LMFDB - Embedded newform 465.2.k.b.32.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [465,2,Mod(32,465)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(465, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 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("465.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			32.3
Character	$\chi$	$=$	465.32
Dual form			465.2.k.b.218.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.78894 + 1.78894i) q^{2} +(-0.177331 + 1.72295i) q^{3} -4.40062i q^{4} +(2.22867 - 0.181744i) q^{5} +(-2.76502 - 3.39949i) q^{6} +(-2.03308 - 2.03308i) q^{7} +(4.29457 + 4.29457i) q^{8} +(-2.93711 - 0.611065i) q^{9} +O(q^{10})$	\(q+(-1.78894 + 1.78894i) q^{2} +(-0.177331 + 1.72295i) q^{3} -4.40062i q^{4} +(2.22867 - 0.181744i) q^{5} +(-2.76502 - 3.39949i) q^{6} +(-2.03308 - 2.03308i) q^{7} +(4.29457 + 4.29457i) q^{8} +(-2.93711 - 0.611065i) q^{9} +(-3.66183 + 4.31209i) q^{10} -3.09835i q^{11} +(7.58205 + 0.780367i) q^{12} +(-1.79379 + 1.79379i) q^{13} +7.27412 q^{14} +(-0.0820773 + 3.87211i) q^{15} -6.56422 q^{16} +(3.85202 - 3.85202i) q^{17} +(6.34747 - 4.16115i) q^{18} -8.58999i q^{19} +(-0.799785 - 9.80753i) q^{20} +(3.86342 - 3.14237i) q^{21} +(5.54276 + 5.54276i) q^{22} +(3.31102 + 3.31102i) q^{23} +(-8.16088 + 6.63776i) q^{24} +(4.93394 - 0.810094i) q^{25} -6.41798i q^{26} +(1.57367 - 4.95213i) q^{27} +(-8.94682 + 8.94682i) q^{28} +1.68272 q^{29} +(-6.78015 - 7.07381i) q^{30} -1.00000 q^{31} +(3.15387 - 3.15387i) q^{32} +(5.33830 + 0.549434i) q^{33} +13.7821i q^{34} +(-4.90057 - 4.16157i) q^{35} +(-2.68907 + 12.9251i) q^{36} +(-5.24547 - 5.24547i) q^{37} +(15.3670 + 15.3670i) q^{38} +(-2.77252 - 3.40871i) q^{39} +(10.3517 + 8.79067i) q^{40} +7.51737i q^{41} +(-1.28993 + 12.5329i) q^{42} +(3.78772 - 3.78772i) q^{43} -13.6347 q^{44} +(-6.65690 - 0.828061i) q^{45} -11.8464 q^{46} +(-1.05449 + 1.05449i) q^{47} +(1.16404 - 11.3098i) q^{48} +1.26683i q^{49} +(-7.37732 + 10.2757i) q^{50} +(5.95376 + 7.31992i) q^{51} +(7.89380 + 7.89380i) q^{52} +(-1.41276 - 1.41276i) q^{53} +(6.04385 + 11.6743i) q^{54} +(-0.563106 - 6.90520i) q^{55} -17.4624i q^{56} +(14.8001 + 1.52327i) q^{57} +(-3.01028 + 3.01028i) q^{58} -6.67934 q^{59} +(17.0397 + 0.361191i) q^{60} +3.28118 q^{61} +(1.78894 - 1.78894i) q^{62} +(4.72903 + 7.21372i) q^{63} -1.84428i q^{64} +(-3.67176 + 4.32378i) q^{65} +(-10.5328 + 8.56700i) q^{66} +(6.78680 + 6.78680i) q^{67} +(-16.9513 - 16.9513i) q^{68} +(-6.29186 + 5.11757i) q^{69} +(16.2116 - 1.32203i) q^{70} +2.68088i q^{71} +(-9.98935 - 15.2379i) q^{72} +(-5.27915 + 5.27915i) q^{73} +18.7677 q^{74} +(0.520809 + 8.64458i) q^{75} -37.8013 q^{76} +(-6.29919 + 6.29919i) q^{77} +(11.0579 + 1.13811i) q^{78} -11.8585i q^{79} +(-14.6295 + 1.19301i) q^{80} +(8.25320 + 3.58953i) q^{81} +(-13.4481 - 13.4481i) q^{82} +(-8.83795 - 8.83795i) q^{83} +(-13.8284 - 17.0015i) q^{84} +(7.88481 - 9.28497i) q^{85} +13.5520i q^{86} +(-0.298398 + 2.89924i) q^{87} +(13.3061 - 13.3061i) q^{88} +16.4412 q^{89} +(13.3902 - 10.4274i) q^{90} +7.29385 q^{91} +(14.5705 - 14.5705i) q^{92} +(0.177331 - 1.72295i) q^{93} -3.77285i q^{94} +(-1.56118 - 19.1443i) q^{95} +(4.87467 + 5.99323i) q^{96} +(-5.68596 - 5.68596i) q^{97} +(-2.26629 - 2.26629i) q^{98} +(-1.89329 + 9.10018i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 4 q^{6}+O(q^{10}) $ 60 * q - 4 * q^6	$ 60 q - 4 q^{6} + 16 q^{10} - 12 q^{13} - 8 q^{15} - 60 q^{16} + 34 q^{18} - 4 q^{21} + 8 q^{22} + 8 q^{25} - 6 q^{27} - 80 q^{28} - 54 q^{30} - 60 q^{31} + 10 q^{33} + 28 q^{36} - 12 q^{37} + 60 q^{40} - 12 q^{42} - 24 q^{43} - 58 q^{45} + 8 q^{46} + 80 q^{48} + 32 q^{51} + 52 q^{52} + 64 q^{55} - 14 q^{57} - 48 q^{58} - 108 q^{60} - 56 q^{61} + 62 q^{63} + 40 q^{66} + 104 q^{67} + 108 q^{70} - 76 q^{72} - 108 q^{73} - 38 q^{75} - 120 q^{76} + 112 q^{78} + 60 q^{81} + 20 q^{82} + 48 q^{85} - 110 q^{87} - 28 q^{88} - 82 q^{90} - 32 q^{91} + 120 q^{96} + 56 q^{97}+O(q^{100}) $ 60 * q - 4 * q^6 + 16 * q^10 - 12 * q^13 - 8 * q^15 - 60 * q^16 + 34 * q^18 - 4 * q^21 + 8 * q^22 + 8 * q^25 - 6 * q^27 - 80 * q^28 - 54 * q^30 - 60 * q^31 + 10 * q^33 + 28 * q^36 - 12 * q^37 + 60 * q^40 - 12 * q^42 - 24 * q^43 - 58 * q^45 + 8 * q^46 + 80 * q^48 + 32 * q^51 + 52 * q^52 + 64 * q^55 - 14 * q^57 - 48 * q^58 - 108 * q^60 - 56 * q^61 + 62 * q^63 + 40 * q^66 + 104 * q^67 + 108 * q^70 - 76 * q^72 - 108 * q^73 - 38 * q^75 - 120 * q^76 + 112 * q^78 + 60 * q^81 + 20 * q^82 + 48 * q^85 - 110 * q^87 - 28 * q^88 - 82 * q^90 - 32 * q^91 + 120 * q^96 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.78894	+	1.78894i	−1.26497	+	1.26497i	−0.316320	+	0.948653i	$0.602447\pi$
$2$	−1.78894	+	1.78894i	−1.26497	+	1.26497i	−0.948653	+	0.316320i	$0.897553\pi$
$3$	−0.177331	+	1.72295i	−0.102382	+	0.994745i
$3$	−0.177331	+	1.72295i	−0.102382	+	0.994745i
$4$		−	4.40062i		−	2.20031i
$5$	2.22867	−	0.181744i	0.996691	−	0.0812783i
$5$	2.22867	−	0.181744i	0.996691	−	0.0812783i
$6$	−2.76502	−	3.39949i	−1.12881	−	1.38784i
$7$	−2.03308	−	2.03308i	−0.768432	−	0.768432i	0.209398	−	0.977830i	$-0.432850\pi$
$7$	−2.03308	−	2.03308i	−0.768432	−	0.768432i	−0.977830	+	0.209398i	$0.932850\pi$
$8$	4.29457	+	4.29457i	1.51836	+	1.51836i
$9$	−2.93711	−	0.611065i	−0.979036	−	0.203688i
$10$	−3.66183	+	4.31209i	−1.15797	+	1.36360i
$11$		−	3.09835i		−	0.934187i	−0.884208	−	0.467094i	$-0.845301\pi$
$11$		−	3.09835i		−	0.934187i	0.884208	−	0.467094i	$-0.154699\pi$
$12$	7.58205	+	0.780367i	2.18875	+	0.225273i
$13$	−1.79379	+	1.79379i	−0.497509	+	0.497509i	−0.910662	−	0.413153i	$-0.864427\pi$
$13$	−1.79379	+	1.79379i	−0.497509	+	0.497509i	0.413153	+	0.910662i	$0.364427\pi$
$14$	7.27412			1.94409
$15$	−0.0820773	+	3.87211i	−0.0211923	+	0.999775i
$16$	−6.56422			−1.64106
$17$	3.85202	−	3.85202i	0.934253	−	0.934253i	−0.0637153	−	0.997968i	$-0.520295\pi$
$17$	3.85202	−	3.85202i	0.934253	−	0.934253i	0.997968	+	0.0637153i	$0.0202950\pi$
$18$	6.34747	−	4.16115i	1.49611	−	0.980793i
$19$		−	8.58999i		−	1.97068i	−0.170603	−	0.985340i	$-0.554571\pi$
$19$		−	8.58999i		−	1.97068i	0.170603	−	0.985340i	$-0.445429\pi$
$20$	−0.799785	−	9.80753i	−0.178837	−	2.19303i
$21$	3.86342	−	3.14237i	0.843068	−	0.685720i
$22$	5.54276	+	5.54276i	1.18172	+	1.18172i
$23$	3.31102	+	3.31102i	0.690395	+	0.690395i	0.962319	−	0.271924i	$-0.0876600\pi$
$23$	3.31102	+	3.31102i	0.690395	+	0.690395i	−0.271924	+	0.962319i	$0.587660\pi$
$24$	−8.16088	+	6.63776i	−1.66583	+	1.35493i
$25$	4.93394	−	0.810094i	0.986788	−	0.162019i
$26$		−	6.41798i		−	1.25867i
$27$	1.57367	−	4.95213i	0.302854	−	0.953037i
$28$	−8.94682	+	8.94682i	−1.69079	+	1.69079i
$29$	1.68272			0.312473			0.156236	−	0.987720i	$-0.450064\pi$
$29$	1.68272			0.312473			0.156236	+	0.987720i	$0.450064\pi$
$30$	−6.78015	−	7.07381i	−1.23788	−	1.29150i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	3.15387	−	3.15387i	0.557530	−	0.557530i
$33$	5.33830	+	0.549434i	0.929278	+	0.0956441i
$34$			13.7821i			2.36361i
$35$	−4.90057	−	4.16157i	−0.828347	−	0.703433i
$36$	−2.68907	+	12.9251i	−0.448178	+	2.15418i
$37$	−5.24547	−	5.24547i	−0.862351	−	0.862351i	0.129260	−	0.991611i	$-0.458740\pi$
$37$	−5.24547	−	5.24547i	−0.862351	−	0.862351i	−0.991611	+	0.129260i	$0.958740\pi$
$38$	15.3670	+	15.3670i	2.49286	+	2.49286i
$39$	−2.77252	−	3.40871i	−0.443958	−	0.545830i
$40$	10.3517	+	8.79067i	1.63675	+	1.38993i
$41$			7.51737i			1.17402i	0.809581	+	0.587008i	$0.199694\pi$
$41$			7.51737i			1.17402i	−0.809581	+	0.587008i	$0.800306\pi$
$42$	−1.28993	+	12.5329i	−0.199040	+	1.93388i
$43$	3.78772	−	3.78772i	0.577622	−	0.577622i	−0.356625	−	0.934248i	$-0.616073\pi$
$43$	3.78772	−	3.78772i	0.577622	−	0.577622i	0.934248	+	0.356625i	$0.116073\pi$
$44$	−13.6347			−2.05550
$45$	−6.65690	−	0.828061i	−0.992352	−	0.123440i
$46$	−11.8464			−1.74666
$47$	−1.05449	+	1.05449i	−0.153813	+	0.153813i	−0.779819	−	0.626005i	$-0.784689\pi$
$47$	−1.05449	+	1.05449i	−0.153813	+	0.153813i	0.626005	+	0.779819i	$0.284689\pi$
$48$	1.16404	−	11.3098i	0.168015	−	1.63243i
$49$			1.26683i			0.180976i
$50$	−7.37732	+	10.2757i	−1.04331	+	1.45321i
$51$	5.95376	+	7.31992i	0.833693	+	1.02499i
$52$	7.89380	+	7.89380i	1.09467	+	1.09467i
$53$	−1.41276	−	1.41276i	−0.194058	−	0.194058i	0.603389	−	0.797447i	$-0.293817\pi$
$53$	−1.41276	−	1.41276i	−0.194058	−	0.194058i	−0.797447	+	0.603389i	$0.793817\pi$
$54$	6.04385	+	11.6743i	0.822464	+	1.58867i
$55$	−0.563106	−	6.90520i	−0.0759292	−	0.931097i
$56$		−	17.4624i		−	2.33351i
$57$	14.8001	+	1.52327i	1.96032	+	0.201762i
$58$	−3.01028	+	3.01028i	−0.395269	+	0.395269i
$59$	−6.67934			−0.869576			−0.434788	−	0.900533i	$-0.643177\pi$
$59$	−6.67934			−0.869576			−0.434788	+	0.900533i	$0.643177\pi$
$60$	17.0397	+	0.361191i	2.19982	+	0.0466295i
