LMFDB - Embedded newform 175.2.n.a.169.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(29,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("175.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.n (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			169.13
Character	$\chi$	$=$	175.169
Dual form			175.2.n.a.29.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.11404 - 0.686892i) q^{2} +(0.515049 + 0.708904i) q^{3} +(2.37929 - 1.72866i) q^{4} +(-1.55449 + 1.60734i) q^{5} +(1.57577 + 1.14486i) q^{6} -1.00000i q^{7} +(1.22941 - 1.69214i) q^{8} +(0.689782 - 2.12293i) q^{9} +O(q^{10})$	\(q+(2.11404 - 0.686892i) q^{2} +(0.515049 + 0.708904i) q^{3} +(2.37929 - 1.72866i) q^{4} +(-1.55449 + 1.60734i) q^{5} +(1.57577 + 1.14486i) q^{6} -1.00000i q^{7} +(1.22941 - 1.69214i) q^{8} +(0.689782 - 2.12293i) q^{9} +(-2.18219 + 4.46575i) q^{10} +(-0.121412 - 0.373666i) q^{11} +(2.45090 + 0.796346i) q^{12} +(-2.20066 - 0.715037i) q^{13} +(-0.686892 - 2.11404i) q^{14} +(-1.94009 - 0.274128i) q^{15} +(-0.380912 + 1.17233i) q^{16} +(-1.50959 + 2.07778i) q^{17} -4.96175i q^{18} +(-2.59114 - 1.88257i) q^{19} +(-0.920054 + 6.51152i) q^{20} +(0.708904 - 0.515049i) q^{21} +(-0.513337 - 0.706547i) q^{22} +(-2.83538 + 0.921271i) q^{23} +1.83277 q^{24} +(-0.167094 - 4.99721i) q^{25} -5.14342 q^{26} +(4.36032 - 1.41675i) q^{27} +(-1.72866 - 2.37929i) q^{28} +(-1.59035 + 1.15546i) q^{29} +(-4.28971 + 0.753116i) q^{30} +(7.28014 + 5.28933i) q^{31} +6.92319i q^{32} +(0.202361 - 0.278525i) q^{33} +(-1.76412 + 5.42942i) q^{34} +(1.60734 + 1.55449i) q^{35} +(-2.02862 - 6.24346i) q^{36} +(5.74156 + 1.86554i) q^{37} +(-6.77088 - 2.19999i) q^{38} +(-0.626553 - 1.92833i) q^{39} +(0.808734 + 4.60651i) q^{40} +(1.76779 - 5.44071i) q^{41} +(1.14486 - 1.57577i) q^{42} -9.34864i q^{43} +(-0.934814 - 0.679182i) q^{44} +(2.34001 + 4.40880i) q^{45} +(-5.36128 + 3.89520i) q^{46} +(1.79851 + 2.47544i) q^{47} +(-1.02726 + 0.333776i) q^{48} -1.00000 q^{49} +(-3.78578 - 10.4495i) q^{50} -2.25046 q^{51} +(-6.47205 + 2.10290i) q^{52} +(6.06474 + 8.34740i) q^{53} +(8.24472 - 5.99014i) q^{54} +(0.789343 + 0.385712i) q^{55} +(-1.69214 - 1.22941i) q^{56} -2.80648i q^{57} +(-2.56839 + 3.53508i) q^{58} +(-1.53233 + 4.71604i) q^{59} +(-5.08991 + 2.70152i) q^{60} +(-3.30596 - 10.1747i) q^{61} +(19.0237 + 6.18116i) q^{62} +(-2.12293 - 0.689782i) q^{63} +(3.99366 + 12.2912i) q^{64} +(4.57022 - 2.42569i) q^{65} +(0.236481 - 0.727812i) q^{66} +(-9.25908 + 12.7440i) q^{67} +7.55320i q^{68} +(-2.11345 - 1.53551i) q^{69} +(4.46575 + 2.18219i) q^{70} +(9.95930 - 7.23586i) q^{71} +(-2.74427 - 3.77716i) q^{72} +(1.27164 - 0.413179i) q^{73} +13.4193 q^{74} +(3.45648 - 2.69226i) q^{75} -9.41939 q^{76} +(-0.373666 + 0.121412i) q^{77} +(-2.64911 - 3.64619i) q^{78} +(0.855018 - 0.621207i) q^{79} +(-1.29220 - 2.43463i) q^{80} +(-2.16750 - 1.57478i) q^{81} -12.7161i q^{82} +(-8.36057 + 11.5073i) q^{83} +(0.796346 - 2.45090i) q^{84} +(-0.993042 - 5.65632i) q^{85} +(-6.42150 - 19.7634i) q^{86} +(-1.63822 - 0.532289i) q^{87} +(-0.781561 - 0.253945i) q^{88} +(-4.34169 - 13.3623i) q^{89} +(7.97523 + 7.71302i) q^{90} +(-0.715037 + 2.20066i) q^{91} +(-5.15363 + 7.09337i) q^{92} +7.88518i q^{93} +(5.50247 + 3.99778i) q^{94} +(7.05385 - 1.23840i) q^{95} +(-4.90787 + 3.56578i) q^{96} +(-10.0074 - 13.7740i) q^{97} +(-2.11404 + 0.686892i) q^{98} -0.877015 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9}+O(q^{10}) $ 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9	$ 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9} - 4 q^{10} + 8 q^{11} - 40 q^{12} - 4 q^{14} - 18 q^{15} - 32 q^{16} + 12 q^{19} + 12 q^{20} + 4 q^{21} - 30 q^{22} + 10 q^{23} - 28 q^{24} + 4 q^{25} + 12 q^{26} + 30 q^{27} - 2 q^{29} + 28 q^{30} + 12 q^{31} + 20 q^{33} + 2 q^{35} - 14 q^{36} - 70 q^{37} - 70 q^{38} - 4 q^{39} - 30 q^{40} + 4 q^{41} + 50 q^{42} + 22 q^{44} - 52 q^{45} - 4 q^{46} - 10 q^{47} + 30 q^{48} - 56 q^{49} - 54 q^{50} - 44 q^{51} - 20 q^{53} + 54 q^{54} - 2 q^{55} + 12 q^{56} + 10 q^{58} - 6 q^{59} + 16 q^{60} - 4 q^{61} + 50 q^{62} + 20 q^{63} + 24 q^{64} - 18 q^{65} - 74 q^{66} + 10 q^{67} - 78 q^{69} + 8 q^{70} - 8 q^{71} + 140 q^{72} + 40 q^{73} + 60 q^{74} - 8 q^{75} + 52 q^{76} - 20 q^{77} - 90 q^{78} + 124 q^{80} - 72 q^{81} - 30 q^{83} - 12 q^{84} + 96 q^{85} - 20 q^{86} + 30 q^{87} + 140 q^{88} + 38 q^{89} - 8 q^{90} + 8 q^{91} + 80 q^{92} + 88 q^{94} - 70 q^{95} - 28 q^{96} - 30 q^{97} + 60 q^{99}+O(q^{100}) $ 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9 - 4 * q^10 + 8 * q^11 - 40 * q^12 - 4 * q^14 - 18 * q^15 - 32 * q^16 + 12 * q^19 + 12 * q^20 + 4 * q^21 - 30 * q^22 + 10 * q^23 - 28 * q^24 + 4 * q^25 + 12 * q^26 + 30 * q^27 - 2 * q^29 + 28 * q^30 + 12 * q^31 + 20 * q^33 + 2 * q^35 - 14 * q^36 - 70 * q^37 - 70 * q^38 - 4 * q^39 - 30 * q^40 + 4 * q^41 + 50 * q^42 + 22 * q^44 - 52 * q^45 - 4 * q^46 - 10 * q^47 + 30 * q^48 - 56 * q^49 - 54 * q^50 - 44 * q^51 - 20 * q^53 + 54 * q^54 - 2 * q^55 + 12 * q^56 + 10 * q^58 - 6 * q^59 + 16 * q^60 - 4 * q^61 + 50 * q^62 + 20 * q^63 + 24 * q^64 - 18 * q^65 - 74 * q^66 + 10 * q^67 - 78 * q^69 + 8 * q^70 - 8 * q^71 + 140 * q^72 + 40 * q^73 + 60 * q^74 - 8 * q^75 + 52 * q^76 - 20 * q^77 - 90 * q^78 + 124 * q^80 - 72 * q^81 - 30 * q^83 - 12 * q^84 + 96 * q^85 - 20 * q^86 + 30 * q^87 + 140 * q^88 + 38 * q^89 - 8 * q^90 + 8 * q^91 + 80 * q^92 + 88 * q^94 - 70 * q^95 - 28 * q^96 - 30 * q^97 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	2.11404	−	0.686892i	1.49485	−	0.485706i	0.556338	−	0.830956i	$-0.312206\pi$
$2$	2.11404	−	0.686892i	1.49485	−	0.485706i	0.938511	+	0.345250i	$0.112206\pi$
$3$	0.515049	+	0.708904i	0.297363	+	0.409286i	0.931388	−	0.364027i	$-0.118598\pi$
$3$	0.515049	+	0.708904i	0.297363	+	0.409286i	−0.634025	+	0.773313i	$0.718598\pi$
$4$	2.37929	−	1.72866i	1.18964	−	0.864328i
$5$	−1.55449	+	1.60734i	−0.695191	+	0.718825i
$5$	−1.55449	+	1.60734i	−0.695191	+	0.718825i
$6$	1.57577	+	1.14486i	0.643306	+	0.467389i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	1.22941	−	1.69214i	0.434663	−	0.598262i
$9$	0.689782	−	2.12293i	0.229927	−	0.707643i
$10$	−2.18219	+	4.46575i	−0.690068	+	1.41219i
$11$	−0.121412	−	0.373666i	−0.0366070	−	0.112665i	0.931083	−	0.364807i	$-0.118865\pi$
$11$	−0.121412	−	0.373666i	−0.0366070	−	0.112665i	−0.967690	+	0.252142i	$0.918865\pi$
$12$	2.45090	+	0.796346i	0.707514	+	0.229885i
$13$	−2.20066	−	0.715037i	−0.610352	−	0.198316i	−0.0125002	−	0.999922i	$-0.503979\pi$
$13$	−2.20066	−	0.715037i	−0.610352	−	0.198316i	−0.597852	+	0.801606i	$0.703979\pi$
$14$	−0.686892	−	2.11404i	−0.183580	−	0.565000i
$15$	−1.94009	−	0.274128i	−0.500929	−	0.0707795i
$16$	−0.380912	+	1.17233i	−0.0952281	+	0.293082i
$17$	−1.50959	+	2.07778i	−0.366130	+	0.503935i	−0.951844	−	0.306583i	$-0.900814\pi$
$17$	−1.50959	+	2.07778i	−0.366130	+	0.503935i	0.585714	+	0.810518i	$0.300814\pi$
$18$		−	4.96175i		−	1.16950i
$19$	−2.59114	−	1.88257i	−0.594448	−	0.431892i	0.249456	−	0.968386i	$-0.419748\pi$
$19$	−2.59114	−	1.88257i	−0.594448	−	0.431892i	−0.843904	+	0.536494i	$0.819748\pi$
$20$	−0.920054	+	6.51152i	−0.205730	+	1.45602i
$21$	0.708904	−	0.515049i	0.154695	−	0.112393i
$22$	−0.513337	−	0.706547i	−0.109444	−	0.150636i
$23$	−2.83538	+	0.921271i	−0.591218	+	0.192098i	−0.589320	−	0.807900i	$-0.700604\pi$
$23$	−2.83538	+	0.921271i	−0.591218	+	0.192098i	−0.00189810	+	0.999998i	$0.500604\pi$
$24$	1.83277			0.374113
$25$	−0.167094	−	4.99721i	−0.0334187	−	0.999441i
$26$	−5.14342			−1.00871
$27$	4.36032	−	1.41675i	0.839144	−	0.272655i
$28$	−1.72866	−	2.37929i	−0.326685	−	0.449644i
$29$	−1.59035	+	1.15546i	−0.295321	+	0.214563i	−0.725572	−	0.688146i	$-0.758425\pi$
$29$	−1.59035	+	1.15546i	−0.295321	+	0.214563i	0.430251	+	0.902709i	$0.358425\pi$
$30$	−4.28971	+	0.753116i	−0.783191	+	0.137500i
$31$	7.28014	+	5.28933i	1.30755	+	0.949992i	0.999999	−	0.00153963i	$-0.000490081\pi$
$31$	7.28014	+	5.28933i	1.30755	+	0.949992i	0.307552	+	0.951531i	$0.400490\pi$
$32$			6.92319i			1.22386i
$33$	0.202361	−	0.278525i	0.0352265	−	0.0484850i
$34$	−1.76412	+	5.42942i	−0.302545	+	0.931137i
$35$	1.60734	+	1.55449i	0.271690	+	0.262758i
$36$	−2.02862	−	6.24346i	−0.338104	−	1.04058i
$37$	5.74156	+	1.86554i	0.943906	+	0.306694i	0.740237	−	0.672346i	$-0.234713\pi$
$37$	5.74156	+	1.86554i	0.943906	+	0.306694i	0.203669	+	0.979040i	$0.434713\pi$
$38$	−6.77088	−	2.19999i	−1.09838	−	0.356886i
$39$	−0.626553	−	1.92833i	−0.100329	−	0.308780i
$40$	0.808734	+	4.60651i	0.127872	+	0.728353i
$41$	1.76779	−	5.44071i	0.276083	−	0.849697i	−0.712848	−	0.701319i	$-0.752595\pi$
$41$	1.76779	−	5.44071i	0.276083	−	0.849697i	0.988931	−	0.148378i	$-0.0474051\pi$
$42$	1.14486	−	1.57577i	0.176656	−	0.243147i
$43$		−	9.34864i		−	1.42565i	−0.701340	−	0.712827i	$-0.747414\pi$
$43$		−	9.34864i		−	1.42565i	0.701340	−	0.712827i	$-0.252586\pi$
$44$	−0.934814	−	0.679182i	−0.140928	−	0.102391i
$45$	2.34001	+	4.40880i	0.348828	+	0.657225i
$46$	−5.36128	+	3.89520i	−0.790478	+	0.574316i
$47$	1.79851	+	2.47544i	0.262339	+	0.361079i	0.919785	−	0.392423i	$-0.128363\pi$
$47$	1.79851	+	2.47544i	0.262339	+	0.361079i	−0.657445	+	0.753502i	$0.728363\pi$
$48$	−1.02726	+	0.333776i	−0.148272	+	0.0481764i
$49$	−1.00000			−0.142857
$50$	−3.78578	−	10.4495i	−0.535390	−	1.47778i
$51$	−2.25046			−0.315127
$52$	−6.47205	+	2.10290i	−0.897512	+	0.291619i
$53$	6.06474	+	8.34740i	0.833056	+	1.14660i	0.987346	+	0.158578i	$0.0506909\pi$
