LMFDB - Embedded newform 273.2.cg.b.124.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(19,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("273.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cg (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			124.8
Character	$\chi$	$=$	273.124
Dual form			273.2.cg.b.262.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.323834 - 1.20856i) q^{2} -1.00000i q^{3} +(0.376291 + 0.217252i) q^{4} +(0.986163 + 3.68041i) q^{5} +(-1.20856 - 0.323834i) q^{6} +(-1.80936 - 1.93034i) q^{7} +(2.15388 - 2.15388i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.323834 - 1.20856i) q^{2} -1.00000i q^{3} +(0.376291 + 0.217252i) q^{4} +(0.986163 + 3.68041i) q^{5} +(-1.20856 - 0.323834i) q^{6} +(-1.80936 - 1.93034i) q^{7} +(2.15388 - 2.15388i) q^{8} -1.00000 q^{9} +4.76737 q^{10} +(3.16350 - 3.16350i) q^{11} +(0.217252 - 0.376291i) q^{12} +(3.57886 + 0.437877i) q^{13} +(-2.91888 + 1.56161i) q^{14} +(3.68041 - 0.986163i) q^{15} +(-1.47110 - 2.54802i) q^{16} +(0.601776 - 1.04231i) q^{17} +(-0.323834 + 1.20856i) q^{18} +(-3.79295 + 3.79295i) q^{19} +(-0.428491 + 1.59915i) q^{20} +(-1.93034 + 1.80936i) q^{21} +(-2.79885 - 4.84774i) q^{22} +(2.92841 - 1.69072i) q^{23} +(-2.15388 - 2.15388i) q^{24} +(-8.24277 + 4.75896i) q^{25} +(1.68816 - 4.18349i) q^{26} +1.00000i q^{27} +(-0.261474 - 1.11946i) q^{28} +(-3.96435 + 6.86645i) q^{29} -4.76737i q^{30} +(-5.16347 - 1.38355i) q^{31} +(2.32867 - 0.623965i) q^{32} +(-3.16350 - 3.16350i) q^{33} +(-1.06482 - 1.06482i) q^{34} +(5.32014 - 8.56280i) q^{35} +(-0.376291 - 0.217252i) q^{36} +(-6.75142 - 1.80904i) q^{37} +(3.35574 + 5.81231i) q^{38} +(0.437877 - 3.57886i) q^{39} +(10.0512 + 5.80308i) q^{40} +(0.914977 + 3.41474i) q^{41} +(1.56161 + 2.91888i) q^{42} +(-8.74306 + 5.04781i) q^{43} +(1.87767 - 0.503121i) q^{44} +(-0.986163 - 3.68041i) q^{45} +(-1.09502 - 4.08668i) q^{46} +(4.98837 - 1.33663i) q^{47} +(-2.54802 + 1.47110i) q^{48} +(-0.452462 + 6.98536i) q^{49} +(3.08223 + 11.5030i) q^{50} +(-1.04231 - 0.601776i) q^{51} +(1.25156 + 0.942283i) q^{52} +(-1.14727 - 1.98713i) q^{53} +(1.20856 + 0.323834i) q^{54} +(14.7627 + 8.52325i) q^{55} +(-8.05487 - 0.260595i) q^{56} +(3.79295 + 3.79295i) q^{57} +(7.01476 + 7.01476i) q^{58} +(-5.88602 + 1.57716i) q^{59} +(1.59915 + 0.428491i) q^{60} +5.40651i q^{61} +(-3.34421 + 5.79234i) q^{62} +(1.80936 + 1.93034i) q^{63} -8.90081i q^{64} +(1.91777 + 13.6035i) q^{65} +(-4.84774 + 2.79885i) q^{66} +(-3.83925 - 3.83925i) q^{67} +(0.452886 - 0.261474i) q^{68} +(-1.69072 - 2.92841i) q^{69} +(-8.62586 - 9.20266i) q^{70} +(3.05313 - 11.3945i) q^{71} +(-2.15388 + 2.15388i) q^{72} +(1.92074 - 7.16831i) q^{73} +(-4.37268 + 7.57370i) q^{74} +(4.75896 + 8.24277i) q^{75} +(-2.25128 + 0.603228i) q^{76} +(-11.8305 - 0.382748i) q^{77} +(-4.18349 - 1.68816i) q^{78} +(5.76343 - 9.98255i) q^{79} +(7.92701 - 7.92701i) q^{80} +1.00000 q^{81} +4.42323 q^{82} +(-5.00708 + 5.00708i) q^{83} +(-1.11946 + 0.261474i) q^{84} +(4.42956 + 1.18690i) q^{85} +(3.26930 + 12.2012i) q^{86} +(6.86645 + 3.96435i) q^{87} -13.6276i q^{88} +(1.36380 - 5.08976i) q^{89} -4.76737 q^{90} +(-5.63018 - 7.70072i) q^{91} +1.46924 q^{92} +(-1.38355 + 5.16347i) q^{93} -6.46162i q^{94} +(-17.7001 - 10.2191i) q^{95} +(-0.623965 - 2.32867i) q^{96} +(2.69756 + 0.722808i) q^{97} +(8.29574 + 2.80893i) q^{98} +(-3.16350 + 3.16350i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 8 * q^7 - 40 * q^9	$ 40 q - 8 q^{7} - 40 q^{9} + 4 q^{11} - 24 q^{12} - 18 q^{14} + 32 q^{16} + 4 q^{17} + 14 q^{19} + 14 q^{20} + 2 q^{21} + 4 q^{22} + 12 q^{23} + 24 q^{25} - 32 q^{26} + 16 q^{28} + 8 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} - 24 q^{34} + 26 q^{35} + 36 q^{37} - 8 q^{38} + 18 q^{39} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 32 q^{44} - 26 q^{46} - 4 q^{47} + 24 q^{48} - 14 q^{49} - 20 q^{50} + 2 q^{52} - 8 q^{53} - 42 q^{55} + 46 q^{56} - 14 q^{57} + 24 q^{58} + 14 q^{59} + 2 q^{60} + 24 q^{62} + 8 q^{63} + 28 q^{65} - 18 q^{66} - 44 q^{67} - 18 q^{68} + 4 q^{69} - 4 q^{70} - 6 q^{71} + 14 q^{73} - 20 q^{74} + 24 q^{75} - 64 q^{76} + 24 q^{77} + 8 q^{78} + 20 q^{80} + 40 q^{81} + 48 q^{82} - 12 q^{83} + 22 q^{84} + 2 q^{85} - 60 q^{86} + 18 q^{87} - 2 q^{89} - 14 q^{91} + 236 q^{92} - 8 q^{93} + 24 q^{95} + 16 q^{96} - 62 q^{97} - 88 q^{98} - 4 q^{99}+O(q^{100}) $ 40 * q - 8 * q^7 - 40 * q^9 + 4 * q^11 - 24 * q^12 - 18 * q^14 + 32 * q^16 + 4 * q^17 + 14 * q^19 + 14 * q^20 + 2 * q^21 + 4 * q^22 + 12 * q^23 + 24 * q^25 - 32 * q^26 + 16 * q^28 + 8 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 - 24 * q^34 + 26 * q^35 + 36 * q^37 - 8 * q^38 + 18 * q^39 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 32 * q^44 - 26 * q^46 - 4 * q^47 + 24 * q^48 - 14 * q^49 - 20 * q^50 + 2 * q^52 - 8 * q^53 - 42 * q^55 + 46 * q^56 - 14 * q^57 + 24 * q^58 + 14 * q^59 + 2 * q^60 + 24 * q^62 + 8 * q^63 + 28 * q^65 - 18 * q^66 - 44 * q^67 - 18 * q^68 + 4 * q^69 - 4 * q^70 - 6 * q^71 + 14 * q^73 - 20 * q^74 + 24 * q^75 - 64 * q^76 + 24 * q^77 + 8 * q^78 + 20 * q^80 + 40 * q^81 + 48 * q^82 - 12 * q^83 + 22 * q^84 + 2 * q^85 - 60 * q^86 + 18 * q^87 - 2 * q^89 - 14 * q^91 + 236 * q^92 - 8 * q^93 + 24 * q^95 + 16 * q^96 - 62 * q^97 - 88 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.323834	−	1.20856i	0.228985	−	0.854584i	−0.751783	−	0.659410i	$-0.770806\pi$
$2$	0.323834	−	1.20856i	0.228985	−	0.854584i	0.980769	−	0.195174i	$-0.0625272\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	0.376291	+	0.217252i	0.188145	+	0.108626i
$5$	0.986163	+	3.68041i	0.441025	+	1.64593i	0.726222	+	0.687460i	$0.241274\pi$
$5$	0.986163	+	3.68041i	0.441025	+	1.64593i	−0.285197	+	0.958469i	$0.592059\pi$
$6$	−1.20856	−	0.323834i	−0.493394	−	0.132205i
$7$	−1.80936	−	1.93034i	−0.683872	−	0.729602i
$7$	−1.80936	−	1.93034i	−0.683872	−	0.729602i
$8$	2.15388	−	2.15388i	0.761511	−	0.761511i
$9$	−1.00000			−0.333333
$10$	4.76737			1.50757
$11$	3.16350	−	3.16350i	0.953831	−	0.953831i	−0.0451488	−	0.998980i	$-0.514376\pi$
$11$	3.16350	−	3.16350i	0.953831	−	0.953831i	0.998980	+	0.0451488i	$0.0143762\pi$
$12$	0.217252	−	0.376291i	0.0627152	−	0.108626i
$13$	3.57886	+	0.437877i	0.992598	+	0.121445i
$13$	3.57886	+	0.437877i	0.992598	+	0.121445i
$14$	−2.91888	+	1.56161i	−0.780103	+	0.417358i
$15$	3.68041	−	0.986163i	0.950278	−	0.254626i
$16$	−1.47110	−	2.54802i	−0.367775	−	0.637005i
$17$	0.601776	−	1.04231i	0.145952	−	0.252796i	−0.783776	−	0.621044i	$-0.786709\pi$
$17$	0.601776	−	1.04231i	0.145952	−	0.252796i	0.929728	+	0.368248i	$0.120042\pi$
$18$	−0.323834	+	1.20856i	−0.0763284	+	0.284861i
$19$	−3.79295	+	3.79295i	−0.870163	+	0.870163i	−0.992490	−	0.122327i	$-0.960964\pi$
$19$	−3.79295	+	3.79295i	−0.870163	+	0.870163i	0.122327	+	0.992490i	$0.460964\pi$
$20$	−0.428491	+	1.59915i	−0.0958135	+	0.357581i
$21$	−1.93034	+	1.80936i	−0.421236	+	0.394834i
$22$	−2.79885	−	4.84774i	−0.596716	−	1.03354i
$23$	2.92841	−	1.69072i	0.610615	−	0.352539i	−0.162591	−	0.986693i	$-0.551985\pi$
$23$	2.92841	−	1.69072i	0.610615	−	0.352539i	0.773206	+	0.634155i	$0.218652\pi$
$24$	−2.15388	−	2.15388i	−0.439659	−	0.439659i
$25$	−8.24277	+	4.75896i	−1.64855	+	0.951793i
$26$	1.68816	−	4.18349i	0.331075	−	0.820449i
$27$			1.00000i			0.192450i
$28$	−0.261474	−	1.11946i	−0.0494139	−	0.211557i
$29$	−3.96435	+	6.86645i	−0.736161	+	1.27507i	0.218051	+	0.975937i	$0.430030\pi$
$29$	−3.96435	+	6.86645i	−0.736161	+	1.27507i	−0.954212	+	0.299131i	$0.903303\pi$
$30$		−	4.76737i		−	0.870398i
$31$	−5.16347	−	1.38355i	−0.927386	−	0.248492i	−0.236646	−	0.971596i	$-0.576048\pi$
$31$	−5.16347	−	1.38355i	−0.927386	−	0.248492i	−0.690740	+	0.723104i	$0.742715\pi$
$32$	2.32867	−	0.623965i	0.411655	−	0.110303i
$33$	−3.16350	−	3.16350i	−0.550695	−	0.550695i
$34$	−1.06482	−	1.06482i	−0.182615	−	0.182615i
$35$	5.32014	−	8.56280i	0.899268	−	1.44738i
$36$	−0.376291	−	0.217252i	−0.0627152	−	0.0362086i
$37$	−6.75142	−	1.80904i	−1.10993	−	0.297404i	−0.343126	−	0.939289i	$-0.611486\pi$
$37$	−6.75142	−	1.80904i	−1.10993	−	0.297404i	−0.766801	+	0.641885i	$0.778153\pi$
$38$	3.35574	+	5.81231i	0.544373	+	0.942882i
$39$	0.437877	−	3.57886i	0.0701165	−	0.573077i
$40$	10.0512	+	5.80308i	1.58924	+	0.917548i
$41$	0.914977	+	3.41474i	0.142895	+	0.533293i	0.999840	+	0.0178844i	$0.00569308\pi$
$41$	0.914977	+	3.41474i	0.142895	+	0.533293i	−0.856945	+	0.515408i	$0.827640\pi$
$42$	1.56161	+	2.91888i	0.240962	+	0.450393i
$43$	−8.74306	+	5.04781i	−1.33330	+	0.769784i	−0.985805	−	0.167896i	$-0.946303\pi$
$43$	−8.74306	+	5.04781i	−1.33330	+	0.769784i	−0.347500	+	0.937680i	$0.612969\pi$
$44$	1.87767	−	0.503121i	0.283070	−	0.0758483i
$45$	−0.986163	−	3.68041i	−0.147008	−	0.548643i
$46$	−1.09502	−	4.08668i	−0.161452	−	0.602548i
$47$	4.98837	−	1.33663i	0.727629	−	0.194968i	0.124056	−	0.992275i	$-0.460410\pi$
$47$	4.98837	−	1.33663i	0.727629	−	0.194968i	0.603573	+	0.797308i	$0.293743\pi$
$48$	−2.54802	+	1.47110i	−0.367775	+	0.212335i
$49$	−0.452462	+	6.98536i	−0.0646374	+	0.997909i
$50$	3.08223	+	11.5030i	0.435893	+	1.62677i
$51$	−1.04231	−	0.601776i	−0.145952	−	0.0842655i
$52$	1.25156	+	0.942283i	0.173561	+	0.130671i
$53$	−1.14727	−	1.98713i	−0.157590	−	0.272953i	0.776409	−	0.630229i	$-0.217039\pi$
$53$	−1.14727	−	1.98713i	−0.157590	−	0.272953i	−0.933999	+	0.357276i	$0.883706\pi$
$54$	1.20856	+	0.323834i	0.164465	+	0.0440682i
$55$	14.7627	+	8.52325i	1.99060	+	1.14928i
$56$	−8.05487	−	0.260595i	−1.07638	−	0.0348235i
