pi$
$468$	8.83098	+	18.0181i	0.408212	+	0.832887i
$469$			20.2946i			0.937119i
$470$	6.45702	+	20.5529i	0.297840	+	0.948036i
$471$	−3.46234	+	1.99898i	−0.159536	+	0.0921083i
$472$	1.79723	−	0.116035i	0.0827241	−	0.00534096i
$473$	−1.80842	+	1.80842i	−0.0831510	+	0.0831510i
$474$	−2.62006	−	5.31732i	−0.120344	−	0.244233i
$475$	34.2325	−	7.53846i	1.57069	−	0.345888i
$476$	−2.84156	−	6.87277i	−0.130243	−	0.315013i
$477$	6.91271	+	25.7986i	0.316511	+	1.18124i
$478$	−28.3020	+	24.8039i	−1.29450	+	1.13450i
$479$	8.45154	−	4.87950i	0.386161	−	0.222950i	−0.294335	−	0.955702i	$-0.595098\pi$
$479$	8.45154	−	4.87950i	0.386161	−	0.222950i	0.680495	+	0.732752i	$0.261765\pi$
$480$	−4.98117	+	3.15705i	−0.227358	+	0.144099i
$481$	19.6517	+	17.2963i	0.896040	+	0.788645i
$482$	6.21206	+	31.2833i	0.282951	+	1.42491i
$483$	−0.730053	+	2.72460i	−0.0332186	+	0.123973i
$484$	−19.1001	−	14.6758i	−0.868188	−	0.667082i
$485$	17.6684	+	24.1323i	0.802279	+	1.09579i
$486$	−8.95663	+	13.3951i	−0.406281	+	0.607614i
$487$	−6.88896	−	25.7099i	−0.312169	−	1.16503i	−0.926597	−	0.376056i	$-0.877280\pi$
$487$	−6.88896	−	25.7099i	−0.312169	−	1.16503i	0.614428	−	0.788973i	$-0.289387\pi$
$488$	−0.809193	−	12.5333i	−0.0366304	−	0.567355i
$489$	5.62455			0.254351
$490$	0.596124	+	13.9844i	0.0269302	+	0.631751i
$491$	−14.2373	+	8.21991i	−0.642521	+	0.370960i	−0.785585	−	0.618754i	$-0.787638\pi$
$491$	−14.2373	+	8.21991i	−0.642521	+	0.370960i	0.143064	+	0.989713i	$0.454304\pi$
$492$	0.858277	+	6.55220i	0.0386941	+	0.295396i
$493$	−0.316009	−	0.316009i	−0.0142323	−	0.0142323i
$494$	−34.5092	−	9.32491i	−1.55264	−	0.419548i
$495$	27.8455	−	10.8059i	1.25156	−	0.485688i
$496$	−12.7711	−	3.43983i	−0.573440	−	0.154453i
$497$	24.1476	+	6.47033i	1.08317	+	0.290234i
$498$	−0.568813	+	1.67388i	−0.0254891	+	0.0750084i
$499$		−	13.2027i		−	0.591034i	−0.955337	−	0.295517i	$-0.904508\pi$
$499$		−	13.2027i		−	0.591034i	0.955337	−	0.295517i	$-0.0954920\pi$
$500$	−12.4744	+	18.5578i	−0.557870	+	0.829928i
$501$	−0.663261	−	0.382934i	−0.0296323	−	0.0171082i
$502$	−1.12393	−	5.66001i	−0.0501636	−	0.252619i
$503$	−4.38365	−	16.3600i	−0.195457	−	0.729456i	−0.992148	−	0.125069i	$-0.960085\pi$
$503$	−4.38365	−	16.3600i	−0.195457	−	0.729456i	0.796691	−	0.604387i	$-0.206582\pi$
$504$	−4.04697	−	11.9603i	−0.180267	−	0.532755i
$505$	−9.70893	+	12.0796i	−0.432042	+	0.537535i
$506$	14.2305	−	21.2824i	0.632621	−	0.946118i
$507$	2.29939	+	5.60787i	0.102120	+	0.249054i
$508$	−37.9440	−	15.7458i	−1.68349	−	0.698609i
$509$	−5.25145	−	9.09578i	−0.232766	−	0.403163i	0.725855	−	0.687848i	$-0.241444\pi$
$509$	−5.25145	−	9.09578i	−0.232766	−	0.403163i	−0.958621	+	0.284685i	$0.908111\pi$
$510$	3.02958	+	1.58107i	0.134152	+	0.0700112i
$511$	9.24205	+	5.33590i	0.408844	+	0.236046i
$512$	−4.34940	−	22.2055i	−0.192218	−	0.981352i
$513$	−4.89183	−	18.2566i	−0.215980	−	0.806047i
$514$	0.745552	+	1.51307i	0.0328849	+	0.0667387i
$515$	−1.29902	−	0.572679i	−0.0572418	−	0.0252353i
$516$	−0.492491	−	0.0651636i	−0.0216807	−	0.00286867i
$517$	−31.5888	−	8.46418i	−1.38927	−	0.372254i
$518$	−10.8576	−	12.3888i	−0.477055	−	0.544334i
$519$	4.54284			0.199409
$520$	20.0304	−	10.8988i	0.878390	−	0.477944i
$521$	26.6575			1.16789			0.583943	−	0.811794i	$-0.301509\pi$
$521$	26.6575			1.16789			0.583943	+	0.811794i	$0.301509\pi$
$522$	−0.500090	−	0.570618i	−0.0218884	−	0.0249753i
$523$	40.3023	+	10.7990i	1.76230	+	0.472206i	0.987180	−	0.159612i	$-0.0510245\pi$
$523$	40.3023	+	10.7990i	1.76230	+	0.472206i	0.775117	+	0.631818i	$0.217691\pi$
$524$	41.1748	+	5.44802i	1.79873	+	0.237998i
$525$	2.52269	+	2.76084i	0.110099	+	0.120493i
$526$	1.90106	+	3.85814i	0.0828903	+	0.168223i
$527$	1.98363	+	7.40302i	0.0864085	+	0.322481i
$528$	0.0116475	−	8.95228i	0.000506894	−	0.389598i
$529$	−7.60208	−	4.38906i	−0.330525	−	0.190829i
$530$	28.9572	−	9.09736i	1.25782	−	0.395164i
$531$	−0.885905	−	1.53443i	−0.0384450	−	0.0665887i
$532$	20.7759	+	8.62150i	0.900750	+	0.373790i
$533$	−1.62558	−	25.5002i	−0.0704119	−	1.10454i
$534$	−4.22299	+	6.31571i	−0.182747	+	0.273308i
$535$	27.5714	−	2.99987i	1.19202	−	0.129696i
$536$	33.8927	−	11.4682i	1.46394	−	0.495349i
$537$	−0.570865	−	2.13050i	−0.0246346	−	0.0919378i
$538$	5.35686	+	26.9766i	0.230951	+	1.16304i
$539$	−18.4011	−	10.6239i	−0.792593	−	0.457604i
$540$	10.2992	+	6.26883i	0.443206	+	0.269767i
$541$			19.1746i			0.824379i	0.911098	+	0.412189i	$0.135236\pi$
$541$			19.1746i			0.824379i	−0.911098	+	0.412189i	$0.864764\pi$
$542$	0.723127	−	2.12799i	0.0310610	−	0.0914050i
$543$	−9.08471	−	2.43424i	−0.389862	−	0.104463i
$544$	−9.87205	+	8.62919i	−0.423261	+	0.369973i
$545$	3.44858	+	8.88657i	0.147721	+	0.380659i
$546$	−0.979316	−	3.68600i	−0.0419109	−	0.157746i
$547$	1.60817	+	1.60817i	0.0687602	+	0.0687602i	0.740651	−	0.671890i	$-0.234517\pi$