$61$	3.28118			0.420112			0.210056	−	0.977689i	$-0.432635\pi$
$61$	3.28118			0.420112			0.210056	+	0.977689i	$0.432635\pi$
$62$	1.78894	−	1.78894i	0.227196	−	0.227196i
$63$	4.72903	+	7.21372i	0.595802	+	0.908843i
$64$		−	1.84428i		−	0.230535i
$65$	−3.67176	+	4.32378i	−0.455426	+	0.536299i
$66$	−10.5328	+	8.56700i	−1.29650	+	1.05452i
$67$	6.78680	+	6.78680i	0.829139	+	0.829139i	0.987398	−	0.158259i	$-0.0505880\pi$
$67$	6.78680	+	6.78680i	0.829139	+	0.829139i	−0.158259	+	0.987398i	$0.550588\pi$
$68$	−16.9513	−	16.9513i	−2.05565	−	2.05565i
$69$	−6.29186	+	5.11757i	−0.757451	+	0.616083i
$70$	16.2116	−	1.32203i	1.93766	−	0.158012i
$71$			2.68088i			0.318162i	0.987266	+	0.159081i	$0.0508531\pi$
$71$			2.68088i			0.318162i	−0.987266	+	0.159081i	$0.949147\pi$
$72$	−9.98935	−	15.2379i	−1.17726	−	1.79580i
$73$	−5.27915	+	5.27915i	−0.617878	+	0.617878i	−0.944987	−	0.327109i	$-0.893926\pi$
$73$	−5.27915	+	5.27915i	−0.617878	+	0.617878i	0.327109	+	0.944987i	$0.393926\pi$
$74$	18.7677			2.18170
$75$	0.520809	+	8.64458i	0.0601379	+	0.998190i
$76$	−37.8013			−4.33611
$77$	−6.29919	+	6.29919i	−0.717860	+	0.717860i
$78$	11.0579	+	1.13811i	1.25206	+	0.128865i
$79$		−	11.8585i		−	1.33419i	−0.744973	−	0.667094i	$-0.767538\pi$
$79$		−	11.8585i		−	1.33419i	0.744973	−	0.667094i	$-0.232462\pi$
$80$	−14.6295	+	1.19301i	−1.63563	+	0.133382i
$81$	8.25320	+	3.58953i	0.917022	+	0.398836i
$82$	−13.4481	−	13.4481i	−1.48510	−	1.48510i
$83$	−8.83795	−	8.83795i	−0.970091	−	0.970091i	0.0294750	−	0.999566i	$-0.490616\pi$
$83$	−8.83795	−	8.83795i	−0.970091	−	0.970091i	−0.999566	+	0.0294750i	$0.990616\pi$
$84$	−13.8284	−	17.0015i	−1.50880	−	1.85501i
$85$	7.88481	−	9.28497i	0.855227	−	1.00710i
$86$			13.5520i			1.46135i
$87$	−0.298398	+	2.89924i	−0.0319916	+	0.310831i
$88$	13.3061	−	13.3061i	1.41843	−	1.41843i
$89$	16.4412			1.74276			0.871379	−	0.490610i	$-0.163226\pi$
$89$	16.4412			1.74276			0.871379	+	0.490610i	$0.163226\pi$
$90$	13.3902	−	10.4274i	1.41145	−	1.09915i
$91$	7.29385			0.764603
$92$	14.5705	−	14.5705i	1.51908	−	1.51908i
$93$	0.177331	−	1.72295i	0.0183884	−	0.178662i
$94$		−	3.77285i		−	0.389140i
$95$	−1.56118	−	19.1443i	−0.160173	−	1.96416i
$96$	4.87467	+	5.99323i	0.497519	+	0.611682i
$97$	−5.68596	−	5.68596i	−0.577322	−	0.577322i	0.356842	−	0.934165i	$-0.383853\pi$
$97$	−5.68596	−	5.68596i	−0.577322	−	0.577322i	−0.934165	+	0.356842i	$0.883853\pi$
$98$	−2.26629	−	2.26629i	−0.228930	−	0.228930i
$99$	−1.89329	+	9.10018i	−0.190283	+	0.914603i
$100$	−3.56492	−	21.7124i	−0.356492	−	2.17124i
$101$		−	10.0900i		−	1.00399i	−0.864871	−	0.501995i	$-0.832600\pi$
$101$		−	10.0900i		−	1.00399i	0.864871	−	0.501995i	$-0.167400\pi$
$102$	−23.7458	−	2.44399i	−2.35119	−	0.241991i
$103$	−0.509078	+	0.509078i	−0.0501610	+	0.0501610i	−0.731742	−	0.681581i	$-0.761293\pi$
$103$	−0.509078	+	0.509078i	−0.0501610	+	0.0501610i	0.681581	+	0.731742i	$0.261293\pi$
$104$	−15.4071			−1.51079
$105$	8.03919	−	7.70545i	0.784545	−	0.751975i
$106$	5.05470			0.490956
$107$	3.22016	−	3.22016i	0.311305	−	0.311305i	−0.534110	−	0.845415i	$-0.679353\pi$
$107$	3.22016	−	3.22016i	0.311305	−	0.311305i	0.845415	+	0.534110i	$0.179353\pi$
$108$	−21.7924	−	6.92515i	−2.09698	−	0.666372i
$109$			15.9595i			1.52865i	0.644833	+	0.764323i	$0.276927\pi$
$109$			15.9595i			1.52865i	−0.644833	+	0.764323i	$0.723073\pi$
$110$	13.3604	+	11.3456i	1.27386	+	1.08176i
$111$	9.96787	−	8.10750i	0.946108	−	0.769530i
$112$	13.3456	+	13.3456i	1.26104	+	1.26104i
$113$	3.20737	+	3.20737i	0.301724	+	0.301724i	0.841688	−	0.539964i	$-0.181562\pi$
$113$	3.20737	+	3.20737i	0.301724	+	0.301724i	−0.539964	+	0.841688i	$0.681562\pi$
$114$	−29.2016	+	23.7515i	−2.73498	+	2.22453i
$115$	7.98092	+	6.77741i	0.744225	+	0.631996i
$116$		−	7.40500i		−	0.687537i
$117$	6.36469	−	4.17244i	0.588415	−	0.385742i
$118$	11.9489	−	11.9489i	1.09999	−	1.09999i
$119$	−15.6629			−1.43582
$120$	−16.9815	+	16.2766i	−1.55020	+	1.48584i
$121$	1.40023			0.127294
$122$	−5.86983	+	5.86983i	−0.531430	+	0.531430i
$123$	−12.9521	−	1.33306i	−1.16785	−	0.120198i
$124$			4.40062i			0.395187i
$125$	10.8489	−	2.70214i	0.970354	−	0.241687i
$126$	−21.3649	−	4.44496i	−1.90333	−	0.395989i
$127$	−11.7311	−	11.7311i	−1.04097	−	1.04097i	−0.999124	−	0.0418417i	$-0.986677\pi$
$127$	−11.7311	−	11.7311i	−1.04097	−	1.04097i	−0.0418417	−	0.999124i	$-0.513323\pi$
$128$	9.60704	+	9.60704i	0.849150	+	0.849150i
$129$	5.85437	+	7.19774i	0.515449	+	0.633725i
$130$	−1.16643	−	14.3036i	−0.102302	−	1.25450i
$131$		−	6.26455i		−	0.547336i	−0.961824	−	0.273668i	$-0.911763\pi$
$131$		−	6.26455i		−	0.547336i	0.961824	−	0.273668i	$-0.0882369\pi$
$132$	2.41785	−	23.4918i	0.210447	−	2.04470i
$133$	−17.4642	+	17.4642i	−1.51433	+	1.51433i
$134$	−24.2824			−2.09768
$135$	2.60718	−	11.3227i	0.224391	−	0.974499i
$136$	33.0856			2.83706
$137$	−9.35395	+	9.35395i	−0.799162	+	0.799162i	−0.982963	−	0.183802i	$-0.941160\pi$
$137$	−9.35395	+	9.35395i	−0.799162	+	0.799162i	0.183802	+	0.982963i	$0.441160\pi$
$138$	2.10074	−	20.4108i	0.178827	−	1.73748i
$139$		−	7.42462i		−	0.629748i	−0.949134	−	0.314874i	$-0.898038\pi$
$139$		−	7.42462i		−	0.629748i	0.949134	−	0.314874i	$-0.101962\pi$
$140$	−18.3135	+	21.5655i	−1.54777	+	1.82262i
$141$	−1.62984	−	2.00383i	−0.137257	−	0.168753i
$142$	−4.79594	−	4.79594i	−0.402466	−	0.402466i
$143$	5.55780	+	5.55780i	0.464766	+	0.464766i
$144$	19.2798	+	4.01117i	1.60665	+	0.334264i
$145$	3.75022	−	0.305823i	0.311439	−	0.0253973i
$146$		−	18.8882i		−	1.56320i
$147$	−2.18269	−	0.224649i	−0.180025	−	0.0185287i
$148$	−23.0833	+	23.0833i	−1.89744	+	1.89744i
$149$	8.55293			0.700683			0.350342	−	0.936622i	$-0.386065\pi$
$149$	8.55293			0.700683			0.350342	+	0.936622i	$0.386065\pi$
$150$	−16.3963	−	14.5329i	−1.33876	−	1.18661i
$151$	1.56714			0.127532			0.0637661	−	0.997965i	$-0.479689\pi$
$151$	1.56714			0.127532			0.0637661	+	0.997965i	$0.479689\pi$
$152$	36.8903	−	36.8903i	2.99220	−	2.99220i
$153$	−13.6676	+	8.95997i	−1.10496	+	0.724371i
$154$		−	22.5378i		−	1.81615i
$155$	−2.22867	+	0.181744i	−0.179011	+	0.0145980i
$156$	−15.0004	+	12.2008i	−1.20100	+	0.976846i
$157$	5.81713	+	5.81713i	0.464258	+	0.464258i	0.900048	−	0.435790i	$-0.143531\pi$
$157$	5.81713	+	5.81713i	0.464258	+	0.464258i	−0.435790	+	0.900048i	$0.643531\pi$
$158$	21.2142	+	21.2142i	1.68771	+	1.68771i
$159$	2.68465	−	2.18359i	0.212906	−	0.173170i
$160$	6.45573	−	7.60212i	0.510370	−	0.601001i
$161$		−	13.4631i		−	1.06104i
$162$	−21.1859	+	8.34303i	−1.66452	+	0.655491i
$163$	7.67554	−	7.67554i	0.601194	−	0.601194i	−0.339435	−	0.940630i	$-0.610236\pi$
$163$	7.67554	−	7.67554i	0.601194	−	0.601194i	0.940630	+	0.339435i	$0.110236\pi$
$164$	33.0811			2.58320
$165$	11.9972	+	0.254304i	0.933978	+	0.0197975i
$166$	31.6211			2.45428
$167$	−8.10948	+	8.10948i	−0.627531	+	0.627531i	−0.947446	−	0.319915i	$-0.896346\pi$
$167$	−8.10948	+	8.10948i	−0.627531	+	0.627531i	0.319915	+	0.947446i	$0.396346\pi$
$168$	30.0868	+	3.09663i	2.32125	+	0.238910i
$169$			6.56461i			0.504970i
$170$	2.50481	+	30.7157i	0.192110	+	2.35579i
$171$	−5.24905	+	25.2297i	−0.401405	+	1.92937i
$172$	−16.6683	−	16.6683i	−1.27095	−	1.27095i
$173$	5.97137	+	5.97137i	0.453995	+	0.453995i	0.896678	−	0.442683i	$-0.145973\pi$
$173$	5.97137	+	5.97137i	0.453995	+	0.453995i	−0.442683	+	0.896678i	$0.645973\pi$
$174$	−4.65275	−	5.72038i	−0.352724	−	0.433661i
$175$	−11.6781	−	8.38411i	−0.882780	−	0.633779i
$176$			20.3382i			1.53305i
$177$	1.18445	−	11.5082i	0.0890291	−	0.865006i
$178$	−29.4123	+	29.4123i	−2.20454	+	2.20454i
$179$	−1.98154			−0.148107			−0.0740537	−	0.997254i	$-0.523594\pi$
$179$	−1.98154			−0.148107			−0.0740537	+	0.997254i	$0.523594\pi$
$180$	−3.64398	+	29.2945i	−0.271607	+	2.18348i
$181$	7.96085			0.591726			0.295863	−	0.955230i	$-0.404393\pi$
$181$	7.96085			0.591726			0.295863	+	0.955230i	$0.404393\pi$
$182$	−13.0483	+	13.0483i	−0.967202	+	0.967202i
$183$	−0.581855	+	5.65330i	−0.0430120	+	0.417904i
$184$			28.4388i			2.09653i
$185$	−12.6438	−	10.7371i	−0.929588	−	0.789407i
$186$	2.76502	+	3.39949i	0.202741	+	0.249263i
$187$	−11.9349	−	11.9349i	−0.872767	−	0.872767i
$188$	4.64042	+	4.64042i	0.338437	+	0.338437i
$189$	−13.2675	+	6.86866i	−0.965067	+	0.499622i
$190$	37.0408	+	31.4551i	2.68722	+	2.28199i
$191$		−	10.5254i		−	0.761591i	−0.924659	−	0.380796i	$-0.875650\pi$
$191$		−	10.5254i		−	0.761591i	0.924659	−	0.380796i	$-0.124350\pi$
$192$	3.17760	+	0.327048i	0.229323	+	0.0236026i
$193$	1.88773	−	1.88773i	0.135882	−	0.135882i	−0.635894	−	0.771776i	$-0.719369\pi$
$193$	1.88773	−	1.88773i	0.135882	−	0.135882i	0.771776	+	0.635894i	$0.219369\pi$
$194$	20.3437			1.46059
$195$	−6.79854	−	7.09300i	−0.486854	−	0.507940i
$196$	5.57486			0.398204
$197$	−3.47099	+	3.47099i	−0.247298	+	0.247298i	−0.819861	−	0.572563i	$-0.805949\pi$