$57$	3.79295	+	3.79295i	0.502389	+	0.502389i
$58$	7.01476	+	7.01476i	0.921083	+	0.921083i
$59$	−5.88602	+	1.57716i	−0.766295	+	0.205328i	−0.620734	−	0.784021i	$-0.713165\pi$
$59$	−5.88602	+	1.57716i	−0.766295	+	0.205328i	−0.145561	+	0.989349i	$0.546499\pi$
$60$	1.59915	+	0.428491i	0.206449	+	0.0553180i
$61$			5.40651i			0.692233i	0.938192	+	0.346116i	$0.112500\pi$
$61$			5.40651i			0.692233i	−0.938192	+	0.346116i	$0.887500\pi$
$62$	−3.34421	+	5.79234i	−0.424715	+	0.735628i
$63$	1.80936	+	1.93034i	0.227957	+	0.243201i
$64$		−	8.90081i		−	1.11260i
$65$	1.91777	+	13.6035i	0.237871	+	1.68731i
$66$	−4.84774	+	2.79885i	−0.596716	+	0.344514i
$67$	−3.83925	−	3.83925i	−0.469039	−	0.469039i	0.432564	−	0.901603i	$-0.357609\pi$
$67$	−3.83925	−	3.83925i	−0.469039	−	0.469039i	−0.901603	+	0.432564i	$0.857609\pi$
$68$	0.452886	−	0.261474i	0.0549205	−	0.0317083i
$69$	−1.69072	−	2.92841i	−0.203538	−	0.352539i
$70$	−8.62586	−	9.20266i	−1.03099	−	1.09993i
$71$	3.05313	−	11.3945i	0.362340	−	1.35227i	−0.508650	−	0.860973i	$-0.669855\pi$
$71$	3.05313	−	11.3945i	0.362340	−	1.35227i	0.870991	−	0.491299i	$-0.163478\pi$
$72$	−2.15388	+	2.15388i	−0.253837	+	0.253837i
$73$	1.92074	−	7.16831i	0.224806	−	0.838987i	−0.757676	−	0.652631i	$-0.773665\pi$
$73$	1.92074	−	7.16831i	0.224806	−	0.838987i	0.982482	−	0.186357i	$-0.0596680\pi$
$74$	−4.37268	+	7.57370i	−0.508313	+	0.880425i
$75$	4.75896	+	8.24277i	0.549518	+	0.951793i
$76$	−2.25128	+	0.603228i	−0.258239	+	0.0691950i
$77$	−11.8305	−	0.382748i	−1.34822	−	0.0436182i
$78$	−4.18349	−	1.68816i	−0.473687	−	0.191147i
$79$	5.76343	−	9.98255i	0.648436	−	1.12312i	−0.335060	−	0.942197i	$-0.608757\pi$
$79$	5.76343	−	9.98255i	0.648436	−	1.12312i	0.983496	−	0.180928i	$-0.0579101\pi$
$80$	7.92701	−	7.92701i	0.886267	−	0.886267i
$81$	1.00000			0.111111
$82$	4.42323			0.488464
$83$	−5.00708	+	5.00708i	−0.549598	+	0.549598i	−0.926325	−	0.376727i	$-0.877050\pi$
$83$	−5.00708	+	5.00708i	−0.549598	+	0.549598i	0.376727	+	0.926325i	$0.377050\pi$
$84$	−1.11946	+	0.261474i	−0.122143	+	0.0285291i
$85$	4.42956	+	1.18690i	0.480454	+	0.128737i
$86$	3.26930	+	12.2012i	0.352538	+	1.31569i
$87$	6.86645	+	3.96435i	0.736161	+	0.425023i
$88$		−	13.6276i		−	1.45271i
$89$	1.36380	−	5.08976i	0.144562	−	0.539514i	−0.855212	−	0.518278i	$-0.826573\pi$
$89$	1.36380	−	5.08976i	0.144562	−	0.539514i	0.999774	−	0.0212358i	$-0.00676006\pi$
$90$	−4.76737			−0.502524
$91$	−5.63018	−	7.70072i	−0.590204	−	0.807254i
$92$	1.46924			0.153179
$93$	−1.38355	+	5.16347i	−0.143467	+	0.535426i
$94$		−	6.46162i		−	0.666465i
$95$	−17.7001	−	10.2191i	−1.81599	−	1.04846i
$96$	−0.623965	−	2.32867i	−0.0636832	−	0.237669i
$97$	2.69756	+	0.722808i	0.273895	+	0.0733901i	0.393152	−	0.919473i	$-0.371385\pi$
$97$	2.69756	+	0.722808i	0.273895	+	0.0733901i	−0.119257	+	0.992863i	$0.538051\pi$
$98$	8.29574	+	2.80893i	0.837996	+	0.283744i
$99$	−3.16350	+	3.16350i	−0.317944	+	0.317944i
$100$	−4.13557			−0.413557
$101$	−6.67768			−0.664454			−0.332227	−	0.943199i	$-0.607800\pi$
$101$	−6.67768			−0.664454			−0.332227	+	0.943199i	$0.607800\pi$
$102$	−1.06482	+	1.06482i	−0.105433	+	0.105433i
$103$	−1.06760	+	1.84913i	−0.105193	+	0.182200i	−0.913817	−	0.406126i	$-0.866880\pi$
$103$	−1.06760	+	1.84913i	−0.105193	+	0.182200i	0.808624	+	0.588326i	$0.200213\pi$
$104$	8.65158	−	6.76531i	0.848357	−	0.663393i
$105$	−8.56280	−	5.32014i	−0.835644	−	0.519192i
$106$	−2.77310	+	0.743050i	−0.269347	+	0.0721714i
$107$	8.96843	+	15.5338i	0.867011	+	1.50171i	0.865036	+	0.501709i	$0.167295\pi$
$107$	8.96843	+	15.5338i	0.867011	+	1.50171i	0.00197496	+	0.999998i	$0.499371\pi$
$108$	−0.217252	+	0.376291i	−0.0209051	+	0.0362086i
$109$	0.0524960	−	0.195918i	0.00502820	−	0.0187655i	−0.963366	−	0.268190i	$-0.913575\pi$
$109$	0.0524960	−	0.195918i	0.00502820	−	0.0187655i	0.968394	+	0.249424i	$0.0802413\pi$
$110$	15.0816	−	15.0816i	1.43797	−	1.43797i
$111$	−1.80904	+	6.75142i	−0.171706	+	0.640817i
$112$	−2.25681	+	7.45001i	−0.213249	+	0.703959i
$113$	2.98143	+	5.16398i	0.280469	+	0.485787i	0.971500	−	0.237038i	$-0.0761767\pi$
$113$	2.98143	+	5.16398i	0.280469	+	0.485787i	−0.691031	+	0.722825i	$0.742843\pi$
$114$	5.81231	−	3.35574i	0.544373	−	0.314294i
$115$	9.11041	+	9.11041i	0.849550	+	0.849550i
$116$	−2.98350	+	1.72252i	−0.277011	+	0.159932i
$117$	−3.57886	−	0.437877i	−0.330866	−	0.0404818i
$118$			7.62437i			0.701881i
$119$	−3.10084	+	0.724268i	−0.284253	+	0.0663936i
$120$	5.80308	−	10.0512i	0.529747	−	0.917548i
$121$		−	9.01548i		−	0.819589i
$122$	6.53412	+	1.75081i	0.591571	+	0.158511i
$123$	3.41474	−	0.914977i	0.307897	−	0.0825007i
$124$	−1.64239	−	1.64239i	−0.147491	−	0.147491i
$125$	−12.1724	−	12.1724i	−1.08873	−	1.08873i
$126$	2.91888	−	1.56161i	0.260034	−	0.139119i
$127$	11.1060	+	6.41205i	0.985497	+	0.568977i	0.903925	−	0.427690i	$-0.140673\pi$
$127$	11.1060	+	6.41205i	0.985497	+	0.568977i	0.0815719	+	0.996667i	$0.474006\pi$
$128$	−6.09986	−	1.63445i	−0.539157	−	0.144467i
$129$	5.04781	+	8.74306i	0.444435	+	0.769784i
$130$	17.0617	+	2.08752i	1.49641	+	0.183088i
$131$	4.86044	+	2.80617i	0.424658	+	0.245177i	0.697068	−	0.717005i	$-0.254487\pi$
$131$	4.86044	+	2.80617i	0.424658	+	0.245177i	−0.272410	+	0.962181i	$0.587821\pi$
$132$	−0.503121	−	1.87767i	−0.0437911	−	0.163430i
$133$	14.1845	+	0.458905i	1.22995	+	0.0397921i
$134$	−5.88326	+	3.39670i	−0.508236	+	0.293430i
$135$	−3.68041	+	0.986163i	−0.316759	+	0.0848754i
$136$	−0.948850	−	3.54116i	−0.0813632	−	0.303652i
$137$	−2.52492	−	9.42312i	−0.215718	−	0.805072i	−0.985912	−	0.167262i	$-0.946507\pi$
$137$	−2.52492	−	9.42312i	−0.215718	−	0.805072i	0.770194	−	0.637810i	$-0.220159\pi$
$138$	−4.08668	+	1.09502i	−0.347881	+	0.0932145i
$139$	−12.9533	+	7.47860i	−1.09869	+	0.634327i	−0.935875	−	0.352331i	$-0.885389\pi$
$139$	−12.9533	+	7.47860i	−1.09869	+	0.634327i	−0.162810	+	0.986657i	$0.552056\pi$
$140$	3.86220	−	2.06630i	0.326416	−	0.174634i
$141$	−1.33663	−	4.98837i	−0.112565	−	0.420097i
$142$	−12.7822	−	7.37982i	−1.07266	−	0.619301i
$143$	12.7070	−	9.93651i	1.06261	−	0.830933i
$144$	1.47110	+	2.54802i	0.122592	+	0.212335i
$145$	−29.1808	−	7.81898i	−2.42334	−	0.649331i
$146$	−8.04137	−	4.64268i	−0.665508	−	0.384231i
$147$	6.98536	+	0.452462i	0.576143	+	0.0373184i
$148$	−2.14748	−	2.14748i	−0.176522	−	0.176522i
$149$	−11.9474	−	11.9474i	−0.978769	−	0.978769i	0.0210106	−	0.999779i	$-0.493312\pi$
$149$	−11.9474	−	11.9474i	−0.978769	−	0.978769i	−0.999779	+	0.0210106i	$0.993312\pi$
$150$	11.5030	−	3.08223i	0.939219	−	0.251663i
$151$	−8.51059	−	2.28041i	−0.692582	−	0.185577i	−0.104677	−	0.994506i	$-0.533381\pi$
$151$	−8.51059	−	2.28041i	−0.692582	−	0.185577i	−0.587906	+	0.808929i	$0.700047\pi$
$152$			16.3391i			1.32528i
$153$	−0.601776	+	1.04231i	−0.0486507	+	0.0842655i
$154$	−4.29371	+	14.1740i	−0.345997	+	1.14218i
$155$		−	20.3681i		−	1.63600i
$156$	0.942283	−	1.25156i	0.0754431	−	0.100205i
$157$	11.2840	−	6.51483i	0.900562	−	0.519940i	0.0231797	−	0.999731i	$-0.492621\pi$
$157$	11.2840	−	6.51483i	0.900562	−	0.519940i	0.877383	+	0.479791i	$0.159288\pi$
$158$	−10.1982	−	10.1982i	−0.811322	−	0.811322i
$159$	−1.98713	+	1.14727i	−0.157590	+	0.0909844i
$160$	4.59290	+	7.95513i	0.363100	+	0.628908i
$161$	−8.56219	−	2.59373i	−0.674795	−	0.204414i
$162$	0.323834	−	1.20856i	0.0254428	−	0.0949538i
$163$	1.98678	−	1.98678i	0.155617	−	0.155617i	−0.625004	−	0.780621i	$-0.714903\pi$
$163$	1.98678	−	1.98678i	0.155617	−	0.155617i	0.780621	+	0.625004i	$0.214903\pi$
$164$	−0.397560	+	1.48372i	−0.0310443	+	0.115859i
$165$	8.52325	−	14.7627i	0.663534	−	1.14928i
$166$	4.42991	+	7.67284i	0.343828	+	0.595528i
$167$	−6.46991	+	1.73361i	−0.500657	+	0.134151i	−0.500305	−	0.865849i	$-0.666779\pi$
$167$	−6.46991	+	1.73361i	−0.500657	+	0.134151i	−0.000351905		1.00000i	$0.500112\pi$
$168$	−0.260595	+	8.05487i	−0.0201054	+	0.621446i
$169$	12.6165	+	3.13421i	0.970502	+	0.241093i
$170$	2.86889	−	4.96906i	0.220033	−	0.381109i
$171$	3.79295	−	3.79295i	0.290054	−	0.290054i
$172$	−4.38658			−0.334474
$173$	9.78650			0.744054			0.372027	−	0.928222i	$-0.378663\pi$
$173$	9.78650			0.744054			0.372027	+	0.928222i	$0.378663\pi$
$174$	7.01476	−	7.01476i	0.531788	−	0.531788i
$175$	24.1005	+	7.30072i	1.82183	+	0.551883i
$176$	−12.7145	−	3.40684i	−0.958391	−	0.256800i
$177$	1.57716	+	5.88602i	0.118546	+	0.442421i
$178$	−5.70966	−	3.29648i	−0.427957	−	0.247081i
$179$			11.5463i			0.863013i	0.902110	+	0.431507i	$0.142018\pi$
$179$			11.5463i			0.863013i	−0.902110	+	0.431507i	$0.857982\pi$
$180$	0.428491	−	1.59915i	0.0319378	−	0.119194i
$181$	16.9576			1.26045			0.630226	−	0.776412i	$-0.282962\pi$
$181$	16.9576			1.26045			0.630226	+	0.776412i	$0.282962\pi$
$182$	−11.1301	+	4.31069i	−0.825015	+	0.319529i
$183$	5.40651			0.399661
$184$	2.66583	−	9.94903i	0.196528	−	0.733452i
$185$		−	26.6320i		−	1.95802i
$186$	5.79234	+	3.34421i	0.424715	+	0.245209i
$187$	−1.39362	−	5.20106i	−0.101911	−	0.380339i
$188$	2.16746	+	0.580770i	0.158079	+	0.0423570i
$189$	1.93034	−	1.80936i	0.140412	−	0.131611i
$190$	−18.0824	+	18.0824i	−1.31183	+	1.31183i
$191$	−1.97758			−0.143093			−0.0715463	−	0.997437i	$-0.522793\pi$
$191$	−1.97758			−0.143093			−0.0715463	+	0.997437i	$0.522793\pi$
$192$	−8.90081			−0.642361
$193$	2.27776	−	2.27776i	0.163957	−	0.163957i	−0.620360	−	0.784317i	$-0.713014\pi$
$193$	2.27776	−	2.27776i	0.163957	−	0.163957i	0.784317	+	0.620360i	$0.213014\pi$
$194$	1.74712	−	3.02610i	0.125436	−	0.217261i
$195$	13.6035	−	1.91777i	0.974167	−	0.137335i