$547$	1.60817	+	1.60817i	0.0687602	+	0.0687602i	−0.671890	+	0.740651i	$0.734517\pi$
$548$	−1.73745	−	13.2639i	−0.0742203	−	0.566607i
$549$	−10.7006	+	6.17801i	−0.456692	+	0.263671i
$550$	−13.6168	−	31.0928i	−0.580620	−	1.32580i
$551$	1.35169			0.0575839
$552$	4.96271	−	0.320410i	0.211227	−	0.0136376i
$553$	−3.73298	−	13.9317i	−0.158743	−	0.592435i
$554$	16.0975	−	24.0747i	0.683918	−	1.02284i
$555$	7.48062	+	1.15678i	0.317535	+	0.0491028i
$556$	4.18564	+	3.21608i	0.177511	+	0.136392i
$557$	−6.58309	+	24.5684i	−0.278934	+	1.04100i	0.674224	+	0.738527i	$0.264478\pi$
$557$	−6.58309	+	24.5684i	−0.278934	+	1.04100i	−0.953159	+	0.302471i	$0.902189\pi$
$558$	2.53438	+	12.7629i	0.107289	+	0.540297i
$559$	1.88334	+	0.378121i	0.0796567	+	0.0159928i
$560$	−13.3839	+	5.17382i	−0.565574	+	0.218634i
$561$	−4.49255	+	2.59378i	−0.189676	+	0.109509i
$562$	18.7372	−	16.4213i	0.790381	−	0.692691i
$563$	2.38978	+	8.91879i	0.100717	+	0.375882i	0.997824	−	0.0659314i	$-0.0210019\pi$
$563$	2.38978	+	8.91879i	0.100717	+	0.375882i	−0.897107	+	0.441814i	$0.854335\pi$
$564$	−2.42717	−	5.87049i	−0.102202	−	0.247192i
$565$	2.75791	+	3.76689i	0.116026	+	0.158474i
$566$	−3.93495	−	7.98583i	−0.165398	−	0.335669i
$567$	−8.04394	+	8.04394i	−0.337814	+	0.337814i
$568$	−2.83974	−	43.9836i	−0.119153	−	1.84551i
$569$	2.35025	−	1.35692i	0.0985276	−	0.0568849i	−0.449927	−	0.893066i	$-0.648550\pi$
$569$	2.35025	−	1.35692i	0.0985276	−	0.0568849i	0.548454	+	0.836181i	$0.315217\pi$
$570$	−9.86076	+	3.09791i	−0.413022	+	0.129757i
$571$		−	2.16500i		−	0.0906026i	−0.998973	−	0.0453013i	$-0.985575\pi$
$571$		−	2.16500i		−	0.0906026i	0.998973	−	0.0453013i	$-0.0144248\pi$
$572$	−2.34822	+	34.5363i	−0.0981841	+	1.44403i
$573$	1.45351	+	1.45351i	0.0607214	+	0.0607214i
$574$	−1.05681	+	16.0438i	−0.0441104	+	0.669657i
$575$	16.7377	−	8.68308i	0.698011	−	0.362110i
$576$	−17.6873	+	13.5172i	−0.736970	+	0.563216i
$577$	0.527902	+	0.527902i	0.0219768	+	0.0219768i	0.718010	−	0.696033i	$-0.245053\pi$
$577$	0.527902	+	0.527902i	0.0219768	+	0.0219768i	−0.696033	+	0.718010i	$0.745053\pi$
$578$	−15.5694	−	5.29074i	−0.647600	−	0.220066i
$579$	−2.46371	−	1.42243i	−0.102388	−	0.0591140i
$580$	−0.623677	+	0.595422i	−0.0258968	+	0.0247236i
$581$	−2.15076	+	3.72522i	−0.0892285	+	0.154548i
$582$	−5.81274	−	6.63251i	−0.240946	−	0.274926i
$583$	−11.9253	+	44.5057i	−0.493894	+	1.84324i
$584$	3.68861	−	18.4498i	0.152636	−	0.763457i
$585$	−18.3449	−	12.9136i	−0.758470	−	0.533910i
$586$	12.3505	−	18.4709i	0.510196	−	0.763025i
$587$	−43.0173	−	11.5264i	−1.77551	−	0.475747i	−0.785759	−	0.618532i	$-0.787728\pi$
$587$	−43.0173	−	11.5264i	−1.77551	−	0.475747i	−0.989754	+	0.142785i	$0.954394\pi$
$588$	−0.536060	−	4.09235i	−0.0221068	−	0.168766i
$589$	−20.0751	−	11.5904i	−0.827182	−	0.477574i
$590$	−1.69932	+	1.08013i	−0.0699600	+	0.0444681i
$591$	−2.36646	+	4.09883i	−0.0973432	+	0.168603i
$592$	−14.5543	+	25.1333i	−0.598180	+	1.03297i
$593$	28.2232	−	28.2232i	1.15899	−	1.15899i	0.174294	−	0.984694i	$-0.444236\pi$
$593$	28.2232	−	28.2232i	1.15899	−	1.15899i	0.984694	−	0.174294i	$-0.0557642\pi$
$594$	−16.4178	+	8.08973i	−0.673631	+	0.331926i
$595$	6.48095	+	5.20904i	0.265693	+	0.213550i
$596$	11.3064	+	8.68743i	0.463130	+	0.355851i
$597$	−1.40338	+	1.40338i	−0.0574365	+	0.0574365i
$598$	−19.2293	−	0.0406377i	−0.786346	−	0.00166180i
$599$	32.2701			1.31852			0.659261	−	0.751915i	$-0.270869\pi$
$599$	32.2701			1.31852			0.659261	+	0.751915i	$0.270869\pi$
$600$	3.18518	−	5.77308i	0.130034	−	0.235685i
$601$	17.3758	+	30.0958i	0.708773	+	1.22763i	0.965312	+	0.261098i	$0.0840845\pi$
$601$	17.3758	+	30.0958i	0.708773	+	1.22763i	−0.256539	+	0.966534i	$0.582582\pi$
$602$	−1.14447	−	0.388910i	−0.0466450	−	0.0158508i
$603$	−24.8909	−	24.8909i	−1.01364	−	1.01364i
$604$	2.10974	−	15.9449i	0.0858442	−	0.648790i
$605$	26.6140	+	4.11552i	1.08201	+	0.167320i
$606$	2.54008	−	3.79882i	0.103184	−	0.154317i
$607$	26.3954	−	7.07262i	1.07136	−	0.287069i	0.320306	−	0.947314i	$-0.396214\pi$
$607$	26.3954	−	7.07262i	1.07136	−	0.287069i	0.751050	+	0.660245i	$0.229548\pi$
$608$	2.65808	−	39.5684i	0.107800	−	1.60471i
$609$	0.0721067	+	0.124892i	0.00292191	+	0.00506090i
$610$	7.53244	+	11.8505i	0.304980	+	0.479813i
$611$	7.85398	+	23.2737i	0.317738	+	0.941554i
$612$	11.9144	+	4.94419i	0.481611	+	0.199857i
$613$	12.3187	+	3.30079i	0.497548	+	0.133317i	0.498862	−	0.866682i	$-0.333752\pi$
$613$	12.3187	+	3.30079i	0.497548	+	0.133317i	−0.00131403	+	0.999999i	$0.500418\pi$
$614$	18.8783	+	1.24352i	0.761867	+	0.0501842i
$615$	−4.36448	−	5.96123i	−0.175993	−	0.240380i
$616$	4.27034	−	21.3595i	0.172057	−	0.860598i
$617$	−32.3997	+	8.68148i	−1.30436	+	0.349503i	−0.843099	−	0.537759i	$-0.819271\pi$
$617$	−32.3997	+	8.68148i	−1.30436	+	0.349503i	−0.461265	+	0.887262i	$0.652604\pi$
$618$	0.396353	+	0.134687i	0.0159437	+	0.00541793i
$619$		−	41.5499i		−	1.67003i	−0.550225	−	0.835016i	$-0.685458\pi$