$53$	6.06474	+	8.34740i	0.833056	+	1.14660i	−0.154290	+	0.988026i	$0.549309\pi$
$54$	8.24472	−	5.99014i	1.12196	−	0.815154i
$55$	0.789343	+	0.385712i	0.106435	+	0.0520095i
$56$	−1.69214	−	1.22941i	−0.226122	−	0.164287i
$57$		−	2.80648i		−	0.371728i
$58$	−2.56839	+	3.53508i	−0.337246	+	0.464179i
$59$	−1.53233	+	4.71604i	−0.199493	+	0.613976i	0.800402	+	0.599464i	$0.204619\pi$
$59$	−1.53233	+	4.71604i	−0.199493	+	0.613976i	−0.999895	+	0.0145120i	$0.995381\pi$
$60$	−5.08991	+	2.70152i	−0.657105	+	0.348765i
$61$	−3.30596	−	10.1747i	−0.423285	−	1.30274i	−0.904627	−	0.426205i	$-0.859850\pi$
$61$	−3.30596	−	10.1747i	−0.423285	−	1.30274i	0.481342	−	0.876533i	$-0.340150\pi$
$62$	19.0237	+	6.18116i	2.41601	+	0.785008i
$63$	−2.12293	−	0.689782i	−0.267464	−	0.0869043i
$64$	3.99366	+	12.2912i	0.499207	+	1.53640i
$65$	4.57022	−	2.42569i	0.566866	−	0.300869i
$66$	0.236481	−	0.727812i	0.0291087	−	0.0895875i
$67$	−9.25908	+	12.7440i	−1.13118	+	1.55693i	−0.345360	+	0.938470i	$0.612243\pi$
$67$	−9.25908	+	12.7440i	−1.13118	+	1.55693i	−0.785816	+	0.618460i	$0.787757\pi$
$68$			7.55320i			0.915959i
$69$	−2.11345	−	1.53551i	−0.254430	−	0.184854i
$70$	4.46575	+	2.18219i	0.533759	+	0.260821i
$71$	9.95930	−	7.23586i	1.18195	−	0.858738i	0.189562	−	0.981869i	$-0.439293\pi$
$71$	9.95930	−	7.23586i	1.18195	−	0.858738i	0.992390	+	0.123130i	$0.0392934\pi$
$72$	−2.74427	−	3.77716i	−0.323415	−	0.445143i
$73$	1.27164	−	0.413179i	0.148834	−	0.0483590i	−0.233653	−	0.972320i	$-0.575068\pi$
$73$	1.27164	−	0.413179i	0.148834	−	0.0483590i	0.382486	+	0.923961i	$0.375068\pi$
$74$	13.4193			1.55996
$75$	3.45648	−	2.69226i	0.399120	−	0.310875i
$76$	−9.41939			−1.08048
$77$	−0.373666	+	0.121412i	−0.0425832	+	0.0138361i
$78$	−2.64911	−	3.64619i	−0.299953	−	0.412849i
$79$	0.855018	−	0.621207i	0.0961970	−	0.0698912i	−0.538647	−	0.842532i	$-0.681064\pi$
$79$	0.855018	−	0.621207i	0.0961970	−	0.0698912i	0.634844	+	0.772640i	$0.281064\pi$
$80$	−1.29220	−	2.43463i	−0.144473	−	0.272200i
$81$	−2.16750	−	1.57478i	−0.240833	−	0.174975i
$82$		−	12.7161i		−	1.40426i
$83$	−8.36057	+	11.5073i	−0.917692	+	1.26309i	0.0467794	+	0.998905i	$0.485104\pi$
$83$	−8.36057	+	11.5073i	−0.917692	+	1.26309i	−0.964471	+	0.264189i	$0.914896\pi$
$84$	0.796346	−	2.45090i	0.0868884	−	0.267415i
$85$	−0.993042	−	5.65632i	−0.107711	−	0.613514i
$86$	−6.42150	−	19.7634i	−0.692448	−	2.13114i
$87$	−1.63822	−	0.532289i	−0.175635	−	0.0570674i
$88$	−0.781561	−	0.253945i	−0.0833147	−	0.0270706i
$89$	−4.34169	−	13.3623i	−0.460218	−	1.41640i	−0.864898	−	0.501947i	$-0.832617\pi$
$89$	−4.34169	−	13.3623i	−0.460218	−	1.41640i	0.404681	−	0.914458i	$-0.367383\pi$
$90$	7.97523	+	7.71302i	0.840663	+	0.813024i
$91$	−0.715037	+	2.20066i	−0.0749562	+	0.230692i
$92$	−5.15363	+	7.09337i	−0.537303	+	0.739535i
$93$			7.88518i			0.817655i
$94$	5.50247	+	3.99778i	0.567536	+	0.412339i
$95$	7.05385	−	1.23840i	0.723710	−	0.127057i
$96$	−4.90787	+	3.56578i	−0.500908	+	0.363931i
$97$	−10.0074	−	13.7740i	−1.01609	−	1.39853i	−0.914906	−	0.403667i	$-0.867736\pi$
$97$	−10.0074	−	13.7740i	−1.01609	−	1.39853i	−0.101188	−	0.994867i	$-0.532264\pi$
$98$	−2.11404	+	0.686892i	−0.213550	+	0.0693865i
$99$	−0.877015			−0.0881433
$100$	−9.03601	−	11.6010i	−0.903601	−	1.16010i
$101$	13.0194			1.29547			0.647737	−	0.761864i	$-0.275715\pi$
$101$	13.0194			1.29547			0.647737	+	0.761864i	$0.275715\pi$
$102$	−4.75754	+	1.54582i	−0.471067	+	0.153059i
$103$	1.66360	+	2.28975i	0.163920	+	0.225616i	0.883073	−	0.469235i	$-0.155470\pi$
$103$	1.66360	+	2.28975i	0.163920	+	0.225616i	−0.719154	+	0.694851i	$0.755470\pi$
$104$	−3.91546	+	2.84475i	−0.383942	+	0.278950i
$105$	−0.274128	+	1.94009i	−0.0267521	+	0.189333i
$106$	18.5548	+	13.4809i	1.80220	+	1.30938i
$107$			7.07518i			0.683984i	0.939703	+	0.341992i	$0.111102\pi$
$107$			7.07518i			0.683984i	−0.939703	+	0.341992i	$0.888898\pi$
$108$	7.92539	−	10.9084i	0.762621	−	1.04966i
$109$	0.531071	−	1.63447i	0.0508674	−	0.156554i	−0.922396	−	0.386245i	$-0.873772\pi$
$109$	0.531071	−	1.63447i	0.0508674	−	0.156554i	0.973263	+	0.229692i	$0.0737718\pi$
$110$	1.93364	+	0.273217i	0.184365	+	0.0260502i
$111$	1.63469	+	5.03105i	0.155158	+	0.477527i
$112$	1.17233	+	0.380912i	0.110775	+	0.0359928i
$113$	1.16490	+	0.378498i	0.109584	+	0.0356061i	0.363296	−	0.931674i	$-0.381651\pi$
$113$	1.16490	+	0.378498i	0.109584	+	0.0356061i	−0.253712	+	0.967280i	$0.581651\pi$
$114$	−1.92775	−	5.93301i	−0.180550	−	0.555677i
$115$	2.92679	−	5.98954i	0.272924	−	0.558527i
$116$	−1.78652	+	5.49835i	−0.165874	+	0.510509i
$117$	−3.03595	+	4.17862i	−0.280673	+	0.386314i
$118$			11.0224i			1.01470i
$119$	2.07778	+	1.50959i	0.190469	+	0.138384i
$120$	−2.84903	+	2.94589i	−0.260080	+	0.268922i
$121$	8.77430	−	6.37490i	0.797664	−	0.579537i
$122$	−13.9778	−	19.2388i	−1.26549	−	1.74180i
$123$	4.76744	−	1.54904i	0.429866	−	0.139672i
$124$	26.4650			2.37663
$125$	8.29196	+	7.49955i	0.741656	+	0.670781i
$126$	−4.96175			−0.442028
$127$	−15.6844	+	5.09616i	−1.39176	+	0.452211i	−0.906518	−	0.422168i	$-0.861269\pi$
$127$	−15.6844	+	5.09616i	−1.39176	+	0.452211i	−0.485244	+	0.874379i	$0.661269\pi$
$128$	8.74676	+	12.0389i	0.773112	+	1.06410i
$129$	6.62728	−	4.81500i	0.583500	−	0.423937i
$130$	7.99542	−	8.26723i	0.701244	−	0.725084i
$131$	−1.31477	−	0.955236i	−0.114872	−	0.0834594i	0.528866	−	0.848705i	$-0.322617\pi$
$131$	−1.31477	−	0.955236i	−0.114872	−	0.0834594i	−0.643738	+	0.765246i	$0.722617\pi$
$132$		−	1.01250i		−	0.0881272i
$133$	−1.88257	+	2.59114i	−0.163240	+	0.224680i
$134$	−10.8202	+	33.3013i	−0.934727	+	2.87679i
$135$	−4.50089	+	9.21086i	−0.387375	+	0.792745i
$136$	1.65998	+	5.10889i	0.142342	+	0.438083i
$137$	11.0561	+	3.59235i	0.944587	+	0.306915i	0.740514	−	0.672041i	$-0.234582\pi$
$137$	11.0561	+	3.59235i	0.944587	+	0.306915i	0.204073	+	0.978956i	$0.434582\pi$
$138$	−5.52264	−	1.79441i	−0.470118	−	0.152751i
$139$	−1.89409	−	5.82941i	−0.160655	−	0.494444i	0.838035	−	0.545616i	$-0.183704\pi$
$139$	−1.89409	−	5.82941i	−0.160655	−	0.494444i	−0.998690	+	0.0511720i	$0.983704\pi$
$140$	6.51152	+	0.920054i	0.550324	+	0.0777587i
$141$	−0.828525	+	2.54994i	−0.0697744	+	0.214744i
$142$	16.0841	−	22.1378i	1.34975	−	1.85776i
$143$			0.909125i			0.0760249i
$144$	2.22602	+	1.61730i	0.185502	+	0.134775i
$145$	0.614978	−	4.35240i	0.0510711	−	0.361447i
$146$	2.40447	−	1.74695i	0.198996	−	0.144579i
$147$	−0.515049	−	0.708904i	−0.0424805	−	0.0584694i
$148$	16.8857	−	5.48650i	1.38800	−	0.450987i
$149$	−15.0483			−1.23281			−0.616404	−	0.787430i	$-0.711411\pi$
$149$	−15.0483			−1.23281			−0.616404	+	0.787430i	$0.711411\pi$
$150$	5.45782	−	8.06575i	0.445629	−	0.658566i
$151$	−4.69108			−0.381755			−0.190878	−	0.981614i	$-0.561133\pi$
$151$	−4.69108			−0.381755			−0.190878	+	0.981614i	$0.561133\pi$
$152$	−6.37116	+	2.07012i	−0.516769	+	0.167909i
$153$	3.36968	+	4.63797i	0.272423	+	0.374958i
$154$	−0.706547	+	0.513337i	−0.0569352	+	0.0413658i
$155$	−19.8187	+	3.47943i	−1.59188	+	0.279475i
$156$	−4.82417	−	3.50497i	−0.386243	−	0.280622i
$157$		−	1.94047i		−	0.154867i	−0.996998	−	0.0774333i	$-0.975328\pi$
$157$		−	1.94047i		−	0.154867i	0.996998	−	0.0774333i	$-0.0246725\pi$
$158$	1.38084	−	1.90056i	0.109853	−	0.151200i
$159$	−2.79386	+	8.59863i	−0.221568	+	0.681916i
$160$	−11.1279	−	10.7621i	−0.879740	−	0.850816i
$161$	0.921271	+	2.83538i	0.0726063	+	0.223459i
$162$	−5.66386	−	1.84030i	−0.444995	−	0.144588i
$163$	15.1542	+	4.92389i	1.18697	+	0.385669i	0.834950	−	0.550325i	$-0.185496\pi$
$163$	15.1542	+	4.92389i	1.18697	+	0.385669i	0.352016	+	0.935994i	$0.385496\pi$
$164$	−5.19902	−	16.0009i	−0.405975	−	1.24946i
$165$	0.133117	+	0.758229i	0.0103632	+	0.0590280i
$166$	−9.77024	+	30.0697i	−0.758318	+	2.33386i
$167$	−6.57134	+	9.04468i	−0.508506	+	0.699898i	−0.983666	−	0.180001i	$-0.942390\pi$
$167$	−6.57134	+	9.04468i	−0.508506	+	0.699898i	0.475161	+	0.879899i	$0.342390\pi$
$168$		−	1.83277i		−	0.141401i
$169$	−6.18561	−	4.49411i	−0.475816	−	0.345701i
$170$	−5.98460	−	11.2755i	−0.458998	−	0.864795i
$171$	−5.78389	+	4.20224i	−0.442305	+	0.321354i
$172$	−16.1606	−	22.2431i	−1.23223	−	1.69602i
$173$	−15.3252	+	4.97945i	−1.16515	+	0.378581i	−0.826831	−	0.562450i	$-0.809859\pi$
$173$	−15.3252	+	4.97945i	−1.16515	+	0.378581i	−0.338321	+	0.941031i	$0.609859\pi$
$174$	−3.82888			−0.290266
$175$	−4.99721	+	0.167094i	−0.377753	+	0.0126311i
$176$	0.484307			0.0365060
$177$	−4.13244	+	1.34271i	−0.310613	+	0.100924i
$178$	−18.3570	−	25.2662i	−1.37591	−	1.89378i
$179$	−19.3867	+	14.0852i	−1.44903	+	1.05278i	−0.462969	+	0.886375i	$0.653216\pi$
$179$	−19.3867	+	14.0852i	−1.44903	+	1.05278i	−0.986058	+	0.166405i	$0.946784\pi$
$180$	13.1889	+	6.44474i	0.983039	+	0.480362i
$181$	−18.7843	−	13.6476i	−1.39623	−	1.01442i	−0.995150	−	0.0983725i	$-0.968636\pi$
$181$	−18.7843	−	13.6476i	−1.39623	−	1.01442i	−0.401076	−	0.916045i	$-0.631364\pi$
$182$			5.14342i			0.381256i
$183$	5.51015	−	7.58408i	0.407322	−	0.560631i
$184$	−1.92693	+	5.93049i	−0.142055	+	0.437201i
$185$	−11.9238	+	6.32866i	−0.876654	+	0.465292i
$186$	5.41626	+	16.6695i	0.397140	+	1.22227i
$187$	0.959677	+	0.311818i	0.0701785	+	0.0228024i
$188$	8.55835	+	2.78078i	0.624182	+	0.202809i
$189$	−1.41675	−	4.36032i	−0.103054	−	0.317167i
$190$	14.0614	−	7.46325i	1.02012	−	0.541441i
$191$	0.159524	−	0.490964i	0.0115427	−	0.0355249i	−0.945119	−	0.326726i	$-0.894055\pi$
$191$	0.159524	−	0.490964i	0.0115427	−	0.0355249i	0.956662	+	0.291201i	$0.0940547\pi$
$192$	−6.65636	+	9.16169i	−0.480381	+	0.661188i