$196$	−1.68784	+	2.53023i	−0.120560	+	0.180731i
$197$	5.66631	−	1.51828i	0.403708	−	0.108173i	−0.0512506	−	0.998686i	$-0.516321\pi$
$197$	5.66631	−	1.51828i	0.403708	−	0.108173i	0.454959	+	0.890513i	$0.349654\pi$
$198$	2.79885	+	4.84774i	0.198905	+	0.344514i
$199$	−0.945648	+	1.63791i	−0.0670352	+	0.116108i	−0.897595	−	0.440821i	$-0.854687\pi$
$199$	−0.945648	+	1.63791i	−0.0670352	+	0.116108i	0.830560	+	0.556930i	$0.188021\pi$
$200$	−7.50369	+	28.0042i	−0.530591	+	1.98019i
$201$	−3.83925	+	3.83925i	−0.270800	+	0.270800i
$202$	−2.16246	+	8.07041i	−0.152150	+	0.567832i
$203$	20.4275	−	4.77130i	1.43373	−	0.334879i
$204$	−0.261474	−	0.452886i	−0.0183068	−	0.0317083i
$205$	−11.6653	+	6.73498i	−0.814742	+	0.470391i
$206$	1.88907	+	1.88907i	0.131618	+	0.131618i
$207$	−2.92841	+	1.69072i	−0.203538	+	0.117513i
$208$	−4.14915	−	9.76318i	−0.287691	−	0.676955i
$209$			23.9980i			1.65998i
$210$	−9.20266	+	8.62586i	−0.635044	+	0.595241i
$211$	0.967437	−	1.67565i	0.0666011	−	0.115357i	−0.830802	−	0.556568i	$-0.812118\pi$
$211$	0.967437	−	1.67565i	0.0666011	−	0.115357i	0.897403	+	0.441212i	$0.145451\pi$
$212$		−	0.996985i		−	0.0684732i
$213$	−11.3945	−	3.05313i	−0.780735	−	0.209197i
$214$	21.6779	−	5.80857i	1.48187	−	0.397065i
$215$	−27.2001	−	27.2001i	−1.85503	−	1.85503i
$216$	2.15388	+	2.15388i	0.146553	+	0.146553i
$217$	6.67183	+	12.4706i	0.452913	+	0.846559i
$218$	−0.219779	−	0.126890i	−0.0148853	−	0.00859405i
$219$	−7.16831	−	1.92074i	−0.484390	−	0.129792i
$220$	3.70338	+	6.41445i	0.249682	+	0.432462i
$221$	2.61008	−	3.46677i	0.175573	−	0.233200i
$222$	7.57370	+	4.37268i	0.508313	+	0.293475i
$223$	−3.88477	−	14.4982i	−0.260144	−	0.970869i	−0.965156	−	0.261674i	$-0.915725\pi$
$223$	−3.88477	−	14.4982i	−0.260144	−	0.970869i	0.705013	−	0.709195i	$-0.250941\pi$
$224$	−5.41786	−	3.36616i	−0.361996	−	0.224911i
$225$	8.24277	−	4.75896i	0.549518	−	0.317264i
$226$	7.20649	−	1.93097i	0.479369	−	0.128446i
$227$	6.31931	+	23.5840i	0.419428	+	1.56533i	0.775799	+	0.630981i	$0.217347\pi$
$227$	6.31931	+	23.5840i	0.419428	+	1.56533i	−0.356371	+	0.934345i	$0.615986\pi$
$228$	0.603228	+	2.25128i	0.0399498	+	0.149095i
$229$	−4.48718	+	1.20234i	−0.296521	+	0.0794526i	−0.404013	−	0.914753i	$-0.632385\pi$
$229$	−4.48718	+	1.20234i	−0.296521	+	0.0794526i	0.107491	+	0.994206i	$0.465718\pi$
$230$	13.9608	−	8.06026i	0.920546	−	0.531478i
$231$	−0.382748	+	11.8305i	−0.0251830	+	0.778393i
$232$	6.25078	+	23.3282i	0.410384	+	1.53157i
$233$	15.1770	+	8.76243i	0.994277	+	0.574046i	0.906550	−	0.422098i	$-0.138706\pi$
$233$	15.1770	+	8.76243i	0.994277	+	0.574046i	0.0877270	+	0.996145i	$0.472040\pi$
$234$	−1.68816	+	4.18349i	−0.110358	+	0.273483i
$235$	9.83869	+	17.0411i	0.641806	+	1.11164i
$236$	−2.55750	−	0.685279i	−0.166479	−	0.0446079i
$237$	−9.98255	−	5.76343i	−0.648436	−	0.374375i
$238$	−0.128831	+	3.98210i	−0.00835088	+	0.258122i
$239$	1.79773	+	1.79773i	0.116285	+	0.116285i	0.762855	−	0.646570i	$-0.223797\pi$
$239$	1.79773	+	1.79773i	0.116285	+	0.116285i	−0.646570	+	0.762855i	$0.723797\pi$
$240$	−7.92701	−	7.92701i	−0.511686	−	0.511686i
$241$	−4.21647	+	1.12980i	−0.271607	+	0.0727768i	−0.392052	−	0.919943i	$-0.628235\pi$
$241$	−4.21647	+	1.12980i	−0.271607	+	0.0727768i	0.120445	+	0.992720i	$0.461568\pi$
$242$	−10.8958	−	2.91952i	−0.700408	−	0.187674i
$243$		−	1.00000i		−	0.0641500i
$244$	−1.17457	+	2.03442i	−0.0751944	+	0.130240i
$245$	−26.1552	+	5.22346i	−1.67099	+	0.333715i
$246$		−	4.42323i		−	0.282015i
$247$	−15.2353	+	11.9136i	−0.969399	+	0.758045i
$248$	−14.1015	+	8.14149i	−0.895445	+	0.516985i
$249$	5.00708	+	5.00708i	0.317311	+	0.317311i
$250$	−18.6530	+	10.7693i	−1.17972	+	0.681111i
$251$	−10.4875	−	18.1649i	−0.661964	−	1.14656i	−0.980099	−	0.198510i	$-0.936390\pi$
$251$	−10.4875	−	18.1649i	−0.661964	−	1.14656i	0.318135	−	0.948046i	$-0.396944\pi$
$252$	0.261474	+	1.11946i	0.0164713	+	0.0705192i
$253$	3.91543	−	14.6126i	0.246161	−	0.918686i
$254$	11.3459	−	11.3459i	0.711903	−	0.711903i
$255$	1.18690	−	4.42956i	0.0743264	−	0.277390i
$256$	4.95013	−	8.57387i	0.309383	−	0.535867i
$257$	3.70449	+	6.41636i	0.231080	+	0.400242i	0.958126	−	0.286347i	$-0.0924409\pi$
$257$	3.70449	+	6.41636i	0.231080	+	0.400242i	−0.727047	+	0.686588i	$0.759108\pi$
$258$	12.2012	−	3.26930i	0.759614	−	0.203538i
$259$	8.72366	+	16.3058i	0.542062	+	1.01319i
$260$	−2.23374	+	5.53551i	−0.138531	+	0.343298i
$261$	3.96435	−	6.86645i	0.245387	−	0.425023i
$262$	4.96542	−	4.96542i	0.306764	−	0.306764i
$263$	22.7469			1.40263			0.701317	−	0.712850i	$-0.252596\pi$
$263$	22.7469			1.40263			0.701317	+	0.712850i	$0.252596\pi$
$264$	−13.6276			−0.838721
$265$	6.18206	−	6.18206i	0.379761	−	0.379761i
$266$	5.14804	−	16.9943i	0.315647	−	1.04199i
$267$	−5.08976	−	1.36380i	−0.311488	−	0.0834631i
$268$	−0.610591	−	2.27876i	−0.0372978	−	0.139197i
$269$	−4.45808	−	2.57388i	−0.271814	−	0.156932i	0.357898	−	0.933761i	$-0.383494\pi$
$269$	−4.45808	−	2.57388i	−0.271814	−	0.156932i	−0.629712	+	0.776829i	$0.716827\pi$
$270$			4.76737i			0.290133i
$271$	4.15851	−	15.5198i	0.252612	−	0.942759i	−0.716792	−	0.697287i	$-0.754390\pi$
$271$	4.15851	−	15.5198i	0.252612	−	0.942759i	0.969404	−	0.245472i	$-0.0789430\pi$
$272$	−3.54109			−0.214710
$273$	−7.70072	+	5.63018i	−0.466069	+	0.340754i
$274$	−12.2061			−0.737398
$275$	−11.0210	+	41.1310i	−0.664592	+	2.48029i
$276$		−	1.46924i		−	0.0884380i
$277$	−6.82673	−	3.94142i	−0.410179	−	0.236817i	0.280688	−	0.959799i	$-0.409437\pi$
$277$	−6.82673	−	3.94142i	−0.410179	−	0.236817i	−0.690867	+	0.722982i	$0.742771\pi$
$278$	4.84365	+	18.0767i	0.290503	+	1.08417i
$279$	5.16347	+	1.38355i	0.309129	+	0.0828308i
$280$	−6.98431	−	29.9022i	−0.417392	−	1.78700i
$281$	12.0099	−	12.0099i	0.716448	−	0.716448i	−0.251428	−	0.967876i	$-0.580900\pi$
$281$	12.0099	−	12.0099i	0.716448	−	0.716448i	0.967876	+	0.251428i	$0.0809001\pi$
$282$	−6.46162			−0.384784
$283$	−12.3954			−0.736831			−0.368416	−	0.929661i	$-0.620100\pi$
$283$	−12.3954			−0.736831			−0.368416	+	0.929661i	$0.620100\pi$
$284$	3.62433	−	3.62433i	0.215064	−	0.215064i
$285$	−10.2191	+	17.7001i	−0.605330	+	1.04846i
$286$	−7.89397	−	18.5750i	−0.466780	−	1.09836i
$287$	4.93611	−	7.94470i	0.291369	−	0.468961i
$288$	−2.32867	+	0.623965i	−0.137218	+	0.0367675i
$289$	7.77573	+	13.4680i	0.457396	+	0.792233i
$290$	−18.8995	+	32.7349i	−1.10982	+	1.92226i
$291$	0.722808	−	2.69756i	0.0423718	−	0.158134i
$292$	2.28009	−	2.28009i	0.133432	−	0.133432i
$293$	2.23957	−	8.35820i	0.130837	−	0.488291i	−0.869143	−	0.494561i	$-0.835329\pi$
$293$	2.23957	−	8.35820i	0.130837	−	0.488291i	0.999980	+	0.00626941i	$0.00199563\pi$
$294$	2.80893	−	8.29574i	0.163820	−	0.483817i
$295$	−11.6092	−	20.1076i	−0.675911	−	1.17071i
$296$	−18.4382	+	10.6453i	−1.07170	+	0.618745i
$297$	3.16350	+	3.16350i	0.183565	+	0.183565i
$298$	−18.3082	+	10.5702i	−1.06056	+	0.612317i
$299$	11.2207	−	4.76856i	0.648909	−	0.275773i
$300$			4.13557i			0.238767i
$301$	25.5633	+	7.74384i	1.47345	+	0.446348i
$302$	−5.51204	+	9.54713i	−0.317182	+	0.549375i
$303$			6.67768i			0.383623i
$304$	15.2443	+	4.08471i	0.874322	+	0.234274i
$305$	−19.8982	+	5.33170i	−1.13937	+	0.305292i
$306$	1.06482	+	1.06482i	0.0608717	+	0.0608717i
$307$	7.24945	+	7.24945i	0.413748	+	0.413748i	0.883042	−	0.469294i	$-0.155492\pi$
$307$	7.24945	+	7.24945i	0.413748	+	0.413748i	−0.469294	+	0.883042i	$0.655492\pi$
$308$	−4.36858	−	2.71423i	−0.248923	−	0.154658i
$309$	1.84913	+	1.06760i	0.105193	+	0.0607335i
$310$	−24.6161	−	6.59587i	−1.39810	−	0.374620i
$311$	−0.447316	−	0.774775i	−0.0253650	−	0.0439334i	0.853064	−	0.521806i	$-0.174741\pi$
$311$	−0.447316	−	0.774775i	−0.0253650	−	0.0439334i	−0.878429	+	0.477872i	$0.841408\pi$
$312$	−6.76531	−	8.65158i	−0.383010	−	0.489799i
$313$	−28.3762	−	16.3830i	−1.60392	−	0.926022i	−0.990693	−	0.136113i	$-0.956539\pi$
$313$	−28.3762	−	16.3830i	−1.60392	−	0.926022i	−0.613224	−	0.789909i	$-0.710128\pi$
$314$	−4.21944	−	15.7472i	−0.238117	−	0.888665i
$315$	−5.32014	+	8.56280i	−0.299756	+	0.482459i
$316$	4.33745	−	2.50423i	0.244001	−	0.140874i
$317$	22.1717	−	5.94088i	1.24529	−	0.333673i	0.424772	−	0.905300i	$-0.360354\pi$
$317$	22.1717	−	5.94088i	1.24529	−	0.333673i	0.820514	+	0.571627i	$0.193688\pi$
$318$	0.743050	+	2.77310i	0.0416682	+	0.155508i
$319$	9.18081	+	34.2632i	0.514027	+	1.91837i
$320$	32.7586	−	8.77765i	1.83126	−	0.490685i
$321$	15.5338	−	8.96843i	0.867011	−	0.500569i
$322$	−5.90741	+	9.50802i	−0.329207	+	0.529861i
$323$	1.67091	+	6.23592i	0.0929720	+	0.346976i
$324$	0.376291	+	0.217252i	0.0209051	+	0.0120695i
$325$	−31.5836	+	13.4224i	−1.75194	+	0.744539i
$326$	−1.75777	−	3.04455i	−0.0973538	−	0.168622i
$327$	−0.195918	−	0.0524960i	−0.0108343	−	0.00290304i
$328$	9.32569	+	5.38419i	0.514925	+	0.297292i
$329$	−11.6059	−	7.21084i	−0.639854	−	0.397546i
$330$	−15.0816	−	15.0816i	−0.830213	−	0.830213i
$331$	11.8814	+	11.8814i	0.653059	+	0.653059i	0.953728	−	0.300670i	$-0.0972102\pi$
$331$	11.8814	+	11.8814i	0.653059	+	0.653059i	−0.300670	+	0.953728i	$0.597210\pi$
$332$	−2.97191	+	0.796322i	−0.163105	+	0.0437038i
$333$	6.75142	+	1.80904i	0.369976	+	0.0991347i
$334$			8.38070i			0.458572i
$335$	10.3439	−	17.9161i	0.565147	−	0.978863i
$336$	7.45001	+	2.25681i	0.406431	+	0.123119i
$337$			26.5544i			1.44651i	0.690582	+	0.723254i	$0.257355\pi$
$337$			26.5544i			1.44651i	−0.690582	+	0.723254i	$0.742645\pi$
$338$	7.87355	−	14.2329i	0.428265	−	0.774169i
$339$	5.16398	−	2.98143i	0.280469	−	0.161929i
$340$	1.40895	+	1.40895i	0.0764110	+	0.0764110i
