LMFDB - Embedded newform 465.2.k.a.32.14

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			32.14
Character	$\chi$	$=$	465.32
Dual form			465.2.k.a.218.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.450084 + 0.450084i) q^{2} +(-1.12935 + 1.31323i) q^{3} +1.59485i q^{4} +(-1.42766 - 1.72099i) q^{5} +(-0.0827594 - 1.09937i) q^{6} +(0.166606 + 0.166606i) q^{7} +(-1.61799 - 1.61799i) q^{8} +(-0.449130 - 2.96619i) q^{9} +O(q^{10})$	\(q+(-0.450084 + 0.450084i) q^{2} +(-1.12935 + 1.31323i) q^{3} +1.59485i q^{4} +(-1.42766 - 1.72099i) q^{5} +(-0.0827594 - 1.09937i) q^{6} +(0.166606 + 0.166606i) q^{7} +(-1.61799 - 1.61799i) q^{8} +(-0.449130 - 2.96619i) q^{9} +(1.41716 + 0.132024i) q^{10} -1.30913i q^{11} +(-2.09440 - 1.80114i) q^{12} +(-2.01795 + 2.01795i) q^{13} -0.149974 q^{14} +(3.87237 + 0.0687627i) q^{15} -1.73324 q^{16} +(0.865338 - 0.865338i) q^{17} +(1.53718 + 1.13289i) q^{18} -6.62828i q^{19} +(2.74471 - 2.27690i) q^{20} +(-0.406948 + 0.0306347i) q^{21} +(0.589219 + 0.589219i) q^{22} +(-3.49738 - 3.49738i) q^{23} +(3.95206 - 0.297507i) q^{24} +(-0.923594 + 4.91396i) q^{25} -1.81649i q^{26} +(4.40251 + 2.76006i) q^{27} +(-0.265711 + 0.265711i) q^{28} +8.04293 q^{29} +(-1.77384 + 1.71195i) q^{30} +1.00000 q^{31} +(4.01607 - 4.01607i) q^{32} +(1.71918 + 1.47847i) q^{33} +0.778950i q^{34} +(0.0488707 - 0.524583i) q^{35} +(4.73062 - 0.716294i) q^{36} +(1.16239 + 1.16239i) q^{37} +(2.98329 + 2.98329i) q^{38} +(-0.371051 - 4.92900i) q^{39} +(-0.474605 + 5.09446i) q^{40} -7.29388i q^{41} +(0.169373 - 0.196949i) q^{42} +(1.00708 - 1.00708i) q^{43} +2.08786 q^{44} +(-4.46357 + 5.00765i) q^{45} +3.14823 q^{46} +(-5.02804 + 5.02804i) q^{47} +(1.95743 - 2.27613i) q^{48} -6.94448i q^{49} +(-1.79600 - 2.62739i) q^{50} +(0.159114 + 2.11366i) q^{51} +(-3.21832 - 3.21832i) q^{52} +(-5.89347 - 5.89347i) q^{53} +(-3.22376 + 0.739238i) q^{54} +(-2.25299 + 1.86899i) q^{55} -0.539132i q^{56} +(8.70444 + 7.48566i) q^{57} +(-3.62000 + 3.62000i) q^{58} -13.9436 q^{59} +(-0.109666 + 6.17585i) q^{60} +3.40260 q^{61} +(-0.450084 + 0.450084i) q^{62} +(0.419358 - 0.569013i) q^{63} +0.148671i q^{64} +(6.35380 + 0.591926i) q^{65} +(-1.43921 + 0.108343i) q^{66} +(-6.19193 - 6.19193i) q^{67} +(1.38008 + 1.38008i) q^{68} +(8.54262 - 0.643081i) q^{69} +(0.214111 + 0.258103i) q^{70} +7.53241i q^{71} +(-4.07257 + 5.52594i) q^{72} +(-5.11366 + 5.11366i) q^{73} -1.04635 q^{74} +(-5.41008 - 6.76247i) q^{75} +10.5711 q^{76} +(0.218109 - 0.218109i) q^{77} +(2.38547 + 2.05146i) q^{78} -10.5143i q^{79} +(2.47447 + 2.98288i) q^{80} +(-8.59657 + 2.66441i) q^{81} +(3.28286 + 3.28286i) q^{82} +(-11.2624 - 11.2624i) q^{83} +(-0.0488577 - 0.649021i) q^{84} +(-2.72464 - 0.253830i) q^{85} +0.906540i q^{86} +(-9.08330 + 10.5622i) q^{87} +(-2.11815 + 2.11815i) q^{88} -3.38615 q^{89} +(-0.244880 - 4.26285i) q^{90} -0.672405 q^{91} +(5.57779 - 5.57779i) q^{92} +(-1.12935 + 1.31323i) q^{93} -4.52608i