$619$		−	41.5499i		−	1.67003i	0.550225	−	0.835016i	$-0.314542\pi$
$620$	14.3684	−	3.49527i	0.577048	−	0.140373i
$621$	−5.08362	−	8.80508i	−0.203998	−	0.353336i
$622$	26.0297	−	22.8125i	1.04370	−	0.914697i
$623$	−13.0714	+	13.0714i	−0.523695	+	0.523695i
$624$	−5.60235	+	3.71839i	−0.224274	+	0.148855i
$625$	2.24921	−	24.8986i	0.0899686	−	0.995945i
$626$	0.332641	−	5.04996i	0.0132950	−	0.201837i
$627$	4.06089	−	15.1555i	0.162176	−	0.605251i
$628$	10.4316	+	13.6130i	0.416264	+	0.543217i
$629$	16.8296			0.671040
$630$	10.3982	+	9.54791i	0.414273	+	0.380398i
$631$	24.2139	−	41.9397i	0.963941	−	1.66959i	0.251507	−	0.967855i	$-0.419074\pi$
$631$	24.2139	−	41.9397i	0.963941	−	1.66959i	0.712434	−	0.701739i	$-0.247593\pi$
$632$	−21.1569	+	14.1068i	−0.841578	+	0.561137i
$633$	5.24449	−	1.40526i	0.208450	−	0.0558540i
$634$	−2.09540	+	31.8111i	−0.0832191	+	1.26338i
$635$	45.6609	−	4.96806i	1.81200	−	0.197152i
$636$	−8.27100	+	3.41966i	−0.327966	+	0.135598i
$637$	1.01530	+	15.9268i	0.0402278	+	0.631044i
$638$	−0.254942	−	1.28386i	−0.0100932	−	0.0508285i
$639$	−37.5522	+	21.6808i	−1.48554	+	0.857679i
$640$	16.2035	+	19.4280i	0.640500	+	0.767958i
$641$	23.1486	−	40.0946i	0.914315	−	1.58364i	0.106414	−	0.994322i	$-0.466063\pi$
$641$	23.1486	−	40.0946i	0.914315	−	1.58364i	0.807901	−	0.589318i	$-0.200603\pi$
$642$	−8.02132	+	1.59283i	−0.316576	+	0.0628639i
$643$	32.2444	−	8.63985i	1.27159	−	0.340722i	0.440952	−	0.897531i	$-0.354641\pi$
$643$	32.2444	−	8.63985i	1.27159	−	0.340722i	0.830641	+	0.556808i	$0.187974\pi$
$644$	11.9956	+	1.58719i	0.472691	+	0.0625439i
$645$	0.517798	−	0.200940i	0.0203883	−	0.00791200i
$646$	−20.6137	+	10.1572i	−0.811033	+	0.399630i
$647$	−4.65013	+	17.3545i	−0.182815	+	0.682276i	0.812272	+	0.583279i	$0.198230\pi$
$647$	−4.65013	+	17.3545i	−0.182815	+	0.682276i	−0.995088	+	0.0989979i	$0.968436\pi$
$648$	17.9792	+	8.88817i	0.706288	+	0.349160i
$649$		−	3.05659i		−	0.119982i
$650$	−13.7742	+	21.4539i	−0.540269	+	0.841492i
$651$		−	2.47319i		−	0.0969318i
$652$	−3.13376	−	23.9235i	−0.122727	−	0.936916i
$653$	−5.00915	+	18.6944i	−0.196023	+	0.731569i	0.795976	+	0.605328i	$0.206958\pi$
$653$	−5.00915	+	18.6944i	−0.196023	+	0.731569i	−0.992000	+	0.126241i	$0.959709\pi$
$654$	−1.24235	−	2.52130i	−0.0485797	−	0.0985907i
$655$	−43.2907	+	16.7996i	−1.69151	+	0.656416i
$656$	27.3910	−	7.30120i	1.06944	−	0.285064i
$657$	−17.8795	+	4.79080i	−0.697547	+	0.186907i
$658$	−3.01047	−	15.1604i	−0.117360	−	0.591015i
$659$	0.691956	−	1.19850i	0.0269548	−	0.0466870i	−0.852233	−	0.523162i	$-0.824752\pi$
$659$	0.691956	−	1.19850i	0.0269548	−	0.0466870i	0.879188	+	0.476475i	$0.158086\pi$
$660$	4.80229	+	8.78165i	0.186929	+	0.341825i
$661$	32.2343	−	18.6105i	1.25377	−	0.723865i	0.281914	−	0.959440i	$-0.409031\pi$
$661$	32.2343	−	18.6105i	1.25377	−	0.723865i	0.971856	+	0.235575i	$0.0756973\pi$
$662$	31.5844	−	6.27186i	1.22756	−	0.243763i
$663$	3.49145	+	1.72956i	0.135597	+	0.0671706i
$664$	7.43661	+	1.48678i	0.288597	+	0.0576982i
$665$	−25.0012	+	2.72022i	−0.969506	+	0.105486i
$666$	28.5112	+	1.87804i	1.10479	+	0.0727725i
$667$	0.702341	−	0.188192i	0.0271947	−	0.00728681i
$668$	−1.25923	+	3.03447i	−0.0487212	+	0.117407i
$669$	−3.11845	+	5.40132i	−0.120566	+	0.208827i
$670$	−27.0565	+	29.4659i	−1.04528	+	1.13837i
$671$	−21.3156			−0.822881
$672$	3.79781	−	1.86520i	0.146504	−	0.0719517i
$673$	1.56866	−	5.85432i	0.0604675	−	0.225668i	−0.929079	−	0.369881i	$-0.879398\pi$
$673$	1.56866	−	5.85432i	0.0604675	−	0.225668i	0.989547	+	0.144213i	$0.0460651\pi$
$674$	16.6651	+	1.09773i	0.641917	+	0.0422831i
$675$	−13.4665	−	0.607010i	−0.518325	−	0.0233638i
$676$	22.5714	−	12.9047i	0.868131	−	0.496335i
$677$	−5.51755	+	5.51755i	−0.212057	+	0.212057i	−0.805141	−	0.593084i	$-0.797910\pi$
$677$	−5.51755	+	5.51755i	−0.212057	+	0.212057i	0.593084	+	0.805141i	$0.297910\pi$
$678$	−0.907330	−	1.03529i	−0.0348458	−	0.0397601i
$679$	−10.7292	−	18.5835i	−0.411748	−	0.713168i
$680$	5.03700	−	13.7670i	0.193160	−	0.527939i
$681$			12.2035i			0.467639i
$682$	−7.22241	+	21.2538i	−0.276560	+	0.813851i
$683$	−47.1219	+	12.6263i	−1.80307	+	0.483131i	−0.994451	−	0.105200i	$-0.966452\pi$
$683$	−47.1219	+	12.6263i	−1.80307	+	0.483131i	−0.808620	+	0.588331i	$0.799785\pi$
$684$	−36.0553	+	14.9071i	−1.37861	+	0.569988i
$685$	8.83523	+	12.0676i	0.337577	+	0.461079i
$686$	1.70392	−	25.8679i	0.0650560	−	0.987640i
$687$	−1.31192	−	0.351528i	−0.0500529	−	0.0134116i
$688$	−0.00277267	+	2.13107i	−0.000105707	+	0.0812462i
$689$	32.7906	−	11.0656i	1.24922	−	0.421564i
$690$	−4.69236	+	2.98257i	−0.178635	+	0.113544i
$691$	−14.4671	−	25.0577i	−0.550353	−	0.953239i	−0.998249	−	0.0591535i	$-0.981160\pi$
$691$	−14.4671	−	25.0577i	−0.550353	−	0.953239i	0.447896	−	0.894086i	$-0.352173\pi$
$692$	−2.53108	−	19.3226i	−0.0962171	−	0.734533i