$193$		−	24.3220i		−	1.75073i	−0.483460	−	0.875367i	$-0.660620\pi$
$193$		−	24.3220i		−	1.75073i	0.483460	−	0.875367i	$-0.339380\pi$
$194$	−30.6172	−	22.2447i	−2.19818	−	1.59707i
$195$	4.07346	+	1.99050i	0.291707	+	0.142542i
$196$	−2.37929	+	1.72866i	−0.169949	+	0.123475i
$197$	6.70301	+	9.22590i	0.477569	+	0.657318i	0.978036	−	0.208438i	$-0.0668380\pi$
$197$	6.70301	+	9.22590i	0.477569	+	0.657318i	−0.500466	+	0.865756i	$0.666838\pi$
$198$	−1.85404	+	0.602414i	−0.131761	+	0.0428117i
$199$	0.916451			0.0649655			0.0324827	−	0.999472i	$-0.489659\pi$
$199$	0.916451			0.0649655			0.0324827	+	0.999472i	$0.489659\pi$
$200$	−8.66141	−	5.86088i	−0.612454	−	0.414427i
$201$	−13.8032			−0.973600
$202$	27.5234	−	8.94289i	1.93654	−	0.629219i
$203$	1.15546	+	1.59035i	0.0810973	+	0.111621i
$204$	−5.35449	+	3.89026i	−0.374889	+	0.272373i
$205$	5.99706	+	11.2990i	0.418853	+	0.789157i
$206$	5.08972	+	3.69790i	0.354618	+	0.257645i
$207$			6.65479i			0.462540i
$208$	1.67651	−	2.30752i	0.116245	−	0.159998i
$209$	−0.388860	+	1.19679i	−0.0268980	+	0.0827835i
$210$	0.753116	+	4.28971i	0.0519700	+	0.296018i
$211$	6.87441	+	21.1573i	0.473254	+	1.45653i	0.848298	+	0.529519i	$0.177628\pi$
$211$	6.87441	+	21.1573i	0.473254	+	1.45653i	−0.375044	+	0.927007i	$0.622372\pi$
$212$	28.8596	+	9.37704i	1.98208	+	0.644018i
$213$	10.2591	+	3.33337i	0.702939	+	0.228399i
$214$	4.85988	+	14.9572i	0.332215	+	1.02245i
$215$	15.0265	+	14.5324i	1.02480	+	0.991102i
$216$	2.96329	−	9.12006i	0.201626	−	0.620541i
$217$	5.28933	−	7.28014i	0.359063	−	0.494208i
$218$		−	3.82011i		−	0.258731i
$219$	0.947858	+	0.688659i	0.0640503	+	0.0465353i
$220$	2.54484	−	0.446780i	0.171573	−	0.0301219i
$221$	4.80778	−	3.49306i	0.323406	−	0.234968i
$222$	6.91158	+	9.51297i	0.463875	+	0.638469i
$223$	−0.824913	+	0.268031i	−0.0552403	+	0.0179487i	−0.336507	−	0.941681i	$-0.609246\pi$
$223$	−0.824913	+	0.268031i	−0.0552403	+	0.0179487i	0.281267	+	0.959630i	$0.409246\pi$
$224$	6.92319			0.462575
$225$	−10.7240	−	3.09225i	−0.714932	−	0.206150i
$226$	2.72262			0.181106
$227$	−2.14652	+	0.697445i	−0.142469	+	0.0462911i	−0.379384	−	0.925239i	$-0.623864\pi$
$227$	−2.14652	+	0.697445i	−0.142469	+	0.0462911i	0.236914	+	0.971531i	$0.423864\pi$
$228$	−4.85145	−	6.67744i	−0.321295	−	0.442224i
$229$	9.47871	−	6.88669i	0.626371	−	0.455085i	−0.228770	−	0.973480i	$-0.573470\pi$
$229$	9.47871	−	6.88669i	0.626371	−	0.455085i	0.855141	+	0.518395i	$0.173470\pi$
$230$	2.07317	−	14.6725i	0.136701	−	0.967474i
$231$	−0.278525	−	0.202361i	−0.0183256	−	0.0133143i
$232$			4.11164i			0.269942i
$233$	3.02185	−	4.15922i	0.197968	−	0.272480i	−0.698479	−	0.715631i	$-0.746139\pi$
$233$	3.02185	−	4.15922i	0.197968	−	0.272480i	0.896447	+	0.443151i	$0.146139\pi$
$234$	−3.54784	+	10.9191i	−0.231929	+	0.713805i
$235$	−6.77464	−	0.957232i	−0.441929	−	0.0624429i
$236$	4.50654	+	13.8697i	0.293351	+	0.902840i
$237$	0.880752	+	0.286174i	0.0572110	+	0.0185890i
$238$	5.42942	+	1.76412i	0.351937	+	0.114351i
$239$	−2.39108	−	7.35899i	−0.154666	−	0.476013i	0.843461	−	0.537191i	$-0.180514\pi$
$239$	−2.39108	−	7.35899i	−0.154666	−	0.476013i	−0.998127	+	0.0611774i	$0.980514\pi$
$240$	1.06037	−	2.17000i	0.0684467	−	0.140073i
$241$	−4.09536	+	12.6042i	−0.263805	+	0.811908i	0.728161	+	0.685406i	$0.240375\pi$
$241$	−4.09536	+	12.6042i	−0.263805	+	0.811908i	−0.991966	+	0.126503i	$0.959625\pi$
$242$	14.1703	−	19.5038i	0.910902	−	1.25375i
$243$		−	16.1018i		−	1.03293i
$244$	−25.4544	−	18.4937i	−1.62955	−	1.18394i
$245$	1.55449	−	1.60734i	0.0993130	−	0.102689i
$246$	9.01452	−	6.54943i	0.574745	−	0.417576i
$247$	4.35610	+	5.99566i	0.277172	+	0.381495i
$248$	17.9006	−	5.81625i	1.13669	−	0.369332i
$249$	−12.4637			−0.789854
$250$	22.6809	+	10.1586i	1.43447	+	0.642489i
$251$	14.1607			0.893818			0.446909	−	0.894579i	$-0.352525\pi$
$251$	14.1607			0.893818			0.446909	+	0.894579i	$0.352525\pi$
$252$	−6.24346	+	2.02862i	−0.393301	+	0.127791i
$253$	0.688496	+	0.947634i	0.0432854	+	0.0595772i
$254$	−29.6568	+	21.5469i	−1.86083	+	1.35197i
$255$	3.49832	−	3.61725i	0.219073	−	0.226521i
$256$	5.84931	+	4.24977i	0.365582	+	0.265611i
$257$		−	12.2713i		−	0.765465i	−0.923859	−	0.382732i	$-0.874983\pi$
$257$		−	12.2713i		−	0.765465i	0.923859	−	0.382732i	$-0.125017\pi$
$258$	10.7029	−	14.7313i	0.666335	−	0.917131i
$259$	1.86554	−	5.74156i	0.115919	−	0.356763i
$260$	6.68070	−	13.6717i	0.414319	−	0.847885i
$261$	1.35596	+	4.17322i	0.0839320	+	0.258316i
$262$	−3.43561	−	1.11630i	−0.212253	−	0.0689651i
$263$	4.01602	+	1.30488i	0.247639	+	0.0804626i	0.430206	−	0.902731i	$-0.358441\pi$
$263$	4.01602	+	1.30488i	0.247639	+	0.0804626i	−0.182568	+	0.983193i	$0.558441\pi$
$264$	−0.222520	−	0.684845i	−0.0136951	−	0.0421493i
$265$	−22.8447	−	3.22788i	−1.40334	−	0.198287i
$266$	−2.19999	+	6.77088i	−0.134890	+	0.415150i
$267$	7.23643	−	9.96009i	0.442862	−	0.609548i
$268$			46.3275i			2.82990i
$269$	15.2520	+	11.0812i	0.929928	+	0.675633i	0.945975	−	0.324239i	$-0.105108\pi$
$269$	15.2520	+	11.0812i	0.929928	+	0.675633i	−0.0160469	+	0.999871i	$0.505108\pi$
$270$	−3.18817	+	22.5637i	−0.194026	+	1.37318i
$271$	17.3216	−	12.5849i	1.05221	−	0.764477i	0.0795805	−	0.996828i	$-0.474642\pi$
$271$	17.3216	−	12.5849i	1.05221	−	0.764477i	0.972632	+	0.232351i	$0.0746419\pi$
$272$	−1.86081	−	2.56119i	−0.112828	−	0.155295i
$273$	−1.92833	+	0.626553i	−0.116708	+	0.0379207i
$274$	25.8406			1.56109
$275$	−1.84700	+	0.669156i	−0.111378	+	0.0403516i
$276$	−7.68289			−0.462455
$277$	−6.46338	+	2.10008i	−0.388347	+	0.126182i	−0.496682	−	0.867933i	$-0.665448\pi$
$277$	−6.46338	+	2.10008i	−0.388347	+	0.126182i	0.108334	+	0.994115i	$0.465448\pi$
$278$	−8.00835	−	11.0225i	−0.480309	−	0.661088i
$279$	16.2506	−	11.8067i	0.972897	−	0.706851i
$280$	4.60651	−	0.808734i	0.275292	−	0.0483311i
$281$	−2.72814	−	1.98211i	−0.162747	−	0.118243i	0.503431	−	0.864035i	$-0.332071\pi$
$281$	−2.72814	−	1.98211i	−0.162747	−	0.118243i	−0.666178	+	0.745793i	$0.732071\pi$
$282$			5.95977i			0.354899i
$283$	1.87527	−	2.58109i	0.111473	−	0.153430i	−0.749635	−	0.661851i	$-0.769771\pi$
$283$	1.87527	−	2.58109i	0.111473	−	0.153430i	0.861108	+	0.508422i	$0.169771\pi$
$284$	11.1878	−	34.4324i	0.663872	−	2.04319i
$285$	4.51098	+	4.36267i	0.267207	+	0.258422i
$286$	0.624470	+	1.92192i	0.0369257	+	0.113646i
$287$	−5.44071	−	1.76779i	−0.321155	−	0.104350i
$288$	14.6974	+	4.77549i	0.866055	+	0.281398i
$289$	3.21501	+	9.89477i	0.189118	+	0.582045i
$290$	−1.68954	−	9.62354i	−0.0992132	−	0.565114i
$291$	4.61013	−	14.1885i	0.270251	−	0.831746i
$292$	2.31134	−	3.18129i	0.135261	−	0.186171i
$293$		−	0.406826i		−	0.0237670i	−0.999929	−	0.0118835i	$-0.996217\pi$
$293$		−	0.406826i		−	0.0237670i	0.999929	−	0.0118835i	$-0.00378273\pi$
$294$	−1.57577	−	1.14486i	−0.0919008	−	0.0667698i
$295$	−5.19828	−	9.79404i	−0.302656	−	0.570231i
$296$	10.2155	−	7.42200i	0.593764	−	0.431395i
$297$	−1.05879	−	1.45730i	−0.0614371	−	0.0845608i
$298$	−31.8127	+	10.3366i	−1.84286	+	0.598782i
$299$	6.89844			0.398947
$300$	3.56997	−	12.3807i	0.206113	−	0.714801i
$301$	−9.34864			−0.538847
$302$	−9.91712	+	3.22227i	−0.570666	+	0.185421i
$303$	6.70560	+	9.22947i	0.385227	+	0.530219i
$304$	3.19399	−	2.32057i	0.183188	−	0.133094i
$305$	21.4933	+	10.5027i	1.23070	+	0.601384i
$306$	10.3094	+	7.49022i	0.589350	+	0.428188i
$307$		−	9.41718i		−	0.537467i	−0.963215	−	0.268733i	$-0.913395\pi$
$307$		−	9.41718i		−	0.537467i	0.963215	−	0.268733i	$-0.0866050\pi$
$308$	−0.679182	+	0.934814i	−0.0387000	+	0.0532659i
$309$	−0.766377	+	2.35867i	−0.0435977	+	0.134180i
$310$	−39.5074	+	20.9689i	−2.24387	+	1.19096i
$311$	2.62208	+	8.06992i	0.148684	+	0.457603i	0.997466	−	0.0711396i	$-0.0226636\pi$
$311$	2.62208	+	8.06992i	0.148684	+	0.457603i	−0.848782	+	0.528743i	$0.822664\pi$
$312$	−4.03330	−	1.31050i	−0.228341	−	0.0741924i
$313$	3.51395	+	1.14175i	0.198620	+	0.0645357i	0.406638	−	0.913589i	$-0.366701\pi$
$313$	3.51395	+	1.14175i	0.198620	+	0.0645357i	−0.208017	+	0.978125i	$0.566701\pi$
$314$	−1.33289	−	4.10223i	−0.0752196	−	0.231502i
$315$	4.40880	−	2.34001i	0.248408	−	0.131845i
$316$	0.960483	−	2.95606i	0.0540314	−	0.166292i
$317$	18.3068	−	25.1971i	1.02821	−	1.41521i	0.121927	−	0.992539i	$-0.461093\pi$
$317$	18.3068	−	25.1971i	1.02821	−	1.41521i	0.906283	−	0.422671i	$-0.138907\pi$
$318$			20.0969i			1.12698i
$319$	0.624844	+	0.453975i	0.0349845	+	0.0254177i
$320$	−25.9643	−	12.6874i	−1.45145	−	0.709250i
$321$	−5.01562	+	3.64406i	−0.279945	+	0.203392i
$322$	3.89520	+	5.36128i	0.217071	+	0.298773i
$323$	7.82313	−	2.54189i	0.435291	−	0.141434i
$324$	−7.87935			−0.437742
$325$	−3.20547	+	11.1166i	−0.177808	+	0.616639i
$326$	35.4186			1.96166
$327$	1.43221	−	0.465353i	0.0792013	−	0.0257341i
$328$	−7.03311	−	9.68024i	−0.388338	−	0.534502i
$329$	2.47544	−	1.79851i	0.136475	−	0.0991550i
$330$	0.802235	+	1.51149i	0.0441616	+	0.0832045i
$331$	3.43895	+	2.49854i	0.189022	+	0.137332i	0.678271	−	0.734811i	$-0.262729\pi$
$331$	3.43895	+	2.49854i	0.189022	+	0.137332i	−0.489250	+	0.872144i	$0.662729\pi$
$332$			41.8318i			2.29582i
$333$	7.92084	−	10.9021i	0.434059	−	0.597431i
$334$	−7.67934	+	23.6346i	−0.420195	+	1.29323i
$335$	−6.09082	−	34.6930i	−0.332777	−	1.89548i
$336$	0.333776	+	1.02726i	0.0182090	+	0.0560414i
$337$	−6.80029	−	2.20955i	−0.370435	−	0.120362i	0.117883	−	0.993028i	$-0.462389\pi$
$337$	−6.80029	−	2.20955i	−0.370435	−	0.120362i	−0.488318	+	0.872666i	$0.662389\pi$
$338$	−16.1636	−	5.25186i	−0.879182	−	0.285663i