q^{94} +(-11.4072 + 9.46291i) q^{95} +(0.738456 + 9.80957i) q^{96} +(4.83829 + 4.83829i) q^{97} +(3.12560 + 3.12560i) q^{98} +(-3.88313 + 0.587969i) 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} - 32 q^{10} + 4 q^{13} + 20 q^{15} - 60 q^{16} - 46 q^{18} - 4 q^{21} + 8 q^{22} - 8 q^{25} - 6 q^{27} + 112 q^{28} + 54 q^{30} + 60 q^{31} - 30 q^{33} - 4 q^{36} - 36 q^{37} - 36 q^{40} + 44 q^{42} + 16 q^{43} + 14 q^{45} + 40 q^{46} - 104 q^{48} - 48 q^{51} - 12 q^{52} - 48 q^{55} + 42 q^{57} + 80 q^{58} + 60 q^{60} - 8 q^{61} - 10 q^{63} - 24 q^{66} - 88 q^{67} - 84 q^{70} + 84 q^{72} + 60 q^{73} + 14 q^{75} + 72 q^{76} - 152 q^{78} - 132 q^{81} - 60 q^{82} - 16 q^{85} + 34 q^{87} + 124 q^{88} + 190 q^{90} + 64 q^{91} - 88 q^{96} - 8 q^{97}+O(q^{100}) $ 60 * q - 4 * q^6 - 32 * q^10 + 4 * q^13 + 20 * q^15 - 60 * q^16 - 46 * q^18 - 4 * q^21 + 8 * q^22 - 8 * q^25 - 6 * q^27 + 112 * q^28 + 54 * q^30 + 60 * q^31 - 30 * q^33 - 4 * q^36 - 36 * q^37 - 36 * q^40 + 44 * q^42 + 16 * q^43 + 14 * q^45 + 40 * q^46 - 104 * q^48 - 48 * q^51 - 12 * q^52 - 48 * q^55 + 42 * q^57 + 80 * q^58 + 60 * q^60 - 8 * q^61 - 10 * q^63 - 24 * q^66 - 88 * q^67 - 84 * q^70 + 84 * q^72 + 60 * q^73 + 14 * q^75 + 72 * q^76 - 152 * q^78 - 132 * q^81 - 60 * q^82 - 16 * q^85 + 34 * q^87 + 124 * q^88 + 190 * q^90 + 64 * q^91 - 88 * q^96 - 8 * 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 $

$2$	−0.450084	+	0.450084i	−0.318258	+	0.318258i	−0.848098	−	0.529840i	$-0.822252\pi$
$2$	−0.450084	+	0.450084i	−0.318258	+	0.318258i	0.529840	+	0.848098i	$0.322252\pi$
$3$	−1.12935	+	1.31323i	−0.652031	+	0.758192i
$3$	−1.12935	+	1.31323i	−0.652031	+	0.758192i
$4$			1.59485i			0.797424i
$5$	−1.42766	−	1.72099i	−0.638467	−	0.769649i
$5$	−1.42766	−	1.72099i	−0.638467	−	0.769649i
$6$	−0.0827594	−	1.09937i	−0.0337864	−	0.448814i
$7$	0.166606	+	0.166606i	0.0629712	+	0.0629712i	0.737891	−	0.674920i	$-0.235822\pi$
$7$	0.166606	+	0.166606i	0.0629712	+	0.0629712i	−0.674920	+	0.737891i	$0.735822\pi$
$8$	−1.61799	−	1.61799i	−0.572044	−	0.572044i
$9$	−0.449130	−	2.96619i	−0.149710	−	0.988730i
$10$	1.41716	+	0.132024i	0.448144	+	0.0417495i
$11$		−	1.30913i		−	0.394717i	−0.980331	−	0.197359i	$-0.936764\pi$
$11$		−	1.30913i		−	0.394717i	0.980331	−	0.197359i	$-0.0632363\pi$
$12$	−2.09440	−	1.80114i	−0.604600	−	0.519946i
$13$	−2.01795	+	2.01795i	−0.559678	+	0.559678i	−0.929216	−	0.369537i	$-0.879516\pi$
$13$	−2.01795	+	2.01795i	−0.559678	+	0.559678i	0.369537	+	0.929216i	$0.379516\pi$
$14$	−0.149974			−0.0400821
$15$	3.87237	+	0.0687627i	0.999842	+	0.0177545i
$16$	−1.73324			−0.433309
$17$	0.865338	−	0.865338i	0.209875	−	0.209875i	−0.594339	−	0.804214i	$-0.702586\pi$
$17$	0.865338	−	0.865338i	0.209875	−	0.209875i	0.804214	+	0.594339i	$0.202586\pi$
$18$	1.53718	+	1.13289i	0.362317	+	0.267025i
$19$		−	6.62828i		−	1.52063i	−0.649553	−	0.760316i	$-0.725044\pi$
$19$		−	6.62828i		−	1.52063i	0.649553	−	0.760316i	$-0.274956\pi$