$693$	−20.6993	+	5.54636i	−0.786301	+	0.210689i
$694$	17.6237	+	11.7841i	0.668988	+	0.447318i
$695$	−5.83224	−	0.901883i	−0.221230	−	0.0342104i
$696$	0.167828	−	0.190995i	0.00636152	−	0.00723966i
$697$	−11.6152	−	11.6152i	−0.439956	−	0.439956i
$698$	−9.21996	+	27.1321i	−0.348981	+	1.02697i
$699$	3.47170	+	6.01316i	0.131312	+	0.227439i
$700$	10.3375	−	12.2682i	0.390719	−	0.463695i
$701$	20.6254			0.779012			0.389506	−	0.921024i	$-0.372646\pi$
$701$	20.6254			0.779012			0.389506	+	0.921024i	$0.372646\pi$
$702$	11.8908	+	6.89869i	0.448789	+	0.260374i
$703$	−35.9933	+	35.9933i	−1.35751	+	1.35751i
$704$	−38.0842	+	4.93828i	−1.43535	+	0.186119i
$705$	5.53581	+	4.44939i	0.208491	+	0.167574i
$706$	−6.82059	−	13.8421i	−0.256696	−	0.520956i
$707$	7.86229	−	7.86229i	0.295692	−	0.295692i
$708$	0.471274	−	0.361135i	0.0177116	−	0.0135723i
$709$	−22.0927	+	38.2656i	−0.829707	+	1.43709i	0.0685613	+	0.997647i	$0.478159\pi$
$709$	−22.0927	+	38.2656i	−0.829707	+	1.43709i	−0.898268	+	0.439448i	$0.855174\pi$
$710$	26.4340	+	41.5876i	0.992049	+	1.56075i
$711$	21.6653	+	12.5085i	0.812513	+	0.469104i
$712$	29.2161	+	14.4433i	1.09492	+	0.541284i
$713$	−12.0448	−	3.22739i	−0.451081	−	0.120867i
$714$	−2.03815	−	1.36280i	−0.0762757	−	0.0510017i
$715$	−16.2686	−	35.1165i	−0.608411	−	1.31328i
$716$	−8.74381	+	3.61514i	−0.326771	+	0.135104i
$717$	−3.21105	+	11.9838i	−0.119919	+	0.447544i
$718$	22.9546	−	20.1175i	0.856660	−	0.750778i
$719$	6.88393	−	11.9233i	0.256727	−	0.444665i	−0.708636	−	0.705574i	$-0.750689\pi$
$719$	6.88393	−	11.9233i	0.256727	−	0.444665i	0.965363	+	0.260910i	$0.0840224\pi$
$720$	10.0695	−	22.7607i	0.375268	−	0.848240i
$721$	0.882084	+	0.509271i	0.0328505	+	0.0189663i
$722$	13.7177	−	40.3680i	0.510521	−	1.50234i
$723$	7.43497	+	7.43497i	0.276510	+	0.276510i
$724$	−5.29220	+	39.9972i	−0.196683	+	1.48648i
$725$	0.291191	−	0.919012i	0.0108146	−	0.0341313i
$726$	−7.92375	−	0.521938i	−0.294078	−	0.0193709i
$727$	−14.1720	−	14.1720i	−0.525611	−	0.525611i	0.393649	−	0.919261i	$-0.371212\pi$
$727$	−14.1720	−	14.1720i	−0.525611	−	0.525611i	−0.919261	+	0.393649i	$0.871212\pi$
$728$	−15.1324	+	6.21911i	−0.560845	+	0.230495i
$729$		−	15.9605i		−	0.591131i
$730$	6.30486	+	20.0686i	0.233353	+	0.742772i
$731$	1.06944	−	0.617442i	0.0395547	−	0.0228369i
$732$	−2.51843	−	3.28651i	−0.0930840	−	0.121473i
$733$	−22.3494	+	22.3494i	−0.825495	+	0.825495i	−0.986890	−	0.161394i	$-0.948401\pi$
$733$	−22.3494	+	22.3494i	−0.825495	+	0.825495i	0.161394	+	0.986890i	$0.448401\pi$
$734$	−11.0397	+	5.43973i	−0.407484	+	0.200784i
$735$	2.72596	+	3.72325i	0.100548	+	0.137334i
$736$	−4.12784	−	20.9299i	−0.152154	−	0.771486i
$737$	−15.7171	−	58.6569i	−0.578946	−	2.16066i
$738$	−18.3813	−	20.9736i	−0.676623	−	0.772047i
$739$	−40.0337	+	23.1135i	−1.47266	+	0.850243i	−0.999527	−	0.0307468i	$-0.990211\pi$
$739$	−40.0337	+	23.1135i	−1.47266	+	0.850243i	−0.473136	+	0.880989i	$0.656878\pi$
$740$	0.752395	−	32.4626i	0.0276586	−	1.19335i
$741$	−11.1661	+	3.76814i	−0.410198	+	0.138426i
$742$	−21.3597	+	4.24148i	−0.784138	+	0.155710i
$743$	10.8066	−	40.3306i	0.396454	−	1.47959i	−0.422835	−	0.906207i	$-0.638965\pi$
$743$	10.8066	−	40.3306i	0.396454	−	1.47959i	0.819289	−	0.573380i	$-0.194368\pi$
$744$	−4.13031	+	1.39756i	−0.151424	+	0.0512369i
$745$	−15.7543	−	2.43621i	−0.577193	−	0.0892558i
$746$	−24.4649	−	16.3585i	−0.895725	−	0.598926i
$747$	−1.93105	−	7.20676i	−0.0706533	−	0.263682i
$748$	13.5354	+	17.6635i	0.494905	+	0.645842i
$749$	−19.8981			−0.727060
$750$	−0.0180108	+	7.37170i	−0.000657662	+	0.269176i
$751$	24.4503	−	14.1164i	0.892202	−	0.515113i	0.0175402	−	0.999846i	$-0.494417\pi$
$751$	24.4503	−	14.1164i	0.892202	−	0.515113i	0.874662	+	0.484733i	$0.161083\pi$
$752$	−23.6173	+	13.5945i	−0.861233	+	0.495740i
$753$	−1.34519	−	1.34519i	−0.0490215	−	0.0490215i
$754$	−0.696648	+	0.693709i	−0.0253704	+	0.0252634i
$755$	6.50565	+	16.7643i	0.236765	+	0.610115i
$756$	−6.85938	−	5.27048i	−0.249473	−	0.191686i
$757$	−8.72011	−	2.33655i	−0.316938	−	0.0849232i	0.0968433	−	0.995300i	$-0.469125\pi$
$757$	−8.72011	−	2.33655i	−0.316938	−	0.0849232i	−0.413781	+	0.910376i	$0.635792\pi$
$758$	0.00280286		0.000952459i	0.000101804		3.45949e-5i
$759$		−	8.44020i		−	0.306360i
$760$	18.6707	+	40.2158i	0.677256	+	1.45878i
$761$	28.9485	+	16.7134i	1.04938	+	0.605861i	0.922476	−	0.386053i	$-0.126162\pi$
$761$	28.9485	+	16.7134i	1.04938	+	0.605861i	0.126906	+	0.991915i	$0.459495\pi$
$762$	−13.2841	+	2.63787i	−0.481231	+	0.0955600i
$763$	−1.77006	−	6.60595i	−0.0640804	−	0.239151i
$764$	5.37255	−	6.99222i	0.194372	−	0.252970i
$765$	−14.3375	+	1.55997i	−0.518374	+	0.0564008i
$766$	−4.54646	−	3.03998i	−0.164270	−	0.109839i
$767$	−1.91116	+	1.27206i	−0.0690080	+	0.0459314i
$768$	−5.26103	−	5.28848i	−0.189841	−	0.190832i
$769$	−18.8909	−	32.7200i	−0.681223	−	1.17991i	−0.974608	−	0.223919i	$-0.928115\pi$