$339$	0.331660	+	1.02075i	0.0180133	+	0.0554393i
$340$	−12.1406	−	11.7414i	−0.658415	−	0.636767i
$341$	1.09255	−	3.36253i	0.0591650	−	0.182091i
$342$	−9.34086	+	12.8566i	−0.505096	+	0.695205i
$343$			1.00000i			0.0539949i
$344$	−15.8192	−	11.4933i	−0.852915	−	0.619679i
$345$	5.75344	−	1.01009i	0.309755	−	0.0543816i
$346$	−28.9776	+	21.0535i	−1.55785	+	1.13184i
$347$	−18.2796	−	25.1597i	−0.981300	−	1.35064i	−0.936126	−	0.351664i	$-0.885616\pi$
$347$	−18.2796	−	25.1597i	−0.981300	−	1.35064i	−0.0451739	−	0.998979i	$-0.514384\pi$
$348$	−4.81794	+	1.56544i	−0.258269	+	0.0839166i
$349$	21.2544			1.13772			0.568861	−	0.822433i	$-0.307384\pi$
$349$	21.2544			1.13772			0.568861	+	0.822433i	$0.307384\pi$
$350$	−10.4495	+	3.78578i	−0.558549	+	0.202359i
$351$	−10.6086			−0.566245
$352$	2.58696	−	0.840555i	0.137886	−	0.0448017i
$353$	14.3710	+	19.7799i	0.764889	+	1.05278i	0.996792	+	0.0800406i	$0.0255050\pi$
$353$	14.3710	+	19.7799i	0.764889	+	1.05278i	−0.231902	+	0.972739i	$0.574495\pi$
$354$	−7.81383	+	5.67708i	−0.415300	+	0.301733i
$355$	−3.85119	+	27.2561i	−0.204400	+	1.44660i
$356$	−33.4290	−	24.2876i	−1.77173	−	1.28724i
$357$			2.25046i			0.119107i
$358$	−31.3090	+	43.0932i	−1.65473	+	2.27755i
$359$	−6.55245	+	20.1664i	−0.345825	+	1.06434i	0.615315	+	0.788281i	$0.289029\pi$
$359$	−6.55245	+	20.1664i	−0.345825	+	1.06434i	−0.961141	+	0.276059i	$0.910971\pi$
$360$	10.3371	+	1.46060i	0.544815	+	0.0769804i
$361$	−2.70140	−	8.31405i	−0.142179	−	0.437582i
$362$	−49.0851	−	15.9487i	−2.57985	−	0.838245i
$363$	9.03838	+	2.93675i	0.474392	+	0.154139i
$364$	2.10290	+	6.47205i	0.110222	+	0.339228i
$365$	−1.31263	+	2.68624i	−0.0687062	+	0.140604i
$366$	6.43922	−	19.8179i	0.336583	−	1.03590i
$367$	−3.70891	+	5.10487i	−0.193603	+	0.266472i	−0.894772	−	0.446523i	$-0.852662\pi$
$367$	−3.70891	+	5.10487i	−0.193603	+	0.266472i	0.701169	+	0.712996i	$0.252662\pi$
$368$		−	3.67492i		−	0.191568i
$369$	−10.3309	−	7.50581i	−0.537803	−	0.390737i
$370$	−20.8602	+	21.5694i	−1.08447	+	1.12134i
$371$	8.34740	−	6.06474i	0.433375	−	0.314866i
$372$	13.6308	+	18.7611i	0.706722	+	0.972719i
$373$	−3.05017	+	0.991061i	−0.157932	+	0.0513152i	−0.386916	−	0.922115i	$-0.626460\pi$
$373$	−3.05017	+	0.991061i	−0.157932	+	0.0513152i	0.228984	+	0.973430i	$0.426460\pi$
$374$	2.24298			0.115981
$375$	−1.04570	+	9.74084i	−0.0539995	+	0.503015i
$376$	6.39989			0.330049
$377$	4.32602	−	1.40561i	0.222801	−	0.0723925i
$378$	−5.99014	−	8.24472i	−0.308099	−	0.424062i
$379$	22.2793	−	16.1869i	1.14441	−	0.831464i	0.156684	−	0.987649i	$-0.449920\pi$
$379$	22.2793	−	16.1869i	1.14441	−	0.831464i	0.987728	+	0.156185i	$0.0499197\pi$
$380$	14.6424	−	15.1402i	0.751139	−	0.776675i
$381$	−11.6909	−	8.49393i	−0.598942	−	0.435157i
$382$		−	1.14749i		−	0.0587108i
$383$	0.399636	−	0.550052i	0.0204205	−	0.0281063i	−0.798685	−	0.601750i	$-0.794470\pi$
$383$	0.399636	−	0.550052i	0.0204205	−	0.0281063i	0.819105	+	0.573643i	$0.194470\pi$
$384$	−4.02940	+	12.4012i	−0.205624	+	0.632847i
$385$	0.385712	−	0.789343i	0.0196577	−	0.0402286i
$386$	−16.7066	−	51.4175i	−0.850341	−	2.61708i
$387$	−19.8465	−	6.44852i	−1.00885	−	0.327797i
$388$	−47.6209	−	15.4730i	−2.41758	−	0.785520i
$389$	−5.81124	−	17.8852i	−0.294642	−	0.906814i	−0.983342	−	0.181768i	$-0.941818\pi$
$389$	−5.81124	−	17.8852i	−0.294642	−	0.906814i	0.688700	−	0.725047i	$-0.258182\pi$
$390$	9.97870	+	1.40995i	0.505291	+	0.0713958i
$391$	2.36607	−	7.28203i	0.119658	−	0.368268i
$392$	−1.22941	+	1.69214i	−0.0620947	+	0.0854660i
$393$		−	1.42404i		−	0.0718332i
$394$	20.5076	+	14.8996i	1.03316	+	0.750633i
$395$	−0.330629	+	2.33997i	−0.0166358	+	0.117737i
$396$	−2.08667	+	1.51606i	−0.104859	+	0.0761847i
$397$	16.1166	+	22.1827i	0.808871	+	1.11332i	0.991497	+	0.130133i	$0.0415404\pi$
$397$	16.1166	+	22.1827i	0.808871	+	1.11332i	−0.182625	+	0.983183i	$0.558460\pi$
$398$	1.93741	−	0.629502i	0.0971135	−	0.0315541i
$399$	−2.80648			−0.140500
$400$	5.92201	+	1.70761i	0.296101	+	0.0853805i
$401$	−20.7884			−1.03812			−0.519062	−	0.854737i	$-0.673719\pi$
$401$	−20.7884			−1.03812			−0.519062	+	0.854737i	$0.673719\pi$
$402$	−29.1804	+	9.48127i	−1.45538	+	0.472883i
$403$	−12.2390	−	16.8456i	−0.609669	−	0.839137i
$404$	30.9768	−	22.5060i	1.54115	−	1.11971i
$405$	5.90057	−	1.03592i	0.293202	−	0.0514754i
$406$	3.53508	+	2.56839i	0.175443	+	0.127467i
$407$		−	2.37192i		−	0.117572i
$408$	−2.76674	+	3.80809i	−0.136974	+	0.188528i
$409$	10.3251	−	31.7774i	0.510543	−	1.57129i	−0.280704	−	0.959794i	$-0.590568\pi$
$409$	10.3251	−	31.7774i	0.510543	−	1.57129i	0.791247	−	0.611496i	$-0.209432\pi$
$410$	20.4392	+	19.7672i	1.00942	+	0.976231i
$411$	3.14781	+	9.68795i	0.155270	+	0.477871i
$412$	7.91638	+	2.57219i	0.390012	+	0.126723i
$413$	4.71604	+	1.53233i	0.232061	+	0.0754012i
$414$	4.57112	+	14.0685i	0.224658	+	0.691427i
$415$	−5.49976	−	31.3264i	−0.269973	−	1.53775i
$416$	4.95034	−	15.2356i	0.242710	−	0.746985i
$417$	3.15694	−	4.34516i	0.154596	−	0.212783i
$418$			2.79716i			0.136813i
$419$	13.2464	+	9.62404i	0.647127	+	0.470165i	0.862291	−	0.506413i	$-0.169029\pi$
$419$	13.2464	+	9.62404i	0.647127	+	0.470165i	−0.215164	+	0.976578i	$0.569029\pi$
$420$	2.70152	+	5.08991i	0.131821	+	0.248362i
$421$	−21.5760	+	15.6759i	−1.05155	+	0.763996i	−0.972507	−	0.232875i	$-0.925187\pi$
$421$	−21.5760	+	15.6759i	−1.05155	+	0.763996i	−0.0790436	+	0.996871i	$0.525187\pi$
$422$	29.0655	+	40.0052i	1.41489	+	1.94742i
$423$	6.49575	−	2.11060i	0.315834	−	0.102621i
$424$	21.5810			1.04807
$425$	10.6353	+	7.19656i	0.515889	+	0.349085i
$426$	23.9777			1.16172
$427$	−10.1747	+	3.30596i	−0.492389	+	0.159987i
$428$	12.2306	+	16.8339i	0.591186	+	0.813698i
$429$	−0.644482	+	0.468244i	−0.0311159	+	0.0226070i
$430$	41.7486	+	20.4005i	2.01330	+	0.983798i
$431$	−18.1907	−	13.2163i	−0.876215	−	0.636607i	0.0560325	−	0.998429i	$-0.482155\pi$
$431$	−18.1907	−	13.2163i	−0.876215	−	0.636607i	−0.932247	+	0.361822i	$0.882155\pi$
$432$			5.65139i			0.271902i
$433$	−21.6486	+	29.7967i	−1.04036	+	1.43194i	−0.143488	+	0.989652i	$0.545832\pi$
$433$	−21.6486	+	29.7967i	−1.04036	+	1.43194i	−0.896875	+	0.442285i	$0.854168\pi$
$434$	6.18116	−	19.0237i	0.296705	−	0.913165i
$435$	3.40217	−	1.80574i	0.163122	−	0.0865784i
$436$	−1.56186	−	4.80691i	−0.0747996	−	0.230209i
$437$	9.08123	+	2.95067i	0.434414	+	0.141150i
$438$	2.47684	+	0.804774i	0.118348	+	0.0384536i
$439$	12.6434	+	38.9123i	0.603435	+	1.85718i	0.507211	+	0.861822i	$0.330677\pi$
$439$	12.6434	+	38.9123i	0.603435	+	1.85718i	0.0962240	+	0.995360i	$0.469323\pi$
$440$	1.62311	−	0.861480i	0.0773786	−	0.0410694i
$441$	−0.689782	+	2.12293i	−0.0328468	+	0.101092i
$442$	7.76446	−	10.6869i	0.369318	−	0.508322i
$443$		−	33.7257i		−	1.60236i	−0.598425	−	0.801178i	$-0.704207\pi$
$443$		−	33.7257i		−	1.60236i	0.598425	−	0.801178i	$-0.295793\pi$
$444$	12.5864	+	9.14452i	0.597322	+	0.433980i
$445$	28.2270	+	13.7931i	1.33809	+	0.653856i
$446$	−1.55979	+	1.13325i	−0.0738581	+	0.0536610i
$447$	−7.75062	−	10.6678i	−0.366592	−	0.504570i
$448$	12.2912	−	3.99366i	0.580705	−	0.188683i
$449$	10.2790			0.485094			0.242547	−	0.970140i	$-0.422017\pi$
$449$	10.2790			0.485094			0.242547	+	0.970140i	$0.422017\pi$
$450$	−24.7949	+	0.829077i	−1.16884	+	0.0390831i
$451$	−2.24764			−0.105837
$452$	3.42592	−	1.11315i	0.161142	−	0.0523582i
$453$	−2.41614	−	3.32553i	−0.113520	−	0.156247i
$454$	−4.05874	+	2.94885i	−0.190486	+	0.138396i
$455$	−2.42569	−	4.57022i	−0.113718	−	0.214255i
$456$	−4.74897	−	3.45033i	−0.222391	−	0.161576i
$457$			1.65826i			0.0775703i	0.999248	+	0.0387851i	$0.0123488\pi$
$457$			1.65826i			0.0775703i	−0.999248	+	0.0387851i	$0.987651\pi$
$458$	15.3079	−	21.0695i	0.715292	−	0.984515i
$459$	−3.63861	+	11.1985i	−0.169836	+	0.522701i
$460$	−3.39017	−	19.3103i	−0.158068	−	0.900345i
$461$	2.33968	+	7.20080i	0.108970	+	0.335375i	0.990642	−	0.136488i	$-0.0435816\pi$
$461$	2.33968	+	7.20080i	0.108970	+	0.335375i	−0.881672	+	0.471863i	$0.843582\pi$
$462$	−0.727812	−	0.236481i	−0.0338609	−	0.0110021i
$463$	−3.96383	−	1.28793i	−0.184215	−	0.0598550i	0.215457	−	0.976513i	$-0.430876\pi$
$463$	−3.96383	−	1.28793i	−0.184215	−	0.0598550i	−0.399672	+	0.916658i	$0.630876\pi$
$464$	−0.748792	−	2.30454i	−0.0347618	−	0.106986i
$465$	−12.6742	−	12.2575i	−0.587751	−	0.568426i
$466$	3.53137	−	10.8684i	0.163587	−	0.503470i
$467$	−7.92551	+	10.9085i	−0.366749	+	0.504787i	−0.952014	−	0.306056i	$-0.900991\pi$
$467$	−7.92551	+	10.9085i	−0.366749	+	0.504787i	0.585265	+	0.810842i	$0.300991\pi$
$468$			15.1903i			0.702170i
$469$	12.7440	+	9.25908i	0.588464	+	0.427544i
$470$	−14.9793	+	2.62982i	−0.690946	+	0.121305i
$471$	1.37561	−	0.999438i	0.0633847	−	0.0460517i
$472$	6.09633	+	8.39088i	0.280606	+	0.386222i
$473$	−3.49327	+	1.13503i	−0.160621	+	0.0521889i
$474$	2.05851			0.0945505
$475$	−8.97465	+	13.2630i	−0.411785	+	0.608549i
$476$	7.55320			0.346200
$477$	21.9043	−	7.11714i	1.00293	−	0.325871i
$478$	−10.1097	−	13.9147i	−0.462405	−	0.636446i
$479$	12.7796	−	9.28493i	0.583916	−	0.424239i	−0.256218	−	0.966619i	$-0.582477\pi$
$479$	12.7796	−	9.28493i	0.583916	−	0.424239i	0.840134	+	0.542380i	$0.182477\pi$
$480$	1.89784	−	13.4316i	0.0866241	−	0.613067i
$481$	−11.3013	−	8.21085i	−0.515293	−	0.374382i
$482$			29.4588i			1.34181i
$483$	−1.53551	+	2.11345i	−0.0698682	+	0.0961654i
$484$	9.85660	−	30.3355i	0.448027	−	1.37889i
$485$	37.6959	+	5.32629i	1.71168	+	0.241854i
$486$	−11.0602	−	34.0397i	−0.501700	−	1.54407i
$487$	7.68880	+	2.49824i	0.348413	+	0.113206i	0.477995	−	0.878363i	$-0.341364\pi$