$20$	2.74471	−	2.27690i	0.613736	−	0.509129i
$21$	−0.406948	+	0.0306347i	−0.0888034	+	0.00668505i
$22$	0.589219	+	0.589219i	0.125622	+	0.125622i
$23$	−3.49738	−	3.49738i	−0.729254	−	0.729254i	0.241218	−	0.970471i	$-0.422453\pi$
$23$	−3.49738	−	3.49738i	−0.729254	−	0.729254i	−0.970471	+	0.241218i	$0.922453\pi$
$24$	3.95206	−	0.297507i	0.806710	−	0.0607284i
$25$	−0.923594	+	4.91396i	−0.184719	+	0.982791i
$26$		−	1.81649i		−	0.356244i
$27$	4.40251	+	2.76006i	0.847263	+	0.531174i
$28$	−0.265711	+	0.265711i	−0.0502147	+	0.0502147i
$29$	8.04293			1.49354			0.746768	−	0.665085i	$-0.231605\pi$
$29$	8.04293			1.49354			0.746768	+	0.665085i	$0.231605\pi$
$30$	−1.77384	+	1.71195i	−0.323858	+	0.312557i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	4.01607	−	4.01607i	0.709948	−	0.709948i
$33$	1.71918	+	1.47847i	0.299271	+	0.257368i
$34$			0.778950i			0.133589i
$35$	0.0488707	−	0.524583i	0.00826065	−	0.0886708i
$36$	4.73062	−	0.716294i	0.788437	−	0.119382i
$37$	1.16239	+	1.16239i	0.191097	+	0.191097i	0.796170	−	0.605073i	$-0.206856\pi$
$37$	1.16239	+	1.16239i	0.191097	+	0.191097i	−0.605073	+	0.796170i	$0.706856\pi$
$38$	2.98329	+	2.98329i	0.483953	+	0.483953i
$39$	−0.371051	−	4.92900i	−0.0594157	−	0.789272i
$40$	−0.474605	+	5.09446i	−0.0750416	+	0.805505i
$41$		−	7.29388i		−	1.13911i	−0.821952	−	0.569556i	$-0.807115\pi$
$41$		−	7.29388i		−	1.13911i	0.821952	−	0.569556i	$-0.192885\pi$
$42$	0.169373	−	0.196949i	0.0261348	−	0.0303899i
$43$	1.00708	−	1.00708i	0.153578	−	0.153578i	−0.626136	−	0.779714i	$-0.715365\pi$
$43$	1.00708	−	1.00708i	0.153578	−	0.153578i	0.779714	+	0.626136i	$0.215365\pi$
$44$	2.08786			0.314757
$45$	−4.46357	+	5.00765i	−0.665390	+	0.746496i
$46$	3.14823			0.464181
$47$	−5.02804	+	5.02804i	−0.733415	+	0.733415i	−0.971295	−	0.237880i	$-0.923548\pi$
$47$	−5.02804	+	5.02804i	−0.733415	+	0.733415i	0.237880	+	0.971295i	$0.423548\pi$
$48$	1.95743	−	2.27613i	0.282531	−	0.328531i
$49$		−	6.94448i		−	0.992069i
$50$	−1.79600	−	2.62739i	−0.253993	−	0.371569i
$51$	0.159114	+	2.11366i	0.0222805	+	0.295971i
$52$	−3.21832	−	3.21832i	−0.446301	−	0.446301i
$53$	−5.89347	−	5.89347i	−0.809531	−	0.809531i	0.175032	−	0.984563i	$-0.443997\pi$
$53$	−5.89347	−	5.89347i	−0.809531	−	0.809531i	−0.984563	+	0.175032i	$0.943997\pi$
$54$	−3.22376	+	0.739238i	−0.438698	+	0.100598i
$55$	−2.25299	+	1.86899i	−0.303794	+	0.252014i
$56$		−	0.539132i		−	0.0720446i
$57$	8.70444	+	7.48566i	1.15293	+	0.991500i
$58$	−3.62000	+	3.62000i	−0.475329	+	0.475329i
$59$	−13.9436			−1.81530			−0.907650	−	0.419727i	$-0.862126\pi$
$59$	−13.9436			−1.81530			−0.907650	+	0.419727i	$0.862126\pi$
$60$	−0.109666	+	6.17585i	−0.0141578	+	0.797298i
$61$	3.40260			0.435658			0.217829	−	0.975987i	$-0.430102\pi$
$61$	3.40260			0.435658			0.217829	+	0.975987i	$0.430102\pi$
$62$	−0.450084	+	0.450084i	−0.0571608	+	0.0571608i
$63$	0.419358	−	0.569013i	0.0528341	−	0.0716889i
$64$			0.148671i			0.0185838i
$65$	6.35380	+	0.591926i	0.788092	+	0.0734194i