$769$	−18.8909	−	32.7200i	−0.681223	−	1.17991i	0.293385	−	0.955995i	$-0.405218\pi$
$770$	7.29920	+	23.2336i	0.263045	+	0.837281i
$771$	0.481585	+	0.278043i	0.0173439	+	0.0100135i
$772$	−4.67748	+	11.2717i	−0.168346	+	0.405677i
$773$	7.17018	+	26.7595i	0.257894	+	0.962472i	0.966458	+	0.256826i	$0.0826766\pi$
$773$	7.17018	+	26.7595i	0.257894	+	0.962472i	−0.708564	+	0.705646i	$0.750657\pi$
$774$	1.88065	−	0.926676i	0.0675987	−	0.0333087i
$775$	−12.2050	+	11.1522i	−0.438418	+	0.400598i
$776$	−24.9721	+	28.4193i	−0.896448	+	1.02019i
$777$	−5.24577	−	1.40560i	−0.188191	−	0.0504256i
$778$	−6.63663	+	5.81635i	−0.237935	+	0.208526i
$779$	49.6825			1.78006
$780$	3.49224	−	6.65734i	0.125042	−	0.238371i
$781$	−74.8040			−2.67670
$782$	−9.29675	+	8.14768i	−0.332451	+	0.291360i
$783$	−0.502104	−	0.134538i	−0.0179437	−	0.00480801i
$784$	−17.1078	+	4.56016i	−0.610992	+	0.162863i
$785$	−17.5452	−	7.73488i	−0.626216	−	0.276070i
$786$	12.2824	−	6.05207i	0.438100	−	0.215870i
$787$	11.0916	+	41.3944i	0.395373	+	1.47555i	0.821144	+	0.570721i	$0.193336\pi$
$787$	11.0916	+	41.3944i	0.395373	+	1.47555i	−0.425771	+	0.904831i	$0.639997\pi$
$788$	18.7525	+	7.78183i	0.668030	+	0.277216i
$789$	1.22798	+	0.708975i	0.0437173	+	0.0252402i
$790$	13.1536	−	25.2043i	0.467983	−	0.896728i
$791$	−1.67475	−	2.90075i	−0.0595473	−	0.103139i
$792$	20.9595	+	31.4344i	0.744762	+	1.11697i
$793$	8.87093	+	13.3278i	0.315016	+	0.473285i
$794$	1.35871	+	0.908499i	0.0482188	+	0.0322414i
$795$	6.26879	−	7.79946i	0.222331	−	0.276618i
$796$	6.75105	+	5.18724i	0.239285	+	0.183857i
$797$	4.75700	+	17.7534i	0.168502	+	0.628857i	0.997568	+	0.0697059i	$0.0222061\pi$
$797$	4.75700	+	17.7534i	0.168502	+	0.628857i	−0.829066	+	0.559151i	$0.811127\pi$
$798$	7.27357	−	1.44434i	0.257482	−	0.0511292i
$799$	13.6752	+	7.89536i	0.483793	+	0.279318i
$800$	−26.3299	−	10.3313i	−0.930902	−	0.365268i
$801$		−	32.0636i		−	1.13291i
$802$	8.10472	+	2.75412i	0.286188	+	0.0972514i
$803$	−30.8444	−	8.26472i	−1.08847	−	0.291656i
$804$	7.18694	−	9.35360i	0.253464	−	0.329876i
$805$	−12.6120	+	4.89428i	−0.444514	+	0.172501i
$806$	16.2949	−	4.32932i	0.573964	−	0.152494i
$807$	6.41142	+	6.41142i	0.225693	+	0.225693i
$808$	−17.5732	−	8.68745i	−0.618222	−	0.305624i
$809$	−4.51084	+	2.60433i	−0.158593	+	0.0915635i	−0.577196	−	0.816606i	$-0.695853\pi$
$809$	−4.51084	+	2.60433i	−0.158593	+	0.0915635i	0.418603	+	0.908169i	$0.362520\pi$
$810$	−22.4031	+	0.954996i	−0.787166	+	0.0335551i
$811$	−1.37463			−0.0482697			−0.0241348	−	0.999709i	$-0.507683\pi$
$811$	−1.37463			−0.0482697			−0.0241348	+	0.999709i	$0.507683\pi$
$812$	0.491043	−	0.376284i	0.0172322	−	0.0132050i
$813$	−0.191770	−	0.715694i	−0.00672566	−	0.0251005i
$814$	40.9758	+	27.3984i	1.43620	+	0.960315i
$815$	15.9357	+	21.7657i	0.558202	+	0.762420i
$816$	−1.12421	+	4.17387i	−0.0393552	+	0.146115i
$817$	−0.966685	+	3.60772i	−0.0338200	+	0.126218i
$818$	9.61562	−	1.90941i	0.336202	−	0.0667611i
$819$	12.0823	+	10.6342i	0.422191	+	0.371589i
$820$	−22.9238	+	21.8853i	−0.800534	+	0.764266i
$821$	−4.96177	+	2.86468i	−0.173167	+	0.0999780i	−0.584078	−	0.811697i	$-0.698544\pi$
$821$	−4.96177	+	2.86468i	−0.173167	+	0.0999780i	0.410911	+	0.911675i	$0.365211\pi$
$822$	−2.90672	−	3.31665i	−0.101383	−	0.115681i
$823$	−11.3713	−	42.4384i	−0.396380	−	1.47931i	−0.819417	−	0.573197i	$-0.805703\pi$
$823$	−11.3713	−	42.4384i	−0.396380	−	1.47931i	0.423038	−	0.906112i	$-0.360964\pi$
$824$	0.352050	−	1.76089i	0.0122642	−	0.0613436i
$825$	−9.42936	−	6.02590i	−0.328288	−	0.209795i
$826$	1.29586	−	0.638523i	0.0450887	−	0.0222171i
$827$	6.62873	−	6.62873i	0.230504	−	0.230504i	−0.582399	−	0.812903i	$-0.697886\pi$
$827$	6.62873	−	6.62873i	0.230504	−	0.230504i	0.812903	+	0.582399i	$0.197886\pi$
$828$	−16.6589	+	12.7656i	−0.578938	+	0.443637i
$829$	35.3796	−	20.4264i	1.22878	−	0.709439i	0.262009	−	0.965065i	$-0.415615\pi$
$829$	35.3796	−	20.4264i	1.22878	−	0.709439i	0.966776	+	0.255626i	$0.0822817\pi$
$830$	−8.08912	+	2.54132i	−0.280777	+	0.0882105i
$831$		−	9.54757i		−	0.331201i
$832$	18.9372	+	21.7573i	0.656530	+	0.754300i
$833$	7.25458	+	7.25458i	0.251356	+	0.251356i
$834$	1.73642	+	0.114378i	0.0601274	+	0.00396060i
$835$	−0.397308	−	3.65161i	−0.0137494	−	0.126369i
$836$	−66.7248	−	8.82866i	−2.30773	−	0.305345i
$837$	6.30357	+	6.30357i	0.217883	+	0.217883i
$838$	3.89328	−	11.4570i	0.134491	−	0.395775i
$839$	−31.7690	−	18.3419i	−1.09679	−	0.633231i	−0.161413	−	0.986887i	$-0.551605\pi$
$839$	−31.7690	−	18.3419i	−1.09679	−	0.633231i	−0.935376	+	0.353656i	$0.884938\pi$
$840$	−2.71983	+	3.87046i	−0.0938432	+	0.133543i
$841$	−14.4814	+	25.0825i	−0.499359	+	0.864915i
$842$	−34.8024	+	30.5008i	−1.19937	+	1.05113i
$843$	2.12587	−	7.93384i	0.0732187	−	0.273256i
$844$	−8.89913	−	21.5240i	−0.306321	−	0.740887i
$845$	−15.1864	+	24.7865i	−0.522429	+	0.852683i