$487$	7.68880	+	2.49824i	0.348413	+	0.113206i	−0.129582	+	0.991569i	$0.541364\pi$
$488$	−21.2814	−	6.91476i	−0.963365	−	0.313016i
$489$	4.31457	+	13.2789i	0.195112	+	0.600492i
$490$	2.18219	−	4.46575i	0.0985811	−	0.201742i
$491$	1.73455	−	5.33838i	0.0782790	−	0.240918i	−0.904258	−	0.426987i	$-0.859575\pi$
$491$	1.73455	−	5.33838i	0.0782790	−	0.240918i	0.982537	+	0.186069i	$0.0595749\pi$
$492$	8.66538	−	11.9269i	0.390665	−	0.537705i
$493$		−	5.04867i		−	0.227381i
$494$	13.3273	+	9.68286i	0.599624	+	0.435653i
$495$	1.36331	−	1.40966i	0.0612764	−	0.0633596i
$496$	−8.97392	+	6.51994i	−0.402941	+	0.292754i
$497$	−7.23586	−	9.95930i	−0.324573	−	0.446736i
$498$	−26.3487	+	8.56120i	−1.18071	+	0.383637i
$499$	−10.2308			−0.457994			−0.228997	−	0.973427i	$-0.573545\pi$
$499$	−10.2308			−0.457994			−0.228997	+	0.973427i	$0.573545\pi$
$500$	32.6931	+	3.50967i	1.46208	+	0.156957i
$501$	−9.79636			−0.437669
$502$	29.9363	−	9.72689i	1.33612	−	0.434132i
$503$	−1.55097	−	2.13472i	−0.0691542	−	0.0951827i	0.773039	−	0.634359i	$-0.218736\pi$
$503$	−1.55097	−	2.13472i	−0.0691542	−	0.0951827i	−0.842193	+	0.539176i	$0.818736\pi$
$504$	−3.77716	+	2.74427i	−0.168248	+	0.122240i
$505$	−20.2385	+	20.9266i	−0.900602	+	0.931220i
$506$	2.10643	+	1.53041i	0.0936421	+	0.0680350i
$507$		−	6.69968i		−	0.297543i
$508$	−28.5081	+	39.2381i	−1.26484	+	1.74091i
$509$	−13.7981	+	42.4661i	−0.611589	+	1.88228i	−0.168802	+	0.985650i	$0.553990\pi$
$509$	−13.7981	+	42.4661i	−0.611589	+	1.88228i	−0.442787	+	0.896627i	$0.646010\pi$
$510$	4.91091	−	10.0500i	0.217459	−	0.445020i
$511$	−0.413179	−	1.27164i	−0.0182780	−	0.0562538i
$512$	−13.0203	−	4.23056i	−0.575423	−	0.186966i
$513$	−13.9653	−	4.53762i	−0.616585	−	0.200341i
$514$	−8.42907	−	25.9420i	−0.371791	−	1.14425i
$515$	−6.26647	−	0.885430i	−0.276134	−	0.0390167i
$516$	7.44475	−	22.9126i	0.327737	−	1.00867i
$517$	0.706627	−	0.972589i	0.0310774	−	0.0427744i
$518$		−	13.4193i		−	0.589609i
$519$	−11.4232	−	8.29942i	−0.501421	−	0.364304i
$520$	1.51408	−	10.7156i	0.0663967	−	0.469911i
$521$	1.78965	−	1.30025i	0.0784058	−	0.0569651i	−0.547892	−	0.836549i	$-0.684569\pi$
$521$	1.78965	−	1.30025i	0.0784058	−	0.0569651i	0.626298	+	0.779584i	$0.284569\pi$
$522$	5.73310	+	7.89094i	0.250931	+	0.345377i
$523$	15.8345	−	5.14494i	0.692394	−	0.224973i	0.0583807	−	0.998294i	$-0.481406\pi$
$523$	15.8345	−	5.14494i	0.692394	−	0.224973i	0.634014	+	0.773322i	$0.281406\pi$
$524$	−4.77949			−0.208793
$525$	−2.69226	−	3.45648i	−0.117500	−	0.150853i
$526$	9.38633			0.409263
$527$	−21.9801	+	7.14176i	−0.957467	+	0.311100i
$528$	0.249441	+	0.343327i	0.0108555	+	0.0149414i
$529$	−11.4167	+	8.29475i	−0.496380	+	0.360641i
$530$	−50.5118	+	8.86801i	−2.19409	+	0.385202i
$531$	8.95484	+	6.50607i	0.388607	+	0.282340i
$532$			9.41939i			0.408382i
$533$	−7.78062	+	10.7091i	−0.337016	+	0.463863i
$534$	8.45656	−	26.0266i	0.365951	−	1.12628i
$535$	−11.3722	−	10.9983i	−0.491665	−	0.475499i
$536$	10.1815	+	31.3353i	0.439772	+	1.35348i
$537$	−19.9701	−	6.48869i	−0.861775	−	0.280008i
$538$	39.8548	+	12.9496i	1.71826	+	0.558297i
$539$	0.121412	+	0.373666i	0.00522957	+	0.0160949i
$540$	5.21349	+	29.6958i	0.224353	+	1.27790i
$541$	8.15227	−	25.0901i	0.350494	−	1.07871i	−0.608083	−	0.793874i	$-0.708061\pi$
$541$	8.15227	−	25.0901i	0.350494	−	1.07871i	0.958577	−	0.284835i	$-0.0919388\pi$
$542$	27.9740	−	38.5029i	1.20159	−	1.65384i
$543$		−	20.3454i		−	0.873106i
$544$	−14.3848	−	10.4512i	−0.616745	−	0.448091i
$545$	1.80160	+	3.39439i	0.0771722	+	0.145399i
$546$	−3.64619	+	2.64911i	−0.156042	+	0.113371i
$547$	21.2825	+	29.2929i	0.909975	+	1.25247i	0.967175	+	0.254110i	$0.0817825\pi$
$547$	21.2825	+	29.2929i	0.909975	+	1.25247i	−0.0572008	+	0.998363i	$0.518218\pi$
$548$	32.5156	−	10.5650i	1.38900	−	0.451313i
$549$	−23.8806			−1.01920
$550$	−3.44499	+	2.68331i	−0.146895	+	0.114417i
$551$	6.29606			0.268221
$552$	−5.19661	+	1.68848i	−0.221182	+	0.0718665i
$553$	−0.621207	−	0.855018i	−0.0264164	−	0.0363591i
$554$	−12.2213	+	8.87929i	−0.519233	+	0.377245i
$555$	−10.6277	−	5.19324i	−0.451122	−	0.220441i
$556$	−14.5836	−	10.5956i	−0.618484	−	0.449355i
$557$			43.3717i			1.83772i	0.394586	+	0.918859i	$0.370888\pi$
$557$			43.3717i			1.83772i	−0.394586	+	0.918859i	$0.629112\pi$
$558$	26.2443	−	36.1222i	1.11101	−	1.52918i
$559$	−6.68462	+	20.5731i	−0.282729	+	0.870151i
$560$	−2.43463	+	1.29220i	−0.102882	+	0.0546056i
$561$	0.273231	+	0.840920i	0.0115358	+	0.0355037i
$562$	−7.12887	−	2.31631i	−0.300713	−	0.0977076i
$563$	−36.5904	−	11.8889i	−1.54210	−	0.501059i	−0.590146	−	0.807297i	$-0.700930\pi$
$563$	−36.5904	−	11.8889i	−1.54210	−	0.501059i	−0.951955	+	0.306237i	$0.900930\pi$
$564$	2.43666	+	7.49928i	0.102602	+	0.315777i
$565$	−2.41920	+	1.28402i	−0.101777	+	0.0540189i
$566$	2.19146	−	6.74461i	0.0921138	−	0.283497i
$567$	−1.57478	+	2.16750i	−0.0661345	+	0.0910263i
$568$		−	25.7484i		−	1.08038i
$569$	18.5065	+	13.4458i	0.775834	+	0.563677i	0.903726	−	0.428111i	$-0.140821\pi$
$569$	18.5065	+	13.4458i	0.775834	+	0.563677i	−0.127892	+	0.991788i	$0.540821\pi$
$570$	12.5330	+	6.12427i	0.524952	+	0.256518i
$571$	−28.9909	+	21.0631i	−1.21323	+	0.881463i	−0.995520	−	0.0945506i	$-0.969859\pi$
$571$	−28.9909	+	21.0631i	−1.21323	+	0.881463i	−0.217710	+	0.976014i	$0.569859\pi$
$572$	1.57156	+	2.16307i	0.0657104	+	0.0904426i
$573$	0.430209	−	0.139783i	0.0179722	−	0.00583953i
$574$	−12.7161			−0.530762
$575$	5.07756	+	14.0150i	0.211749	+	0.584468i
$576$	28.8481			1.20201
$577$	28.6157	−	9.29780i	1.19129	−	0.387072i	0.354738	−	0.934966i	$-0.384570\pi$
$577$	28.6157	−	9.29780i	1.19129	−	0.387072i	0.836548	+	0.547893i	$0.184570\pi$
$578$	13.5933	+	18.7095i	0.565406	+	0.778214i
$579$	17.2419	−	12.5270i	0.716550	−	0.520604i
$580$	−6.06058	−	11.4187i	−0.251652	−	0.474136i
$581$	11.5073	+	8.36057i	0.477405	+	0.346855i
$582$		−	33.1617i		−	1.37460i
$583$	2.38281	−	3.27966i	0.0986860	−	0.135830i
$584$	0.864206	−	2.65975i	0.0357611	−	0.110061i
$585$	−1.99711	−	11.3754i	−0.0825703	−	0.470317i
$586$	−0.279446	−	0.860045i	−0.0115438	−	0.0355281i
$587$	−13.5840	−	4.41371i	−0.560671	−	0.182173i	0.0149519	−	0.999888i	$-0.495240\pi$
$587$	−13.5840	−	4.41371i	−0.560671	−	0.182173i	−0.575623	+	0.817715i	$0.695240\pi$
$588$	−2.45090	−	0.796346i	−0.101073	−	0.0328407i
$589$	−8.90630	−	27.4108i	−0.366978	−	1.12944i
$590$	−17.7168	−	17.1343i	−0.729389	−	0.705407i
$591$	−3.08790	+	9.50357i	−0.127019	+	0.390925i
$592$	−4.37406	+	6.02037i	−0.179773	+	0.247436i
$593$			3.32432i			0.136514i	0.997668	+	0.0682568i	$0.0217437\pi$
$593$			3.32432i			0.136514i	−0.997668	+	0.0682568i	$0.978256\pi$
$594$	−3.23932	−	2.35350i	−0.132911	−	0.0965653i
$595$	−5.65632	+	0.993042i	−0.231887	+	0.0407108i
$596$	−35.8043	+	26.0134i	−1.46660	+	1.06555i
$597$	0.472017	+	0.649675i	0.0193184	+	0.0265894i
$598$	14.5836	−	4.73848i	0.596366	−	0.193771i
$599$	−6.84699			−0.279761			−0.139880	−	0.990168i	$-0.544672\pi$
$599$	−6.84699			−0.279761			−0.139880	+	0.990168i	$0.544672\pi$
$600$	−0.306245	−	9.15874i	−0.0125024	−	0.373904i
$601$	46.2226			1.88546			0.942729	−	0.333561i	$-0.108250\pi$
$601$	46.2226			1.88546			0.942729	+	0.333561i	$0.108250\pi$
$602$	−19.7634	+	6.42150i	−0.805494	+	0.261721i
$603$	20.6679	+	28.4470i	0.841663	+	1.15845i
$604$	−11.1615	+	8.10927i	−0.454153	+	0.329961i
$605$	−3.39296	+	24.0131i	−0.137943	+	0.976269i
$606$	20.5155	+	14.9054i	0.833386	+	0.605491i
$607$		−	11.3032i		−	0.458782i	−0.973334	−	0.229391i	$-0.926327\pi$
$607$		−	11.3032i		−	0.458782i	0.973334	−	0.229391i	$-0.0736735\pi$
$608$	13.0334	−	17.9390i	0.528575	−	0.727521i
$609$	−0.532289	+	1.63822i	−0.0215695	+	0.0663840i
$610$	52.6519	+	7.43952i	2.13181	+	0.301217i
$611$	−2.18787	−	6.73358i	−0.0885119	−	0.272412i
$612$	16.0349	+	5.21006i	0.648173	+	0.210604i
$613$	10.9140	+	3.54616i	0.440811	+	0.143228i	0.521010	−	0.853551i	$-0.325556\pi$
$613$	10.9140	+	3.54616i	0.440811	+	0.143228i	−0.0801988	+	0.996779i	$0.525556\pi$
$614$	−6.46858	−	19.9082i	−0.261051	−	0.803431i
$615$	−4.92113	+	10.0709i	−0.198439	+	0.406097i
$616$	−0.253945	+	0.781561i	−0.0102317	+	0.0314900i
$617$	22.4184	−	30.8562i	0.902530	−	1.24223i	−0.0671242	−	0.997745i	$-0.521382\pi$
$617$	22.4184	−	30.8562i	0.902530	−	1.24223i	0.969654	−	0.244481i	$-0.0786176\pi$
$618$			5.51272i			0.221754i
$619$	6.87598	+	4.99569i	0.276369	+	0.200794i	0.717332	−	0.696731i	$-0.245363\pi$
$619$	6.87598	+	4.99569i	0.276369	+	0.200794i	−0.440963	+	0.897525i	$0.645363\pi$
$620$	−41.1397	+	42.5383i	−1.65221	+	1.70838i
$621$	−11.0580	+	8.03408i	−0.443741	+	0.322396i
$622$	11.0863	+	15.2590i	0.444521	+	0.611831i
$623$	−13.3623	+	4.34169i	−0.535351	+	0.173946i
$624$	2.49930			0.100052
$625$	−24.9442	+	1.67000i	−0.997766	+	0.0668001i
$626$	8.21288			0.328253
$627$	−1.04869	+	0.340740i	−0.0418806	+	0.0136078i
$628$	−3.35441	−	4.61695i	−0.133855	−	0.184236i
$629$	−12.5436	+	9.11345i	−0.500146	+	0.363377i
$630$	7.71302	−	7.97523i	0.307294	−	0.317741i
$631$	21.3561	+	15.5161i	0.850173	+	0.617687i	0.925194	−	0.379495i	$-0.123902\pi$
$631$	21.3561	+	15.5161i	0.850173	+	0.617687i	−0.0750210	+	0.997182i	$0.523902\pi$
$632$		−	2.21053i		−	0.0879302i
$633$	−11.4578	+	15.7703i	−0.455407	+	0.626814i
$634$	21.3935	−	65.8423i	0.849643	−	2.61493i
$635$	16.1900	−	33.1321i	0.642480	−	1.31481i
$636$	8.21666	+	25.2883i	0.325812	+	1.00275i
$637$	2.20066	+	0.715037i	0.0871932	+	0.0283308i
$638$	1.63277	+	0.530520i	0.0646421	+	0.0210035i