$341$	−20.7115	+	11.9578i	−1.12159	+	0.647550i
$342$	−3.35574	−	5.81231i	−0.181458	−	0.314294i
$343$	14.3028	−	11.7656i	0.772280	−	0.635283i
$344$	−7.95913	+	29.7039i	−0.429128	+	1.60153i
$345$	9.11041	−	9.11041i	0.490488	−	0.490488i
$346$	3.16920	−	11.8276i	0.170377	−	0.635856i
$347$	9.40270	−	16.2860i	0.504763	−	0.874276i	−0.495221	−	0.868767i	$-0.664913\pi$
$347$	9.40270	−	16.2860i	0.504763	−	0.874276i	0.999985	−	0.00550914i	$-0.00175362\pi$
$348$	1.72252	+	2.98350i	0.0923369	+	0.159932i
$349$	−28.4085	+	7.61204i	−1.52067	+	0.407463i	−0.919963	−	0.392005i	$-0.871782\pi$
$349$	−28.4085	+	7.61204i	−1.52067	+	0.407463i	−0.600709	+	0.799468i	$0.705115\pi$
$350$	16.6280	−	26.7628i	0.888802	−	1.43053i
$351$	−0.437877	+	3.57886i	−0.0233722	+	0.191026i
$352$	5.39284	−	9.34067i	0.287439	−	0.497859i
$353$	−5.59741	+	5.59741i	−0.297920	+	0.297920i	−0.840199	−	0.542279i	$-0.817562\pi$
$353$	−5.59741	+	5.59741i	−0.297920	+	0.297920i	0.542279	+	0.840199i	$0.317562\pi$
$354$	7.62437			0.405231
$355$	44.9471			2.38555
$356$	1.61894	−	1.61894i	0.0858039	−	0.0858039i
$357$	0.724268	+	3.10084i	0.0383323	+	0.164114i
$358$	13.9545	+	3.73909i	0.737517	+	0.197617i
$359$	6.59681	+	24.6196i	0.348166	+	1.29937i	0.888870	+	0.458160i	$0.151491\pi$
$359$	6.59681	+	24.6196i	0.348166	+	1.29937i	−0.540703	+	0.841213i	$0.681842\pi$
$360$	−10.0512	−	5.80308i	−0.529747	−	0.305849i
$361$		−	9.77296i		−	0.514366i
$362$	5.49146	−	20.4944i	0.288625	−	1.07716i
$363$	−9.01548			−0.473190
$364$	−0.445594	−	4.12088i	−0.0233555	−	0.215993i
$365$	28.2765			1.48006
$366$	1.75081	−	6.53412i	0.0915164	−	0.341544i
$367$		−	33.4625i		−	1.74673i	−0.487068	−	0.873364i	$-0.661934\pi$
$367$		−	33.4625i		−	1.74673i	0.487068	−	0.873364i	$-0.338066\pi$
$368$	−8.61595	−	4.97442i	−0.449138	−	0.259310i
$369$	−0.914977	−	3.41474i	−0.0476318	−	0.177764i
$370$	−32.1865	−	8.62434i	−1.67330	−	0.448358i
$371$	−1.76003	+	5.81005i	−0.0913760	+	0.301643i
$372$	−1.64239	+	1.64239i	−0.0851538	+	0.0851538i
$373$	1.88815			0.0977649			0.0488825	−	0.998805i	$-0.484434\pi$
$373$	1.88815			0.0977649			0.0488825	+	0.998805i	$0.484434\pi$
$374$	−6.73711			−0.348368
$375$	−12.1724	+	12.1724i	−0.628581	+	0.628581i
$376$	7.86541	−	13.6233i	0.405628	−	0.702568i
$377$	−17.1945	+	22.8382i	−0.885563	+	1.17623i
$378$	−1.56161	−	2.91888i	−0.0803207	−	0.150131i
$379$	−1.67371	+	0.448469i	−0.0859726	+	0.0230363i	−0.301549	−	0.953451i	$-0.597504\pi$
$379$	−1.67371	+	0.448469i	−0.0859726	+	0.0230363i	0.215576	+	0.976487i	$0.430837\pi$
$380$	−4.44025	−	7.69074i	−0.227780	−	0.394527i
$381$	6.41205	−	11.1060i	0.328499	−	0.568977i
$382$	−0.640407	+	2.39003i	−0.0327661	+	0.122285i
$383$	3.76832	−	3.76832i	0.192552	−	0.192552i	−0.604246	−	0.796798i	$-0.706526\pi$
$383$	3.76832	−	3.76832i	0.192552	−	0.192552i	0.796798	+	0.604246i	$0.206526\pi$
$384$	−1.63445	+	6.09986i	−0.0834078	+	0.311282i
$385$	−10.2582	−	43.9187i	−0.522805	−	2.23830i
$386$	−2.01520	−	3.49043i	−0.102571	−	0.177658i
$387$	8.74306	−	5.04781i	0.444435	−	0.256595i
$388$	0.858035	+	0.858035i	0.0435601	+	0.0435601i
$389$	13.5597	−	7.82869i	0.687503	−	0.396930i	−0.115173	−	0.993345i	$-0.536742\pi$
$389$	13.5597	−	7.82869i	0.687503	−	0.396930i	0.802676	+	0.596415i	$0.203409\pi$
$390$	2.08752	−	17.0617i	0.105706	−	0.863955i
$391$		−	4.06973i		−	0.205815i
$392$	14.0711	+	16.0202i	0.710697	+	0.809141i
$393$	2.80617	−	4.86044i	0.141553	−	0.245177i
$394$		−	7.33978i		−	0.369773i
$395$	42.4235	+	11.3674i	2.13456	+	0.571954i
$396$	−1.87767	+	0.503121i	−0.0943566	+	0.0252828i
$397$	14.9475	+	14.9475i	0.750192	+	0.750192i	0.974515	−	0.224323i	$-0.0720170\pi$
$397$	14.9475	+	14.9475i	0.750192	+	0.750192i	−0.224323	+	0.974515i	$0.572017\pi$
$398$	1.67329	+	1.67329i	0.0838743	+	0.0838743i
$399$	0.458905	−	14.1845i	0.0229740	−	0.710113i
$400$	24.2519	+	14.0018i	1.21259	+	0.700091i
$401$	8.10958	+	2.17296i	0.404973	+	0.108512i	0.455555	−	0.890208i	$-0.349441\pi$
$401$	8.10958	+	2.17296i	0.404973	+	0.108512i	−0.0505817	+	0.998720i	$0.516108\pi$
$402$	3.39670	+	5.88326i	0.169412	+	0.293430i
$403$	−17.8735	−	7.21249i	−0.890343	−	0.359280i
$404$	−2.51275	−	1.45074i	−0.125014	−	0.0721769i
$405$	0.986163	+	3.68041i	0.0490028	+	0.182881i
$406$	0.848707	−	26.2331i	0.0421206	−	1.30193i
$407$	−27.0810	+	15.6352i	−1.34236	+	0.775010i
$408$	−3.54116	+	0.948850i	−0.175313	+	0.0469751i
$409$	−3.52993	−	13.1739i	−0.174544	−	0.651407i	−0.996629	−	0.0820418i	$-0.973856\pi$
$409$	−3.52993	−	13.1739i	−0.174544	−	0.651407i	0.822085	−	0.569365i	$-0.192811\pi$
$410$	4.36203	+	16.2793i	0.215425	+	0.803978i
$411$	−9.42312	+	2.52492i	−0.464808	+	0.124545i
$412$	−0.803454	+	0.463874i	−0.0395833	+	0.0228535i
$413$	13.6944	+	8.50842i	0.673856	+	0.418672i
$414$	1.09502	+	4.08668i	0.0538174	+	0.200849i
$415$	−23.3659	−	13.4903i	−1.14699	−	0.662213i
$416$	8.60721	−	1.21341i	0.422003	−	0.0594925i
$417$	7.47860	+	12.9533i	0.366229	+	0.634327i
$418$	29.0031	+	7.77137i	1.41859	+	0.380110i
$419$	−14.4313	−	8.33192i	−0.705015	−	0.407041i	0.104197	−	0.994557i	$-0.466773\pi$
$419$	−14.4313	−	8.33192i	−0.705015	−	0.407041i	−0.809213	+	0.587516i	$0.800106\pi$
$420$	−2.06630	−	3.86220i	−0.100825	−	0.188456i
$421$	−23.8562	−	23.8562i	−1.16268	−	1.16268i	−0.983887	−	0.178794i	$-0.942780\pi$
$421$	−23.8562	−	23.8562i	−1.16268	−	1.16268i	−0.178794	−	0.983887i	$-0.557220\pi$
$422$	−1.71184	−	1.71184i	−0.0833312	−	0.0833312i
$423$	−4.98837	+	1.33663i	−0.242543	+	0.0649892i
$424$	−6.75112	−	1.80896i	−0.327863	−	0.0878507i
$425$			11.4553i			0.555665i
$426$	−7.37982	+	12.7822i	−0.357553	+	0.619301i
$427$	10.4364	−	9.78230i	0.505054	−	0.473399i
$428$			7.79363i			0.376719i
$429$	−9.93651	−	12.7070i	−0.479739	−	0.613498i
$430$	−41.6814	+	24.0648i	−2.01005	+	1.16051i
$431$	6.36851	+	6.36851i	0.306760	+	0.306760i	0.843652	−	0.536891i	$-0.180401\pi$
$431$	6.36851	+	6.36851i	0.306760	+	0.306760i	−0.536891	+	0.843652i	$0.680401\pi$
$432$	2.54802	−	1.47110i	0.122592	−	0.0707783i
$433$	−7.92993	−	13.7350i	−0.381088	−	0.660064i	0.610130	−	0.792301i	$-0.291117\pi$
$433$	−7.92993	−	13.7350i	−0.381088	−	0.660064i	−0.991218	+	0.132238i	$0.957784\pi$
$434$	17.2321	−	4.02493i	0.827166	−	0.193203i
$435$	−7.81898	+	29.1808i	−0.374892	+	1.39911i
$436$	0.0623172	−	0.0623172i	0.00298445	−	0.00298445i
$437$	−4.69450	+	17.5201i	−0.224568	+	0.838100i
$438$	−4.64268	+	8.04137i	−0.221836	+	0.384231i
$439$	9.64300	+	16.7022i	0.460235	+	0.797151i	0.998972	−	0.0453228i	$-0.0144316\pi$
$439$	9.64300	+	16.7022i	0.460235	+	0.797151i	−0.538737	+	0.842474i	$0.681098\pi$
$440$	50.1552	−	13.4390i	2.39105	−	0.640681i
$441$	0.452462	−	6.98536i	0.0215458	−	0.332636i
$442$	−3.34458	−	4.27710i	−0.159086	−	0.203441i
$443$	14.7573	−	25.5603i	0.701139	−	1.21441i	−0.266928	−	0.963716i	$-0.586009\pi$
$443$	14.7573	−	25.5603i	0.701139	−	1.21441i	0.968067	−	0.250692i	$-0.0806581\pi$
$444$	−2.14748	+	2.14748i	−0.101915	+	0.101915i
$445$	20.0773			0.951757
$446$	−18.7800			−0.889258
$447$	−11.9474	+	11.9474i	−0.565092	+	0.565092i
$448$	−17.1816	+	16.1047i	−0.811756	+	0.760877i
$449$	−14.6691	−	3.93057i	−0.692276	−	0.185495i	−0.104508	−	0.994524i	$-0.533327\pi$
$449$	−14.6691	−	3.93057i	−0.692276	−	0.185495i	−0.587768	+	0.809029i	$0.699993\pi$
$450$	−3.08223	−	11.5030i	−0.145298	−	0.542258i
$451$	13.6971	+	7.90800i	0.644970	+	0.372373i
$452$			2.59088i			0.121865i
$453$	−2.28041	+	8.51059i	−0.107143	+	0.399863i
$454$	30.5492			1.43374
$455$	22.7895	−	28.3155i	1.06839	−	1.32745i
$456$	16.3391			0.765150
$457$	7.98659	−	29.8063i	0.373597	−	1.39428i	−0.481788	−	0.876288i	$-0.660012\pi$
$457$	7.98659	−	29.8063i	0.373597	−	1.39428i	0.855384	−	0.517994i	$-0.173321\pi$
$458$			5.81240i			0.271596i
$459$	1.04231	+	0.601776i	0.0486507	+	0.0280885i
$460$	1.44891	+	5.40742i	0.0675559	+	0.252122i
$461$	25.0349	+	6.70809i	1.16599	+	0.312427i	0.789357	−	0.613934i	$-0.210414\pi$
$461$	25.0349	+	6.70809i	1.16599	+	0.312427i	0.376636	+	0.926361i	$0.377081\pi$
$462$	14.1740	+	4.29371i	0.659436	+	0.199761i
$463$	12.0612	−	12.0612i	0.560529	−	0.560529i	−0.368928	−	0.929458i	$-0.620275\pi$
$463$	12.0612	−	12.0612i	0.560529	−	0.560529i	0.929458	+	0.368928i	$0.120275\pi$
$464$	23.3278			1.08297
$465$	−20.3681			−0.944546
$466$	15.5048	−	15.5048i	0.718245	−	0.718245i
$467$	11.5656	−	20.0323i	0.535193	−	0.926982i	−0.463961	−	0.885856i	$-0.653572\pi$
$467$	11.5656	−	20.0323i	0.535193	−	0.926982i	0.999154	−	0.0411263i	$-0.0130946\pi$
$468$	−1.25156	−	0.942283i	−0.0578536	−	0.0435571i
$469$	−0.464506	+	14.3576i	−0.0214489	+	0.662974i
$470$	23.7814	−	6.37220i	1.09695	−	0.293928i
$471$	−6.51483	−	11.2840i	−0.300187	−	0.519940i
$472$	−9.28078	+	16.0748i	−0.427183	+	0.739902i
$473$	−11.6899	+	43.6274i	−0.537504	+	2.00599i
$474$	−10.1982	+	10.1982i	−0.468417	+	0.468417i
$475$	13.2139	−	49.3149i	0.606295	−	2.26272i
$476$	−1.32417	−	0.401127i	−0.0606930	−	0.0183856i
$477$	1.14727	+	1.98713i	0.0525299	+	0.0909844i
$478$	2.75483	−	1.59050i	0.126003	−	0.0727479i
$479$	−20.3154	−	20.3154i	−0.928236	−	0.928236i	0.0693556	−	0.997592i	$-0.477906\pi$
$479$	−20.3154	−	20.3154i	−0.928236	−	0.928236i	−0.997592	+	0.0693556i	$0.977906\pi$
$480$	7.95513	−	4.59290i	0.363100	−	0.209636i
$481$	−23.3703	−	9.43059i	−1.06559	−	0.429998i
$482$			5.46174i			0.248776i
$483$	−2.59373	+	8.56219i	−0.118019	+	0.389593i
$484$	1.95863	−	3.39244i	0.0890285	−	0.154202i
$485$			10.6409i			0.483179i
$486$	−1.20856	−	0.323834i	−0.0548216	−	0.0146894i