$66$	−1.43921	+	0.108343i	−0.177155	+	0.0133361i
$67$	−6.19193	−	6.19193i	−0.756464	−	0.756464i	0.219213	−	0.975677i	$-0.429651\pi$
$67$	−6.19193	−	6.19193i	−0.756464	−	0.756464i	−0.975677	+	0.219213i	$0.929651\pi$
$68$	1.38008	+	1.38008i	0.167360	+	0.167360i
$69$	8.54262	−	0.643081i	1.02841	−	0.0774179i
$70$	0.214111	+	0.258103i	0.0255911	+	0.0308492i
$71$			7.53241i			0.893933i	0.894551	+	0.446966i	$0.147496\pi$
$71$			7.53241i			0.893933i	−0.894551	+	0.446966i	$0.852504\pi$
$72$	−4.07257	+	5.52594i	−0.479956	+	0.651238i
$73$	−5.11366	+	5.11366i	−0.598509	+	0.598509i	−0.939916	−	0.341407i	$-0.889097\pi$
$73$	−5.11366	+	5.11366i	−0.598509	+	0.598509i	0.341407	+	0.939916i	$0.389097\pi$
$74$	−1.04635			−0.121636
$75$	−5.41008	−	6.76247i	−0.624702	−	0.780863i
$76$	10.5711			1.21259
$77$	0.218109	−	0.218109i	0.0248558	−	0.0248558i
$78$	2.38547	+	2.05146i	0.270101	+	0.232282i
$79$		−	10.5143i		−	1.18296i	−0.806321	−	0.591478i	$-0.798545\pi$
$79$		−	10.5143i		−	1.18296i	0.806321	−	0.591478i	$-0.201455\pi$
$80$	2.47447	+	2.98288i	0.276654	+	0.333496i
$81$	−8.59657	+	2.66441i	−0.955174	+	0.296045i
$82$	3.28286	+	3.28286i	0.362531	+	0.362531i
$83$	−11.2624	−	11.2624i	−1.23621	−	1.23621i	−0.961538	−	0.274671i	$-0.911431\pi$
$83$	−11.2624	−	11.2624i	−1.23621	−	1.23621i	−0.274671	−	0.961538i	$-0.588569\pi$
$84$	−0.0488577	−	0.649021i	−0.00533082	−	0.0708140i
$85$	−2.72464	−	0.253830i	−0.295529	−	0.0275317i
$86$			0.906540i			0.0977547i
$87$	−9.08330	+	10.5622i	−0.973832	+	1.13239i
$88$	−2.11815	+	2.11815i	−0.225796	+	0.225796i
$89$	−3.38615			−0.358931			−0.179466	−	0.983764i	$-0.557437\pi$
$89$	−3.38615			−0.358931			−0.179466	+	0.983764i	$0.557437\pi$
$90$	−0.244880	−	4.26285i	−0.0258126	−	0.449344i
$91$	−0.672405			−0.0704872
$92$	5.57779	−	5.57779i	0.581524	−	0.581524i
$93$	−1.12935	+	1.31323i	−0.117108	+	0.136175i
$94$		−	4.52608i		−	0.466830i
$95$	−11.4072	+	9.46291i	−1.17035	+	0.970874i
$96$	0.738456	+	9.80957i	0.0753684	+	1.00119i
$97$	4.83829	+	4.83829i	0.491254	+	0.491254i	0.908701	−	0.417447i	$-0.137075\pi$
$97$	4.83829	+	4.83829i	0.491254	+	0.491254i	−0.417447	+	0.908701i	$0.637075\pi$
$98$	3.12560	+	3.12560i	0.315734	+	0.315734i
$99$	−3.88313	+	0.587969i	−0.390269	+	0.0590931i
$100$	−7.83702	−	1.47299i	−0.783702	−	0.147299i
$101$		−	0.709895i		−	0.0706371i	−0.999376	−	0.0353186i	$-0.988755\pi$
$101$		−	0.709895i		−	0.0706371i	0.999376	−	0.0353186i	$-0.0112446\pi$
$102$	−1.02294	−	0.879709i	−0.101286	−	0.0871042i
$103$	−4.71170	+	4.71170i	−0.464258	+	0.464258i	−0.900048	−	0.435790i	$-0.856469\pi$
$103$	−4.71170	+	4.71170i	−0.464258	+	0.464258i	0.435790	+	0.900048i	$0.356469\pi$
$104$	6.53002			0.640321
$105$	0.633705	+	0.656617i	0.0618432	+	0.0640793i
$106$	5.30512			0.515279
$107$	−4.30015	+	4.30015i	−0.415711	+	0.415711i	−0.883723	−	0.468011i	$-0.844971\pi$
$107$	−4.30015	+	4.30015i	−0.415711	+	0.415711i	0.468011	+	0.883723i	$0.344971\pi$