$639$	−8.49147	−	26.1341i	−0.335918	−	1.03385i
$640$	−32.9474	−	4.65535i	−1.30236	−	0.184019i
$641$	−4.60640	+	14.1770i	−0.181942	+	0.559959i	−0.999882	−	0.0153438i	$-0.995116\pi$
$641$	−4.60640	+	14.1770i	−0.181942	+	0.559959i	0.817941	+	0.575303i	$0.195116\pi$
$642$	−8.10013	+	11.1489i	−0.319686	+	0.440011i
$643$		−	23.5452i		−	0.928534i	−0.885695	−	0.464267i	$-0.846318\pi$
$643$		−	23.5452i		−	0.928534i	0.885695	−	0.464267i	$-0.153682\pi$
$644$	7.09337	+	5.15363i	0.279518	+	0.203082i
$645$	−2.56272	+	18.1372i	−0.100907	+	0.714152i
$646$	14.7924	−	10.7473i	0.581998	−	0.422846i
$647$	−14.0204	−	19.2974i	−0.551199	−	0.758660i	0.438976	−	0.898499i	$-0.355341\pi$
$647$	−14.0204	−	19.2974i	−0.551199	−	0.758660i	−0.990174	+	0.139839i	$0.955341\pi$
$648$	−5.32949	+	1.73166i	−0.209362	+	0.0680259i
$649$	1.94827			0.0764762
$650$	0.859432	+	25.7027i	0.0337097	+	1.00814i
$651$	7.88518			0.309044
$652$	44.5679	−	14.4810i	1.74541	−	0.567119i
$653$	1.43317	+	1.97258i	0.0560842	+	0.0771932i	0.836138	−	0.548519i	$-0.184808\pi$
$653$	1.43317	+	1.97258i	0.0560842	+	0.0771932i	−0.780054	+	0.625713i	$0.784808\pi$
$654$	2.70809	−	1.96754i	0.105895	−	0.0769370i
$655$	3.57919	−	0.628375i	0.139851	−	0.0245526i
$656$	5.70492	+	4.14487i	0.222740	+	0.161830i
$657$		−	2.98460i		−	0.116440i
$658$	3.99778	−	5.50247i	0.155850	−	0.214508i
$659$	−1.21619	+	3.74306i	−0.0473761	+	0.145809i	−0.971946	−	0.235203i	$-0.924424\pi$
$659$	−1.21619	+	3.74306i	−0.0473761	+	0.145809i	0.924570	+	0.381012i	$0.124424\pi$
$660$	1.62744	+	1.57393i	0.0633480	+	0.0612652i
$661$	11.9984	+	36.9272i	0.466682	+	1.43630i	0.856854	+	0.515559i	$0.172416\pi$
$661$	11.9984	+	36.9272i	0.466682	+	1.43630i	−0.390172	+	0.920742i	$0.627584\pi$
$662$	8.98628	+	2.91982i	0.349262	+	0.113482i
$663$	4.95248	+	1.60916i	0.192338	+	0.0624945i
$664$	9.19345	+	28.2945i	0.356775	+	1.09804i
$665$	−1.23840	−	7.05385i	−0.0480230	−	0.273537i
$666$	9.25637	−	28.4882i	0.358677	−	1.10389i
$667$	3.44477	−	4.74131i	0.133382	−	0.183584i
$668$			32.8795i			1.27215i
$669$	−0.614878	−	0.446735i	−0.0237726	−	0.0172718i
$670$	−36.7065	−	69.1585i	−1.41810	−	2.67183i
$671$	−3.40056	+	2.47065i	−0.131277	+	0.0953785i
$672$	3.56578	+	4.90787i	0.137553	+	0.189325i
$673$	−36.8913	+	11.9867i	−1.42205	+	0.462054i	−0.916254	−	0.400597i	$-0.868803\pi$
$673$	−36.8913	+	11.9867i	−1.42205	+	0.462054i	−0.505800	+	0.862650i	$0.668803\pi$
$674$	−15.8938			−0.612205
$675$	−7.80840	−	21.5527i	−0.300545	−	0.829564i
$676$	−22.4861			−0.864851
$677$	−17.2975	+	5.62028i	−0.664795	+	0.216005i	−0.621926	−	0.783076i	$-0.713650\pi$
$677$	−17.2975	+	5.62028i	−0.664795	+	0.216005i	−0.0428687	+	0.999081i	$0.513650\pi$
$678$	1.40228	+	1.93008i	0.0538544	+	0.0741242i
$679$	−13.7740	+	10.0074i	−0.528596	+	0.384048i
$680$	−10.7922	−	5.27358i	−0.413860	−	0.202233i
$681$	−1.59998	−	1.16245i	−0.0613114	−	0.0445453i
$682$		−	7.85897i		−	0.300935i
$683$	6.57676	−	9.05213i	0.251653	−	0.346370i	−0.664437	−	0.747345i	$-0.731328\pi$
$683$	6.57676	−	9.05213i	0.251653	−	0.346370i	0.916089	+	0.400974i	$0.131328\pi$
$684$	−6.49733	+	19.9967i	−0.248431	+	0.764593i
$685$	−22.9608	+	12.1867i	−0.877287	+	0.465628i
$686$	0.686892	+	2.11404i	0.0262256	+	0.0807142i
$687$	9.76399	+	3.17251i	0.372520	+	0.121039i
$688$	10.9597	+	3.56101i	0.417833	+	0.135762i
$689$	−7.37772	−	22.7063i	−0.281069	−	0.865040i
$690$	11.4692	−	6.08736i	0.436623	−	0.231742i
$691$	9.70842	−	29.8795i	0.369326	−	1.13667i	−0.577902	−	0.816106i	$-0.696128\pi$
$691$	9.70842	−	29.8795i	0.369326	−	1.13667i	0.947228	−	0.320562i	$-0.103872\pi$
$692$	−27.8553	+	38.3395i	−1.05890	+	1.45745i
$693$			0.877015i			0.0333150i
$694$	−55.9257	−	40.6324i	−2.12291	−	1.54238i
$695$	12.3142	+	6.01734i	0.467104	+	0.228251i
$696$	−2.91476	+	2.11769i	−0.110484	+	0.0802710i
$697$	8.63593	+	11.8863i	0.327109	+	0.450227i
$698$	44.9326	−	14.5995i	1.70072	−	0.552599i
$699$	4.50489			0.170390
$700$	−11.6010	+	9.03601i	−0.438475	+	0.341529i
$701$	−32.9719			−1.24533			−0.622665	−	0.782489i	$-0.713950\pi$
$701$	−32.9719			−1.24533			−0.622665	+	0.782489i	$0.713950\pi$
$702$	−22.4270	+	7.28696i	−0.846451	+	0.275029i
$703$	−11.3651	−	15.6428i	−0.428645	−	0.589979i
$704$	4.10794	−	2.98459i	0.154824	−	0.112486i
$705$	−2.81068	−	5.29559i	−0.105856	−	0.199443i
$706$	43.9674	+	31.9442i	1.65473	+	1.20224i
$707$		−	13.0194i		−	0.489643i
$708$	−7.51119	+	10.3383i	−0.282288	+	0.388536i
$709$	5.66249	−	17.4274i	0.212659	−	0.654498i	−0.786652	−	0.617396i	$-0.788187\pi$
$709$	5.66249	−	17.4274i	0.212659	−	0.654498i	0.999311	−	0.0371016i	$-0.0118125\pi$
$710$	10.5804	+	60.2657i	0.397077	+	2.26173i
$711$	−0.729003	−	2.24364i	−0.0273398	−	0.0841431i
$712$	−27.9487	−	9.08108i	−1.04742	−	0.340328i
$713$	−25.5149	−	8.29028i	−0.955539	−	0.310474i
$714$	1.54582	+	4.75754i	0.0578508	+	0.178047i
$715$	−1.46127	−	1.41323i	−0.0546486	−	0.0528518i
$716$	−21.7780	+	67.0257i	−0.813881	+	2.50487i
$717$	3.98529	−	5.48528i	0.148833	−	0.204852i
$718$			47.1332i			1.75900i
$719$	2.31422	+	1.68138i	0.0863058	+	0.0627048i	0.630101	−	0.776513i	$-0.283013\pi$
$719$	2.31422	+	1.68138i	0.0863058	+	0.0627048i	−0.543796	+	0.839218i	$0.683013\pi$
$720$	−6.05990	+	1.06389i	−0.225839	+	0.0396490i
$721$	2.28975	−	1.66360i	0.0852748	−	0.0619558i
$722$	−11.4217	−	15.7206i	−0.425072	−	0.585061i
$723$	−11.0445	+	3.58857i	−0.410748	+	0.133460i
$724$	−68.2853			−2.53780
$725$	6.03981	+	7.75426i	0.224313	+	0.287986i
$726$	21.1247			0.784011
$727$	24.0204	−	7.80469i	0.890866	−	0.289460i	0.172404	−	0.985026i	$-0.444846\pi$
$727$	24.0204	−	7.80469i	0.890866	−	0.289460i	0.718462	+	0.695566i	$0.244846\pi$
$728$	2.84475	+	3.91546i	0.105433	+	0.145117i
$729$	4.91212	−	3.56886i	0.181930	−	0.132180i
$730$	−0.929791	+	6.58043i	−0.0344131	+	0.243553i
$731$	19.4244	+	14.1126i	0.718436	+	0.521975i
$732$		−	27.5699i		−	1.01901i
$733$	2.31886	−	3.19164i	0.0856491	−	0.117886i	−0.764042	−	0.645166i	$-0.776788\pi$
$733$	2.31886	−	3.19164i	0.0856491	−	0.117886i	0.849691	+	0.527280i	$0.176788\pi$
$734$	−4.33427	+	13.3395i	−0.159981	+	0.492370i
$735$	1.94009	+	0.274128i	0.0715613	+	0.0101114i
$736$	−6.37814	−	19.6299i	−0.235101	−	0.723567i
$737$	5.88617	+	1.91253i	0.216820	+	0.0704491i
$738$	−26.9955	−	8.77136i	−0.993717	−	0.322878i
$739$	4.75260	+	14.6270i	0.174827	+	0.538063i	0.999626	−	0.0273640i	$-0.00871131\pi$
$739$	4.75260	+	14.6270i	0.174827	+	0.538063i	−0.824798	+	0.565427i	$0.808711\pi$
$740$	−17.4301	+	35.6698i	−0.640742	+	1.31125i
$741$	−2.00674	+	6.17611i	−0.0737194	+	0.226885i
$742$	13.4809	−	18.5548i	0.494898	−	0.681169i
$743$			2.93096i			0.107527i	0.998554	+	0.0537633i	$0.0171217\pi$
$743$			2.93096i			0.107527i	−0.998554	+	0.0537633i	$0.982878\pi$
$744$	13.3428	+	9.69413i	0.489172	+	0.355404i
$745$	23.3925	−	24.1878i	0.857037	−	0.886173i
$746$	−5.76742	+	4.19028i	−0.211160	+	0.153417i
$747$	18.6623	+	25.6864i	0.682818	+	0.939818i
$748$	2.82237	−	0.917045i	0.103196	−	0.0335305i
$749$	7.07518			0.258522
$750$	4.48026	+	21.3108i	0.163596	+	0.778159i
$751$	−14.1736			−0.517202			−0.258601	−	0.965984i	$-0.583262\pi$
$751$	−14.1736			−0.517202			−0.258601	+	0.965984i	$0.583262\pi$
$752$	−3.58710	+	1.16552i	−0.130808	+	0.0425021i
$753$	7.29347	+	10.0386i	0.265789	+	0.365827i
$754$	8.17985	−	5.94301i	0.297893	−	0.216432i
$755$	7.29227	−	7.54018i	0.265393	−	0.274415i
$756$	−10.9084	−	7.92539i	−0.396733	−	0.288244i
$757$		−	0.724796i		−	0.0263432i	−0.999913	−	0.0131716i	$-0.995807\pi$
$757$		−	0.724796i		−	0.0263432i	0.999913	−	0.0131716i	$-0.00419276\pi$
$758$	35.9806	−	49.5231i	1.30688	−	1.79876i
$759$	−0.317172	+	0.976155i	−0.0115126	+	0.0354322i
$760$	6.57655	−	13.4586i	0.238557	−	0.488195i
$761$	5.57065	+	17.1447i	0.201936	+	0.621495i	0.999825	+	0.0186911i	$0.00594991\pi$
$761$	5.57065	+	17.1447i	0.201936	+	0.621495i	−0.797889	+	0.602804i	$0.794050\pi$
$762$	−30.5494	−	9.92609i	−1.10669	−	0.359584i
$763$	−1.63447	−	0.531071i	−0.0591717	−	0.0192261i
$764$	−0.469154	−	1.44391i	−0.0169734	−	0.0522388i
$765$	−12.6930	−	1.79347i	−0.458915	−	0.0648430i
$766$	0.467019	−	1.43734i	0.0168741	−	0.0519331i
$767$	6.74428	−	9.28271i	0.243522	−	0.335179i
$768$			6.33544i			0.228610i
$769$	−3.39252	−	2.46481i	−0.122337	−	0.0888832i	0.524934	−	0.851143i	$-0.324090\pi$
$769$	−3.39252	−	2.46481i	−0.122337	−	0.0888832i	−0.647271	+	0.762260i	$0.724090\pi$
$770$	0.273217	−	1.93364i	0.00984604	−	0.0696836i
$771$	8.69919	−	6.32033i	0.313294	−	0.227621i
$772$	−42.0443	−	57.8690i	−1.51321	−	2.08275i
$773$	−9.01645	+	2.92962i	−0.324299	+	0.105371i	−0.466642	−	0.884446i	$-0.654536\pi$
$773$	−9.01645	+	2.92962i	−0.324299	+	0.105371i	0.142343	+	0.989817i	$0.454536\pi$
$774$	−46.3856			−1.66730
$775$	25.2154	−	37.2642i	0.905764	−	1.33857i
$776$	−35.6107			−1.27835
$777$	5.03105	−	1.63469i	0.180488	−	0.0586441i
$778$	−24.5703	−	33.8182i	−0.880890	−	1.21244i
$779$	−14.8231	+	10.7696i	−0.531094	+	0.385863i
$780$	13.1328	−	2.30564i	0.470231	−	0.0825552i
$781$	−3.91297	−	2.84294i	−0.140017	−	0.101728i
$782$		−	17.0197i		−	0.608623i
$783$	−5.29745	+	7.29132i	−0.189315	+	0.260570i
$784$	0.380912	−	1.17233i	0.0136040	−	0.0418688i
$785$	3.11900	+	3.01645i	0.111322	+	0.107662i
$786$	−0.978160	−	3.01047i	−0.0348898	−	0.107380i
$787$	20.6190	+	6.69952i	0.734988	+	0.238812i	0.652509	−	0.757781i	$-0.273716\pi$
$787$	20.6190	+	6.69952i	0.734988	+	0.238812i	0.0824786	+	0.996593i	$0.473716\pi$
$788$	31.8968	+	10.3639i	1.13628	+	0.369198i
$789$	1.14341	+	3.51905i	0.0407064	+	0.125282i