$487$	16.7161	−	4.47906i	0.757478	−	0.202966i	0.140646	−	0.990060i	$-0.455082\pi$
$487$	16.7161	−	4.47906i	0.757478	−	0.202966i	0.616833	+	0.787094i	$0.288415\pi$
$488$	11.6450	+	11.6450i	0.527143	+	0.527143i
$489$	−1.98678	−	1.98678i	−0.0898455	−	0.0898455i
$490$	−2.15705	+	33.3018i	−0.0974456	+	1.50442i
$491$	−30.2502	−	17.4649i	−1.36517	−	0.788182i	−0.374865	−	0.927080i	$-0.622311\pi$
$491$	−30.2502	−	17.4649i	−1.36517	−	0.788182i	−0.990307	+	0.138898i	$0.955644\pi$
$492$	1.48372	+	0.397560i	0.0668911	+	0.0179234i
$493$	4.77130	+	8.26413i	0.214888	+	0.372198i
$494$	9.46466	+	22.2709i	0.425835	+	1.00201i
$495$	−14.7627	−	8.52325i	−0.663534	−	0.383092i
$496$	4.07067	+	15.1919i	0.182778	+	0.682139i
$497$	−27.5194	+	14.7230i	−1.23441	+	0.660418i
$498$	7.67284	−	4.42991i	0.343828	−	0.198509i
$499$	23.0606	−	6.17906i	1.03233	−	0.276613i	0.297400	−	0.954753i	$-0.403880\pi$
$499$	23.0606	−	6.17906i	1.03233	−	0.276613i	0.734933	+	0.678140i	$0.237214\pi$
$500$	−1.93589	−	7.22485i	−0.0865757	−	0.323105i
$501$	1.73361	+	6.46991i	0.0774519	+	0.289054i
$502$	−25.3496	+	6.79241i	−1.13141	+	0.303160i
$503$	−23.7508	+	13.7125i	−1.05900	+	0.611412i	−0.925155	−	0.379591i	$-0.876065\pi$
$503$	−23.7508	+	13.7125i	−1.05900	+	0.611412i	−0.133842	+	0.991003i	$0.542732\pi$
$504$	8.05487	+	0.260595i	0.358792	+	0.0116078i
$505$	−6.58528	−	24.5766i	−0.293041	−	1.09364i
$506$	−16.3923	−	9.46411i	−0.728727	−	0.420731i
$507$	3.13421	−	12.6165i	0.139195	−	0.560320i
$508$	2.78606	+	4.82559i	0.123611	+	0.214101i
$509$	−1.60605	−	0.430339i	−0.0711868	−	0.0190744i	0.223050	−	0.974807i	$-0.428399\pi$
$509$	−1.60605	−	0.430339i	−0.0711868	−	0.0190744i	−0.294237	+	0.955733i	$0.595065\pi$
$510$	−4.96906	−	2.86889i	−0.220033	−	0.127036i
$511$	−17.3126	+	9.26233i	−0.765865	+	0.409741i
$512$	−17.6899	−	17.6899i	−0.781789	−	0.781789i
$513$	−3.79295	−	3.79295i	−0.167463	−	0.167463i
$514$	8.95422	−	2.39928i	0.394954	−	0.105828i
$515$	−7.85839	−	2.10565i	−0.346282	−	0.0927860i
$516$			4.38658i			0.193108i
$517$	11.5523	−	20.0092i	0.508069	−	0.880001i
$518$	22.5316	−	5.26274i	0.989981	−	0.231232i
$519$		−	9.78650i		−	0.429580i
$520$	33.4310	+	25.1697i	1.46604	+	1.10376i
$521$	−31.3898	+	18.1229i	−1.37521	+	0.793979i	−0.991579	−	0.129507i	$-0.958661\pi$
$521$	−31.3898	+	18.1229i	−1.37521	+	0.793979i	−0.383633	+	0.923486i	$0.625327\pi$
$522$	−7.01476	−	7.01476i	−0.307028	−	0.307028i
$523$	−33.5801	+	19.3875i	−1.46835	+	0.847754i	−0.999371	−	0.0354536i	$-0.988712\pi$
$523$	−33.5801	+	19.3875i	−1.46835	+	0.847754i	−0.468982	+	0.883208i	$0.655379\pi$
$524$	1.21929	+	2.11188i	0.0532650	+	0.0922577i
$525$	7.30072	−	24.1005i	0.318630	−	1.05183i
$526$	7.36622	−	27.4911i	0.321182	−	1.19867i
$527$	−4.54933	+	4.54933i	−0.198172	+	0.198172i
$528$	−3.40684	+	12.7145i	−0.148264	+	0.553327i
$529$	−5.78296	+	10.0164i	−0.251433	+	0.435495i
$530$	−5.46945	−	9.47337i	−0.237578	−	0.411497i
$531$	5.88602	−	1.57716i	0.255432	−	0.0684427i
$532$	5.23780	+	3.25429i	0.227088	+	0.141091i
$533$	1.77934	+	12.6215i	0.0770718	+	0.546699i
$534$	−3.29648	+	5.70966i	−0.142652	+	0.247081i
$535$	−48.3263	+	48.3263i	−2.08933	+	2.08933i
$536$	−16.5386			−0.714357
$537$	11.5463			0.498261
$538$	−4.55437	+	4.55437i	−0.196353	+	0.196353i
$539$	20.6668	+	23.5296i	0.890184	+	1.01349i
$540$	−1.59915	−	0.428491i	−0.0688165	−	0.0184393i
$541$	6.82499	+	25.4712i	0.293429	+	1.09509i	0.942457	+	0.334328i	$0.108509\pi$
$541$	6.82499	+	25.4712i	0.293429	+	1.09509i	−0.649028	+	0.760765i	$0.724824\pi$
$542$	−17.4100	−	10.0517i	−0.747823	−	0.431756i
$543$		−	16.9576i		−	0.727722i
$544$	0.750975	−	2.80268i	0.0321978	−	0.120164i
$545$	0.772827			0.0331043
$546$	4.31069	+	11.1301i	0.184480	+	0.476322i
$547$	−1.40037			−0.0598755			−0.0299378	−	0.999552i	$-0.509531\pi$
$547$	−1.40037			−0.0598755			−0.0299378	+	0.999552i	$0.509531\pi$
$548$	1.09709	−	4.09438i	0.0468652	−	0.174903i
$549$		−	5.40651i		−	0.230744i
$550$	46.1405	+	26.6392i	1.96744	+	1.13590i
$551$	−11.0075	−	41.0807i	−0.468937	−	1.75010i
$552$	−9.94903	−	2.66583i	−0.423459	−	0.113465i
$553$	−29.6979	+	6.93658i	−1.26288	+	0.294974i
$554$	−6.97419	+	6.97419i	−0.296305	+	0.296305i
$555$	−26.6320			−1.13047
$556$	−6.49895			−0.275617
$557$	−15.9249	+	15.9249i	−0.674760	+	0.674760i	−0.958810	−	0.284049i	$-0.908322\pi$
$557$	−15.9249	+	15.9249i	−0.674760	+	0.674760i	0.284049	+	0.958810i	$0.408322\pi$
$558$	3.34421	−	5.79234i	0.141572	−	0.245209i
$559$	−33.5006	+	14.2370i	−1.41692	+	0.602162i
$560$	−29.6447	−	0.959079i	−1.25272	−	0.0405285i
$561$	−5.20106	+	1.39362i	−0.219589	+	0.0588386i
$562$	−10.6255	−	18.4039i	−0.448209	−	0.776321i
$563$	4.63798	−	8.03322i	0.195468	−	0.338560i	−0.751586	−	0.659635i	$-0.770711\pi$
$563$	4.63798	−	8.03322i	0.195468	−	0.338560i	0.947054	+	0.321075i	$0.104044\pi$
$564$	0.580770	−	2.16746i	0.0244548	−	0.0912667i
$565$	−16.0654	+	16.0654i	−0.675876	+	0.675876i
$566$	−4.01406	+	14.9807i	−0.168723	+	0.629684i
$567$	−1.80936	−	1.93034i	−0.0759858	−	0.0810669i
$568$	−17.9662	−	31.1184i	−0.753845	−	1.30570i
$569$	19.3383	−	11.1650i	0.810705	−	0.468061i	−0.0364957	−	0.999334i	$-0.511620\pi$
$569$	19.3383	−	11.1650i	0.810705	−	0.468061i	0.847201	+	0.531273i	$0.178286\pi$
$570$	18.0824	+	18.0824i	0.757388	+	0.757388i
$571$	−9.81204	+	5.66499i	−0.410621	+	0.237072i	−0.691057	−	0.722801i	$-0.742855\pi$
$571$	−9.81204	+	5.66499i	−0.410621	+	0.237072i	0.280435	+	0.959873i	$0.409521\pi$
$572$	6.94024	−	0.978411i	0.290186	−	0.0409094i
$573$			1.97758i			0.0826146i
$574$	−8.00320	−	8.53837i	−0.334047	−	0.356385i
$575$	−16.0921	+	27.8724i	−0.671087	+	1.16236i
$576$			8.90081i			0.370867i
$577$	29.0695	+	7.78915i	1.21018	+	0.324267i	0.806832	−	0.590781i	$-0.201180\pi$
$577$	29.0695	+	7.78915i	1.21018	+	0.324267i	0.403347	+	0.915047i	$0.367847\pi$
$578$	18.7949	−	5.03609i	0.781767	−	0.209474i
$579$	−2.27776	−	2.27776i	−0.0946604	−	0.0946604i
$580$	−9.28180	−	9.28180i	−0.385406	−	0.385406i
$581$	18.7250	+	0.605800i	0.776842	+	0.0251328i
$582$	−3.02610	−	1.74712i	−0.125436	−	0.0724205i
$583$	−9.91568	−	2.65690i	−0.410665	−	0.110037i
$584$	−11.3026	−	19.5767i	−0.467706	−	0.810091i
$585$	−1.91777	−	13.6035i	−0.0792902	−	0.562436i
$586$	−9.37618	−	5.41334i	−0.387326	−	0.223623i
$587$	−8.03018	−	29.9690i	−0.331441	−	1.23695i	−0.907676	−	0.419671i	$-0.862145\pi$
$587$	−8.03018	−	29.9690i	−0.331441	−	1.23695i	0.576235	−	0.817284i	$-0.304521\pi$
$588$	2.53023	+	1.68784i	0.104345	+	0.0696053i
$589$	24.8325	−	14.3370i	1.02321	−	0.590748i
$590$	−28.0608	+	7.51887i	−1.15525	+	0.309547i
$591$	−1.51828	−	5.66631i	−0.0624539	−	0.233081i
$592$	5.32255	+	19.8640i	0.218756	+	0.816407i
$593$	3.81290	−	1.02166i	0.156577	−	0.0419547i	−0.179679	−	0.983725i	$-0.557506\pi$
$593$	3.81290	−	1.02166i	0.156577	−	0.0419547i	0.336256	+	0.941771i	$0.390839\pi$
$594$	4.84774	−	2.79885i	0.198905	−	0.114838i
$595$	−5.72353	−	10.6981i	−0.234642	−	0.438580i
$596$	−1.90010	−	7.09129i	−0.0778313	−	0.290470i
$597$	1.63791	+	0.945648i	0.0670352	+	0.0387028i
$598$	−2.12947	−	15.1051i	−0.0870805	−	0.617695i
$599$	−9.50796	−	16.4683i	−0.388485	−	0.672876i	0.603761	−	0.797165i	$-0.293668\pi$
$599$	−9.50796	−	16.4683i	−0.388485	−	0.672876i	−0.992246	+	0.124290i	$0.960335\pi$
$600$	28.0042	+	7.50369i	1.14327	+	0.306337i
$601$	17.8089	+	10.2820i	0.726440	+	0.419410i	0.817118	−	0.576470i	$-0.195570\pi$
$601$	17.8089	+	10.2820i	0.726440	+	0.419410i	−0.0906786	+	0.995880i	$0.528904\pi$
$602$	17.6372	−	28.3872i	0.718839	−	1.15698i
$603$	3.83925	+	3.83925i	0.156346	+	0.156346i
$604$	−2.70704	−	2.70704i	−0.110148	−	0.110148i
$605$	33.1806	−	8.89073i	1.34899	−	0.361459i
$606$	8.07041	+	2.16246i	0.327838	+	0.0878439i
$607$			27.5412i			1.11786i	0.829214	+	0.558931i	$0.188788\pi$
$607$			27.5412i			1.11786i	−0.829214	+	0.558931i	$0.811212\pi$
$608$	−6.46586	+	11.1992i	−0.262225	+	0.454188i
$609$	−4.77130	−	20.4275i	−0.193343	−	0.827766i
$610$			25.7748i			1.04359i
$611$	18.4380	−	2.59932i	0.745921	−	0.105157i
$612$	−0.452886	+	0.261474i	−0.0183068	+	0.0105694i
$613$	−6.76040	−	6.76040i	−0.273050	−	0.273050i	0.557277	−	0.830327i	$-0.311846\pi$
$613$	−6.76040	−	6.76040i	−0.273050	−	0.273050i	−0.830327	+	0.557277i	$0.811846\pi$
$614$	11.1090	−	6.41381i	0.448325	−	0.258840i
$615$	6.73498	+	11.6653i	0.271581	+	0.470391i
$616$	−26.3060	+	24.6572i	−1.05990	+	0.993466i
$617$	−0.316773	+	1.18221i	−0.0127528	+	0.0475941i	−0.972009	−	0.234943i	$-0.924510\pi$
$617$	−0.316773	+	1.18221i	−0.0127528	+	0.0475941i	0.959256	+	0.282538i	$0.0911762\pi$
$618$	1.88907	−	1.88907i	0.0759896	−	0.0759896i
$619$	−5.25875	+	19.6259i	−0.211367	+	0.788832i	0.776047	+	0.630675i	$0.217222\pi$
$619$	−5.25875	+	19.6259i	−0.211367	+	0.788832i	−0.987414	+	0.158157i	$0.949445\pi$
$620$	4.42500	−	7.66432i	0.177712	−	0.307806i
$621$	1.69072	+	2.92841i	0.0678461	+	0.117513i
$622$	−1.08122	+	0.289712i	−0.0433530	+	0.0116164i
$623$	−12.2926	+	6.57659i	−0.492492	+	0.263486i
$624$	−9.76318	+	4.14915i	−0.390840	+	0.166099i
$625$	9.00066	−	15.5896i	0.360027	−	0.623584i
$626$	−28.9891	+	28.9891i	−1.15864	+	1.15864i
$627$	23.9980			0.958388
$628$	5.66143			0.225916
$629$	−5.94841	+	5.94841i	−0.237179	+	0.237179i
$630$	8.62586	+	9.20266i	0.343663	+	0.366643i
$631$	0.282038	+	0.0755720i	0.0112278	+	0.00300847i	0.264429	−	0.964405i	$-0.414817\pi$
$631$	0.282038	+	0.0755720i	0.0112278	+	0.00300847i	−0.253201	+	0.967414i	$0.581483\pi$
$632$	−9.08748	−	33.9149i	−0.361481	−	1.34906i
$633$	−1.67565	−	0.967437i	−0.0666011	−	0.0384522i