$846$	22.2862	+	14.9016i	0.766215	+	0.512329i
$847$	−18.6630	−	5.00074i	−0.641268	−	0.171827i
$848$	19.1534	+	33.2746i	0.657732	+	1.14266i
$849$	−2.54176	−	1.46748i	−0.0872329	−	0.0503639i
$850$	2.46513	+	16.2034i	0.0845531	+	0.555770i
$851$	−13.6909	+	23.7134i	−0.469320	+	0.812886i
$852$	−8.83806	−	11.5335i	−0.302787	−	0.395132i
$853$	17.9810	−	17.9810i	0.615656	−	0.615656i	−0.328758	−	0.944414i	$-0.606630\pi$
$853$	17.9810	−	17.9810i	0.615656	−	0.615656i	0.944414	+	0.328758i	$0.106630\pi$
$854$	−4.45285	−	9.03690i	−0.152373	−	0.309236i
$855$	27.3272	−	33.9997i	0.934569	−	1.16277i
$856$	11.2441	+	33.2305i	0.384315	+	1.13579i
$857$	8.67656	−	8.67656i	0.296386	−	0.296386i	−0.543211	−	0.839596i	$-0.682792\pi$
$857$	8.67656	−	8.67656i	0.296386	−	0.296386i	0.839596	+	0.543211i	$0.182792\pi$
$858$	5.68509	+	9.89510i	0.194086	+	0.337813i
$859$	−33.4337			−1.14074			−0.570372	−	0.821386i	$-0.693201\pi$
$859$	−33.4337			−1.14074			−0.570372	+	0.821386i	$0.693201\pi$
$860$	−1.14317	−	2.09045i	−0.0389819	−	0.0712838i
$861$	2.65034	+	4.59053i	0.0903235	+	0.156445i
$862$	−3.47514	+	10.2265i	−0.118364	+	0.348316i
$863$	−4.64391	−	4.64391i	−0.158080	−	0.158080i	0.623635	−	0.781716i	$-0.285655\pi$
$863$	−4.64391	−	4.64391i	−0.158080	−	0.158080i	−0.781716	+	0.623635i	$0.785655\pi$
$864$	−4.92577	+	14.4337i	−0.167578	+	0.491044i
$865$	12.8709	+	17.5798i	0.437625	+	0.597730i
$866$	−6.04491	−	4.04192i	−0.205414	−	0.137350i
$867$	−5.23635	+	1.40308i	−0.177836	+	0.0476510i
$868$	−10.5195	+	1.37795i	−0.357054	+	0.0467707i
$869$	21.5786	+	37.3753i	0.732005	+	1.26787i
$870$	−0.0618126	+	0.277464i	−0.00209564	+	0.00940691i
$871$	−30.1348	+	34.2385i	−1.02108	+	1.16013i
$872$	−10.0319	+	6.68897i	−0.339724	+	0.226517i
$873$	35.9513	+	9.63312i	1.21677	+	0.326032i
$874$	2.45750	−	37.3082i	0.0831260	−	1.26197i
$875$	−3.53647	+	17.5843i	−0.119555	+	0.594459i
$876$	−2.36997	−	5.73215i	−0.0800738	−	0.193671i
$877$	24.9987	−	6.69837i	0.844144	−	0.226188i	0.189270	−	0.981925i	$-0.439388\pi$
$877$	24.9987	−	6.69837i	0.844144	−	0.226188i	0.654875	+	0.755737i	$0.272721\pi$
$878$	16.8927	−	49.7110i	0.570100	−	1.67767i
$879$		−	7.32520i		−	0.247073i
$880$	34.6763	−	25.3188i	1.16894	−	0.853498i
$881$	16.9633	+	29.3813i	0.571508	+	0.989881i	0.996411	+	0.0846424i	$0.0269748\pi$
$881$	16.9633	+	29.3813i	0.571508	+	0.989881i	−0.424903	+	0.905239i	$0.639692\pi$
$882$	11.4805	+	13.0996i	0.386569	+	0.441087i
$883$	−19.8045	+	19.8045i	−0.666475	+	0.666475i	−0.956898	−	0.290423i	$-0.906204\pi$
$883$	−19.8045	+	19.8045i	−0.666475	+	0.666475i	0.290423	+	0.956898i	$0.406204\pi$
$884$	5.41124	−	15.8142i	0.182000	−	0.531889i
$885$	−0.267777	+	0.607406i	−0.00900123	+	0.0204177i
$886$	43.3530	+	2.85567i	1.45647	+	0.0959379i
$887$	5.88071	−	21.9471i	0.197455	−	0.736912i	−0.794163	−	0.607705i	$-0.792090\pi$
$887$	5.88071	−	21.9471i	0.197455	−	0.736912i	0.991618	−	0.129207i	$-0.0412431\pi$
$888$	0.616898	+	9.55489i	0.0207017	+	0.320641i
$889$	−32.9531			−1.10521
$890$	−36.4051	+	1.55187i	−1.22030	+	0.0520187i
$891$	17.0196	−	29.4787i	0.570177	−	0.987575i
$892$	24.7115	+	10.2547i	0.827401	+	0.343351i
$893$	−46.1326	+	12.3612i	−1.54377	+	0.413652i
$894$	4.69051	+	0.308964i	0.156874	+	0.0103333i
$895$	6.62714	−	8.24532i	0.221521	−	0.275611i
$896$	−10.0494	−	15.1144i	−0.335728	−	0.504937i
$897$	−5.27732	+	3.51256i	−0.176204	+	0.117281i
$898$	−27.3693	+	5.43484i	−0.913326	+	0.181363i
$899$	−0.552120	+	0.318766i	−0.0184142	+	0.0106315i
$900$	2.36804	+	27.7254i	0.0789348	+	0.924179i
$901$	11.1239	−	19.2671i	0.370589	−	0.641880i
$902$	−9.37061	−	47.1894i	−0.312007	−	1.57124i
$903$	−0.384912	+	0.103137i	−0.0128091	+	0.00343218i
$904$	−3.89799	+	4.43606i	−0.129645	+	0.147541i
$905$	−16.3192	−	42.0525i	−0.542467	−	1.39787i
$906$	−2.34366	−	4.75637i	−0.0778629	−	0.158020i
$907$	8.42212	−	31.4318i	0.279652	−	1.04367i	−0.673008	−	0.739636i	$-0.734998\pi$
$907$	8.42212	−	31.4318i	0.279652	−	1.04367i	0.952659	−	0.304039i	$-0.0983354\pi$
$908$	51.9064	−	6.79926i	1.72258	−	0.225641i
$909$			19.2859i			0.639671i
$910$	11.4893	−	14.2330i	0.380868	−	0.471820i
$911$			6.27808i			0.208002i	0.994577	+	0.104001i	$0.0331645\pi$
$911$			6.27808i			0.208002i	−0.994577	+	0.104001i	$0.966835\pi$
$912$	−6.52229	−	11.3309i	−0.215974	−	0.375205i
$913$	3.33129	−	12.4325i	0.110250	−	0.411457i
$914$	−11.2460	+	5.54138i	−0.371986	+	0.183293i
$915$	4.23585	+	1.86739i	0.140033	+	0.0617340i
$916$	−0.764246	+	5.77598i	−0.0252514	+	0.190844i
$917$	32.1807	−	8.62279i	1.06270	−	0.284750i
$918$	8.66822	−	1.72129i	0.286094	−	0.0568109i
$919$	4.44945	−	7.70667i	0.146774	−	0.254220i	−0.783260	−	0.621695i	$-0.786444\pi$
$919$	4.44945	−	7.70667i	0.146774	−	0.254220i	0.930033	+	0.367475i	$0.119778\pi$
$920$	15.3004	+	18.2968i	0.504441	+	0.603226i
$921$	5.40154	−	3.11858i	0.177987	−	0.102761i
$922$	2.37616	+	11.9661i	0.0782547	+	0.394083i