$790$	0.908344	+	5.17388i	0.0323174	+	0.184078i
$791$	0.378498	−	1.16490i	0.0134579	−	0.0414190i
$792$	−1.07821	+	1.48403i	−0.0383126	+	0.0527328i
$793$			24.7549i			0.879073i
$794$	49.3082	+	35.8245i	1.74988	+	1.27136i
$795$	−9.47789	−	17.8572i	−0.336146	−	0.633330i
$796$	2.18050	−	1.58423i	0.0772858	−	0.0561515i
$797$	−1.73319	−	2.38553i	−0.0613926	−	0.0844996i	0.777217	−	0.629233i	$-0.216631\pi$
$797$	−1.73319	−	2.38553i	−0.0613926	−	0.0844996i	−0.838609	+	0.544733i	$0.816631\pi$
$798$	−5.93301	+	1.92775i	−0.210026	+	0.0682416i
$799$	−7.85841			−0.278011
$800$	34.5966	−	1.15682i	1.22318	−	0.0408998i
$801$	−31.3621			−1.10813
$802$	−43.9474	+	14.2794i	−1.55184	+	0.504223i
$803$	−0.308782	−	0.425003i	−0.0108967	−	0.0149980i
$804$	−32.8417	+	23.8609i	−1.15824	+	0.841509i
$805$	−5.98954	−	2.92679i	−0.211103	−	0.103156i
$806$	−37.4448	−	27.2052i	−1.31894	−	0.958263i
$807$			16.5195i			0.581515i
$808$	16.0062	−	22.0306i	0.563095	−	0.775034i
$809$	12.0825	−	37.1862i	0.424799	−	1.30740i	−0.478388	−	0.878148i	$-0.658779\pi$
$809$	12.0825	−	37.1862i	0.424799	−	1.30740i	0.903187	−	0.429247i	$-0.141221\pi$
$810$	11.7624	−	6.24303i	0.413290	−	0.219358i
$811$	3.25685	+	10.0236i	0.114363	+	0.351975i	0.991814	−	0.127693i	$-0.0407572\pi$
$811$	3.25685	+	10.0236i	0.114363	+	0.351975i	−0.877450	+	0.479668i	$0.840757\pi$
$812$	5.49835	+	1.78652i	0.192954	+	0.0626946i
$813$	17.8429	+	5.79752i	0.625779	+	0.203328i
$814$	−1.62926	−	5.01433i	−0.0571054	−	0.175752i
$815$	−31.4714	+	16.7038i	−1.10240	+	0.585107i
$816$	0.857226	−	2.63827i	0.0300089	−	0.0923580i
$817$	−17.5995	+	24.2236i	−0.615728	+	0.847478i
$818$		−	74.2707i		−	2.59681i
$819$	4.17862	+	3.03595i	0.146013	+	0.106085i
$820$	33.8008	+	16.5168i	1.18038	+	0.576791i
$821$	16.3552	−	11.8827i	0.570799	−	0.414710i	−0.264596	−	0.964359i	$-0.585239\pi$
$821$	16.3552	−	11.8827i	0.570799	−	0.414710i	0.835395	+	0.549649i	$0.185239\pi$
$822$	13.3091	+	18.3185i	0.464210	+	0.638930i
$823$	44.3253	−	14.4022i	1.54508	−	0.502028i	0.592310	−	0.805710i	$-0.298216\pi$
$823$	44.3253	−	14.4022i	1.54508	−	0.502028i	0.952773	+	0.303682i	$0.0982161\pi$
$824$	5.91984			0.206227
$825$	−1.42566	−	0.964698i	−0.0496352	−	0.0335865i
$826$	11.0224			0.383519
$827$	42.4453	−	13.7913i	1.47597	−	0.479571i	0.543062	−	0.839693i	$-0.317265\pi$
$827$	42.4453	−	13.7913i	1.47597	−	0.479571i	0.932905	+	0.360122i	$0.117265\pi$
$828$	11.5038	+	15.8337i	0.399786	+	0.550258i
$829$	−23.8942	+	17.3602i	−0.829880	+	0.602943i	−0.919525	−	0.393031i	$-0.871427\pi$
$829$	−23.8942	+	17.3602i	−0.829880	+	0.602943i	0.0896454	+	0.995974i	$0.471427\pi$
$830$	−33.1445	−	62.4473i	−1.15046	−	2.16758i
$831$	−4.81771	−	3.50027i	−0.167125	−	0.121423i
$832$		−	29.9043i		−	1.03675i
$833$	1.50959	−	2.07778i	0.0523043	−	0.0719907i
$834$	3.68923	−	11.3543i	0.127748	−	0.393167i
$835$	−4.32277	−	24.6223i	−0.149596	−	0.852090i
$836$	1.14362	+	3.51971i	0.0395530	+	0.121732i
$837$	39.2374	+	12.7490i	1.35624	+	0.440670i
$838$	34.6139	+	11.2467i	1.19572	+	0.388512i
$839$	7.63057	+	23.4845i	0.263436	+	0.810774i	0.992049	+	0.125849i	$0.0401653\pi$
$839$	7.63057	+	23.4845i	0.263436	+	0.810774i	−0.728613	+	0.684926i	$0.759835\pi$
$840$	2.94589	+	2.84903i	0.101643	+	0.0983010i
$841$	−7.76736	+	23.9055i	−0.267840	+	0.824326i
$842$	−34.8448	+	47.9597i	−1.20083	+	1.65280i
$843$		−	2.95487i		−	0.101771i
$844$	52.9298	+	38.4558i	1.82192	+	1.32370i
$845$	16.8391	−	2.95632i	0.579281	−	0.101700i
$846$	12.2825	−	8.92376i	0.422281	−	0.306805i
$847$	−6.37490	−	8.77430i	−0.219044	−	0.301489i
$848$	−12.0960	+	3.93024i	−0.415379	+	0.134965i
$849$	2.79560			0.0959446
$850$	27.4267	+	7.90847i	0.940728	+	0.271258i
$851$	−17.9982			−0.616969
$852$	30.1715	−	9.80332i	1.03366	−	0.335856i
$853$	15.2163	+	20.9435i	0.520997	+	0.717091i	0.985725	−	0.168362i	$-0.0538479\pi$
$853$	15.2163	+	20.9435i	0.520997	+	0.717091i	−0.464728	+	0.885454i	$0.653848\pi$
$854$	−19.2388	+	13.9778i	−0.658340	+	0.478312i
$855$	2.23659	−	15.8291i	0.0764897	−	0.541342i
$856$	11.9722	+	8.69832i	0.409202	+	0.297302i
$857$		−	29.4598i		−	1.00633i	−0.864191	−	0.503164i	$-0.832169\pi$
$857$		−	29.4598i		−	1.00633i	0.864191	−	0.503164i	$-0.167831\pi$
$858$	−1.04082	+	1.43257i	−0.0355332	+	0.0489072i
$859$	−14.5480	+	44.7740i	−0.496370	+	1.52767i	0.318441	+	0.947943i	$0.396841\pi$
$859$	−14.5480	+	44.7740i	−0.496370	+	1.52767i	−0.814811	+	0.579727i	$0.803159\pi$
$860$	60.8738	+	8.60125i	2.07578	+	0.293300i
$861$	−1.54904	−	4.76744i	−0.0527910	−	0.162474i
$862$	−47.5339	−	15.4447i	−1.61901	−	0.526049i
$863$	−12.2300	−	3.97378i	−0.416315	−	0.135269i	0.0933669	−	0.995632i	$-0.470237\pi$
$863$	−12.2300	−	3.97378i	−0.416315	−	0.135269i	−0.509682	+	0.860363i	$0.670237\pi$
$864$	9.80846	+	30.1873i	0.333691	+	1.02699i
$865$	15.8192	−	32.3733i	0.537870	−	1.10073i
$866$	−25.2987	+	77.8614i	−0.859685	+	2.64584i
$867$	−5.35856	+	7.37542i	−0.181986	+	0.250482i
$868$		−	26.4650i		−	0.898280i
$869$	−0.335933	−	0.244070i	−0.0113958	−	0.00827950i
$870$	5.95197	−	6.15431i	0.201791	−	0.208651i
$871$	29.4885	−	21.4246i	0.999180	−	0.725946i
$872$	−2.11285	−	2.90808i	−0.0715500	−	0.0984801i
$873$	−36.1441	+	11.7439i	−1.22329	+	0.397471i
$874$	21.2248			0.717941
$875$	7.49955	−	8.29196i	0.253531	−	0.280320i
$876$	3.44568			0.116419
$877$	−20.9771	+	6.81587i	−0.708346	+	0.230156i	−0.640963	−	0.767572i	$-0.721465\pi$
$877$	−20.9771	+	6.81587i	−0.708346	+	0.230156i	−0.0673828	+	0.997727i	$0.521465\pi$
$878$	53.4570	+	73.5773i	1.80409	+	2.48311i
$879$	0.288401	−	0.209535i	0.00972751	−	0.00706745i
$880$	−0.752852	+	0.778446i	−0.0253786	+	0.0262414i
$881$	−1.95911	−	1.42338i	−0.0660042	−	0.0479549i	0.554294	−	0.832321i	$-0.312988\pi$
$881$	−1.95911	−	1.42338i	−0.0660042	−	0.0479549i	−0.620298	+	0.784366i	$0.712988\pi$
$882$			4.96175i			0.167071i
$883$	6.35144	−	8.74201i	0.213743	−	0.294192i	−0.688661	−	0.725084i	$-0.741801\pi$
$883$	6.35144	−	8.74201i	0.213743	−	0.294192i	0.902404	+	0.430892i	$0.141801\pi$
$884$	5.40081	−	16.6220i	0.181649	−	0.559058i
$885$	4.26566	−	8.72948i	0.143389	−	0.293438i
$886$	−23.1659	−	71.2973i	−0.778274	−	2.39528i
$887$	−26.5749	−	8.63470i	−0.892297	−	0.289925i	−0.173243	−	0.984879i	$-0.555425\pi$
$887$	−26.5749	−	8.63470i	−0.892297	−	0.289925i	−0.719054	+	0.694954i	$0.755425\pi$
$888$	10.5230	+	3.41912i	0.353127	+	0.114738i
$889$	5.09616	+	15.6844i	0.170920	+	0.526036i
$890$	69.1472	+	9.77024i	2.31782	+	0.327499i
$891$	−0.325283	+	1.00112i	−0.0108974	+	0.0335387i
$892$	−1.49938	+	2.06371i	−0.0502028	+	0.0690982i
$893$		−	9.80002i		−	0.327945i
$894$	−23.7127	−	17.2283i	−0.793072	−	0.576200i
$895$	7.49667	−	53.0564i	0.250586	−	1.77348i
$896$	12.0389	−	8.74676i	0.402191	−	0.292209i
$897$	3.55303	+	4.89033i	0.118632	+	0.163283i
$898$	21.7301	−	7.06053i	0.725142	−	0.235613i
$899$	−17.6896			−0.589981
$900$	−30.8609	+	11.1807i	−1.02870	+	0.372690i
$901$	−26.4993			−0.882820
$902$	−4.75159	+	1.54389i	−0.158211	+	0.0514058i
$903$	−4.81500	−	6.62728i	−0.160233	−	0.220542i
$904$	2.07261	−	1.50584i	0.0689341	−	0.0500835i
$905$	51.1364	−	8.97767i	1.69983	−	0.298428i
$906$	−7.39207	−	5.37066i	−0.245585	−	0.178428i
$907$			19.6907i			0.653818i	0.945056	+	0.326909i	$0.106007\pi$
$907$			19.6907i			0.653818i	−0.945056	+	0.326909i	$0.893993\pi$
$908$	−3.90154	+	5.37001i	−0.129477	+	0.178210i
$909$	8.98052	−	27.6392i	0.297865	−	0.916734i
$910$	−8.26723	−	7.99542i	−0.274056	−	0.265045i
$911$	8.32087	+	25.6090i	0.275683	+	0.848464i	0.989038	+	0.147662i	$0.0471746\pi$
$911$	8.32087	+	25.6090i	0.275683	+	0.848464i	−0.713355	+	0.700803i	$0.752825\pi$
$912$	3.29012	+	1.06902i	0.108947	+	0.0353989i
$913$	5.31497	+	1.72694i	0.175900	+	0.0571534i
$914$	1.13905	+	3.50563i	0.0376763	+	0.115956i
$915$	3.62470	+	20.6461i	0.119829	+	0.682539i
$916$	10.6479	−	32.7708i	0.351816	−	1.08278i
$917$	−0.955236	+	1.31477i	−0.0315447	+	0.0434175i
$918$			26.1733i			0.863849i
$919$	24.5160	+	17.8119i	0.808710	+	0.587562i	0.913456	−	0.406937i	$-0.133403\pi$
$919$	24.5160	+	17.8119i	0.808710	+	0.587562i	−0.104747	+	0.994499i	$0.533403\pi$
$920$	−6.53691	−	12.3161i	−0.215516	−	0.406051i
$921$	6.67587	−	4.85030i	0.219977	−	0.159823i
$922$	9.89234	+	13.6156i	0.325787	+	0.448407i
$923$	−27.0909	+	8.80237i	−0.891708	+	0.289734i
$924$	−1.01250			−0.0333089
$925$	8.36313	−	29.0035i	0.274978	−	0.953628i
$926$	−9.26434			−0.304445
$927$	6.00851	−	1.95228i	0.197345	−	0.0641213i
$928$	−7.99946	−	11.0103i	−0.262595	−	0.361431i
$929$	10.6834	−	7.76191i	0.350509	−	0.254660i	−0.398573	−	0.917136i	$-0.630495\pi$
$929$	10.6834	−	7.76191i	0.350509	−	0.254660i	0.749083	+	0.662477i	$0.230495\pi$
$930$	−35.2132	−	17.2069i	−1.15469	−	0.564237i
$931$	2.59114	+	1.88257i	0.0849212	+	0.0616988i
$932$		−	15.1197i		−	0.495263i
$933$	−4.37030	+	6.01520i	−0.143077	+	0.196929i
$934$	−9.26183	+	28.5050i	−0.303056	+	0.932712i
$935$	−1.99301	+	1.05781i	−0.0651784	+	0.0345941i
$936$	3.33839	+	10.2745i	0.109119	+	0.335832i
$937$	−15.0738	−	4.89777i	−0.492439	−	0.160003i	0.0522621	−	0.998633i	$-0.483357\pi$
$937$	−15.0738	−	4.89777i	−0.492439	−	0.160003i	−0.544701	+	0.838630i	$0.683357\pi$
$938$	33.3013	+	10.8202i	1.08733	+	0.353294i
$939$	1.00046	+	3.07911i	0.0326489	+	0.100483i
$940$	−17.7736	+	9.43349i	−0.579710	+	0.307686i
$941$	0.922511	−	2.83920i	0.0300730	−	0.0925552i	−0.934893	−	0.354929i	$-0.884505\pi$
$941$	0.922511	−	2.83920i	0.0300730	−	0.0925552i	0.964966	+	0.262373i	$0.0845052\pi$
$942$	2.22158	−	3.05774i	0.0723829	−	0.0996265i