$634$		−	28.7198i		−	1.14061i
$635$	−12.6466	+	47.1979i	−0.501867	+	1.87299i
$636$	−0.996985			−0.0395330
$637$	−4.67803	+	24.8015i	−0.185350	+	0.982673i
$638$	44.3824			1.75712
$639$	−3.05313	+	11.3945i	−0.120780	+	0.450758i
$640$		−	24.0618i		−	0.951127i
$641$	33.4427	+	19.3082i	1.32091	+	0.762626i	0.983873	−	0.178866i	$-0.0572430\pi$
$641$	33.4427	+	19.3082i	1.32091	+	0.762626i	0.337034	+	0.941493i	$0.390576\pi$
$642$	−5.80857	−	21.6779i	−0.229246	−	0.855557i
$643$	−20.7961	−	5.57229i	−0.820116	−	0.219749i	−0.175719	−	0.984440i	$-0.556225\pi$
$643$	−20.7961	−	5.57229i	−0.820116	−	0.219749i	−0.644397	+	0.764691i	$0.722892\pi$
$644$	−2.65838	−	2.83615i	−0.104755	−	0.111760i
$645$	−27.2001	+	27.2001i	−1.07100	+	1.07100i
$646$	8.07761			0.317809
$647$	−7.27173			−0.285881			−0.142941	−	0.989731i	$-0.545656\pi$
$647$	−7.27173			−0.285881			−0.142941	+	0.989731i	$0.545656\pi$
$648$	2.15388	−	2.15388i	0.0846124	−	0.0846124i
$649$	−13.6311	+	23.6098i	−0.535068	+	0.926765i
$650$	5.99396	+	42.5174i	0.235102	+	1.66767i
$651$	12.4706	−	6.67183i	0.488761	−	0.261489i
$652$	1.17924	−	0.315977i	0.0461827	−	0.0123746i
$653$	9.18591	+	15.9105i	0.359473	+	0.622625i	0.987873	−	0.155265i	$-0.0496233\pi$
$653$	9.18591	+	15.9105i	0.359473	+	0.622625i	−0.628400	+	0.777890i	$0.716290\pi$
$654$	−0.126890	+	0.219779i	−0.00496178	+	0.00859405i
$655$	−5.53469	+	20.6557i	−0.216258	+	0.807086i
$656$	7.35480	−	7.35480i	0.287157	−	0.287157i
$657$	−1.92074	+	7.16831i	−0.0749353	+	0.279662i
$658$	−12.4731	+	11.6914i	−0.486254	+	0.455777i
$659$	7.69490	+	13.3280i	0.299751	+	0.519183i	0.976079	−	0.217417i	$-0.0697632\pi$
$659$	7.69490	+	13.3280i	0.299751	+	0.519183i	−0.676328	+	0.736600i	$0.736430\pi$
$660$	6.41445	−	3.70338i	0.249682	−	0.144154i
$661$	22.9763	+	22.9763i	0.893676	+	0.893676i	0.994867	−	0.101191i	$-0.0322654\pi$
$661$	22.9763	+	22.9763i	0.893676	+	0.893676i	−0.101191	+	0.994867i	$0.532265\pi$
$662$	18.2070	−	10.5118i	0.707634	−	0.408553i
$663$	−3.46677	−	2.61008i	−0.134638	−	0.101367i
$664$			21.5693i			0.837050i
$665$	12.2993	+	52.6573i	0.476945	+	2.04196i
$666$	4.37268	−	7.57370i	0.169438	−	0.293475i
$667$			26.8103i			1.03810i
$668$	−2.81120	−	0.753258i	−0.108768	−	0.0291444i
$669$	−14.4982	+	3.88477i	−0.560531	+	0.150194i
$670$	−18.3031	−	18.3031i	−0.707111	−	0.707111i
$671$	17.1035	+	17.1035i	0.660273	+	0.660273i
$672$	−3.36616	+	5.41786i	−0.129852	+	0.208999i
$673$	−31.0836	−	17.9461i	−1.19818	−	0.691772i	−0.238034	−	0.971257i	$-0.576503\pi$
$673$	−31.0836	−	17.9461i	−1.19818	−	0.691772i	−0.960150	+	0.279485i	$0.909836\pi$
$674$	32.0927	+	8.59921i	1.23616	+	0.331229i
$675$	−4.75896	−	8.24277i	−0.183173	−	0.317264i
$676$	4.06657	+	3.92034i	0.156407	+	0.150782i
$677$	−5.45989	−	3.15227i	−0.209840	−	0.121151i	0.391397	−	0.920222i	$-0.371992\pi$
$677$	−5.45989	−	3.15227i	−0.209840	−	0.121151i	−0.601237	+	0.799071i	$0.705325\pi$
$678$	−1.93097	−	7.20649i	−0.0741586	−	0.276764i
$679$	−3.48557	−	6.51503i	−0.133764	−	0.250024i
$680$	12.0972	−	6.98431i	0.463906	−	0.267836i
$681$	23.5840	−	6.31931i	0.903741	−	0.242157i
$682$	7.74467	+	28.9035i	0.296559	+	1.10677i
$683$	−0.964556	−	3.59977i	−0.0369077	−	0.137741i	0.945014	−	0.327031i	$-0.106048\pi$
$683$	−0.964556	−	3.59977i	−0.0369077	−	0.137741i	−0.981921	+	0.189290i	$0.939382\pi$
$684$	2.25128	−	0.603228i	0.0860798	−	0.0230650i
$685$	32.1910	−	18.5855i	1.22995	−	0.710114i
$686$	−9.58775	−	21.0960i	−0.366062	−	0.805448i
$687$	1.20234	+	4.48718i	0.0458720	+	0.171197i
$688$	25.7238	+	14.8517i	0.980712	+	0.566215i
$689$	−3.23580	−	7.61403i	−0.123274	−	0.290071i
$690$	−8.06026	−	13.9608i	−0.306849	−	0.531478i
$691$	39.3550	+	10.5451i	1.49713	+	0.401156i	0.912139	−	0.409882i	$-0.134430\pi$
$691$	39.3550	+	10.5451i	1.49713	+	0.401156i	0.584994	+	0.811037i	$0.301097\pi$
$692$	3.68257	+	2.12613i	0.139990	+	0.0808235i
$693$	11.8305	+	0.382748i	0.449405	+	0.0145394i
$694$	−16.6377	−	16.6377i	−0.631559	−	0.631559i
$695$	−40.2984	−	40.2984i	−1.52860	−	1.52860i
$696$	23.3282	−	6.25078i	0.884255	−	0.236935i
$697$	4.10982	+	1.10122i	0.155670	+	0.0417118i
$698$			36.7985i			1.39285i
$699$	8.76243	−	15.1770i	0.331426	−	0.574046i
$700$	7.48272	+	7.98308i	0.282820	+	0.301732i
$701$		−	26.1623i		−	0.988136i	−0.869423	−	0.494068i	$-0.835509\pi$
$701$		−	26.1623i		−	0.988136i	0.869423	−	0.494068i	$-0.164491\pi$
$702$	4.18349	+	1.68816i	0.157896	+	0.0637155i
$703$	32.4694	−	18.7462i	1.22461	−	0.707027i
$704$	−28.1577	−	28.1577i	−1.06123	−	1.06123i
$705$	17.0411	−	9.83869i	0.641806	−	0.370547i
$706$	4.95220	+	8.57746i	0.186378	+	0.322817i
$707$	12.0823	+	12.8902i	0.454402	+	0.484787i
$708$	−0.685279	+	2.55750i	−0.0257544	+	0.0961166i
$709$	−33.1997	+	33.1997i	−1.24684	+	1.24684i	−0.289731	+	0.957108i	$0.593566\pi$
$709$	−33.1997	+	33.1997i	−1.24684	+	1.24684i	−0.957108	+	0.289731i	$0.906434\pi$
$710$	14.5554	−	54.3215i	0.546255	−	2.03865i
$711$	−5.76343	+	9.98255i	−0.216145	+	0.374375i
$712$	−8.02528	−	13.9002i	−0.300760	−	0.520932i
$713$	−17.4599	+	4.67837i	−0.653878	+	0.175206i
$714$	3.98210	+	0.128831i	0.149027	+	0.00482138i
$715$	49.1016	+	36.9678i	1.83629	+	1.38252i
$716$	−2.50846	+	4.34478i	−0.0937455	+	0.162372i
$717$	1.79773	−	1.79773i	0.0671373	−	0.0671373i
$718$	31.8907			1.19015
$719$	−10.5889			−0.394898			−0.197449	−	0.980313i	$-0.563266\pi$
$719$	−10.5889			−0.394898			−0.197449	+	0.980313i	$0.563266\pi$
$720$	−7.92701	+	7.92701i	−0.295422	+	0.295422i
$721$	5.50113	−	1.28491i	0.204873	−	0.0478525i
$722$	−11.8113	−	3.16482i	−0.439569	−	0.117782i
$723$	1.12980	+	4.21647i	0.0420177	+	0.156812i
$724$	6.38101	+	3.68408i	0.237148	+	0.136918i
$725$		−	75.4648i		−	2.80269i
$726$	−2.91952	+	10.8958i	−0.108353	+	0.404381i
$727$	−23.3269			−0.865148			−0.432574	−	0.901598i	$-0.642395\pi$
$727$	−23.3269			−0.865148			−0.432574	+	0.901598i	$0.642395\pi$
$728$	−28.7132	−	4.45968i	−1.06418	−	0.165287i
$729$	−1.00000			−0.0370370
$730$	9.15688	−	34.1740i	0.338911	−	1.26483i
$731$			12.1506i			0.449406i
$732$	2.03442	+	1.17457i	0.0751944	+	0.0434135i
$733$	−10.7328	−	40.0554i	−0.396426	−	1.47948i	−0.819338	−	0.573311i	$-0.805659\pi$
$733$	−10.7328	−	40.0554i	−0.396426	−	1.47948i	0.422912	−	0.906171i	$-0.361008\pi$
$734$	−40.4416	−	10.8363i	−1.49273	−	0.399975i
$735$	5.22346	+	26.1552i	0.192670	+	0.964749i
$736$	5.76434	−	5.76434i	0.212476	−	0.212476i
$737$	−24.2909			−0.894768
$738$	−4.42323			−0.162821
$739$	3.17436	−	3.17436i	0.116771	−	0.116771i	−0.646307	−	0.763078i	$-0.723687\pi$
$739$	3.17436	−	3.17436i	0.116771	−	0.116771i	0.763078	+	0.646307i	$0.223687\pi$
$740$	5.78585	−	10.0214i	0.212692	−	0.368393i
$741$	11.9136	+	15.2353i	0.437657	+	0.559683i
$742$	6.45187	+	4.00860i	0.236855	+	0.147160i
$743$	−11.0839	+	2.96992i	−0.406629	+	0.108956i	−0.456335	−	0.889808i	$-0.650838\pi$
$743$	−11.0839	+	2.96992i	−0.406629	+	0.108956i	0.0497063	+	0.998764i	$0.484171\pi$
$744$	8.14149	+	14.1015i	0.298482	+	0.516985i
$745$	32.1892	−	55.7534i	1.17932	−	2.04265i
$746$	0.611448	−	2.28196i	0.0223867	−	0.0835484i
$747$	5.00708	−	5.00708i	0.183199	−	0.183199i
$748$	0.605532	−	2.25988i	0.0221404	−	0.0826293i
$749$	13.7585	−	45.4183i	0.502723	−	1.65955i
$750$	10.7693	+	18.6530i	0.393240	+	0.681111i
$751$	−13.4143	+	7.74474i	−0.489494	+	0.282609i	−0.724365	−	0.689417i	$-0.757867\pi$
$751$	−13.4143	+	7.74474i	−0.489494	+	0.282609i	0.234871	+	0.972027i	$0.424533\pi$
$752$	−10.7442	−	10.7442i	−0.391799	−	0.391799i
$753$	−18.1649	+	10.4875i	−0.661964	+	0.382185i
$754$	22.0333	+	28.1765i	0.802404	+	1.02613i
$755$		−	33.5713i		−	1.22179i
$756$	1.11946	−	0.261474i	0.0407143	−	0.00950970i
$757$	−20.6838	+	35.8253i	−0.751765	+	1.30209i	0.195202	+	0.980763i	$0.437464\pi$
$757$	−20.6838	+	35.8253i	−0.751765	+	1.30209i	−0.946967	+	0.321331i	$0.895870\pi$
$758$			2.16801i			0.0787458i
$759$	−14.6126	−	3.91543i	−0.530403	−	0.142121i
$760$	−60.1347	+	16.1130i	−2.18131	+	0.584481i
$761$	15.5732	+	15.5732i	0.564529	+	0.564529i	0.930591	−	0.366062i	$-0.119294\pi$
$761$	15.5732	+	15.5732i	0.564529	+	0.564529i	−0.366062	+	0.930591i	$0.619294\pi$
$762$	−11.3459	−	11.3459i	−0.411017	−	0.411017i
$763$	−0.473173	+	0.253150i	−0.0171300	+	0.00916463i
$764$	−0.744145	−	0.429632i	−0.0269222	−	0.0155436i
$765$	−4.42956	−	1.18690i	−0.160151	−	0.0429124i
$766$	−3.33395	−	5.77456i	−0.120460	−	0.208643i
$767$	−21.7559	+	3.06707i	−0.785559	+	0.110745i
$768$	−8.57387	−	4.95013i	−0.309383	−	0.178622i
$769$	8.12503	+	30.3230i	0.292996	+	1.09348i	0.942796	+	0.333371i	$0.108186\pi$
$769$	8.12503	+	30.3230i	0.292996	+	1.09348i	−0.649799	+	0.760106i	$0.725147\pi$
$770$	−56.4005	−	1.82470i	−2.03253	−	0.0657576i
$771$	6.41636	−	3.70449i	0.231080	−	0.133414i
$772$	1.35195	−	0.362253i	0.0486576	−	0.0130378i
$773$	−4.35215	−	16.2425i	−0.156536	−	0.584201i	−0.998969	−	0.0453993i	$-0.985544\pi$
$773$	−4.35215	−	16.2425i	−0.156536	−	0.584201i	0.842433	−	0.538801i	$-0.181123\pi$
$774$	−3.26930	−	12.2012i	−0.117513	−	0.438563i
$775$	49.1455	−	13.1685i	1.76536	−	0.473026i
$776$	7.36706	−	4.25337i	0.264462	−	0.152687i
$777$	16.3058	−	8.72366i	0.584966	−	0.312959i
$778$	−5.07039	−	18.9229i	−0.181782	−	0.678421i
$779$	−16.4224	−	9.48148i	−0.588394	−	0.339709i
$780$	5.53551	+	2.23374i	0.198203	+	0.0799808i
$781$	−26.3878	−	45.7049i	−0.944228	−	1.63545i
$782$	−4.91853	−	1.31792i	−0.175886	−	0.0471286i
$783$	−6.86645	−	3.96435i	−0.245387	−	0.141674i
$784$	18.4645	−	9.12328i	0.659445	−	0.325832i
$785$	35.1051	+	35.1051i	1.25295	+	1.25295i