$108$	−4.40188	+	7.02133i	−0.423571	+	0.675628i
$109$		−	9.17913i		−	0.879201i	−0.898193	−	0.439601i	$-0.855120\pi$
$109$		−	9.17913i		−	0.879201i	0.898193	−	0.439601i	$-0.144880\pi$
$110$	0.172836	−	1.85524i	0.0164793	−	0.176890i
$111$	−2.83924	+	0.213736i	−0.269489	+	0.0202869i
$112$	−0.288768	−	0.288768i	−0.0272860	−	0.0272860i
$113$	0.442971	+	0.442971i	0.0416712	+	0.0416712i	0.727635	−	0.685964i	$-0.240619\pi$
$113$	0.442971	+	0.442971i	0.0416712	+	0.0416712i	−0.685964	+	0.727635i	$0.740619\pi$
$114$	−7.28691	+	0.548552i	−0.682482	+	0.0513766i
$115$	−1.02589	+	11.0120i	−0.0956645	+	1.02687i
$116$			12.8273i			1.19098i
$117$	6.89194	+	5.07930i	0.637160	+	0.469581i
$118$	6.27579	−	6.27579i	0.577734	−	0.577734i
$119$	0.288341			0.0264322
$120$	−6.15418	−	6.37670i	−0.561798	−	0.582110i
$121$	9.28618			0.844198
$122$	−1.53146	+	1.53146i	−0.138652	+	0.138652i
$123$	9.57852	+	8.23735i	0.863666	+	0.742737i
$124$			1.59485i			0.143222i
$125$	9.77543	−	5.42595i	0.874341	−	0.485312i
$126$	0.0673576	+	0.444850i	0.00600069	+	0.0396304i
$127$	−2.28068	−	2.28068i	−0.202377	−	0.202377i	0.598641	−	0.801018i	$-0.295708\pi$
$127$	−2.28068	−	2.28068i	−0.202377	−	0.202377i	−0.801018	+	0.598641i	$0.795708\pi$
$128$	7.96523	+	7.96523i	0.704034	+	0.704034i
$129$	0.185177	+	2.45987i	0.0163039	+	0.216579i
$130$	−3.12616	+	2.59333i	−0.274183	+	0.227450i
$131$		−	9.37330i		−	0.818949i	−0.912321	−	0.409475i	$-0.865712\pi$
$131$		−	9.37330i		−	0.818949i	0.912321	−	0.409475i	$-0.134288\pi$
$132$	−2.35793	+	2.74184i	−0.205231	+	0.238646i
$133$	1.10431	−	1.10431i	0.0957560	−	0.0957560i
$134$	5.57378			0.481501
$135$	−1.53523	−	11.5171i	−0.132132	−	0.991232i
$136$	−2.80021			−0.240116
$137$	1.99002	−	1.99002i	0.170019	−	0.170019i	−0.616969	−	0.786988i	$-0.711639\pi$
$137$	1.99002	−	1.99002i	0.170019	−	0.170019i	0.786988	+	0.616969i	$0.211639\pi$
$138$	−3.55546	+	4.13434i	−0.302661	+	0.351938i
$139$			16.3387i			1.38583i	0.721017	+	0.692917i	$0.243675\pi$
$139$			16.3387i			1.38583i	−0.721017	+	0.692917i	$0.756325\pi$
$140$	0.836631	+	0.0779413i	0.0707082	+	0.00658724i
$141$	−0.924532	−	12.2814i	−0.0778596	−	1.03428i
$142$	−3.39022	−	3.39022i	−0.284501	−	0.284501i
$143$	2.64176	+	2.64176i	0.220915	+	0.220915i
$144$	0.778448	+	5.14111i	0.0648707	+	0.428426i
$145$	−11.4825	−	13.8418i	−0.953573	−	1.14950i
$146$		−	4.60316i		−	0.380960i
$147$	9.11968	+	7.84277i	0.752179	+	0.646860i
$148$	−1.85384	+	1.85384i	−0.152385	+	0.152385i
$149$	−15.6124			−1.27902			−0.639510	−	0.768782i	$-0.720863\pi$
$149$	−15.6124			−1.27902			−0.639510	+	0.768782i	$0.720863\pi$
$150$	5.47868	+	0.608692i	0.447332	+	0.0496995i
$151$	18.8848			1.53682			0.768411	−	0.639956i	$-0.221048\pi$
$151$	18.8848			1.53682			0.768411	+	0.639956i	$0.221048\pi$
$152$	−10.7245	+	10.7245i	−0.869869	+	0.869869i
$153$	−2.95541	−	2.17811i	−0.238930	−	0.176090i
$154$			0.196335i			0.0158211i
$155$	−1.42766	−	1.72099i	−0.114672	−	0.138233i