$197$	−3.47099	+	3.47099i	−0.247298	+	0.247298i	0.572563	+	0.819861i	$0.305949\pi$
$198$	−12.8927	−	19.6667i	−0.916245	−	1.39765i
$199$		−	13.8644i		−	0.982818i	−0.870929	−	0.491409i	$-0.836482\pi$
$199$		−	13.8644i		−	0.982818i	0.870929	−	0.491409i	$-0.163518\pi$
$200$	24.6681	+	17.7101i	1.74430	+	1.25230i
$201$	−12.8968	+	10.4898i	−0.909671	+	0.739893i
$202$	18.0504	+	18.0504i	1.27002	+	1.27002i
$203$	−3.42110	−	3.42110i	−0.240114	−	0.240114i
$204$	32.2122	−	26.2002i	2.25531	−	1.83438i
$205$	1.36624	+	16.7537i	0.0954221	+	1.17013i
$206$		−	1.82142i		−	0.126905i
$207$	−7.70156	−	11.7481i	−0.535296	−	0.816546i
$208$	11.7749	−	11.7749i	0.816439	−	0.816439i
$209$	−26.6148			−1.84098
$210$	−0.597040	+	28.1662i	−0.0411997	+	1.94365i
$211$	14.0033			0.964026			0.482013	−	0.876164i	$-0.339906\pi$
$211$	14.0033			0.964026			0.482013	+	0.876164i	$0.339906\pi$
$212$	−6.21704	+	6.21704i	−0.426988	+	0.426988i
$213$	−4.61902	−	0.475404i	−0.316490	−	0.0325741i
$214$			11.5214i			0.787583i
$215$	7.75319	−	9.12998i	0.528763	−	0.622660i
$216$	28.0255	−	14.5090i	1.90689	−	0.987212i
$217$	2.03308	+	2.03308i	0.138015	+	0.138015i
$218$	−28.5507	−	28.5507i	−1.93370	−	1.93370i
$219$	−8.15955	−	10.0319i	−0.551371	−	0.677890i
$220$	−30.3872	+	2.47801i	−2.04870	+	0.167068i
$221$			13.8195i			0.929598i
$222$	−3.32810	+	32.3358i	−0.223367	+	2.17023i
$223$	0.243503	−	0.243503i	0.0163062	−	0.0163062i	−0.698907	−	0.715213i	$-0.746330\pi$
$223$	0.243503	−	0.243503i	0.0163062	−	0.0163062i	0.715213	+	0.698907i	$0.246330\pi$
$224$	−12.8241			−0.856848
$225$	−14.9865	−	0.635625i	−0.999102	−	0.0423750i
$226$	−11.4756			−0.763346
$227$	9.23695	−	9.23695i	0.613078	−	0.613078i	−0.330669	−	0.943747i	$-0.607274\pi$
$227$	9.23695	−	9.23695i	0.613078	−	0.613078i	0.943747	+	0.330669i	$0.107274\pi$
$228$	6.70335	−	65.1297i	0.443940	−	4.31332i
$229$			15.0444i			0.994161i	0.867704	+	0.497080i	$0.165595\pi$
$229$			15.0444i			0.994161i	−0.867704	+	0.497080i	$0.834405\pi$
$230$	−26.4018	+	2.15301i	−1.74088	+	0.141966i
$231$	−9.73615	−	11.9702i	−0.640591	−	0.787583i
$232$	7.22655	+	7.22655i	0.474446	+	0.474446i
$233$	−10.6075	−	10.6075i	−0.694921	−	0.694921i	0.268389	−	0.963311i	$-0.413509\pi$
$233$	−10.6075	−	10.6075i	−0.694921	−	0.694921i	−0.963311	+	0.268389i	$0.913509\pi$
$234$	−3.92180	+	18.8503i	−0.256376	+	1.23228i
$235$	−2.15847	+	2.54176i	−0.140803	+	0.165806i
$236$			29.3932i			1.91334i
$237$	20.4316	+	2.10289i	1.32718	+	0.136597i
$238$	28.0201	−	28.0201i	1.81627	−	1.81627i
$239$	−20.6254			−1.33415			−0.667074	−	0.744991i	$-0.732454\pi$
$239$	−20.6254			−1.33415			−0.667074	+	0.744991i	$0.732454\pi$
$240$	0.538773	−	25.4174i	0.0347777	−	1.64069i
$241$	14.2002			0.914713			0.457356	−	0.889283i	$-0.348796\pi$
$241$	14.2002			0.914713			0.457356	+	0.889283i	$0.348796\pi$
$242$	−2.50494	+	2.50494i	−0.161023	+	0.161023i
$243$	−7.64812	+	13.5833i	−0.490627	+	0.871370i
$244$		−	14.4392i		−	0.924376i
$245$	0.230239	+	2.82335i	0.0147094	+	0.180378i
$246$	25.5552	−	20.7857i	1.62934	−	1.32525i
$247$	15.4087	+	15.4087i	0.980430	+	0.980430i
$248$	−4.29457	−	4.29457i	−0.272705	−	0.272705i
$249$	16.7946	−	13.6601i	1.06431	−	0.865673i
$250$	−14.5740	+	24.2420i	−0.921744	+	1.53320i
$251$			18.6181i			1.17517i	0.809164	+	0.587583i	$0.199920\pi$
$251$			18.6181i			1.17517i	−0.809164	+	0.587583i	$0.800080\pi$
$252$	31.7448	−	20.8107i	1.99974	−	1.31095i
$253$	10.2587	−	10.2587i	0.644958	−	0.644958i
$254$	41.9725			2.63359
$255$	14.5993	+	15.2316i	0.914244	+	0.953842i
$256$	−30.6843			−1.91777
$257$	−17.4181	+	17.4181i	−1.08651	+	1.08651i	−0.0906243	+	0.995885i	$0.528886\pi$
$257$	−17.4181	+	17.4181i	−1.08651	+	1.08651i	−0.995885	+	0.0906243i	$0.971114\pi$
$258$	−23.3495	−	2.40320i	−1.45367	−	0.149617i
$259$			21.3289i			1.32532i
$260$	19.0273	+	16.1580i	1.18002	+	1.00208i
$261$	−4.94232	−	1.02825i	−0.305922	−	0.0636471i
$262$	11.2069	+	11.2069i	0.692365	+	0.692365i
$263$	18.5231	+	18.5231i	1.14218	+	1.14218i	0.988050	+	0.154132i	$0.0492582\pi$
$263$	18.5231	+	18.5231i	1.14218	+	1.14218i	0.154132	+	0.988050i	$0.450742\pi$
$264$	20.5661	+	25.2853i	1.26576	+	1.55620i
$265$	−3.40535	−	2.89182i	−0.209189	−	0.177643i
$266$		−	62.4847i		−	3.83118i
$267$	−2.91553	+	28.3273i	−0.178427	+	1.73360i
$268$	29.8661	−	29.8661i	1.82436	−	1.82436i
$269$	15.4852			0.944150			0.472075	−	0.881559i	$-0.343505\pi$
$269$	15.4852			0.944150			0.472075	+	0.881559i	$0.343505\pi$
$270$	15.5915	+	24.9197i	0.948867	+	1.51656i
$271$	−10.6059			−0.644263			−0.322131	−	0.946695i	$-0.604399\pi$
$271$	−10.6059			−0.644263			−0.322131	+	0.946695i	$0.604399\pi$
$272$	−25.2855	+	25.2855i	−1.53316	+	1.53316i
$273$	−1.29343	+	12.5669i	−0.0782818	+	0.760585i
$274$		−	33.4673i		−	2.02184i
$275$	−2.50995	−	15.2871i	−0.151356	−	0.921845i
$276$	22.5205	+	27.6881i	1.35557	+	1.66663i
$277$	−15.8937	−	15.8937i	−0.954962	−	0.954962i	0.0440667	−	0.999029i	$-0.485969\pi$
$277$	−15.8937	−	15.8937i	−0.954962	−	0.954962i	−0.999029	+	0.0440667i	$0.985969\pi$
$278$	13.2822	+	13.2822i	0.796613	+	0.796613i
$279$	2.93711	+	0.611065i	0.175840	+	0.0365835i
$280$	−3.17368	−	38.9179i	−0.189664	−	2.32579i
$281$		−	28.2673i		−	1.68629i	−0.537688	−	0.843144i	$-0.680702\pi$
$281$		−	28.2673i		−	1.68629i	0.537688	−	0.843144i	$-0.319298\pi$
$282$	6.50042	+	0.669043i	0.387095	+	0.0398410i
$283$	14.0744	−	14.0744i	0.836634	−	0.836634i	−0.151780	−	0.988414i	$-0.548501\pi$
$283$	14.0744	−	14.0744i	0.836634	−	0.836634i	0.988414	+	0.151780i	$0.0485005\pi$
$284$	11.7975			0.700055
$285$	33.2614	+	0.705043i	1.97024	+	0.0417632i
$286$	−19.8851			−1.17583
$287$	15.2834	−	15.2834i	0.902152	−	0.902152i
$288$	−11.1905	+	7.33603i	−0.659404	+	0.432280i
$289$		−	12.6762i		−	0.745657i
$290$	−6.16183	+	7.25603i	−0.361835	+	0.426089i
$291$	10.8049	−	8.78833i	0.633396	−	0.515181i
$292$	23.2315	+	23.2315i	1.35952	+	1.35952i
$293$	9.54775	+	9.54775i	0.557786	+	0.557786i	0.928676	−	0.370891i	$-0.120948\pi$
$293$	9.54775	+	9.54775i	0.557786	+	0.557786i	−0.370891	+	0.928676i	$0.620948\pi$
$294$	4.30659	−	3.50282i	0.251165	−	0.204289i
$295$	−14.8860	+	1.21393i	−0.866699	+	0.0706776i
$296$		−	45.0541i		−	2.61872i
$297$	−15.3434	−	4.87579i	−0.890315	−	0.282922i
$298$	−15.3007	+	15.3007i	−0.886345	+	0.886345i
$299$	−11.8786			−0.686955
$300$	38.0415	−	2.29188i	2.19633	−	0.132322i
$301$	−15.4015			−0.887727
$302$	−2.80352	+	2.80352i	−0.161325	+	0.161325i
$303$	17.3845	+	1.78927i	0.998713	+	0.102791i
$304$			56.3866i			3.23399i
$305$	7.31266	−	0.596334i	0.418722	−	0.0341460i
$306$	8.42175	−	40.4795i	0.481439	−	2.31406i
$307$	−10.4566	−	10.4566i	−0.596788	−	0.596788i	0.342668	−	0.939456i	$-0.388669\pi$
$307$	−10.4566	−	10.4566i	−0.596788	−	0.596788i	−0.939456	+	0.342668i	$0.888669\pi$
$308$	27.7204	+	27.7204i	1.57951	+	1.57951i
$309$	−0.786841	−	0.967392i	−0.0447618	−	0.0550330i
$310$	3.66183	−	4.31209i	0.207978	−	0.244910i
$311$			22.0375i			1.24963i	0.780771	+	0.624817i	$0.214827\pi$
$311$			22.0375i			1.24963i	−0.780771	+	0.624817i	$0.785173\pi$
$312$	2.73216	−	26.5457i	0.154678	−	1.50285i
$313$	6.66715	−	6.66715i	0.376849	−	0.376849i	−0.493115	−	0.869964i	$-0.664142\pi$
$313$	6.66715	−	6.66715i	0.376849	−	0.376849i	0.869964	+	0.493115i	$0.164142\pi$
$314$	−20.8130			−1.17455
$315$	11.8505	+	15.2175i	0.667700	+	0.857411i
$316$	−52.1849			−2.93563
$317$	−9.19212	+	9.19212i	−0.516281	+	0.516281i	−0.916444	−	0.400163i	$-0.868953\pi$
$317$	−9.19212	+	9.19212i	−0.516281	+	0.516281i	0.400163	+	0.916444i	$0.368953\pi$
$318$	−0.896356	+	8.70900i	−0.0502652	+	0.488376i
$319$		−	5.21365i		−	0.291908i
$320$	−0.335186	−	4.11029i	−0.0187375	−	0.229772i
$321$	4.97714	+	6.11921i	0.277797	+	0.341541i
$322$	24.0847	+	24.0847i	1.34219	+	1.34219i
$323$	−33.0889	−	33.0889i	−1.84111	−	1.84111i
$324$	15.7961	−	36.3192i	0.877564	−	2.01773i
$325$	−7.39732	+	10.3036i	−0.410330	+	0.571541i
$326$			27.4622i			1.52099i
$327$	−27.4975	−	2.83012i	−1.52061	−	0.156506i
$328$	−32.2839	+	32.2839i	−1.78258	+	1.78258i
$329$	4.28773			0.236390
$330$	−21.9171	+	21.0073i	−1.20650	+	1.15641i
$331$	−5.96304			−0.327759			−0.163879	−	0.986480i	$-0.552401\pi$
$331$	−5.96304			−0.327759			−0.163879	+	0.986480i	$0.552401\pi$
$332$	−38.8924	+	38.8924i	−2.13450	+	2.13450i
$333$	12.2012	+	18.6118i	0.668621	+	1.01992i
$334$		−	29.0148i		−	1.58762i
$335$	16.3590	+	13.8921i	0.893787	+	0.759005i
$336$	−25.3604	+	20.6272i	−1.38352	+	1.12531i
$337$	−9.29229	−	9.29229i	−0.506183	−	0.506183i	0.407169	−	0.913353i	$-0.366516\pi$
$337$	−9.29229	−	9.29229i	−0.506183	−	0.506183i	−0.913353	+	0.407169i	$0.866516\pi$
$338$	−11.7437	−	11.7437i	−0.638774	−	0.638774i
$339$	−6.09491	+	4.95737i	−0.331030	+	0.269247i
$340$	−40.8596	−	34.6980i	−2.21592	−	1.88177i