$786$	−4.96542	−	4.96542i	−0.177111	−	0.177111i
$787$	10.6185	−	2.84522i	0.378508	−	0.101421i	−0.0645484	−	0.997915i	$-0.520561\pi$
$787$	10.6185	−	2.84522i	0.378508	−	0.101421i	0.443057	+	0.896494i	$0.353894\pi$
$788$	2.46203	+	0.659699i	0.0877063	+	0.0235008i
$789$		−	22.7469i		−	0.809811i
$790$	27.4764	−	47.5905i	0.977565	−	1.69319i
$791$	4.57380	−	15.0987i	0.162626	−	0.536847i
$792$			13.6276i			0.484236i
$793$	−2.36739	+	19.3492i	−0.0840684	+	0.687109i
$794$	22.9055	−	13.2245i	0.812885	−	0.469319i
$795$	−6.18206	−	6.18206i	−0.219255	−	0.219255i
$796$	−0.711678	+	0.410887i	−0.0252247	+	0.0145635i
$797$	−2.77166	−	4.80066i	−0.0981772	−	0.170048i	0.812753	−	0.582608i	$-0.197968\pi$
$797$	−2.77166	−	4.80066i	−0.0981772	−	0.170048i	−0.910930	+	0.412560i	$0.864635\pi$
$798$	−16.9943	−	5.14804i	−0.601591	−	0.182239i
$799$	1.60870	−	6.00376i	0.0569118	−	0.212398i
$800$	−16.2253	+	16.2253i	−0.573650	+	0.573650i
$801$	−1.36380	+	5.08976i	−0.0481874	+	0.179838i
$802$	5.25232	−	9.09728i	0.185466	−	0.321236i
$803$	−16.6007	−	28.7532i	−0.585826	−	1.01468i
$804$	−2.27876	+	0.610591i	−0.0803656	+	0.0215339i
$805$	1.10226	−	34.0702i	0.0388495	−	1.20082i
$806$	−14.5048	+	19.2656i	−0.510910	+	0.678603i
$807$	−2.57388	+	4.45808i	−0.0906047	+	0.156932i
$808$	−14.3829	+	14.3829i	−0.505989	+	0.505989i
$809$	47.6802			1.67635			0.838174	−	0.545403i	$-0.183623\pi$
$809$	47.6802			1.67635			0.838174	+	0.545403i	$0.183623\pi$
$810$	4.76737			0.167508
$811$	−3.30449	+	3.30449i	−0.116036	+	0.116036i	−0.762741	−	0.646704i	$-0.776147\pi$
$811$	−3.30449	+	3.30449i	−0.116036	+	0.116036i	0.646704	+	0.762741i	$0.276147\pi$
$812$	8.72327	+	2.64252i	0.306127	+	0.0927343i
$813$	−15.5198	−	4.15851i	−0.544302	−	0.145845i
$814$	10.1264	+	37.7924i	0.354931	+	1.32462i
$815$	9.27147	+	5.35289i	0.324766	+	0.187503i
$816$			3.54109i			0.123963i
$817$	14.0159	−	52.3081i	0.490355	−	1.83003i
$818$	−17.0646			−0.596650
$819$	5.63018	+	7.70072i	0.196735	+	0.269085i
$820$	−5.85274			−0.204387
$821$	11.0324	−	41.1736i	0.385035	−	1.43697i	−0.453077	−	0.891471i	$-0.649674\pi$
$821$	11.0324	−	41.1736i	0.385035	−	1.43697i	0.838112	−	0.545498i	$-0.183660\pi$
$822$			12.2061i			0.425737i
$823$	−27.8995	−	16.1078i	−0.972517	−	0.561483i	−0.0725142	−	0.997367i	$-0.523102\pi$
$823$	−27.8995	−	16.1078i	−0.972517	−	0.561483i	−0.900003	+	0.435885i	$0.856436\pi$
$824$	1.68333	+	6.28228i	0.0586417	+	0.218854i
$825$	41.1310	+	11.0210i	1.43200	+	0.383703i
$826$	14.7177	−	13.7952i	0.512093	−	0.479997i
$827$	−16.5275	+	16.5275i	−0.574718	+	0.574718i	−0.933443	−	0.358725i	$-0.883211\pi$
$827$	−16.5275	+	16.5275i	−0.574718	+	0.574718i	0.358725	+	0.933443i	$0.383211\pi$
$828$	−1.46924			−0.0510597
$829$	24.3425			0.845451			0.422725	−	0.906258i	$-0.361073\pi$
$829$	24.3425			0.845451			0.422725	+	0.906258i	$0.361073\pi$
$830$	−23.8706	+	23.8706i	−0.828559	+	0.828559i
$831$	−3.94142	+	6.82673i	−0.136726	+	0.236817i
$832$	3.89746	−	31.8548i	0.135120	−	1.10437i
$833$	7.00861	+	4.67523i	0.242834	+	0.161987i
$834$	18.0767	−	4.84365i	0.625946	−	0.167722i
$835$	−12.7608	−	22.1023i	−0.441605	−	0.764882i
$836$	−5.21361	+	9.03023i	−0.180316	+	0.312317i
$837$	1.38355	−	5.16347i	0.0478224	−	0.178475i
$838$	−14.7430	+	14.7430i	−0.509289	+	0.509289i
$839$	−7.84399	+	29.2742i	−0.270805	+	1.01066i	0.687797	+	0.725904i	$0.258578\pi$
$839$	−7.84399	+	29.2742i	−0.270805	+	1.01066i	−0.958601	+	0.284753i	$0.908089\pi$
$840$	−29.9022	+	6.98431i	−1.03172	+	0.240982i
$841$	−16.9321	−	29.3273i	−0.583866	−	1.01129i
$842$	−36.5572	+	21.1063i	−1.25985	+	0.727372i
$843$	−12.0099	−	12.0099i	−0.413642	−	0.413642i
$844$	0.728076	−	0.420355i	0.0250614	−	0.0144692i
$845$	0.906785	+	49.5248i	0.0311943	+	1.70371i
$846$			6.46162i			0.222155i
$847$	−17.4030	+	16.3122i	−0.597973	+	0.560494i
$848$	−3.37550	+	5.84653i	−0.115915	+	0.200771i
$849$			12.3954i			0.425410i
$850$	13.8445	+	3.70962i	0.474862	+	0.127239i
$851$	−22.8295	+	6.11714i	−0.782584	+	0.209693i
$852$	−3.62433	−	3.62433i	−0.124168	−	0.124168i
$853$	29.1952	+	29.1952i	0.999624	+	0.999624i	1.00000		0.000375643i	$-0.000119571\pi$
$853$	29.1952	+	29.1952i	0.999624	+	0.999624i	−0.000375643		1.00000i	$0.500120\pi$
$854$	−8.44287	−	15.7809i	−0.288909	−	0.540013i
$855$	17.7001	+	10.2191i	0.605330	+	0.349487i
$856$	52.7748	+	14.1410i	1.80381	+	0.483328i
$857$	19.8885	+	34.4479i	0.679379	+	1.17672i	0.975168	+	0.221465i	$0.0710840\pi$
$857$	19.8885	+	34.4479i	0.679379	+	1.17672i	−0.295790	+	0.955253i	$0.595583\pi$
$858$	−18.5750	+	7.89397i	−0.634139	+	0.269496i
$859$	2.87941	+	1.66243i	0.0982443	+	0.0567214i	0.548317	−	0.836270i	$-0.315269\pi$
$859$	2.87941	+	1.66243i	0.0982443	+	0.0567214i	−0.450073	+	0.892992i	$0.648602\pi$
$860$	−4.32588	−	16.1444i	−0.147511	−	0.550520i
$861$	−7.94470	−	4.93611i	−0.270755	−	0.168222i
$862$	9.75910	−	5.63442i	0.332396	−	0.191909i
$863$	−29.0179	+	7.77531i	−0.987779	+	0.264675i	−0.716317	−	0.697775i	$-0.754174\pi$
$863$	−29.0179	+	7.77531i	−0.987779	+	0.264675i	−0.271462	+	0.962449i	$0.587507\pi$
$864$	0.623965	+	2.32867i	0.0212277	+	0.0792230i
$865$	9.65108	+	36.0183i	0.328147	+	1.22466i
$866$	−19.1677	+	5.13596i	−0.651343	+	0.174527i
$867$	13.4680	−	7.77573i	0.457396	−	0.264078i
$868$	−0.198710	+	6.14204i	−0.00674467	+	0.208474i
$869$	−13.3472	−	49.8124i	−0.452773	−	1.68977i
$870$	32.7349	+	18.8995i	1.10982	+	0.640753i
$871$	−12.0590	−	15.4213i	−0.408605	−	0.522530i
$872$	−0.308913	−	0.535053i	−0.0104611	−	0.0181192i
$873$	−2.69756	−	0.722808i	−0.0912985	−	0.0244634i
$874$	19.6539	+	11.3472i	0.664804	+	0.383825i
$875$	−1.47273	+	45.5212i	−0.0497872	+	1.53890i
$876$	−2.28009	−	2.28009i	−0.0770370	−	0.0770370i
$877$	−6.09999	−	6.09999i	−0.205982	−	0.205982i	0.596575	−	0.802557i	$-0.296528\pi$
$877$	−6.09999	−	6.09999i	−0.205982	−	0.205982i	−0.802557	+	0.596575i	$0.796528\pi$
$878$	23.3084	−	6.24546i	0.786620	−	0.210774i
$879$	−8.35820	−	2.23957i	−0.281915	−	0.0755389i
$880$		−	50.1542i		−	1.69070i
$881$	−1.81740	+	3.14783i	−0.0612299	+	0.106053i	−0.895015	−	0.446035i	$-0.852836\pi$
$881$	−1.81740	+	3.14783i	−0.0612299	+	0.106053i	0.833786	+	0.552088i	$0.186169\pi$
$882$	−8.29574	−	2.80893i	−0.279332	−	0.0945815i
$883$		−	9.84592i		−	0.331342i	−0.986181	−	0.165671i	$-0.947021\pi$
$883$		−	9.84592i		−	0.331342i	0.986181	−	0.165671i	$-0.0529789\pi$
$884$	1.73531	−	0.737470i	0.0583648	−	0.0248038i
$885$	−20.1076	+	11.6092i	−0.675911	+	0.390237i
$886$	−26.1124	−	26.1124i	−0.877264	−	0.877264i
$887$	35.4119	−	20.4450i	1.18901	−	0.686478i	0.230932	−	0.972970i	$-0.425823\pi$
$887$	35.4119	−	20.4450i	1.18901	−	0.686478i	0.958083	+	0.286492i	$0.0924893\pi$
$888$	10.6453	+	18.4382i	0.357233	+	0.618745i
$889$	−7.71723	−	33.0401i	−0.258828	−	1.10813i
$890$	6.50172	−	24.2648i	0.217938	−	0.813356i
$891$	3.16350	−	3.16350i	0.105981	−	0.105981i
$892$	1.68795	−	6.29950i	0.0565166	−	0.210923i
$893$	−13.8509	+	23.9904i	−0.463502	+	0.802809i
$894$	10.5702	+	18.3082i	0.353521	+	0.612317i
$895$	−42.4952	+	11.3866i	−1.42046	+	0.380611i
$896$	7.88176	+	14.7321i	0.263311	+	0.492166i
$897$	−4.76856	−	11.2207i	−0.159217	−	0.374648i
$898$	−9.50068	+	16.4557i	−0.317042	+	0.549133i
$899$	29.9698	−	29.9698i	0.999550	−	0.999550i
$900$	4.13557			0.137852
$901$	−2.76160			−0.0920022
$902$	13.9929	−	13.9929i	0.465913	−	0.465913i
$903$	7.74384	−	25.5633i	0.257699	−	0.850694i
$904$	17.5442	+	4.70096i	0.583512	+	0.156352i
$905$	16.7230	+	62.4110i	0.555891	+	2.07461i
$906$	9.54713	+	5.51204i	0.317182	+	0.183125i
$907$			19.1425i			0.635618i	0.948155	+	0.317809i	$0.102947\pi$
$907$			19.1425i			0.635618i	−0.948155	+	0.317809i	$0.897053\pi$
$908$	−2.74576	+	10.2473i	−0.0911214	+	0.340070i
$909$	6.67768			0.221485
$910$	−26.8411	−	36.7121i	−0.889775	−	1.21700i
$911$	2.12009			0.0702418			0.0351209	−	0.999383i	$-0.488818\pi$
$911$	2.12009			0.0702418			0.0351209	+	0.999383i	$0.488818\pi$
$912$	4.08471	−	15.2443i	0.135258	−	0.504790i
$913$			31.6798i			1.04845i
$914$	−33.4366	−	19.3046i	−1.10598	−	0.638540i
$915$	5.33170	+	19.8982i	0.176261	+	0.657813i
$916$	−1.94970	−	0.522419i	−0.0644197	−	0.0172612i
$917$	−3.37738	−	14.4597i	−0.111531	−	0.477501i
$918$	1.06482	−	1.06482i	0.0351443	−	0.0351443i
$919$	7.19783			0.237435			0.118717	−	0.992928i	$-0.462122\pi$
$919$	7.19783			0.237435			0.118717	+	0.992928i	$0.462122\pi$
$920$	39.2454			1.29388
$921$	7.24945	−	7.24945i	0.238877	−	0.238877i
$922$	16.2143	−	28.0840i	0.533990	−	0.924898i
$923$	15.9161	−	39.4423i	0.523886	−	1.29826i
$924$	−2.71423	+	4.36858i	−0.0892916	+	0.143716i
$925$	64.2595	−	17.2183i	2.11284	−	0.566134i
$926$	−10.6709	−	18.4825i	−0.350667	−	0.607372i
$927$	1.06760	−	1.84913i	0.0350645	−	0.0607335i
$928$	−4.94723	+	18.4633i	−0.162401	+	0.606088i
$929$	−19.6636	+	19.6636i	−0.645141	+	0.645141i	−0.951815	−	0.306674i	$-0.900784\pi$
$929$	−19.6636	+	19.6636i	−0.645141	+	0.645141i	0.306674	+	0.951815i	$0.400784\pi$
$930$	−6.59587	+	24.6161i	−0.216287	+	0.807194i
$931$	−24.7790	−	28.2113i	−0.812098	−	0.924588i
$932$	3.80731	+	6.59445i	0.124712	+	0.216008i
$933$	−0.774775	+	0.447316i	−0.0253650	+	0.0146445i
$934$	−20.4649	−	20.4649i	−0.669633	−	0.669633i
$935$	17.7677	−	10.2582i	0.581065	−	0.335478i
$936$	−8.65158	+	6.76531i	−0.282786	+	0.221131i
$937$		−	47.3785i		−	1.54779i	−0.633315	−	0.773894i	$-0.718306\pi$
$937$		−	47.3785i		−	1.54779i	0.633315	−	0.773894i	$-0.281694\pi$
$938$	17.2017	+	5.21088i	0.561656	+	0.170141i
$939$	−16.3830	+	28.3762i	−0.534639	+	0.926022i
$940$			8.54989i			0.278867i