$156$	7.86100	−	0.591770i	0.629384	−	0.0473795i
$157$	4.14917	+	4.14917i	0.331140	+	0.331140i	0.853019	−	0.521879i	$-0.174769\pi$
$157$	4.14917	+	4.14917i	0.331140	+	0.331140i	−0.521879	+	0.853019i	$0.674769\pi$
$158$	4.73234	+	4.73234i	0.376485	+	0.376485i
$159$	14.3953	−	1.08366i	1.14162	−	0.0859401i
$160$	−12.6452	−	1.17804i	−0.999689	−	0.0931320i
$161$		−	1.16537i		−	0.0918439i
$162$	2.66997	−	5.06839i	0.209773	−	0.398210i
$163$	2.08017	−	2.08017i	0.162932	−	0.162932i	−0.620932	−	0.783864i	$-0.713246\pi$
$163$	2.08017	−	2.08017i	0.162932	−	0.162932i	0.783864	+	0.620932i	$0.213246\pi$
$164$	11.6326			0.908356
$165$	0.0900193	−	5.06944i	0.00700799	−	0.394655i
$166$	10.1381			0.786866
$167$	−4.70505	+	4.70505i	−0.364088	+	0.364088i	−0.865316	−	0.501227i	$-0.832882\pi$
$167$	−4.70505	+	4.70505i	−0.364088	+	0.364088i	0.501227	+	0.865316i	$0.332882\pi$
$168$	0.708003	+	0.608870i	0.0546236	+	0.0469753i
$169$			4.85576i			0.373520i
$170$	1.34056	−	1.11207i	0.102817	−	0.0852922i
$171$	−19.6607	+	2.97696i	−1.50349	+	0.227654i
$172$	1.60614	+	1.60614i	0.122467	+	0.122467i
$173$	−9.53000	−	9.53000i	−0.724553	−	0.724553i	0.244976	−	0.969529i	$-0.421220\pi$
$173$	−9.53000	−	9.53000i	−0.724553	−	0.724553i	−0.969529	+	0.244976i	$0.921220\pi$
$174$	−0.665628	−	8.84213i	−0.0504611	−	0.670320i
$175$	−0.972572	+	0.664819i	−0.0735195	+	0.0502556i
$176$			2.26903i			0.171035i
$177$	15.7472	−	18.3111i	1.18363	−	1.37635i
$178$	1.52405	−	1.52405i	0.114233	−	0.114233i
$179$	−14.9589			−1.11808			−0.559042	−	0.829139i	$-0.688831\pi$
$179$	−14.9589			−1.11808			−0.559042	+	0.829139i	$0.688831\pi$
$180$	−7.98644	−	7.11872i	−0.595274	−	0.530598i
$181$	−9.69759			−0.720817			−0.360408	−	0.932795i	$-0.617363\pi$
$181$	−9.69759			−0.720817			−0.360408	+	0.932795i	$0.617363\pi$
$182$	0.302639	−	0.302639i	0.0224331	−	0.0224331i
$183$	−3.84273	+	4.46839i	−0.284063	+	0.330313i
$184$			11.3174i			0.834330i
$185$	0.340966	−	3.65997i	0.0250683	−	0.269086i
$186$	−0.0827594	−	1.09937i	−0.00606821	−	0.0806095i
$187$	−1.13284	−	1.13284i	−0.0828414	−	0.0828414i
$188$	−8.01896	−	8.01896i	−0.584843	−	0.584843i
$189$	0.273641	+	1.19333i	0.0199045	+	0.0868018i
$190$	0.875089	−	9.39330i	0.0634856	−	0.681462i
$191$			22.6760i			1.64078i	0.571806	+	0.820389i	$0.306243\pi$
$191$			22.6760i			1.64078i	−0.571806	+	0.820389i	$0.693757\pi$
$192$	−0.195238	−	0.167901i	−0.0140901	−	0.0121172i
$193$	16.1784	−	16.1784i	1.16455	−	1.16455i	0.181076	−	0.983469i	$-0.442042\pi$
$193$	16.1784	−	16.1784i	1.16455	−	1.16455i	0.983469	−	0.181076i	$-0.0579580\pi$
$194$	−4.35528			−0.312691
$195$	−7.95301	+	7.67549i	−0.569527	+	0.549653i
$196$	11.0754			0.791100
$197$	9.79366	−	9.79366i	0.697769	−	0.697769i	−0.266160	−	0.963929i	$-0.585755\pi$
$197$	9.79366	−	9.79366i	0.697769	−	0.697769i	0.963929	+	0.266160i	$0.0857549\pi$
$198$	1.48310	−	2.01237i	0.105399	−	0.143013i
$199$		−	3.91459i		−	0.277498i	−0.990328	−	0.138749i	$-0.955692\pi$