$341$			3.09835i			0.167785i
$342$	−35.7443	−	54.5247i	−1.93283	−	2.94836i
$343$	−11.6560	+	11.6560i	−0.629364	+	0.629364i
$344$	32.5333			1.75408
$345$	−13.0924	+	12.5489i	−0.704871	+	0.675609i
$346$	−21.3649			−1.14858
$347$	0.468364	−	0.468364i	0.0251431	−	0.0251431i	−0.694423	−	0.719567i	$-0.744341\pi$
$347$	0.468364	−	0.468364i	0.0251431	−	0.0251431i	0.719567	+	0.694423i	$0.244341\pi$
$348$	12.7584	+	1.31314i	0.683924	+	0.0703916i
$349$			28.5347i			1.52743i	0.645556	+	0.763713i	$0.276626\pi$
$349$			28.5347i			1.52743i	−0.645556	+	0.763713i	$0.723374\pi$
$350$	35.8901	−	5.89272i	1.91841	−	0.314979i
$351$	6.06024	+	11.7059i	0.323472	+	0.624817i
$352$	−9.77178	−	9.77178i	−0.520838	−	0.520838i
$353$	−14.5689	−	14.5689i	−0.775422	−	0.775422i	0.203627	−	0.979049i	$-0.434727\pi$
$353$	−14.5689	−	14.5689i	−0.775422	−	0.775422i	−0.979049	+	0.203627i	$0.934727\pi$
$354$	18.4685	+	22.7063i	0.981590	+	1.20683i
$355$	0.487233	+	5.97480i	0.0258597	+	0.317109i
$356$		−	72.3513i		−	3.83461i
$357$	2.77753	−	26.9865i	0.147002	−	1.42827i
$358$	3.54486	−	3.54486i	0.187352	−	0.187352i
$359$	−8.99489			−0.474732			−0.237366	−	0.971420i	$-0.576284\pi$
$359$	−8.99489			−0.474732			−0.237366	+	0.971420i	$0.576284\pi$
$360$	−25.0323	−	32.1447i	−1.31932	−	1.69417i
$361$	−54.7880			−2.88358
$362$	−14.2415	+	14.2415i	−0.748517	+	0.748517i
$363$	−0.248305	+	2.41253i	−0.0130326	+	0.126625i
$364$		−	32.0975i		−	1.68236i
$365$	−10.8060	+	12.7249i	−0.565613	+	0.666053i
$366$	−9.07252	−	11.1543i	−0.474228	−	0.583046i
$367$	1.27316	+	1.27316i	0.0664583	+	0.0664583i	0.739555	−	0.673096i	$-0.235036\pi$
$367$	1.27316	+	1.27316i	0.0664583	+	0.0664583i	−0.673096	+	0.739555i	$0.735036\pi$
$368$	−21.7342	−	21.7342i	−1.13298	−	1.13298i
$369$	4.59361	−	22.0793i	0.239134	−	1.14940i
$370$	41.8270	−	3.41091i	2.17448	−	0.177325i
$371$			5.74453i			0.298241i
$372$	−7.58205	−	0.780367i	−0.393111	−	0.0404601i
$373$	−1.69061	+	1.69061i	−0.0875367	+	0.0875367i	−0.749519	−	0.661983i	$-0.769715\pi$
$373$	−1.69061	+	1.69061i	−0.0875367	+	0.0875367i	0.661983	+	0.749519i	$0.269715\pi$
$374$	42.7017			2.20805
$375$	2.73181	+	19.1713i	0.141070	+	0.990000i
$376$	−9.05718			−0.467088
$377$	−3.01845	+	3.01845i	−0.155458	+	0.155458i
$378$	11.4471	−	36.0224i	0.588775	−	1.85279i
$379$			30.4886i			1.56610i	0.621961	+	0.783048i	$0.286336\pi$
$379$			30.4886i			1.56610i	−0.621961	+	0.783048i	$0.713664\pi$
$380$	−84.2466	+	6.87015i	−4.32176	+	0.352431i
$381$	22.2924	−	18.1318i	1.14207	−	0.928919i
$382$	18.8293	+	18.8293i	0.963392	+	0.963392i
$383$	12.9172	+	12.9172i	0.660036	+	0.660036i	0.955388	−	0.295352i	$-0.0954370\pi$
$383$	12.9172	+	12.9172i	0.660036	+	0.660036i	−0.295352	+	0.955388i	$0.595437\pi$
$384$	−18.2561	+	14.8488i	−0.931626	+	0.757750i
$385$	−12.8940	+	15.1837i	−0.657138	+	0.773831i
$386$			6.75407i			0.343773i
$387$	−13.4395	+	8.81041i	−0.683168	+	0.447858i
$388$	−25.0218	+	25.0218i	−1.27029	+	1.27029i
$389$	1.61562			0.0819150			0.0409575	−	0.999161i	$-0.486959\pi$
$389$	1.61562			0.0819150			0.0409575	+	0.999161i	$0.486959\pi$
$390$	24.8511	+	0.526770i	1.25839	+	0.0266740i
$391$	25.5082			1.29001
$392$	−5.44051	+	5.44051i	−0.274787	+	0.274787i
$393$	10.7935	+	1.11090i	0.544460	+	0.0560374i
$394$		−	12.4188i		−	0.625650i
$395$	−2.15521	−	26.4287i	−0.108441	−	1.32977i
$396$	40.0465	+	8.33166i	2.01241	+	0.418682i
$397$	21.8692	+	21.8692i	1.09758	+	1.09758i	0.994693	+	0.102890i	$0.0328090\pi$
$397$	21.8692	+	21.8692i	1.09758	+	1.09758i	0.102890	+	0.994693i	$0.467191\pi$
$398$	24.8025	+	24.8025i	1.24324	+	1.24324i
$399$	−26.9929	−	33.1868i	−1.35134	−	1.66142i
$400$	−32.3875	+	5.31763i	−1.61937	+	0.265882i
$401$		−	2.94725i		−	0.147179i	−0.997289	−	0.0735893i	$-0.976555\pi$
$401$		−	2.94725i		−	0.147179i	0.997289	−	0.0735893i	$-0.0234454\pi$
$402$	4.30602	−	41.8373i	0.214765	−	2.08665i
$403$	1.79379	−	1.79379i	0.0893552	−	0.0893552i
$404$	−44.4021			−2.20909
$405$	19.0460	+	6.49990i	0.946405	+	0.322983i
$406$	12.2403			0.607476
$407$	−16.2523	+	16.2523i	−0.805597	+	0.805597i
$408$	−5.86710	+	57.0047i	−0.290465	+	2.82215i
$409$		−	23.0697i		−	1.14072i	−0.821394	−	0.570361i	$-0.806803\pi$
$409$		−	23.0697i		−	1.14072i	0.821394	−	0.570361i	$-0.193197\pi$
$410$	−32.4156	−	27.5273i	−1.60089	−	1.35948i
$411$	−14.4576	−	17.7751i	−0.713142	−	0.876782i
$412$	2.24026	+	2.24026i	0.110370	+	0.110370i
$413$	13.5796	+	13.5796i	0.668210	+	0.668210i
$414$	34.7942	+	7.23894i	1.71004	+	0.355774i
$415$	−21.3031	−	18.0906i	−1.04573	−	0.888034i
$416$			11.3148i			0.554752i
$417$	12.7922	+	1.31662i	0.626438	+	0.0644749i
$418$	47.6123	−	47.6123i	2.32879	−	2.32879i
$419$	−11.6376			−0.568532			−0.284266	−	0.958745i	$-0.591750\pi$
$419$	−11.6376			−0.568532			−0.284266	+	0.958745i	$0.591750\pi$
$420$	−33.9088	−	35.3774i	−1.65458	−	1.72624i
$421$	−31.2859			−1.52478			−0.762392	−	0.647116i	$-0.775975\pi$
$421$	−31.2859			−1.52478			−0.762392	+	0.647116i	$0.775975\pi$
$422$	−25.0510	+	25.0510i	−1.21947	+	1.21947i
$423$	3.74152	−	2.45279i	0.181919	−	0.119259i
$424$		−	12.1344i		−	0.589300i
$425$	15.8851	−	22.1261i	0.770543	−	1.07328i
$426$	9.11363	−	7.41269i	0.441557	−	0.359146i
$427$	−6.67090	−	6.67090i	−0.322827	−	0.322827i
$428$	−14.1707	−	14.1707i	−0.684967	−	0.684967i
$429$	−10.5614	+	8.59023i	−0.509908	+	0.414740i
$430$	2.46300	+	30.2030i	0.118776	+	1.45652i
$431$			19.9312i			0.960050i	0.877255	+	0.480025i	$0.159372\pi$
$431$			19.9312i			0.960050i	−0.877255	+	0.480025i	$0.840628\pi$
$432$	−10.3299	+	32.5068i	−0.497000	+	1.56399i
$433$	−5.65049	+	5.65049i	−0.271545	+	0.271545i	−0.829722	−	0.558177i	$-0.811501\pi$
$433$	−5.65049	+	5.65049i	−0.271545	+	0.271545i	0.558177	+	0.829722i	$0.311501\pi$
$434$	−7.27412			−0.349169
$435$	−0.138113	+	6.51567i	−0.00662200	+	0.312403i
$436$	70.2319			3.36350
$437$	28.4416	−	28.4416i	1.36055	−	1.36055i
$438$	32.5434	+	3.34946i	1.55498	+	0.160043i
$439$		−	16.2225i		−	0.774256i	−0.922026	−	0.387128i	$-0.873467\pi$
$439$		−	16.2225i		−	0.774256i	0.922026	−	0.387128i	$-0.126533\pi$
$440$	27.2365	−	32.0731i	1.29845	−	1.52903i
$441$	0.774118	−	3.72083i	0.0368628	−	0.177182i
$442$	−24.7222	−	24.7222i	−1.17592	−	1.17592i
$443$	20.7919	+	20.7919i	0.987855	+	0.987855i	0.999927	−	0.0120725i	$-0.00384287\pi$
$443$	20.7919	+	20.7919i	0.987855	+	0.987855i	−0.0120725	+	0.999927i	$0.503843\pi$
$444$	−35.6780	−	43.8648i	−1.69320	−	2.08173i
$445$	36.6419	−	2.98808i	1.73699	−	0.141648i
$446$			0.871226i			0.0412538i
$447$	−1.51670	+	14.7363i	−0.0717375	+	0.697001i
$448$	−3.74956	+	3.74956i	−0.177150	+	0.177150i
$449$	22.7008			1.07132			0.535658	−	0.844435i	$-0.320064\pi$
$449$	22.7008			1.07132			0.535658	+	0.844435i	$0.320064\pi$
$450$	27.9471	−	25.6729i	1.31744	−	1.21023i
$451$	23.2914			1.09675
$452$	14.1144	−	14.1144i	0.663887	−	0.663887i
$453$	−0.277903	+	2.70010i	−0.0130570	+	0.126862i
$454$			33.0487i			1.55105i
$455$	16.2556	−	1.32561i	0.762074	−	0.0621457i
$456$	57.0183	+	70.1020i	2.67013	+	3.28282i
$457$	1.60714	+	1.60714i	0.0751789	+	0.0751789i	0.743696	−	0.668518i	$-0.233071\pi$
$457$	1.60714	+	1.60714i	0.0751789	+	0.0751789i	−0.668518	+	0.743696i	$0.733071\pi$
$458$	−26.9135	−	26.9135i	−1.25759	−	1.25759i
$459$	−13.0139	−	25.1375i	−0.607435	−	1.17332i
$460$	29.8248	−	35.1210i	1.39059	−	1.63752i
$461$			25.9977i			1.21083i	0.795909	+	0.605416i	$0.206993\pi$
$461$			25.9977i			1.21083i	−0.795909	+	0.605416i	$0.793007\pi$
$462$	38.8314	+	3.99665i	1.80660	+	0.185941i
$463$	−10.8312	+	10.8312i	−0.503368	+	0.503368i	−0.912483	−	0.409115i	$-0.865837\pi$
$463$	−10.8312	+	10.8312i	−0.503368	+	0.503368i	0.409115	+	0.912483i	$0.365837\pi$
$464$	−11.0457			−0.512785
$465$	0.0820773	−	3.87211i	0.00380624	−	0.179565i
$466$	37.9524			1.75811
$467$	7.55402	−	7.55402i	0.349559	−	0.349559i	−0.510387	−	0.859945i	$-0.670498\pi$
$467$	7.55402	−	7.55402i	0.349559	−	0.349559i	0.859945	+	0.510387i	$0.170498\pi$
$468$	−18.3613	−	28.0086i	−0.848752	−	1.29470i
$469$		−	27.5962i		−	1.27427i
$470$	−0.685692	−	8.40843i	−0.0316286	−	0.387852i
$471$	−11.0542	+	8.99107i	−0.509350	+	0.414286i
$472$	−28.6849	−	28.6849i	−1.32033	−	1.32033i
$473$	−11.7357	−	11.7357i	−0.539608	−	0.539608i
$474$	−40.3129	+	32.7891i	−1.85163	+	1.50605i
$475$	−6.95870	−	42.3825i	−0.319287	−	1.94464i
$476$			68.9267i			3.15925i
$477$	3.28615	+	5.01273i	0.150462	+	0.229517i
$478$	36.8977	−	36.8977i	1.68766	−	1.68766i
$479$	24.3686			1.11343			0.556714	−	0.830704i	$-0.312062\pi$
$479$	24.3686			1.11343			0.556714	+	0.830704i	$0.312062\pi$
$480$	11.9533	+	12.4710i	0.545590	+	0.569220i
$481$	18.8186			0.858054
$482$	−25.4033	+	25.4033i	−1.15709	+	1.15709i
$483$	23.1963	+	2.38743i	1.05547	+	0.108632i
$484$		−	6.16190i		−	0.280086i