$941$	29.0378	+	7.78065i	0.946604	+	0.253642i	0.698921	−	0.715199i	$-0.253664\pi$
$941$	29.0378	+	7.78065i	0.946604	+	0.253642i	0.247683	+	0.968841i	$0.420331\pi$
$942$	−15.7472	+	4.21944i	−0.513071	+	0.137477i
$943$	8.45278	+	8.45278i	0.275260	+	0.275260i
$944$	12.6776	+	12.6776i	0.412619	+	0.412619i
$945$	8.56280	+	5.32014i	0.278548	+	0.173064i
$946$	48.9410	+	28.2561i	1.59121	+	0.918685i
$947$	1.50945	+	0.404457i	0.0490506	+	0.0131431i	0.283261	−	0.959043i	$-0.408584\pi$
$947$	1.50945	+	0.404457i	0.0490506	+	0.0131431i	−0.234210	+	0.972186i	$0.575250\pi$
$948$	−2.50423	−	4.33745i	−0.0813336	−	0.140874i
$949$	10.0129	−	24.8134i	0.325033	−	0.805476i
$950$	−55.3212	−	31.9397i	−1.79486	−	1.03626i
$951$	−5.94088	−	22.1717i	−0.192646	−	0.718966i
$952$	−5.11884	+	8.23882i	−0.165903	+	0.267022i
$953$	20.1615	−	11.6403i	0.653096	−	0.377065i	−0.136545	−	0.990634i	$-0.543600\pi$
$953$	20.1615	−	11.6403i	0.653096	−	0.377065i	0.789641	+	0.613569i	$0.210267\pi$
$954$	2.77310	−	0.743050i	0.0897824	−	0.0240571i
$955$	−1.95021	−	7.27830i	−0.0631075	−	0.235520i
$956$	0.285909	+	1.06703i	0.00924696	+	0.0345101i
$957$	34.2632	−	9.18081i	1.10757	−	0.296773i
$958$	−31.1314	+	17.9737i	−1.00581	+	0.580704i
$959$	−13.6214	+	21.9237i	−0.439858	+	0.707955i
$960$	−8.77765	−	32.7586i	−0.283297	−	1.05728i
$961$	−2.09961	−	1.21221i	−0.0677295	−	0.0391037i
$962$	−18.9656	+	25.1905i	−0.611475	+	0.812176i
$963$	−8.96843	−	15.5338i	−0.289004	−	0.500569i
$964$	−1.83207	−	0.490902i	−0.0590070	−	0.0158109i
$965$	10.6293	+	6.13684i	0.342170	+	0.197552i
$966$	9.50802	+	5.90741i	0.305916	+	0.190068i
$967$	−5.77720	−	5.77720i	−0.185782	−	0.185782i	0.608088	−	0.793870i	$-0.291937\pi$
$967$	−5.77720	−	5.77720i	−0.185782	−	0.185782i	−0.793870	+	0.608088i	$0.791937\pi$
$968$	−19.4183	−	19.4183i	−0.624126	−	0.624126i
$969$	6.23592	−	1.67091i	0.200327	−	0.0536774i
$970$	12.8602	+	3.44589i	0.412917	+	0.110641i
$971$			15.5472i			0.498934i	0.968383	+	0.249467i	$0.0802554\pi$
$971$			15.5472i			0.498934i	−0.968383	+	0.249467i	$0.919745\pi$
$972$	0.217252	−	0.376291i	0.00696835	−	0.0120695i
$973$	37.8734	+	11.4729i	1.21417	+	0.367805i
$974$		−	21.6529i		−	0.693805i
$975$	13.4224	+	31.5836i	0.429860	+	1.01148i
$976$	13.7759	−	7.95352i	0.440956	−	0.254586i
$977$	21.0735	+	21.0735i	0.674200	+	0.674200i	0.958682	−	0.284481i	$-0.0918214\pi$
$977$	21.0735	+	21.0735i	0.674200	+	0.674200i	−0.284481	+	0.958682i	$0.591821\pi$
$978$	−3.04455	+	1.75777i	−0.0973538	+	0.0562073i
$979$	−11.7871	−	20.4158i	−0.376717	−	0.652493i
$980$	−10.9768	−	3.71672i	−0.350640	−	0.118726i
$981$	−0.0524960	+	0.195918i	−0.00167607	+	0.00625517i
$982$	−30.9035	+	30.9035i	−0.986172	+	0.986172i
$983$	13.2861	−	49.5845i	0.423762	−	1.58150i	−0.342850	−	0.939390i	$-0.611392\pi$
$983$	13.2861	−	49.5845i	0.423762	−	1.58150i	0.766612	−	0.642111i	$-0.221941\pi$
$984$	5.38419	−	9.32569i	0.171642	−	0.297292i
$985$	11.1758	+	19.3571i	0.356091	+	0.616768i
$986$	11.5328	−	3.09022i	0.367281	−	0.0984125i
$987$	−7.21084	+	11.6059i	−0.229523	+	0.369420i
$988$	−8.32116	+	1.17309i	−0.264731	+	0.0373209i
$989$	−17.0688	+	29.5641i	−0.542757	+	0.940083i
$990$	−15.0816	+	15.0816i	−0.479324	+	0.479324i
$991$	−20.0235			−0.636069			−0.318034	−	0.948079i	$-0.603023\pi$
$991$	−20.0235			−0.636069			−0.318034	+	0.948079i	$0.603023\pi$
$992$	−12.8873			−0.409172
$993$	11.8814	−	11.8814i	0.377044	−	0.377044i
$994$	8.88199	+	38.0268i	0.281720	+	1.20614i
$995$	−6.96074	−	1.86513i	−0.220670	−	0.0591285i
$996$	0.796322	+	2.97191i	0.0252324	+	0.0941687i
$997$	−10.6118	−	6.12675i	−0.336080	−	0.194036i	0.322457	−	0.946584i	$-0.395491\pi$
$997$	−10.6118	−	6.12675i	−0.336080	−	0.194036i	−0.658537	+	0.752548i	$0.728825\pi$
$998$		−	29.8712i		−	0.945555i
$999$	1.80904	−	6.75142i	0.0572354	−	0.213606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.b.124.8	yes	40
3.2	odd	2		819.2.gh.d.397.3		40
7.3	odd	6		273.2.bt.b.241.8	yes	40
13.2	odd	12		273.2.bt.b.145.8	✓	40
21.17	even	6		819.2.et.d.514.3		40
39.2	even	12		819.2.et.d.145.3		40
91.80	even	12	inner	273.2.cg.b.262.8	yes	40
273.80	odd	12		819.2.gh.d.262.3		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.145.8	✓	40	13.2	odd	12
273.2.bt.b.241.8	yes	40	7.3	odd	6
273.2.cg.b.124.8	yes	40	1.1	even	1	trivial
273.2.cg.b.262.8	yes	40	91.80	even	12	inner
819.2.et.d.145.3		40	39.2	even	12
819.2.et.d.514.3		40	21.17	even	6
819.2.gh.d.262.3		40	273.80	odd	12
819.2.gh.d.397.3		40	3.2	odd	2

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.323834 - 1.20856i) q^{2} -1.00000i q^{3} +(0.376291 + 0.217252i) q^{4} +(0.986163 + 3.68041i) q^{5} +(-1.20856 - 0.323834i) q^{6} +(-1.80936 - 1.93034i) q^{7} +(2.15388 - 2.15388i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.323834 - 1.20856i) q^{2} -1.00000i q^{3} +(0.376291 + 0.217252i) q^{4} +(0.986163 + 3.68041i) q^{5} +(-1.20856 - 0.323834i) q^{6} +(-1.80936 - 1.93034i) q^{7} +(2.15388 - 2.15388i) q^{8} -1.00000 q^{9} +4.76737 q^{10} +(3.16350 - 3.16350i) q^{11} +(0.217252 - 0.376291i) q^{12} +(3.57886 + 0.437877i) q^{13} +(-2.91888 + 1.56161i) q^{14} +(3.68041 - 0.986163i) q^{15} +(-1.47110 - 2.54802i) q^{16} +(0.601776 - 1.04231i) q^{17} +(-0.323834 + 1.20856i) q^{18} +(-3.79295 + 3.79295i) q^{19} +(-0.428491 + 1.59915i) q^{20} +(-1.93034 + 1.80936i) q^{21} +(-2.79885 - 4.84774i) q^{22} +(2.92841 - 1.69072i) q^{23} +(-2.15388 - 2.15388i) q^{24} +(-8.24277 + 4.75896i) q^{25} +(1.68816 - 4.18349i) q^{26} +1.00000i q^{27} +(-0.261474 - 1.11946i) q^{28} +(-3.96435 + 6.86645i) q^{29} -4.76737i q^{30} +(-5.16347 - 1.38355i) q^{31} +(2.32867 - 0.623965i) q^{32} +(-3.16350 - 3.16350i) q^{33} +(-1.06482 - 1.06482i) q^{34} +(5.32014 - 8.56280i) q^{35} +(-0.376291 - 0.217252i) q^{36} +(-6.75142 - 1.80904i) q^{37} +(3.35574 + 5.81231i) q^{38} +(0.437877 - 3.57886i) q^{39} +(10.0512 + 5.80308i) q^{40} +(0.914977 + 3.41474i) q^{41} +(1.56161 + 2.91888i) q^{42} +(-8.74306 + 5.04781i) q^{43} +(1.87767 - 0.503121i) q^{44} +(-0.986163 - 3.68041i) q^{45} +(-1.09502 - 4.08668i) q^{46} +(4.98837 - 1.33663i) q^{47} +(-2.54802 + 1.47110i) q^{48} +(-0.452462 + 6.98536i) q^{49} +(3.08223 + 11.5030i) q^{50} +(-1.04231 - 0.601776i) q^{51} +(1.25156 + 0.942283i) q^{52} +(-1.14727 - 1.98713i) q^{53} +(1.20856 + 0.323834i) q^{54} +(14.7627 + 8.52325i) q^{55} +(-8.05487 - 0.260595i) q^{56} +(3.79295 + 3.79295i) q^{57} +(7.01476 + 7.01476i) q^{58} +(-5.88602 + 1.57716i) q^{59} +(1.59915 + 0.428491i) q^{60} +5.40651i q^{61} +(-3.34421 + 5.79234i) q^{62} +(1.80936 + 1.93034i) q^{63} -8.90081i q^{64} +(1.91777 + 13.6035i) q^{65} +(-4.84774 + 2.79885i) q^{66} +(-3.83925 - 3.83925i) q^{67} +(0.452886 - 0.261474i) q^{68} +(-1.69072 - 2.92841i) q^{69} +(-8.62586 - 9.20266i) q^{70} +(3.05313 - 11.3945i) q^{71} +(-2.15388 + 2.15388i) q^{72} +(1.92074 - 7.16831i) q^{73} +(-4.37268 + 7.57370i) q^{74} +(4.75896 + 8.24277i) q^{75} +(-2.25128 + 0.603228i) q^{76} +(-11.8305 - 0.382748i) q^{77} +(-4.18349 - 1.68816i) q^{78} +(5.76343 - 9.98255i) q^{79} +(7.92701 - 7.92701i) q^{80} +1.00000 q^{81} +4.42323 q^{82} +(-5.00708 + 5.00708i) q^{83} +(-1.11946 + 0.261474i) q^{84} +(4.42956 + 1.18690i) q^{85} +(3.26930 + 12.2012i) q^{86} +(6.86645 + 3.96435i) q^{87} -13.6276i q^{88} +(1.36380 - 5.08976i) q^{89} -4.76737 q^{90} +(-5.63018 - 7.70072i) q^{91} +1.46924 q^{92} +(-1.38355 + 5.16347i) q^{93} -6.46162i q^{94} +(-17.7001 - 10.2191i) q^{95} +(-0.623965 - 2.32867i) q^{96} +(2.69756 + 0.722808i) q^{97} +(8.29574 + 2.80893i) q^{98} +(-3.16350 + 3.16350i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 8 * q^7 - 40 * q^9	\( 40 q - 8 q^{7} - 40 q^{9} + 4 q^{11} - 24 q^{12} - 18 q^{14} + 32 q^{16} + 4 q^{17} + 14 q^{19} + 14 q^{20} + 2 q^{21} + 4 q^{22} + 12 q^{23} + 24 q^{25} - 32 q^{26} + 16 q^{28} + 8 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} - 24 q^{34} + 26 q^{35} + 36 q^{37} - 8 q^{38} + 18 q^{39} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 32 q^{44} - 26 q^{46} - 4 q^{47} + 24 q^{48} - 14 q^{49} - 20 q^{50} + 2 q^{52} - 8 q^{53} - 42 q^{55} + 46 q^{56} - 14 q^{57} + 24 q^{58} + 14 q^{59} + 2 q^{60} + 24 q^{62} + 8 q^{63} + 28 q^{65} - 18 q^{66} - 44 q^{67} - 18 q^{68} + 4 q^{69} - 4 q^{70} - 6 q^{71} + 14 q^{73} - 20 q^{74} + 24 q^{75} - 64 q^{76} + 24 q^{77} + 8 q^{78} + 20 q^{80} + 40 q^{81} + 48 q^{82} - 12 q^{83} + 22 q^{84} + 2 q^{85} - 60 q^{86} + 18 q^{87} - 2 q^{89} - 14 q^{91} + 236 q^{92} - 8 q^{93} + 24 q^{95} + 16 q^{96} - 62 q^{97} - 88 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q - 8 * q^7 - 40 * q^9 + 4 * q^11 - 24 * q^12 - 18 * q^14 + 32 * q^16 + 4 * q^17 + 14 * q^19 + 14 * q^20 + 2 * q^21 + 4 * q^22 + 12 * q^23 + 24 * q^25 - 32 * q^26 + 16 * q^28 + 8 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 - 24 * q^34 + 26 * q^35 + 36 * q^37 - 8 * q^38 + 18 * q^39 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 32 * q^44 - 26 * q^46 - 4 * q^47 + 24 * q^48 - 14 * q^49 - 20 * q^50 + 2 * q^52 - 8 * q^53 - 42 * q^55 + 46 * q^56 - 14 * q^57 + 24 * q^58 + 14 * q^59 + 2 * q^60 + 24 * q^62 + 8 * q^63 + 28 * q^65 - 18 * q^66 - 44 * q^67 - 18 * q^68 + 4 * q^69 - 4 * q^70 - 6 * q^71 + 14 * q^73 - 20 * q^74 + 24 * q^75 - 64 * q^76 + 24 * q^77 + 8 * q^78 + 20 * q^80 + 40 * q^81 + 48 * q^82 - 12 * q^83 + 22 * q^84 + 2 * q^85 - 60 * q^86 + 18 * q^87 - 2 * q^89 - 14 * q^91 + 236 * q^92 - 8 * q^93 + 24 * q^95 + 16 * q^96 - 62 * q^97 - 88 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more