$199$		−	3.91459i		−	0.277498i	0.990328	−	0.138749i	$-0.0443081\pi$
$200$	9.44507	−	6.45635i	0.667867	−	0.456533i
$201$	15.1243	−	1.13854i	1.06678	−	0.0803066i
$202$	0.319512	+	0.319512i	0.0224808	+	0.0224808i
$203$	1.34000	+	1.34000i	0.0940497	+	0.0940497i
$204$	−3.37096	+	0.253763i	−0.236014	+	0.0177670i
$205$	−12.5527	+	10.4132i	−0.876717	+	0.727286i
$206$		−	4.24133i		−	0.295507i
$207$	−8.80311	+	11.9447i	−0.611858	+	0.830211i
$208$	3.49758	−	3.49758i	0.242514	−	0.242514i
$209$	−8.67728			−0.600220
$210$	−0.580754	−	0.0103126i	−0.0400758	−	0.000711637i
$211$	−14.3888			−0.990568			−0.495284	−	0.868731i	$-0.664936\pi$
$211$	−14.3888			−0.990568			−0.495284	+	0.868731i	$0.664936\pi$
$212$	9.39920	−	9.39920i	0.645540	−	0.645540i
$213$	−9.89177	−	8.50674i	−0.677773	−	0.582872i
$214$		−	3.87086i		−	0.264607i
$215$	−3.17093	−	0.295407i	−0.216255	−	0.0201466i
$216$	−2.65745	−	11.5889i	−0.180816	−	0.788527i
$217$	0.166606	+	0.166606i	0.0113100	+	0.0113100i
$218$	4.13138	+	4.13138i	0.279813	+	0.279813i
$219$	−0.940276	−	12.4905i	−0.0635380	−	0.844031i
$220$	−2.98075	−	3.59318i	−0.200962	−	0.242252i
$221$			3.49242i			0.234925i
$222$	1.18170	−	1.37410i	0.0793104	−	0.0922233i
$223$	18.4037	−	18.4037i	1.23240	−	1.23240i	0.269366	−	0.963038i	$-0.413186\pi$
$223$	18.4037	−	18.4037i	1.23240	−	1.23240i	0.963038	−	0.269366i	$-0.0868141\pi$
$224$	1.33820			0.0894125
$225$	14.9905	+	0.532550i	0.999370	+	0.0355033i
$226$	−0.398749			−0.0265244
$227$	15.7435	−	15.7435i	1.04493	−	1.04493i	0.0459902	−	0.998942i	$-0.485356\pi$
$227$	15.7435	−	15.7435i	1.04493	−	1.04493i	0.998942	−	0.0459902i	$-0.0146443\pi$
$228$	−11.9385	+	13.8823i	−0.790646	+	0.919375i
$229$		−	10.7145i		−	0.708037i	−0.935238	−	0.354018i	$-0.884815\pi$
$229$		−	10.7145i		−	0.708037i	0.935238	−	0.354018i	$-0.115185\pi$
$230$	−4.49459	−	5.41806i	−0.296365	−	0.357256i
$231$	0.0401048	+	0.532748i	0.00263870	+	0.0350523i
$232$	−13.0133	−	13.0133i	−0.854368	−	0.854368i
$233$	8.99413	+	8.99413i	0.589225	+	0.589225i	0.937421	−	0.348197i	$-0.113206\pi$
$233$	8.99413	+	8.99413i	0.589225	+	0.589225i	−0.348197	+	0.937421i	$0.613206\pi$
$234$	−5.38807	+	0.815842i	−0.352229	+	0.0533332i
$235$	15.8315	+	1.47488i	1.03273	+	0.0962104i
$236$		−	22.2379i		−	1.44756i
$237$	13.8077	+	11.8744i	0.896908	+	0.771325i
$238$	−0.129778	+	0.129778i	−0.00841225	+	0.00841225i
$239$	21.1887			1.37059			0.685293	−	0.728268i	$-0.259674\pi$
$239$	21.1887			1.37059			0.685293	+	0.728268i	$0.259674\pi$
$240$	−6.71174	−	0.119182i	−0.433241	−	0.00769317i
$241$	−10.3050			−0.663806			−0.331903	−	0.943314i	$-0.607691\pi$
$241$	−10.3050			−0.663806			−0.331903	+	0.943314i	$0.607691\pi$
$242$	−4.17957	+	4.17957i	−0.268673	+	0.268673i
$243$	6.20957	−	14.2983i	0.398344	−	0.917236i
$244$			5.42663i			0.347405i
$245$	−11.9514	+	9.91434i	−0.763545	+	0.633404i
$246$	−8.01865	+	0.603637i	−0.511250	+	0.0384865i
$247$	13.3755	+	13.3755i	0.851065	+	0.851065i