$485$	−13.7055	−	11.6387i	−0.622336	−	0.528488i
$486$	−10.6177	−	37.9818i	−0.481628	−	1.72289i
$487$	22.8705	+	22.8705i	1.03636	+	1.03636i	0.999314	+	0.0370473i	$0.0117952\pi$
$487$	22.8705	+	22.8705i	1.03636	+	1.03636i	0.0370473	+	0.999314i	$0.488205\pi$
$488$	14.0912	+	14.0912i	0.637881	+	0.637881i
$489$	11.8634	+	14.5857i	0.536484	+	0.659587i
$490$	−5.46270	−	4.63893i	−0.246780	−	0.209566i
$491$			25.9062i			1.16913i	0.811347	+	0.584564i	$0.198735\pi$
$491$			25.9062i			1.16913i	−0.811347	+	0.584564i	$0.801265\pi$
$492$	−5.86631	+	56.9971i	−0.264474	+	2.56963i
$493$	6.48187	−	6.48187i	0.291929	−	0.291929i
$494$	−55.1304			−2.48043
$495$	−2.56562	+	20.6254i	−0.115316	+	0.927043i
$496$	6.56422			0.294742
$497$	5.45045	−	5.45045i	0.244486	−	0.244486i
$498$	−5.60741	+	54.4816i	−0.251274	+	2.44138i
$499$			28.8706i			1.29243i	0.763157	+	0.646213i	$0.223648\pi$
$499$			28.8706i			1.29243i	−0.763157	+	0.646213i	$0.776352\pi$
$500$	−11.8911	−	47.7419i	−0.531787	−	2.13508i
$501$	−12.5342	−	15.4103i	−0.559985	−	0.688481i
$502$	−33.3067	−	33.3067i	−1.48655	−	1.48655i
$503$	−7.89509	−	7.89509i	−0.352024	−	0.352024i	0.508838	−	0.860862i	$-0.330075\pi$
$503$	−7.89509	−	7.89509i	−0.352024	−	0.352024i	−0.860862	+	0.508838i	$0.830075\pi$
$504$	−10.6707	+	51.2890i	−0.475309	+	2.28459i
$505$	−1.83379	−	22.4872i	−0.0816025	−	1.00067i
$506$			36.7044i			1.63171i
$507$	−11.3105	−	1.16411i	−0.502317	−	0.0517000i
$508$	−51.6241	+	51.6241i	−2.29045	+	2.29045i
$509$	23.0254			1.02058			0.510291	−	0.860002i	$-0.329538\pi$
$509$	23.0254			1.02058			0.510291	+	0.860002i	$0.329538\pi$
$510$	−53.3658	−	1.13120i	−2.36308	−	0.0500902i
$511$	21.4659			0.949594
$512$	35.6783	−	35.6783i	1.57677	−	1.57677i
$513$	−42.5387	−	13.5179i	−1.87813	−	0.596828i
$514$		−	62.3198i		−	2.74881i
$515$	−1.04205	+	1.22709i	−0.0459180	+	0.0540720i
$516$	31.6745	−	25.7629i	1.39439	−	1.13415i
$517$	3.26718	+	3.26718i	0.143691	+	0.143691i
$518$	−38.1562	−	38.1562i	−1.67649	−	1.67649i
$519$	−11.3473	+	9.22946i	−0.498090	+	0.405128i
$520$	−34.3374	+	2.80015i	−1.50580	+	0.122795i
$521$			27.7930i			1.21763i	0.793311	+	0.608816i	$0.208355\pi$
$521$			27.7930i			1.21763i	−0.793311	+	0.608816i	$0.791645\pi$
$522$	10.6810	−	7.00204i	0.467495	−	0.306471i
$523$	16.2315	−	16.2315i	0.709752	−	0.709752i	−0.256731	−	0.966483i	$-0.582645\pi$
$523$	16.2315	−	16.2315i	0.709752	−	0.709752i	0.966483	+	0.256731i	$0.0826455\pi$
$524$	−27.5679			−1.20431
$525$	16.5163	−	18.6340i	0.720830	−	0.813253i
$526$	−66.2734			−2.88966
$527$	−3.85202	+	3.85202i	−0.167797	+	0.167797i
$528$	−35.0418	−	3.60660i	−1.52500	−	0.156957i
$529$		−	1.07434i		−	0.0467104i
$530$	11.2653	−	0.918661i	0.489332	−	0.0399041i
$531$	19.6179	+	4.08151i	0.851346	+	0.177122i
$532$	76.8531	+	76.8531i	3.33200	+	3.33200i
$533$	−13.4846	−	13.4846i	−0.584083	−	0.584083i
$534$	−45.4601	−	55.8915i	−1.96725	−	2.41866i
$535$	6.59143	−	7.76192i	0.284972	−	0.335577i
$536$			58.2927i			2.51786i
$537$	0.351389	−	3.41409i	0.0151636	−	0.147329i
$538$	−27.7021	+	27.7021i	−1.19432	+	1.19432i
$539$	3.92509			0.169066
$540$	−49.8267	−	11.4732i	−2.14420	−	0.493729i
$541$	6.90893			0.297038			0.148519	−	0.988910i	$-0.452549\pi$
$541$	6.90893			0.297038			0.148519	+	0.988910i	$0.452549\pi$
$542$	18.9733	−	18.9733i	0.814975	−	0.814975i
$543$	−1.41171	+	13.7161i	−0.0605822	+	0.588616i
$544$		−	24.2975i		−	1.04175i
$545$	2.90055	+	35.5685i	0.124246	+	1.52359i
$546$	−20.1676	−	24.7954i	−0.863095	−	1.06114i
$547$	13.2480	+	13.2480i	0.566445	+	0.566445i	0.931131	−	0.364686i	$-0.118824\pi$
$547$	13.2480	+	13.2480i	0.566445	+	0.566445i	−0.364686	+	0.931131i	$0.618824\pi$
$548$	41.1632	+	41.1632i	1.75840	+	1.75840i
$549$	−9.63717	−	2.00501i	−0.411305	−	0.0855719i
$550$	31.8378	+	22.8575i	1.35757	+	0.974647i
$551$		−	14.4545i		−	0.615784i
$552$	−48.9986	−	5.04308i	−2.08552	−	0.214648i
$553$	−24.1093	+	24.1093i	−1.02523	+	1.02523i
$554$	56.8659			2.41600
$555$	20.7416	−	19.8805i	0.880432	−	0.843882i
$556$	−32.6729			−1.38564
$557$	16.3344	−	16.3344i	0.692111	−	0.692111i	−0.270585	−	0.962696i	$-0.587217\pi$
$557$	16.3344	−	16.3344i	0.692111	−	0.692111i	0.962696	+	0.270585i	$0.0872172\pi$
$558$	−6.34747	+	4.16115i	−0.268710	+	0.176156i
$559$			13.5888i			0.574744i
$560$	32.1684	+	27.3174i	1.35936	+	1.15437i
$561$	22.6797	−	18.4468i	0.957537	−	0.778825i
$562$	50.5686	+	50.5686i	2.13311	+	2.13311i
$563$	−7.03183	−	7.03183i	−0.296356	−	0.296356i	0.543229	−	0.839585i	$-0.317202\pi$
$563$	−7.03183	−	7.03183i	−0.296356	−	0.296356i	−0.839585	+	0.543229i	$0.817202\pi$
$564$	−8.81810	+	7.17231i	−0.371309	+	0.302009i
$565$	7.73109	+	6.56525i	0.325250	+	0.276202i
$566$			50.3564i			2.11664i
$567$	−9.48162	−	24.0772i	−0.398191	−	1.01115i
$568$	−11.5132	+	11.5132i	−0.483084	+	0.483084i
$569$	1.33493			0.0559633			0.0279817	−	0.999608i	$-0.491092\pi$
$569$	1.33493			0.0559633			0.0279817	+	0.999608i	$0.491092\pi$
$570$	−60.7640	+	58.2415i	−2.54512	+	2.43947i
$571$	−25.0425			−1.04800			−0.523998	−	0.851720i	$-0.675560\pi$
$571$	−25.0425			−1.04800			−0.523998	+	0.851720i	$0.675560\pi$
$572$	24.4578	−	24.4578i	1.02263	−	1.02263i
$573$	18.1347	+	1.86648i	0.757589	+	0.0779734i
$574$			54.6823i			2.28240i
$575$	19.0186	+	13.6541i	0.793130	+	0.569416i
$576$	−1.12697	+	5.41684i	−0.0469572	+	0.225702i
$577$	−7.17231	−	7.17231i	−0.298587	−	0.298587i	0.541873	−	0.840460i	$-0.317715\pi$
$577$	−7.17231	−	7.17231i	−0.298587	−	0.298587i	−0.840460	+	0.541873i	$0.817715\pi$
$578$	22.6769	+	22.6769i	0.943235	+	0.943235i
$579$	2.91771	+	3.58721i	0.121256	+	0.149079i
$580$	−1.34581	−	16.5033i	−0.0558818	−	0.685262i
$581$			35.9365i			1.49090i
$582$	−3.60757	+	35.0512i	−0.149539	+	1.45292i
$583$	−4.37724	+	4.37724i	−0.181287	+	0.181287i
$584$	−45.3433			−1.87632
$585$	13.4265	−	10.4557i	0.555116	−	0.432291i
$586$	−34.1607			−1.41117
$587$	−27.9482	+	27.9482i	−1.15355	+	1.15355i	−0.167710	+	0.985836i	$0.553637\pi$
$587$	−27.9482	+	27.9482i	−1.15355	+	1.15355i	−0.985836	+	0.167710i	$0.946363\pi$
$588$	−0.988596	+	9.60519i	−0.0407690	+	0.396111i
$589$			8.58999i			0.353945i
$590$	24.4586	−	28.8019i	1.00694	−	1.18576i
$591$	−5.36483	−	6.59586i	−0.220680	−	0.271317i
$592$	34.4325	+	34.4325i	1.41517	+	1.41517i
$593$	18.9672	+	18.9672i	0.778889	+	0.778889i	0.979642	−	0.200753i	$-0.0643388\pi$
$593$	18.9672	+	18.9672i	0.778889	+	0.778889i	−0.200753	+	0.979642i	$0.564339\pi$
$594$	36.1710	−	18.7260i	1.48411	−	0.768335i
$595$	−34.9075	+	2.84664i	−1.43107	+	0.116701i
$596$		−	37.6382i		−	1.54172i
$597$	23.8876	+	2.45858i	0.977654	+	0.100623i
$598$	21.2500	−	21.2500i	0.868979	−	0.868979i
$599$	39.6677			1.62078			0.810389	−	0.585892i	$-0.199256\pi$
$599$	39.6677			1.62078			0.810389	+	0.585892i	$0.199256\pi$
$600$	−34.8881	+	39.3614i	−1.42430	+	1.60692i
$601$	42.4796			1.73278			0.866389	−	0.499370i	$-0.166435\pi$
$601$	42.4796			1.73278			0.866389	+	0.499370i	$0.166435\pi$
$602$	27.5524	−	27.5524i	1.12295	−	1.12295i
$603$	−15.7864	−	24.0807i	−0.642871	−	0.980643i
$604$		−	6.89639i		−	0.280610i
$605$	3.12066	−	0.254484i	0.126873	−	0.0103462i
$606$	−34.3007	+	27.8990i	−1.39337	+	1.13332i
$607$	13.1603	+	13.1603i	0.534160	+	0.534160i	0.921808	−	0.387647i	$-0.126712\pi$
$607$	13.1603	+	13.1603i	0.534160	+	0.534160i	−0.387647	+	0.921808i	$0.626712\pi$
$608$	−27.0917	−	27.0917i	−1.09871	−	1.09871i
$609$	6.50105	−	5.28771i	0.263436	−	0.214269i
$610$	−12.0151	+	14.1487i	−0.486478	+	0.572865i
$611$		−	3.78308i		−	0.153047i
$612$	39.4294	+	60.1461i	1.59384	+	2.43126i
$613$	22.4091	−	22.4091i	0.905097	−	0.905097i	−0.0907747	−	0.995871i	$-0.528934\pi$
$613$	22.4091	−	22.4091i	0.905097	−	0.905097i	0.995871	+	0.0907747i	$0.0289343\pi$
$614$	37.4124			1.50984
$615$	−29.1081	−	0.617006i	−1.17375	−	0.0248801i
$616$	−54.1046			−2.17994
$617$	3.69104	−	3.69104i	0.148596	−	0.148596i	−0.628895	−	0.777490i	$-0.716492\pi$
$617$	3.69104	−	3.69104i	0.148596	−	0.148596i	0.777490	+	0.628895i	$0.216492\pi$
$618$	3.13822	+	0.322995i	0.126238	+	0.0129928i
$619$		−	12.8016i		−	0.514540i	−0.966340	−	0.257270i	$-0.917177\pi$
$619$		−	12.8016i		−	0.514540i	0.966340	−	0.257270i	$-0.0828229\pi$
$620$	0.799785	+	9.80753i	0.0321202	+	0.393880i
$621$	21.6070	−	11.1861i	0.867060	−	0.448883i
$622$	−39.4239	−	39.4239i	−1.58075	−	1.58075i
$623$	−33.4262	−	33.4262i	−1.33919	−	1.33919i
$624$	18.1994	+	22.3755i	0.728560	+	0.895738i
$625$	23.6875	−	7.99391i	0.947500	−	0.319756i
$626$			23.8543i			0.953408i
$627$	4.71963	−	45.8559i	0.188484	−	1.83131i
$628$	25.5990	−	25.5990i	1.02151	−	1.02151i
$629$	−40.4114			−1.61131
$630$	−48.4231	−	6.02342i	−1.92922	−	0.239979i
$631$	−37.5421			−1.49453			−0.747264	−	0.664527i	$-0.768633\pi$
$631$	−37.5421			−1.49453			−0.747264	+	0.664527i	$0.768633\pi$