$923$	31.1312	+	46.7719i	1.02470	+	1.53952i
$924$	−2.74373	−	6.63617i	−0.0902622	−	0.218314i
$925$	16.7179	+	32.2257i	0.549680	+	1.05958i
$926$	0.663365	−	10.0708i	0.0217995	−	0.330947i
$927$	−1.70647	+	0.457246i	−0.0560477	+	0.0150179i
$928$	−0.905888	−	0.607428i	−0.0297372	−	0.0199398i
$929$	22.1120	−	38.2991i	0.725472	−	1.25655i	−0.233308	−	0.972403i	$-0.574955\pi$
$929$	22.1120	−	38.2991i	0.725472	−	1.25655i	0.958780	−	0.284151i	$-0.0917116\pi$
$930$	3.29722	−	3.59084i	0.108120	−	0.117748i
$931$	−31.0306			−1.01699
$932$	23.6421	−	18.1168i	0.774423	−	0.593436i
$933$	2.95325	−	11.0217i	0.0966851	−	0.360834i
$934$	−0.0548860	+	0.833245i	−0.00179592	+	0.0272646i
$935$	−22.7658	−	10.0364i	−0.744521	−	0.328225i
$936$	10.9320	−	26.1872i	0.357323	−	0.855954i
$937$	22.7928	−	22.7928i	0.744608	−	0.744608i	−0.228853	−	0.973461i	$-0.573497\pi$
$937$	22.7928	−	22.7928i	0.744608	−	0.744608i	0.973461	+	0.228853i	$0.0734975\pi$
$938$	21.5847	−	18.9168i	0.704764	−	0.617656i
$939$	−0.834222	−	1.44492i	−0.0272238	−	0.0471530i
$940$	15.8407	−	26.0251i	0.516668	−	0.848844i
$941$		−	38.0886i		−	1.24165i	−0.783948	−	0.620827i	$-0.786797\pi$
$941$		−	38.0886i		−	1.24165i	0.783948	−	0.620827i	$-0.213203\pi$
$942$	5.35333	+	1.81915i	0.174421	+	0.0592712i
$943$	25.8151	−	6.91715i	0.840657	−	0.225253i
$944$	−1.79863	−	1.80331i	−0.0585403	−	0.0586928i
$945$	9.55782	+	1.47800i	0.310916	+	0.0480793i
$946$	3.60901	+	0.237726i	0.117339	+	0.00772914i
$947$	−15.5139	−	4.15694i	−0.504135	−	0.135082i	−0.00221640	−	0.999998i	$-0.500706\pi$
$947$	−15.5139	−	4.15694i	−0.504135	−	0.135082i	−0.501918	+	0.864915i	$0.667372\pi$
$948$	−3.21313	+	7.74294i	−0.104358	+	0.251479i
$949$	7.66890	+	22.7253i	0.248943	+	0.737693i
$950$	−39.9261	−	29.3818i	−1.29537	−	0.953271i
$951$	5.25500	+	9.10193i	0.170405	+	0.295150i
$952$	−4.66099	+	9.42836i	−0.151064	+	0.305575i
$953$	−47.8050	+	12.8093i	−1.54855	+	0.414934i	−0.929018	−	0.370034i	$-0.879346\pi$
$953$	−47.8050	+	12.8093i	−1.54855	+	0.414934i	−0.619536	+	0.784968i	$0.712679\pi$
$954$	20.9951	−	31.3993i	0.679741	−	1.01659i
$955$	−1.50662	+	9.74291i	−0.0487531	+	0.315273i
$956$	52.7611	+	6.98105i	1.70642	+	0.225783i
$957$	−0.305130	−	0.305130i	−0.00986345	−	0.00986345i
$958$	−13.0674	−	4.44054i	−0.422190	−	0.143467i
$959$	−5.36522	−	9.29283i	−0.173252	−	0.300081i
$960$	8.00073	+	2.35509i	0.258222	+	0.0760101i
$961$	−20.0666			−0.647311
$962$	0.0782413	−	37.0229i	0.00252260	−	1.19367i
$963$	24.4045	−	24.4045i	0.786425	−	0.786425i
$964$	27.4815	−	35.7664i	0.885120	−	1.15196i
$965$	−1.47582	−	13.5641i	−0.0475083	−	0.436643i
$966$	3.57827	−	1.76316i	0.115129	−	0.0567288i
$967$	−18.8015	+	18.8015i	−0.604614	+	0.604614i	−0.941534	−	0.336919i	$-0.890615\pi$
$967$	−18.8015	+	18.8015i	−0.604614	+	0.604614i	0.336919	+	0.941534i	$0.390615\pi$
$968$	2.19475	+	33.9937i	0.0705421	+	1.09260i
$969$	−3.78799	+	6.56099i	−0.121688	+	0.210769i
$970$	9.19744	−	41.2854i	0.295312	−	1.32560i
$971$	−10.1188	−	5.84210i	−0.324728	−	0.187482i	0.328770	−	0.944410i	$-0.393366\pi$
$971$	−10.1188	−	5.84210i	−0.324728	−	0.187482i	−0.653498	+	0.756928i	$0.726699\pi$
$972$	22.5951	−	2.95975i	0.724739	−	0.0949341i
$973$	4.08984	+	1.09587i	0.131114	+	0.0351320i
$974$	−20.9229	+	31.2914i	−0.670414	+	1.00264i
$975$	0.156464	+	8.40360i	0.00501087	+	0.269131i
$976$	−12.5757	+	12.5430i	−0.402539	+	0.401492i
$977$	−0.205364	+	0.766427i	−0.00657016	+	0.0245202i	−0.969133	−	0.246538i	$-0.920707\pi$
$977$	−0.205364	+	0.766427i	−0.00657016	+	0.0245202i	0.962563	+	0.271058i	$0.0873736\pi$
$978$	−5.24270	−	5.98208i	−0.167643	−	0.191286i
$979$	27.6568	−	47.9029i	0.883914	−	1.53098i
$980$	14.3177	−	13.6690i	0.457362	−	0.436641i
$981$	10.2730	+	5.93111i	0.327991	+	0.189366i
$982$	22.0132	+	7.48044i	0.702468	+	0.238711i
$983$	15.9514	+	15.9514i	0.508772	+	0.508772i	0.914149	−	0.405378i	$-0.132860\pi$
$983$	15.9514	+	15.9514i	0.508772	+	0.508772i	−0.405378	+	0.914149i	$0.632860\pi$
$984$	6.16868	−	7.02020i	0.196650	−	0.223796i
$985$	−22.5663	+	2.45529i	−0.719022	+	0.0782320i
$986$	−0.0415411	+	0.630651i	−0.00132294	+	0.0200840i
$987$	−3.60312	−	3.60312i	−0.114688	−	0.114688i
$988$	22.2487	+	45.3946i	0.707825	+	1.44419i
$989$			2.00917i			0.0638878i
$990$	−37.4478	−	19.5432i	−1.19017	−	0.621124i
$991$	5.92977	−	3.42356i	0.188365	−	0.108753i	−0.402852	−	0.915265i	$-0.631981\pi$
$991$	5.92977	−	3.42356i	0.188365	−	0.108753i	0.591217	+	0.806512i	$0.298648\pi$
$992$	8.24560	+	16.7892i	0.261798	+	0.533058i
$993$	7.50654	−	7.50654i	0.238213	−	0.238213i
$994$	−15.6266	−	31.7136i	−0.495646	−	1.00590i
$995$	−9.40687	−	1.45465i	−0.298218	−	0.0461156i
$996$	2.31048	−	0.955271i	0.0732103	−	0.0302689i
$997$	5.38526	+	20.0981i	0.170553	+	0.636512i	0.997266	+	0.0738892i	$0.0235411\pi$
$997$	5.38526	+	20.0981i	0.170553	+	0.636512i	−0.826713	+	0.562623i	$0.809792\pi$