$943$			17.0551i			0.555391i
$944$	−4.94506	−	3.59279i	−0.160948	−	0.116935i
$945$	9.21086	+	4.50089i	0.299629	+	0.146414i
$946$	−6.60525	+	4.79900i	−0.214755	+	0.156029i
$947$	−4.62559	−	6.36657i	−0.150311	−	0.206886i	0.727221	−	0.686404i	$-0.240812\pi$
$947$	−4.62559	−	6.36657i	−0.150311	−	0.206886i	−0.877532	+	0.479518i	$0.840812\pi$
$948$	2.59026	−	0.841626i	0.0841277	−	0.0273347i
$949$	−3.09387			−0.100431
$950$	−9.86245	+	34.2031i	−0.319980	+	1.10970i
$951$	27.2912			0.884977
$952$	5.10889	−	1.65998i	0.165580	−	0.0538002i
$953$	−17.5180	−	24.1115i	−0.567465	−	0.781048i	0.424787	−	0.905293i	$-0.360349\pi$
$953$	−17.5180	−	24.1115i	−0.567465	−	0.781048i	−0.992252	+	0.124245i	$0.960349\pi$
$954$	41.4177	−	30.0917i	1.34095	−	0.974256i
$955$	0.541168	+	1.01961i	0.0175118	+	0.0329938i
$956$	−18.4102	−	13.3758i	−0.595429	−	0.432605i
$957$			0.676773i			0.0218770i
$958$	20.6388	−	28.4069i	0.666810	−	0.917785i
$959$	3.59235	−	11.0561i	0.116003	−	0.357020i
$960$	−4.37869	−	24.9408i	−0.141322	−	0.804962i
$961$	15.4439	+	47.5313i	0.498189	+	1.53327i
$962$	−29.5312	−	9.59527i	−0.952125	−	0.309364i
$963$	15.0201	+	4.88033i	0.484017	+	0.157267i
$964$	12.0443	+	37.0685i	0.387921	+	1.19390i
$965$	39.0937	+	37.8084i	1.25847	+	1.21709i
$966$	−1.79441	+	5.52264i	−0.0577344	+	0.177688i
$967$	−32.4097	+	44.6081i	−1.04222	+	1.43450i	−0.146864	+	0.989157i	$0.546918\pi$
$967$	−32.4097	+	44.6081i	−1.04222	+	1.43450i	−0.895360	+	0.445342i	$0.853082\pi$
$968$		−	22.6847i		−	0.729115i
$969$	5.83125	+	4.23665i	0.187327	+	0.136101i
$970$	83.3490	−	14.6330i	2.67617	−	0.469838i
$971$	31.4461	−	22.8469i	1.00915	−	0.733193i	0.0451227	−	0.998981i	$-0.485632\pi$
$971$	31.4461	−	22.8469i	1.00915	−	0.733193i	0.964031	+	0.265788i	$0.0856321\pi$
$972$	−27.8344	−	38.3108i	−0.892789	−	1.22882i
$973$	−5.82941	+	1.89409i	−0.186882	+	0.0607217i
$974$	17.9704			0.575809
$975$	−9.53158	+	3.45323i	−0.305255	+	0.110592i
$976$	13.1874			0.422117
$977$	2.23004	−	0.724583i	0.0713452	−	0.0231815i	−0.273127	−	0.961978i	$-0.588058\pi$
$977$	2.23004	−	0.724583i	0.0713452	−	0.0231815i	0.344472	+	0.938797i	$0.388058\pi$
$978$	18.2423	+	25.1084i	0.583325	+	0.802878i
$979$	−4.46592	+	3.24468i	−0.142732	+	0.103701i
$980$	0.920054	−	6.51152i	0.0293900	−	0.208003i
$981$	−3.10354	−	2.25485i	−0.0990884	−	0.0719919i
$982$		−	12.4770i		−	0.398156i
$983$	−24.4023	+	33.5869i	−0.778314	+	1.07126i	0.217152	+	0.976138i	$0.430323\pi$
$983$	−24.4023	+	33.5869i	−0.778314	+	1.07126i	−0.995466	+	0.0951194i	$0.969677\pi$
$984$	3.23996	−	9.97159i	0.103286	−	0.317883i
$985$	−25.2490	−	3.56759i	−0.804499	−	0.113673i
$986$	−3.46789	−	10.6731i	−0.110440	−	0.339900i
$987$	2.54994	+	0.828525i	0.0811654	+	0.0263723i
$988$	20.7289	+	6.73521i	0.659473	+	0.214276i
$989$	8.61263	+	26.5070i	0.273866	+	0.842872i
$990$	1.91381	−	3.91653i	0.0608249	−	0.124475i
$991$	−4.89864	+	15.0765i	−0.155610	+	0.478920i	−0.998222	−	0.0596019i	$-0.981017\pi$
$991$	−4.89864	+	15.0765i	−0.155610	+	0.478920i	0.842612	+	0.538521i	$0.181017\pi$
$992$	−36.6190	+	50.4018i	−1.16266	+	1.60026i
$993$			3.72475i			0.118201i
$994$	−22.1378	−	16.0841i	−0.702169	−	0.510156i
$995$	−1.42462	+	1.47305i	−0.0451634	+	0.0466988i
$996$	−29.6547	+	21.5454i	−0.939646	+	0.682693i
$997$	−6.95994	−	9.57954i	−0.220424	−	0.303387i	0.684456	−	0.729054i	$-0.260040\pi$
$997$	−6.95994	−	9.57954i	−0.220424	−	0.303387i	−0.904880	+	0.425667i	$0.860040\pi$
$998$	−21.6283	+	7.02745i	−0.684631	+	0.222450i
$999$	27.6780			0.875695

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.n.a.169.13	yes	56
5.2	odd	4		875.2.h.e.526.14		56
5.3	odd	4		875.2.h.d.526.1		56
5.4	even	2		875.2.n.c.99.2		56
25.2	odd	20		4375.2.a.o.1.26		28
25.3	odd	20		875.2.h.d.351.1		56
25.4	even	10	inner	175.2.n.a.29.13	✓	56
25.21	even	5		875.2.n.c.274.2		56
25.22	odd	20		875.2.h.e.351.14		56
25.23	odd	20		4375.2.a.p.1.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.n.a.29.13	✓	56	25.4	even	10	inner
175.2.n.a.169.13	yes	56	1.1	even	1	trivial
875.2.h.d.351.1		56	25.3	odd	20
875.2.h.d.526.1		56	5.3	odd	4
875.2.h.e.351.14		56	25.22	odd	20
875.2.h.e.526.14		56	5.2	odd	4
875.2.n.c.99.2		56	5.4	even	2
875.2.n.c.274.2		56	25.21	even	5
4375.2.a.o.1.26		28	25.2	odd	20
4375.2.a.p.1.3		28	25.23	odd	20

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.11404 - 0.686892i) q^{2} +(0.515049 + 0.708904i) q^{3} +(2.37929 - 1.72866i) q^{4} +(-1.55449 + 1.60734i) q^{5} +(1.57577 + 1.14486i) q^{6} -1.00000i q^{7} +(1.22941 - 1.69214i) q^{8} +(0.689782 - 2.12293i) q^{9} +O(q^{10})\)	\(q+(2.11404 - 0.686892i) q^{2} +(0.515049 + 0.708904i) q^{3} +(2.37929 - 1.72866i) q^{4} +(-1.55449 + 1.60734i) q^{5} +(1.57577 + 1.14486i) q^{6} -1.00000i q^{7} +(1.22941 - 1.69214i) q^{8} +(0.689782 - 2.12293i) q^{9} +(-2.18219 + 4.46575i) q^{10} +(-0.121412 - 0.373666i) q^{11} +(2.45090 + 0.796346i) q^{12} +(-2.20066 - 0.715037i) q^{13} +(-0.686892 - 2.11404i) q^{14} +(-1.94009 - 0.274128i) q^{15} +(-0.380912 + 1.17233i) q^{16} +(-1.50959 + 2.07778i) q^{17} -4.96175i q^{18} +(-2.59114 - 1.88257i) q^{19} +(-0.920054 + 6.51152i) q^{20} +(0.708904 - 0.515049i) q^{21} +(-0.513337 - 0.706547i) q^{22} +(-2.83538 + 0.921271i) q^{23} +1.83277 q^{24} +(-0.167094 - 4.99721i) q^{25} -5.14342 q^{26} +(4.36032 - 1.41675i) q^{27} +(-1.72866 - 2.37929i) q^{28} +(-1.59035 + 1.15546i) q^{29} +(-4.28971 + 0.753116i) q^{30} +(7.28014 + 5.28933i) q^{31} +6.92319i q^{32} +(0.202361 - 0.278525i) q^{33} +(-1.76412 + 5.42942i) q^{34} +(1.60734 + 1.55449i) q^{35} +(-2.02862 - 6.24346i) q^{36} +(5.74156 + 1.86554i) q^{37} +(-6.77088 - 2.19999i) q^{38} +(-0.626553 - 1.92833i) q^{39} +(0.808734 + 4.60651i) q^{40} +(1.76779 - 5.44071i) q^{41} +(1.14486 - 1.57577i) q^{42} -9.34864i q^{43} +(-0.934814 - 0.679182i) q^{44} +(2.34001 + 4.40880i) q^{45} +(-5.36128 + 3.89520i) q^{46} +(1.79851 + 2.47544i) q^{47} +(-1.02726 + 0.333776i) q^{48} -1.00000 q^{49} +(-3.78578 - 10.4495i) q^{50} -2.25046 q^{51} +(-6.47205 + 2.10290i) q^{52} +(6.06474 + 8.34740i) q^{53} +(8.24472 - 5.99014i) q^{54} +(0.789343 + 0.385712i) q^{55} +(-1.69214 - 1.22941i) q^{56} -2.80648i q^{57} +(-2.56839 + 3.53508i) q^{58} +(-1.53233 + 4.71604i) q^{59} +(-5.08991 + 2.70152i) q^{60} +(-3.30596 - 10.1747i) q^{61} +(19.0237 + 6.18116i) q^{62} +(-2.12293 - 0.689782i) q^{63} +(3.99366 + 12.2912i) q^{64} +(4.57022 - 2.42569i) q^{65} +(0.236481 - 0.727812i) q^{66} +(-9.25908 + 12.7440i) q^{67} +7.55320i q^{68} +(-2.11345 - 1.53551i) q^{69} +(4.46575 + 2.18219i) q^{70} +(9.95930 - 7.23586i) q^{71} +(-2.74427 - 3.77716i) q^{72} +(1.27164 - 0.413179i) q^{73} +13.4193 q^{74} +(3.45648 - 2.69226i) q^{75} -9.41939 q^{76} +(-0.373666 + 0.121412i) q^{77} +(-2.64911 - 3.64619i) q^{78} +(0.855018 - 0.621207i) q^{79} +(-1.29220 - 2.43463i) q^{80} +(-2.16750 - 1.57478i) q^{81} -12.7161i q^{82} +(-8.36057 + 11.5073i) q^{83} +(0.796346 - 2.45090i) q^{84} +(-0.993042 - 5.65632i) q^{85} +(-6.42150 - 19.7634i) q^{86} +(-1.63822 - 0.532289i) q^{87} +(-0.781561 - 0.253945i) q^{88} +(-4.34169 - 13.3623i) q^{89} +(7.97523 + 7.71302i) q^{90} +(-0.715037 + 2.20066i) q^{91} +(-5.15363 + 7.09337i) q^{92} +7.88518i q^{93} +(5.50247 + 3.99778i) q^{94} +(7.05385 - 1.23840i) q^{95} +(-4.90787 + 3.56578i) q^{96} +(-10.0074 - 13.7740i) q^{97} +(-2.11404 + 0.686892i) q^{98} -0.877015 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9}+O(q^{10}) \) 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9	\( 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9} - 4 q^{10} + 8 q^{11} - 40 q^{12} - 4 q^{14} - 18 q^{15} - 32 q^{16} + 12 q^{19} + 12 q^{20} + 4 q^{21} - 30 q^{22} + 10 q^{23} - 28 q^{24} + 4 q^{25} + 12 q^{26} + 30 q^{27} - 2 q^{29} + 28 q^{30} + 12 q^{31} + 20 q^{33} + 2 q^{35} - 14 q^{36} - 70 q^{37} - 70 q^{38} - 4 q^{39} - 30 q^{40} + 4 q^{41} + 50 q^{42} + 22 q^{44} - 52 q^{45} - 4 q^{46} - 10 q^{47} + 30 q^{48} - 56 q^{49} - 54 q^{50} - 44 q^{51} - 20 q^{53} + 54 q^{54} - 2 q^{55} + 12 q^{56} + 10 q^{58} - 6 q^{59} + 16 q^{60} - 4 q^{61} + 50 q^{62} + 20 q^{63} + 24 q^{64} - 18 q^{65} - 74 q^{66} + 10 q^{67} - 78 q^{69} + 8 q^{70} - 8 q^{71} + 140 q^{72} + 40 q^{73} + 60 q^{74} - 8 q^{75} + 52 q^{76} - 20 q^{77} - 90 q^{78} + 124 q^{80} - 72 q^{81} - 30 q^{83} - 12 q^{84} + 96 q^{85} - 20 q^{86} + 30 q^{87} + 140 q^{88} + 38 q^{89} - 8 q^{90} + 8 q^{91} + 80 q^{92} + 88 q^{94} - 70 q^{95} - 28 q^{96} - 30 q^{97} + 60 q^{99}+O(q^{100}) \) 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9 - 4 * q^10 + 8 * q^11 - 40 * q^12 - 4 * q^14 - 18 * q^15 - 32 * q^16 + 12 * q^19 + 12 * q^20 + 4 * q^21 - 30 * q^22 + 10 * q^23 - 28 * q^24 + 4 * q^25 + 12 * q^26 + 30 * q^27 - 2 * q^29 + 28 * q^30 + 12 * q^31 + 20 * q^33 + 2 * q^35 - 14 * q^36 - 70 * q^37 - 70 * q^38 - 4 * q^39 - 30 * q^40 + 4 * q^41 + 50 * q^42 + 22 * q^44 - 52 * q^45 - 4 * q^46 - 10 * q^47 + 30 * q^48 - 56 * q^49 - 54 * q^50 - 44 * q^51 - 20 * q^53 + 54 * q^54 - 2 * q^55 + 12 * q^56 + 10 * q^58 - 6 * q^59 + 16 * q^60 - 4 * q^61 + 50 * q^62 + 20 * q^63 + 24 * q^64 - 18 * q^65 - 74 * q^66 + 10 * q^67 - 78 * q^69 + 8 * q^70 - 8 * q^71 + 140 * q^72 + 40 * q^73 + 60 * q^74 - 8 * q^75 + 52 * q^76 - 20 * q^77 - 90 * q^78 + 124 * q^80 - 72 * q^81 - 30 * q^83 - 12 * q^84 + 96 * q^85 - 20 * q^86 + 30 * q^87 + 140 * q^88 + 38 * q^89 - 8 * q^90 + 8 * q^91 + 80 * q^92 + 88 * q^94 - 70 * q^95 - 28 * q^96 - 30 * q^97 + 60 * q^99

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