$632$	50.9273	−	50.9273i	2.02578	−	2.02578i
$633$	−2.48322	+	24.1269i	−0.0986990	+	0.958960i
$634$		−	32.8883i		−	1.30616i
$635$	−28.2768	−	24.0127i	−1.12213	−	0.952914i
$636$	−9.60917	−	11.8141i	−0.381028	−	0.468460i
$637$	−2.27244	−	2.27244i	−0.0900373	−	0.0900373i
$638$	9.32691	+	9.32691i	0.369256	+	0.369256i
$639$	1.63819	−	7.87404i	0.0648059	−	0.311492i
$640$	23.1569	+	19.6649i	0.915358	+	0.777323i
$641$			27.0280i			1.06754i	0.845629	+	0.533770i	$0.179225\pi$
$641$			27.0280i			1.06754i	−0.845629	+	0.533770i	$0.820775\pi$
$642$	−19.8507	−	2.04309i	−0.783445	−	0.0806345i
$643$	−23.3491	+	23.3491i	−0.920799	+	0.920799i	−0.997086	−	0.0762869i	$-0.975694\pi$
$643$	−23.3491	+	23.3491i	−0.920799	+	0.920799i	0.0762869	+	0.997086i	$0.475694\pi$
$644$	−59.2461			−2.33462
$645$	14.3556	+	14.9774i	0.565252	+	0.589734i
$646$	118.388			4.65791
$647$	−15.1252	+	15.1252i	−0.594633	+	0.594633i	−0.938879	−	0.344246i	$-0.888134\pi$
$647$	−15.1252	+	15.1252i	−0.594633	+	0.594633i	0.344246	+	0.938879i	$0.388134\pi$
$648$	20.0285	+	50.8594i	0.786792	+	1.99795i
$649$			20.6949i			0.812347i
$650$	−5.19917	−	31.6659i	−0.203928	−	1.24204i
$651$	−3.86342	+	3.14237i	−0.151419	+	0.123159i
$652$	−33.7771	−	33.7771i	−1.32281	−	1.32281i
$653$	−22.5839	−	22.5839i	−0.883776	−	0.883776i	0.110140	−	0.993916i	$-0.464870\pi$
$653$	−22.5839	−	22.5839i	−0.883776	−	0.883776i	−0.993916	+	0.110140i	$0.964870\pi$
$654$	54.2543	−	44.1284i	2.12151	−	1.72556i
$655$	−1.13854	−	13.9616i	−0.0444865	−	0.545525i
$656$		−	49.3457i		−	1.92663i
$657$	18.7313	−	12.2795i	0.730779	−	0.479070i
$658$	−7.67050	+	7.67050i	−0.299027	+	0.299027i
$659$	19.2074			0.748215			0.374108	−	0.927385i	$-0.377949\pi$
$659$	19.2074			0.748215			0.374108	+	0.927385i	$0.377949\pi$
$660$	1.11910	−	52.7949i	0.0435607	−	2.05504i
$661$	14.4208			0.560902			0.280451	−	0.959868i	$-0.409516\pi$
$661$	14.4208			0.560902			0.280451	+	0.959868i	$0.409516\pi$
$662$	10.6675	−	10.6675i	0.414605	−	0.414605i
$663$	−23.8102	−	2.45062i	−0.924713	−	0.0951742i
$664$		−	75.9103i		−	2.94589i
$665$	−35.7478	+	42.0958i	−1.38624	+	1.63241i
$666$	−55.1227	−	11.4683i	−2.13596	−	0.444387i
$667$	5.57151	+	5.57151i	0.215730	+	0.215730i
$668$	35.6868	+	35.6868i	1.38076	+	1.38076i
$669$	0.376363	+	0.462725i	0.0145510	+	0.0178900i
$670$	−54.1173	+	4.41317i	−2.09074	+	0.170496i
$671$		−	10.1662i		−	0.392463i
$672$	2.27412	−	22.0953i	0.0877260	−	0.852346i
$673$	−2.93474	+	2.93474i	−0.113126	+	0.113126i	−0.761404	−	0.648278i	$-0.775490\pi$
$673$	−2.93474	+	2.93474i	−0.113126	+	0.113126i	0.648278	+	0.761404i	$0.275490\pi$
$674$	33.2467			1.28062
$675$	3.75273	−	25.7083i	0.144443	−	0.989513i
$676$	28.8884			1.11109
$677$	−3.45098	+	3.45098i	−0.132632	+	0.132632i	−0.770306	−	0.637674i	$-0.779897\pi$
$677$	−3.45098	+	3.45098i	−0.132632	+	0.132632i	0.637674	+	0.770306i	$0.279897\pi$
$678$	2.03498	−	19.7719i	0.0781530	−	0.759334i
$679$			23.1200i			0.887266i
$680$	73.7368	−	6.01309i	2.82768	−	0.230592i
$681$	14.2768	+	17.5528i	0.547088	+	0.672625i
$682$	−5.54276	−	5.54276i	−0.212243	−	0.212243i
$683$	−12.4788	−	12.4788i	−0.477489	−	0.477489i	0.426839	−	0.904328i	$-0.359627\pi$
$683$	−12.4788	−	12.4788i	−0.477489	−	0.477489i	−0.904328	+	0.426839i	$0.859627\pi$
$684$	111.026	+	23.0991i	4.24520	+	0.883215i
$685$	−19.1468	+	22.5469i	−0.731563	+	0.861472i
$686$		−	41.7038i		−	1.59226i
$687$	−25.9207	−	2.66784i	−0.988937	−	0.101784i
$688$	−24.8635	+	24.8635i	−0.947910	+	0.947910i
$689$	5.06841			0.193091
$690$	0.972322	−	45.8707i	0.0370157	−	1.74627i
$691$	41.9694			1.59659			0.798296	−	0.602265i	$-0.205735\pi$
$691$	41.9694			1.59659			0.798296	+	0.602265i	$0.205735\pi$
$692$	26.2777	−	26.2777i	0.998930	−	0.998930i
$693$	22.3506	−	14.6522i	0.849030	−	0.556591i
$694$			1.67575i			0.0636107i
$695$	−1.34938	−	16.5470i	−0.0511848	−	0.627664i
$696$	−13.7325	+	11.1695i	−0.520528	+	0.423378i
$697$	28.9571	+	28.9571i	1.09683	+	1.09683i
$698$	−51.0469	−	51.0469i	−1.93215	−	1.93215i
$699$	20.1572	−	16.3952i	0.762417	−	0.620122i
$700$	−36.8953	+	51.3908i	−1.39451	+	1.94239i
$701$		−	4.29543i		−	0.162236i	−0.996704	−	0.0811181i	$-0.974151\pi$
$701$		−	4.29543i		−	0.162236i	0.996704	−	0.0811181i	$-0.0258491\pi$
$702$	−31.7826	−	10.0998i	−1.19956	−	0.381193i
$703$	−45.0586	+	45.0586i	−1.69942	+	1.69942i
$704$	−5.71421			−0.215363
$705$	−3.99656	−	4.16966i	−0.150519	−	0.157039i
$706$	52.1257			1.96177
$707$	−20.5137	+	20.5137i	−0.771498	+	0.771498i
$708$	−50.6431	−	5.21234i	−1.90328	−	0.195892i
$709$			30.6837i			1.15235i	0.817326	+	0.576175i	$0.195455\pi$
$709$			30.6837i			1.15235i	−0.817326	+	0.576175i	$0.804545\pi$
$710$	−11.5602	−	9.81693i	−0.433846	−	0.368423i
$711$	−7.24633	+	34.8298i	−0.271759	+	1.30622i
$712$	70.6077	+	70.6077i	2.64613	+	2.64613i
$713$	−3.31102	−	3.31102i	−0.123999	−	0.123999i
$714$	43.3084	+	53.2460i	1.62077	+	1.99268i
$715$	13.3966	+	11.3764i	0.501004	+	0.425453i
$716$			8.72001i			0.325882i
$717$	3.65753	−	35.5366i	0.136593	−	1.32714i
$718$	16.0913	−	16.0913i	0.600523	−	0.600523i
$719$	−2.17986			−0.0812950			−0.0406475	−	0.999174i	$-0.512942\pi$
$719$	−2.17986			−0.0812950			−0.0406475	+	0.999174i	$0.512942\pi$
$720$	43.6974	+	5.43558i	1.62850	+	0.202572i
$721$	2.06999			0.0770906
$722$	98.0125	−	98.0125i	3.64765	−	3.64765i
$723$	−2.51813	+	24.4662i	−0.0936503	+	0.909906i
$724$		−	35.0327i		−	1.30198i
$725$	8.30242	−	1.36316i	0.308344	−	0.0506265i
$726$	−3.87167	−	4.76008i	−0.143691	−	0.176663i
$727$	−23.1728	−	23.1728i	−0.859432	−	0.859432i	0.131840	−	0.991271i	$-0.457912\pi$
$727$	−23.1728	−	23.1728i	−0.859432	−	0.859432i	−0.991271	+	0.131840i	$0.957912\pi$
$728$	31.3239	+	31.3239i	1.16094	+	1.16094i
$729$	−22.0471	−	15.5861i	−0.816559	−	0.577262i
$730$	−3.43281	−	42.0955i	−0.127054	−	1.55802i
$731$		−	29.1808i		−	1.07929i
$732$	24.8780	+	2.56052i	0.919519	+	0.0946397i
$733$	20.6691	−	20.6691i	0.763429	−	0.763429i	−0.213511	−	0.976941i	$-0.568490\pi$
$733$	20.6691	−	20.6691i	0.763429	−	0.763429i	0.976941	+	0.213511i	$0.0684900\pi$
$734$	−4.55521			−0.168136
$735$	−4.90533	−	0.103978i	−0.180936	−	0.00383530i
$736$	20.8850			0.769832
$737$	21.0279	−	21.0279i	0.774571	−	0.774571i
$738$	31.2809	+	47.7163i	1.15147	+	1.75646i
$739$			8.03631i			0.295620i	0.989016	+	0.147810i	$0.0472225\pi$
$739$			8.03631i			0.295620i	−0.989016	+	0.147810i	$0.952778\pi$
$740$	−47.2499	+	55.6404i	−1.73694	+	2.04538i
$741$	−29.2808	+	23.8159i	−1.07566	+	0.874900i
$742$	−10.2766	−	10.2766i	−0.377267	−	0.377267i
$743$	7.34801	+	7.34801i	0.269572	+	0.269572i	0.828928	−	0.559356i	$-0.188951\pi$
$743$	7.34801	+	7.34801i	0.269572	+	0.269572i	−0.559356	+	0.828928i	$0.688951\pi$
$744$	8.16088	−	6.63776i	0.299193	−	0.243352i
$745$	19.0617	−	1.55444i	0.698365	−	0.0569503i
$746$		−	6.04882i		−	0.221463i
$747$	20.5574	+	31.3586i	0.752157	+	1.14735i
$748$	−52.5210	+	52.5210i	−1.92036	+	1.92036i
$749$	−13.0937			−0.478433
$750$	−39.1833	−	29.4092i	−1.43077	−	1.07387i
$751$	24.2277			0.884083			0.442041	−	0.896995i	$-0.354254\pi$
$751$	24.2277			0.884083			0.442041	+	0.896995i	$0.354254\pi$
$752$	6.92192	−	6.92192i	0.252416	−	0.252416i
$753$	−32.0781	−	3.30157i	−1.16899	−	0.120316i
$754$		−	10.7996i		−	0.393300i
$755$	3.49264	−	0.284818i	0.127110	−	0.0103656i
$756$	30.2264	+	58.3851i	1.09932	+	2.12345i
$757$	−6.91262	−	6.91262i	−0.251243	−	0.251243i	0.570237	−	0.821480i	$-0.306851\pi$
$757$	−6.91262	−	6.91262i	−0.251243	−	0.251243i	−0.821480	+	0.570237i	$0.806851\pi$
$758$	−54.5424	−	54.5424i	−1.98107	−	1.98107i
$759$	15.8560	+	19.4944i	0.575537	+	0.707601i
$760$	75.5118	−	88.9209i	2.73910	−	3.22550i
$761$		−	9.47758i		−	0.343562i	−0.985135	−	0.171781i	$-0.945048\pi$
$761$		−	9.47758i		−	0.343562i	0.985135	−	0.171781i	$-0.0549521\pi$
$762$	−7.44302	+	72.3164i	−0.269632	+	2.61975i
$763$	32.4470	−	32.4470i	1.17466	−	1.17466i
$764$	−46.3183			−1.67574
$765$	−28.8322	+	22.4528i	−1.04243	+	0.811783i
$766$	−46.2161			−1.66986
$767$	11.9813	−	11.9813i	0.432621	−	0.432621i
$768$	5.44128	−	52.8675i	0.196345	−	1.90769i
$769$			7.20588i			0.259851i	0.991524	+	0.129925i	$0.0414738\pi$
$769$			7.20588i			0.259851i	−0.991524	+	0.129925i	$0.958526\pi$
$770$	−4.09610	−	50.2293i	−0.147613	−	1.81014i
$771$	−26.9217	−	33.0992i	−0.969561	−	1.19204i
$772$	−8.30718	−	8.30718i	−0.298982	−	0.298982i
$773$	−12.9574	−	12.9574i	−0.466047	−	0.466047i	0.434584	−	0.900631i	$-0.356895\pi$
$773$	−12.9574	−	12.9574i	−0.466047	−	0.466047i	−0.900631	+	0.434584i	$0.856895\pi$
$774$	8.28117	−	39.8038i	0.297661	−	1.43072i
$775$	−4.93394	+	0.810094i	−0.177232	+	0.0290994i
$776$		−	48.8375i		−	1.75317i
$777$	−36.7487	−	3.78229i	−1.31835	−	0.135689i
$778$	−2.89024	+	2.89024i	−0.103620	+	0.103620i
$779$	64.5742			2.31361