$998$	−14.0419	+	12.3064i	−0.444490	+	0.389551i
$999$	16.9528	−	9.78768i	0.536361	−	0.309668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bg.c.23.11	✓	144
4.3	odd	2	inner	260.2.bg.c.23.33	yes	144
5.2	odd	4	inner	260.2.bg.c.127.29	yes	144
13.4	even	6	inner	260.2.bg.c.43.22	yes	144
20.7	even	4	inner	260.2.bg.c.127.22	yes	144
52.43	odd	6	inner	260.2.bg.c.43.29	yes	144
65.17	odd	12	inner	260.2.bg.c.147.33	yes	144
260.147	even	12	inner	260.2.bg.c.147.11	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bg.c.23.11	✓	144	1.1	even	1	trivial
260.2.bg.c.23.33	yes	144	4.3	odd	2	inner
260.2.bg.c.43.22	yes	144	13.4	even	6	inner
260.2.bg.c.43.29	yes	144	52.43	odd	6	inner
260.2.bg.c.127.22	yes	144	20.7	even	4	inner
260.2.bg.c.127.29	yes	144	5.2	odd	4	inner
260.2.bg.c.147.11	yes	144	260.147	even	12	inner
260.2.bg.c.147.33	yes	144	65.17	odd	12	inner

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.bg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.932110 - 1.06357i) q^{2} +(-0.450342 - 0.120669i) q^{3} +(-0.262342 + 1.98272i) q^{4} +(-0.808965 - 2.08460i) q^{5} +(0.291429 + 0.591445i) q^{6} +(0.415219 + 1.54962i) q^{7} +(2.35328 - 1.56909i) q^{8} +(-2.40983 - 1.39132i) q^{9} +(-1.46307 + 2.80347i) q^{10} +(-2.40019 - 4.15725i) q^{11} +(0.357396 - 0.861246i) q^{12} +(-1.60047 + 3.23086i) q^{13} +(1.26109 - 1.88603i) q^{14} +(0.112764 + 1.03640i) q^{15} +(-3.86235 - 1.04030i) q^{16} +(0.599908 + 2.23889i) q^{17} +(0.766471 + 3.85987i) q^{18} +(-6.07130 - 3.50527i) q^{19} +(4.34541 - 1.05707i) q^{20} -0.747963i q^{21} +(-2.18427 + 6.42777i) q^{22} +(-3.64269 - 0.976056i) q^{23} +(-1.24912 + 0.422661i) q^{24} +(-3.69115 + 3.37274i) q^{25} +(4.92805 - 1.30931i) q^{26} +(1.90638 + 1.90638i) q^{27} +(-3.18139 + 0.416732i) q^{28} +(-0.166977 + 0.0964041i) q^{29} +(0.997173 - 1.08597i) q^{30} +3.30656 q^{31} +(2.49371 + 5.07754i) q^{32} +(0.579256 + 2.16181i) q^{33} +(1.82202 - 2.72493i) q^{34} +(2.89444 - 2.11915i) q^{35} +(3.39079 - 4.41301i) q^{36} +(1.87924 - 7.01341i) q^{37} +(1.93104 + 9.72452i) q^{38} +(1.11063 - 1.26187i) q^{39} +(-5.17466 - 3.63632i) q^{40} +(-6.13738 + 3.54342i) q^{41} +(-0.795507 + 0.697183i) q^{42} +(-0.137890 - 0.514614i) q^{43} +(8.87233 - 3.66828i) q^{44} +(-0.950876 + 6.14907i) q^{45} +(2.35729 + 4.78403i) q^{46} +(4.81724 - 4.81724i) q^{47} +(1.61385 + 0.934558i) q^{48} +(3.83327 - 2.21314i) q^{49} +(7.02769 + 0.782015i) q^{50} -1.08066i q^{51} +(-5.98603 - 4.02088i) q^{52} +(-6.78706 - 6.78706i) q^{53} +(0.250604 - 3.80451i) q^{54} +(-6.72455 + 8.36651i) q^{55} +(3.40863 + 2.99517i) q^{56} +(2.31119 + 2.31119i) q^{57} +(0.258173 + 0.0877316i) q^{58} +(0.551432 + 0.318370i) q^{59} +(-2.08448 - 0.0483125i) q^{60} +(2.22021 - 3.84551i) q^{61} +(-3.08208 - 3.51675i) q^{62} +(1.15540 - 4.31202i) q^{63} +(3.07589 - 7.38505i) q^{64} +(8.02980 + 0.722701i) q^{65} +(1.75930 - 2.63112i) q^{66} +(12.2192 + 3.27413i) q^{67} +(-4.59647 + 0.602095i) q^{68} +(1.52268 + 0.879118i) q^{69} +(-4.95180 - 1.10315i) q^{70} +(7.79147 - 13.4952i) q^{71} +(-7.85412 + 0.507089i) q^{72} +(4.70372 - 4.70372i) q^{73} +(-9.21087 + 4.53857i) q^{74} +(2.06927 - 1.07348i) q^{75} +(8.54272 - 11.1181i) q^{76} +(5.44554 - 5.44554i) q^{77} +(-2.37730 - 0.00502400i) q^{78} -8.99039 q^{79} +(0.955888 + 8.89305i) q^{80} +(3.54546 + 6.14092i) q^{81} +(9.48937 + 3.22465i) q^{82} +(1.89595 + 1.89595i) q^{83} +(1.48300 + 0.196222i) q^{84} +(4.18189 - 3.06175i) q^{85} +(-0.418797 + 0.626332i) q^{86} +(0.0868297 - 0.0232660i) q^{87} +(-12.1714 - 6.01706i) q^{88} +(5.76138 + 9.97900i) q^{89} +(7.42625 - 4.72029i) q^{90} +(-5.67115 - 1.13861i) q^{91} +(2.89088 - 6.96637i) q^{92} +(-1.48909 - 0.398999i) q^{93} +(-9.61365 - 0.633252i) q^{94} +(-2.39563 + 15.4919i) q^{95} +(-0.510321 - 2.58754i) q^{96} +(-12.9199 + 3.46187i) q^{97} +(-5.92684 - 2.01404i) q^{98} +13.3577i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 6 q^{2} - 12 q^{6} + 12 q^{10} - 12 q^{12} + 4 q^{13} - 12 q^{16} - 24 q^{17} - 42 q^{20} - 12 q^{22} - 24 q^{25} - 36 q^{26} - 6 q^{28} - 36 q^{32} - 12 q^{33} - 76 q^{36} + 48 q^{37} - 16 q^{38}+ \cdots - 162 q^{98}+O(q^{100}) \) 144 * q - 6 * q^2 - 12 * q^6 + 12 * q^10 - 12 * q^12 + 4 * q^13 - 12 * q^16 - 24 * q^17 - 42 * q^20 - 12 * q^22 - 24 * q^25 - 36 * q^26 - 6 * q^28 - 36 * q^32 - 12 * q^33 - 76 * q^36 + 48 * q^37 - 16 * q^38 + 76 * q^40 - 72 * q^41 + 40 * q^42 - 120 * q^45 - 12 * q^46 - 40 * q^48 + 120 * q^50 - 10 * q^52 + 8 * q^53 - 20 * q^56 + 126 * q^58 + 16 * q^61 - 44 * q^62 + 32 * q^65 + 96 * q^66 - 64 * q^68 - 54 * q^72 - 12 * q^76 + 40 * q^77 - 100 * q^78 - 24 * q^80 - 32 * q^81 - 78 * q^82 - 24 * q^85 - 10 * q^88 - 8 * q^90 + 100 * q^92 - 48 * q^93 - 12 * q^97 - 162 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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