$780$	−31.2136	+	29.9178i	−1.11763	+	1.07123i
$781$	8.30631			0.297223
$782$	−45.6327	+	45.6327i	−1.63182	+	1.63182i
$783$	2.64805	−	8.33303i	0.0946336	−	0.297798i
$784$		−	8.31578i		−	0.296992i
$785$	14.0217	+	11.9072i	0.500456	+	0.424988i
$786$	−21.2963	+	17.3216i	−0.759612	+	0.617841i
$787$	−19.3624	−	19.3624i	−0.690193	−	0.690193i	0.272081	−	0.962274i	$-0.412288\pi$
$787$	−19.3624	−	19.3624i	−0.690193	−	0.690193i	−0.962274	+	0.272081i	$0.912288\pi$
$788$	15.2745	+	15.2745i	0.544132	+	0.544132i
$789$	−35.1991	+	28.6296i	−1.25312	+	1.01924i
$790$	51.1350	+	43.4239i	1.81930	+	1.54495i
$791$		−	13.0417i		−	0.463709i
$792$	−47.2122	+	30.9505i	−1.67761	+	1.09978i
$793$	−5.88575	+	5.88575i	−0.209009	+	0.209009i
$794$	−78.2454			−2.77682
$795$	5.58634	−	5.35443i	0.198127	−	0.189902i
$796$	−61.0118			−2.16251
$797$	2.15731	−	2.15731i	0.0764159	−	0.0764159i	−0.667866	−	0.744282i	$-0.732792\pi$
$797$	2.15731	−	2.15731i	0.0764159	−	0.0764159i	0.744282	+	0.667866i	$0.232792\pi$
$798$	107.658	+	11.0805i	3.81105	+	0.392245i
$799$			8.12385i			0.287401i
$800$	13.0061	−	18.1159i	0.459834	−	0.640494i
$801$	−48.2894	−	10.0466i	−1.70622	−	0.354980i
$802$	5.27246	+	5.27246i	0.186177	+	0.186177i
$803$	16.3566	+	16.3566i	0.577213	+	0.577213i
$804$	46.1616	+	56.7540i	1.62799	+	2.00156i
$805$	−2.44684	−	30.0049i	−0.0862398	−	1.05753i
$806$			6.41798i			0.226064i
$807$	−2.74601	+	26.6802i	−0.0966641	+	0.939188i
$808$	43.3321	−	43.3321i	1.52442	−	1.52442i
$809$	7.12301			0.250432			0.125216	−	0.992130i	$-0.460038\pi$
$809$	7.12301			0.250432			0.125216	+	0.992130i	$0.460038\pi$
$810$	−45.7002	+	22.4443i	−1.60574	+	0.788612i
$811$	−38.2583			−1.34343			−0.671716	−	0.740809i	$-0.734442\pi$
$811$	−38.2583			−1.34343			−0.671716	+	0.740809i	$0.734442\pi$
$812$	−15.0550	+	15.0550i	−0.528326	+	0.528326i
$813$	1.88076	−	18.2734i	0.0659610	−	0.640877i
$814$		−	58.1488i		−	2.03812i
$815$	15.7113	−	18.5012i	0.550341	−	0.648069i
$816$	−39.0818	−	48.0496i	−1.36814	−	1.68207i
$817$	−32.5365	−	32.5365i	−1.13831	−	1.13831i
$818$	41.2703	+	41.2703i	1.44298	+	1.44298i
$819$	−21.4228	−	4.45702i	−0.748574	−	0.155741i
$820$	73.7269	−	6.01229i	2.57465	−	0.209958i
$821$			4.38496i			0.153036i	0.997068	+	0.0765181i	$0.0243803\pi$
$821$			4.38496i			0.153036i	−0.997068	+	0.0765181i	$0.975620\pi$
$822$	57.6625	+	5.93480i	2.01121	+	0.207000i
$823$	−6.09556	+	6.09556i	−0.212478	+	0.212478i	−0.805319	−	0.592841i	$-0.798006\pi$
$823$	−6.09556	+	6.09556i	−0.212478	+	0.212478i	0.592841	+	0.805319i	$0.298006\pi$
$824$	−4.37254			−0.152325
$825$	26.7839	−	1.61365i	0.932497	−	0.0561801i
$826$	−48.5863			−1.69053
$827$	−13.9463	+	13.9463i	−0.484959	+	0.484959i	−0.906711	−	0.421752i	$-0.861415\pi$
$827$	−13.9463	+	13.9463i	−0.484959	+	0.484959i	0.421752	+	0.906711i	$0.361415\pi$
$828$	−51.6987	+	33.8917i	−1.79666	+	1.17782i
$829$		−	24.6081i		−	0.854674i	−0.904092	−	0.427337i	$-0.859452\pi$
$829$		−	24.6081i		−	0.854674i	0.904092	−	0.427337i	$-0.140548\pi$
$830$	70.4731	−	5.74694i	2.44616	−	0.199479i
$831$	30.2025	−	24.5656i	1.04771	−	0.852173i
$832$	3.30825	+	3.30825i	0.114693	+	0.114693i
$833$	4.87987	+	4.87987i	0.169078	+	0.169078i
$834$	−25.2399	+	20.5292i	−0.873986	+	0.710868i
$835$	−16.5995	+	19.5472i	−0.574450	+	0.676459i
$836$			117.122i			4.05074i
$837$	−1.57367	+	4.95213i	−0.0543942	+	0.171171i
$838$	20.8189	−	20.8189i	0.719177	−	0.719177i
$839$	−40.9270			−1.41296			−0.706479	−	0.707734i	$-0.749718\pi$
$839$	−40.9270			−1.41296			−0.706479	+	0.707734i	$0.749718\pi$
$840$	67.6164	+	1.43327i	2.33299	+	0.0494524i
$841$	−26.1685			−0.902361
$842$	55.9687	−	55.9687i	1.92881	−	1.92881i
$843$	48.7032	+	5.01268i	1.67743	+	0.172646i
$844$		−	61.6231i		−	2.12116i
$845$	1.19308	+	14.6304i	0.0410431	+	0.503300i
$846$	−2.30546	+	11.0813i	−0.0792632	+	0.380981i
$847$	−2.84679	−	2.84679i	−0.0978168	−	0.0978168i
$848$	9.27370	+	9.27370i	0.318460	+	0.318460i
$849$	21.7536	+	26.7452i	0.746581	+	0.917894i
$850$	11.1648	+	68.0000i	0.382949	+	2.33238i
$851$		−	34.7357i		−	1.19072i
$852$	−2.09207	+	20.3266i	−0.0716732	+	0.696377i
$853$	35.5421	−	35.5421i	1.21694	−	1.21694i	0.248241	−	0.968698i	$-0.420148\pi$
$853$	35.5421	−	35.5421i	1.21694	−	1.21694i	0.968698	−	0.248241i	$-0.0798524\pi$
$854$	23.8677			0.816736
$855$	−7.11304	+	57.1827i	−0.243261	+	1.95561i
$856$	27.6584			0.945345
$857$	−11.6636	+	11.6636i	−0.398420	+	0.398420i	−0.877675	−	0.479256i	$-0.840907\pi$
$857$	−11.6636	+	11.6636i	−0.398420	+	0.398420i	0.479256	+	0.877675i	$0.340907\pi$
$858$	3.52625	−	34.2611i	0.120384	−	1.16965i
$859$		−	20.0932i		−	0.685570i	−0.939414	−	0.342785i	$-0.888630\pi$
$859$		−	20.0932i		−	0.685570i	0.939414	−	0.342785i	$-0.111370\pi$
$860$	−40.1776	−	34.1189i	−1.37004	−	1.16344i
$861$	23.6223	+	29.0428i	0.805047	+	0.989776i
$862$	−35.6557	−	35.6557i	−1.21444	−	1.21444i
$863$	−18.4605	−	18.4605i	−0.628402	−	0.628402i	0.319264	−	0.947666i	$-0.396564\pi$
$863$	−18.4605	−	18.4605i	−0.628402	−	0.628402i	−0.947666	+	0.319264i	$0.896564\pi$
$864$	−10.6552	−	20.5815i	−0.362497	−	0.700197i
$865$	14.3935	+	12.2230i	0.489393	+	0.415593i
$866$		−	20.2168i		−	0.686995i
$867$	21.8404	+	2.24788i	0.741738	+	0.0763420i
$868$	8.94682	−	8.94682i	0.303675	−	0.303675i
$869$	−36.7419			−1.24638
$870$	−11.4091	−	11.9032i	−0.386804	−	0.403557i
$871$	−24.3482			−0.825008
$872$	−68.5394	+	68.5394i	−2.32104	+	2.32104i
$873$	13.2258	+	20.1748i	0.447625	+	0.682813i
$874$			101.761i			3.44211i
$875$	−27.5503	−	16.5630i	−0.931372	−	0.559931i
$876$	−44.1464	+	35.9071i	−1.49157	+	1.21319i
$877$	3.55273	+	3.55273i	0.119967	+	0.119967i	0.764542	−	0.644574i	$-0.222965\pi$
$877$	3.55273	+	3.55273i	0.119967	+	0.119967i	−0.644574	+	0.764542i	$0.722965\pi$
$878$	29.0210	+	29.0210i	0.979412	+	0.979412i
$879$	−18.1434	+	14.7572i	−0.611962	+	0.497747i
$880$	3.69635	+	45.3272i	0.124604	+	1.52798i
$881$		−	54.9231i		−	1.85041i	−0.379473	−	0.925203i	$-0.623895\pi$
$881$		−	54.9231i		−	1.85041i	0.379473	−	0.925203i	$-0.376105\pi$
$882$	5.27149	+	8.04119i	0.177500	+	0.270761i
$883$	13.8216	−	13.8216i	0.465135	−	0.465135i	−0.435199	−	0.900334i	$-0.643322\pi$
$883$	13.8216	−	13.8216i	0.465135	−	0.465135i	0.900334	+	0.435199i	$0.143322\pi$
$884$	60.8142			2.04540
$885$	0.548222	−	25.8632i	0.0184283	−	0.869381i
$886$	−74.3911			−2.49922
$887$	9.54020	−	9.54020i	0.320329	−	0.320329i	−0.528565	−	0.848893i	$-0.677270\pi$
$887$	9.54020	−	9.54020i	0.320329	−	0.320329i	0.848893	+	0.528565i	$0.177270\pi$
$888$	77.6259	+	7.98950i	2.60496	+	0.268110i
$889$			47.7005i			1.59982i
$890$	−60.2047	+	70.8957i	−2.01807	+	2.37643i
$891$	11.1216	−	25.5713i	0.372588	−	0.856670i
$892$	−1.07157	−	1.07157i	−0.0358787	−	0.0358787i
$893$	9.05808	+	9.05808i	0.303117	+	0.303117i
$894$	−23.6490	−	29.0756i	−0.790942	−	0.972433i
$895$	−4.41620	+	0.360133i	−0.147617	+	0.0120379i
$896$		−	39.0638i		−	1.30503i
$897$	2.10644	−	20.4661i	0.0703319	−	0.683345i
$898$	−40.6104	+	40.6104i	−1.35519	+	1.35519i
$899$	−1.68272			−0.0561218
$900$	−2.79714	+	65.9500i	−0.0932382	+	2.19833i
$901$	−10.8840			−0.362599
$902$	−41.6670	+	41.6670i	−1.38736	+	1.38736i
$903$	2.73116	−	26.5360i	0.0908875	−	0.883063i
$904$			27.5486i			0.916252i
$905$	17.7421	−	1.44684i	0.589768	−	0.0480944i
$906$	−4.33318	−	5.32748i	−0.143960	−	0.176994i
$907$	30.6550	+	30.6550i	1.01788	+	1.01788i	0.999837	+	0.0180453i	$0.00574432\pi$
$907$	30.6550	+	30.6550i	1.01788	+	1.01788i	0.0180453	+	0.999837i	$0.494256\pi$
$908$	−40.6483	−	40.6483i	−1.34896	−	1.34896i
$909$	−6.16563	+	29.6353i	−0.204501	+	0.982941i
$910$	−26.7088	+	31.4517i	−0.885390	+	1.04261i
$911$			39.2231i			1.29952i	0.760140	+	0.649760i	$0.225131\pi$
$911$			39.2231i			1.29952i	−0.760140	+	0.649760i	$0.774869\pi$
$912$	−97.1513	−	9.99910i	−3.21700	−	0.331103i
$913$	−27.3830	+	27.3830i	−0.906246	+	0.906246i
$914$	−5.75016			−0.190198
$915$	−0.269310	+	12.7051i	−0.00890312	+	0.420017i
$916$	66.2046			2.18746
$917$	−12.7363	+	12.7363i	−0.420591	+	0.420591i
$918$	68.2506	+	21.6885i	2.25261	+	0.715828i
$919$			45.5043i			1.50105i	0.660843	+	0.750525i	$0.270199\pi$
$919$			45.5043i			1.50105i	−0.660843	+	0.750525i	$0.729801\pi$
$920$	5.16857	+	63.3806i	0.170403	+	2.08960i
$921$	19.8704	−	16.1619i	0.654752	−	0.532551i
$922$	−46.5083	−	46.5083i	−1.53167	−	1.53167i
$923$	−4.80895	−	4.80895i	−0.158288	−	0.158288i
$924$	−52.6765	+	42.8451i	−1.73293	+	1.40950i
$925$	−30.1302	−	21.6315i	−0.990674	−	0.711240i
$926$		−	38.7527i		−	1.27349i
$927$	1.80630	−	1.18414i	0.0593266	−	0.0388922i
$928$	5.30707	−	5.30707i	0.174213	−	0.174213i
$929$	−7.13362			−0.234046			−0.117023	−	0.993129i	$-0.537335\pi$
$929$	−7.13362			−0.234046			−0.117023	+	0.993129i	$0.537335\pi$
$930$	6.78015	+	7.07381i	0.222330	+	0.231960i
$931$	10.8821			0.356646
$932$	−46.6796	+	46.6796i	−1.52904	+	1.52904i
$933$	−37.9696	−	3.90794i	−1.24307	−	0.127940i
$934$			27.0274i			0.884364i
$935$	−28.7681	−	24.4299i	−0.940817	−	0.798943i
$936$	45.2524	+	9.41476i	1.47912	+	0.307731i
$937$	21.6182	+	21.6182i	0.706235	+	0.706235i	0.965741	−	0.259506i	$-0.0835598\pi$
$937$	21.6182	+	21.6182i	0.706235	+	0.706235i	−0.259506	+	0.965741i	$0.583560\pi$
$938$	49.3680	+	49.3680i	1.61192	+	1.61192i
$939$	10.3049	+	12.6694i	0.336286	+	0.413452i
$940$	11.1853	+	9.49859i	0.364825	+	0.309810i
$941$		−	4.99491i		−	0.162830i	−0.996680	−	0.0814148i	$-0.974056\pi$
$941$		−	4.99491i		−	0.162830i	0.996680	−	0.0814148i	$-0.0259438\pi$
$942$	3.69080	−	35.8598i	0.120253	−	1.16837i
$943$	−24.8902	+	24.8902i	−0.810535	+	0.810535i
$944$	43.8447			1.42702
$945$	−28.3205	+	17.7193i	−0.921266	+	0.576408i
$946$	41.9889			1.36518
$947$	9.48497	−	9.48497i	0.308220	−	0.308220i	−0.535999	−	0.844219i	$-0.680065\pi$
$947$	9.48497	−	9.48497i	0.308220	−	0.308220i	0.844219	+	0.535999i	$0.180065\pi$
$948$	9.25401	−	89.9119i	0.300556	−	2.92020i
$949$		−	18.9394i		−	0.614799i
$950$	88.2685	+	63.3711i	2.86381	+	2.05603i
$951$	−14.2075	−	17.4676i	−0.460710	−	0.566426i
$952$	−67.2656	−	67.2656i	−2.18009	−	2.18009i
$953$	−39.4892	−	39.4892i	−1.27918	−	1.27918i	−0.941127	−	0.338054i	$-0.890231\pi$
$953$	−39.4892	−	39.4892i	−1.27918	−	1.27918i	−0.338054	−	0.941127i	$-0.609769\pi$
$954$	−14.8462	−	3.08875i	−0.480664	−	0.100002i
$955$	−1.91293	−	23.4576i	−0.0619008	−	0.759072i
$956$			90.7647i			2.93554i
$957$	8.98285	+	0.924542i	0.290374	+	0.0298862i
$958$	−43.5939	+	43.5939i	−1.40846	+	1.40846i
$959$	38.0347			1.22820
$960$	7.14125	+	0.151373i	0.230483	+	0.00488555i
$961$	1.00000			0.0322581
$962$	−33.6653	+	33.6653i	−1.08541	+	1.08541i
$963$	−11.4257	+	7.49023i	−0.368187	+	0.241369i
$964$		−	62.4895i		−	2.01265i
$965$	3.86404	−	4.55021i	0.124388	−	0.146476i
$966$	−45.7678	+	37.2258i	−1.47255	+	1.19772i
$967$	15.2441	+	15.2441i	0.490217	+	0.490217i	0.908375	−	0.418158i	$-0.137324\pi$
$967$	15.2441	+	15.2441i	0.490217	+	0.490217i	−0.418158	+	0.908375i	$0.637324\pi$
$968$	6.01340	+	6.01340i	0.193278	+	0.193278i
$969$	62.8781	−	51.1427i	2.01994	−	1.64294i
$970$	45.3394	−	3.69734i	1.45576	−	0.118715i
$971$		−	28.6356i		−	0.918961i	−0.888188	−	0.459480i	$-0.848036\pi$
$971$		−	28.6356i		−	0.918961i	0.888188	−	0.459480i	$-0.151964\pi$
$972$	59.7750	+	33.6565i	1.91728	+	1.07953i
$973$	−15.0948	+	15.0948i	−0.483918	+	0.483918i
$974$	−81.8279			−2.62194
$975$	−16.4408	−	14.5724i	−0.526527	−	0.466689i
$976$	−21.5384			−0.689427
$977$	16.9567	−	16.9567i	0.542493	−	0.542493i	−0.381766	−	0.924259i	$-0.624684\pi$
$977$	16.9567	−	16.9567i	0.542493	−	0.542493i	0.924259	+	0.381766i	$0.124684\pi$
$978$	−47.3159	−	4.86990i	−1.51300	−	0.155722i
$979$		−	50.9404i		−	1.62806i
$980$	12.4245	−	1.01320i	0.396887	−	0.0323653i
$981$	9.75232	−	46.8749i	0.311368	−	1.49660i
$982$	−46.3446	−	46.3446i	−1.47892	−	1.47892i
$983$	17.0347	+	17.0347i	0.543323	+	0.543323i	0.924501	−	0.381179i	$-0.124482\pi$
$983$	17.0347	+	17.0347i	0.543323	+	0.543323i	−0.381179	+	0.924501i	$0.624482\pi$
$984$	−49.8986	−	61.3484i	−1.59071	−	1.95572i
$985$	−7.10487	+	8.36653i	−0.226380	+	0.266580i
$986$			23.1914i			0.738563i
$987$	−0.760349	+	7.38755i	−0.0242022	+	0.235148i
$988$	67.8077	−	67.8077i	2.15725	−	2.15725i
$989$	25.0824			0.797575
$990$	−32.3079	−	41.4874i	−1.02681	−	1.31856i
$991$	20.5761			0.653622			0.326811	−	0.945090i	$-0.394026\pi$
$991$	20.5761			0.653622			0.326811	+	0.945090i	$0.394026\pi$
$992$	−3.15387	+	3.15387i	−0.100135	+	0.100135i
$993$	1.05743	−	10.2740i	0.0335566	−	0.326036i
$994$			19.5011i			0.618536i
$995$	−2.51976	−	30.8991i	−0.0798818	−	0.979567i
$996$	−60.1129	−	73.9065i	−1.90475	−	2.34182i
$997$	16.7354	+	16.7354i	0.530014	+	0.530014i	0.920576	−	0.390562i	$-0.127719\pi$
$997$	16.7354	+	16.7354i	0.530014	+	0.530014i	−0.390562	+	0.920576i	$0.627719\pi$
$998$	−51.6478	−	51.6478i	−1.63488	−	1.63488i
$999$	−34.2309	+	17.7216i	−1.08302	+	0.560686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.k.b.32.3	✓	60
3.2	odd	2	inner	465.2.k.b.32.28	yes	60
5.3	odd	4	inner	465.2.k.b.218.28	yes	60
15.8	even	4	inner	465.2.k.b.218.3	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.k.b.32.3	✓	60	1.1	even	1	trivial
465.2.k.b.32.28	yes	60	3.2	odd	2	inner
465.2.k.b.218.3	yes	60	15.8	even	4	inner
465.2.k.b.218.28	yes	60	5.3	odd	4	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:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.78894 + 1.78894i) q^{2} +(-0.177331 + 1.72295i) q^{3} -4.40062i q^{4} +(2.22867 - 0.181744i) q^{5} +(-2.76502 - 3.39949i) q^{6} +(-2.03308 - 2.03308i) q^{7} +(4.29457 + 4.29457i) q^{8} +(-2.93711 - 0.611065i) q^{9} +O(q^{10})\)	\(q+(-1.78894 + 1.78894i) q^{2} +(-0.177331 + 1.72295i) q^{3} -4.40062i q^{4} +(2.22867 - 0.181744i) q^{5} +(-2.76502 - 3.39949i) q^{6} +(-2.03308 - 2.03308i) q^{7} +(4.29457 + 4.29457i) q^{8} +(-2.93711 - 0.611065i) q^{9} +(-3.66183 + 4.31209i) q^{10} -3.09835i q^{11} +(7.58205 + 0.780367i) q^{12} +(-1.79379 + 1.79379i) q^{13} +7.27412 q^{14} +(-0.0820773 + 3.87211i) q^{15} -6.56422 q^{16} +(3.85202 - 3.85202i) q^{17} +(6.34747 - 4.16115i) q^{18} -8.58999i q^{19} +(-0.799785 - 9.80753i) q^{20} +(3.86342 - 3.14237i) q^{21} +(5.54276 + 5.54276i) q^{22} +(3.31102 + 3.31102i) q^{23} +(-8.16088 + 6.63776i) q^{24} +(4.93394 - 0.810094i) q^{25} -6.41798i q^{26} +(1.57367 - 4.95213i) q^{27} +(-8.94682 + 8.94682i) q^{28} +1.68272 q^{29} +(-6.78015 - 7.07381i) q^{30} -1.00000 q^{31} +(3.15387 - 3.15387i) q^{32} +(5.33830 + 0.549434i) q^{33} +13.7821i q^{34} +(-4.90057 - 4.16157i) q^{35} +(-2.68907 + 12.9251i) q^{36} +(-5.24547 - 5.24547i) q^{37} +(15.3670 + 15.3670i) q^{38} +(-2.77252 - 3.40871i) q^{39} +(10.3517 + 8.79067i) q^{40} +7.51737i q^{41} +(-1.28993 + 12.5329i) q^{42} +(3.78772 - 3.78772i) q^{43} -13.6347 q^{44} +(-6.65690 - 0.828061i) q^{45} -11.8464 q^{46} +(-1.05449 + 1.05449i) q^{47} +(1.16404 - 11.3098i) q^{48} +1.26683i q^{49} +(-7.37732 + 10.2757i) q^{50} +(5.95376 + 7.31992i) q^{51} +(7.89380 + 7.89380i) q^{52} +(-1.41276 - 1.41276i) q^{53} +(6.04385 + 11.6743i) q^{54} +(-0.563106 - 6.90520i) q^{55} -17.4624i q^{56} +(14.8001 + 1.52327i) q^{57} +(-3.01028 + 3.01028i) q^{58} -6.67934 q^{59} +(17.0397 + 0.361191i) q^{60} +3.28118 q^{61} +(1.78894 - 1.78894i) q^{62} +(4.72903 + 7.21372i) q^{63} -1.84428i q^{64} +(-3.67176 + 4.32378i) q^{65} +(-10.5328 + 8.56700i) q^{66} +(6.78680 + 6.78680i) q^{67} +(-16.9513 - 16.9513i) q^{68} +(-6.29186 + 5.11757i) q^{69} +(16.2116 - 1.32203i) q^{70} +2.68088i q^{71} +(-9.98935 - 15.2379i) q^{72} +(-5.27915 + 5.27915i) q^{73} +18.7677 q^{74} +(0.520809 + 8.64458i) q^{75} -37.8013 q^{76} +(-6.29919 + 6.29919i) q^{77} +(11.0579 + 1.13811i) q^{78} -11.8585i q^{79} +(-14.6295 + 1.19301i) q^{80} +(8.25320 + 3.58953i) q^{81} +(-13.4481 - 13.4481i) q^{82} +(-8.83795 - 8.83795i) q^{83} +(-13.8284 - 17.0015i) q^{84} +(7.88481 - 9.28497i) q^{85} +13.5520i q^{86} +(-0.298398 + 2.89924i) q^{87} +(13.3061 - 13.3061i) q^{88} +16.4412 q^{89} +(13.3902 - 10.4274i) q^{90} +7.29385 q^{91} +(14.5705 - 14.5705i) q^{92} +(0.177331 - 1.72295i) q^{93} -3.77285i q^{94} +(-1.56118 - 19.1443i) q^{95} +(4.87467 + 5.99323i) q^{96} +(-5.68596 - 5.68596i) q^{97} +(-2.26629 - 2.26629i) q^{98} +(-1.89329 + 9.10018i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 4 q^{6}+O(q^{10}) \) 60 * q - 4 * q^6	\( 60 q - 4 q^{6} + 16 q^{10} - 12 q^{13} - 8 q^{15} - 60 q^{16} + 34 q^{18} - 4 q^{21} + 8 q^{22} + 8 q^{25} - 6 q^{27} - 80 q^{28} - 54 q^{30} - 60 q^{31} + 10 q^{33} + 28 q^{36} - 12 q^{37} + 60 q^{40} - 12 q^{42} - 24 q^{43} - 58 q^{45} + 8 q^{46} + 80 q^{48} + 32 q^{51} + 52 q^{52} + 64 q^{55} - 14 q^{57} - 48 q^{58} - 108 q^{60} - 56 q^{61} + 62 q^{63} + 40 q^{66} + 104 q^{67} + 108 q^{70} - 76 q^{72} - 108 q^{73} - 38 q^{75} - 120 q^{76} + 112 q^{78} + 60 q^{81} + 20 q^{82} + 48 q^{85} - 110 q^{87} - 28 q^{88} - 82 q^{90} - 32 q^{91} + 120 q^{96} + 56 q^{97}+O(q^{100}) \) 60 * q - 4 * q^6 + 16 * q^10 - 12 * q^13 - 8 * q^15 - 60 * q^16 + 34 * q^18 - 4 * q^21 + 8 * q^22 + 8 * q^25 - 6 * q^27 - 80 * q^28 - 54 * q^30 - 60 * q^31 + 10 * q^33 + 28 * q^36 - 12 * q^37 + 60 * q^40 - 12 * q^42 - 24 * q^43 - 58 * q^45 + 8 * q^46 + 80 * q^48 + 32 * q^51 + 52 * q^52 + 64 * q^55 - 14 * q^57 - 48 * q^58 - 108 * q^60 - 56 * q^61 + 62 * q^63 + 40 * q^66 + 104 * q^67 + 108 * q^70 - 76 * q^72 - 108 * q^73 - 38 * q^75 - 120 * q^76 + 112 * q^78 + 60 * q^81 + 20 * q^82 + 48 * q^85 - 110 * q^87 - 28 * q^88 - 82 * q^90 - 32 * q^91 + 120 * q^96 + 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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