$248$	−1.61799	−	1.61799i	−0.102742	−	0.102742i
$249$	27.5093	−	2.07088i	1.74333	−	0.131236i
$250$	−1.95763	+	6.84190i	−0.123812	+	0.432720i
$251$			6.76751i			0.427162i	0.976925	+	0.213581i	$0.0685127\pi$
$251$			6.76751i			0.427162i	−0.976925	+	0.213581i	$0.931487\pi$
$252$	0.907489	+	0.668812i	0.0571665	+	0.0421312i
$253$	−4.57852	+	4.57852i	−0.287849	+	0.287849i
$254$	2.05299			0.128816
$255$	3.41042	−	3.29141i	0.213568	−	0.206116i
$256$	−7.46739			−0.466712
$257$	−3.42845	+	3.42845i	−0.213861	+	0.213861i	−0.805905	−	0.592045i	$-0.798321\pi$
$257$	−3.42845	+	3.42845i	−0.213861	+	0.213861i	0.592045	+	0.805905i	$0.298321\pi$
$258$	−1.19049	−	1.02380i	−0.0741168	−	0.0637391i
$259$			0.387324i			0.0240671i
$260$	−0.944032	+	10.1334i	−0.0585464	+	0.628444i
$261$	−3.61232	−	23.8569i	−0.223597	−	1.47670i
$262$	4.21878	+	4.21878i	0.260637	+	0.260637i
$263$	15.2074	+	15.2074i	0.937727	+	0.937727i	0.998172	−	0.0604447i	$-0.0192519\pi$
$263$	15.2074	+	15.2074i	0.937727	+	0.937727i	−0.0604447	+	0.998172i	$0.519252\pi$
$264$	−0.389476	−	5.17375i	−0.0239706	−	0.318422i
$265$	−1.72874	+	18.5565i	−0.106195	+	1.13991i
$266$			0.994067i			0.0609502i
$267$	3.82415	−	4.44678i	0.234034	−	0.272139i
$268$	9.87518	−	9.87518i	0.603223	−	0.603223i
$269$	3.85492			0.235039			0.117519	−	0.993071i	$-0.462506\pi$
$269$	3.85492			0.235039			0.117519	+	0.993071i	$0.462506\pi$
$270$	5.87464	+	4.49267i	0.357519	+	0.273415i
$271$	−8.26158			−0.501856			−0.250928	−	0.968006i	$-0.580736\pi$
$271$	−8.26158			−0.501856			−0.250928	+	0.968006i	$0.580736\pi$
$272$	−1.49984	+	1.49984i	−0.0909409	+	0.0909409i
$273$	0.759382	−	0.883021i	0.0459599	−	0.0534428i
$274$			1.79136i			0.108220i
$275$	6.43300	+	1.20910i	0.387925	+	0.0729117i
$276$	1.02562	+	13.6242i	0.0617349	+	0.820079i
$277$	−2.44738	−	2.44738i	−0.147049	−	0.147049i	0.629749	−	0.776798i	$-0.283158\pi$
$277$	−2.44738	−	2.44738i	−0.147049	−	0.147049i	−0.776798	+	0.629749i	$0.783158\pi$
$278$	−7.35381	−	7.35381i	−0.441052	−	0.441052i
$279$	−0.449130	−	2.96619i	−0.0268887	−	0.177581i
$280$	−0.927840	+	0.769696i	−0.0554490	+	0.0459981i
$281$			20.0205i			1.19432i	0.802121	+	0.597162i	$0.203705\pi$
$281$			20.0205i			1.19432i	−0.802121	+	0.597162i	$0.796295\pi$
$282$	5.94378	+	5.11154i	0.353947	+	0.304388i
$283$	−18.1293	+	18.1293i	−1.07768	+	1.07768i	−0.0809604	+	0.996717i	$0.525799\pi$
$283$	−18.1293	+	18.1293i	−1.07768	+	1.07768i	−0.996717	+	0.0809604i	$0.974201\pi$
$284$	−12.0131			−0.712844
$285$	0.455779	−	25.6672i	0.0269980	−	1.52039i
$286$	−2.37803			−0.140616
$287$	1.21520	−	1.21520i	0.0717313	−	0.0717313i
$288$	−13.7162	−	10.1087i	−0.808233	−	0.595661i
$289$			15.5024i			0.911905i
$290$	11.3981	+	1.06186i	0.669319	+	0.0623544i
$291$	−11.8179	+	0.889641i	−0.692777	+	0.0521517i
$292$	−8.15552	−	8.15552i	−0.477265	−	0.477265i
$293$	4.41602	+	4.41602i	0.257986	+	0.257986i	0.824235	−	0.566248i	$-0.191606\pi$
$293$	4.41602	+	4.41602i	0.257986	+	0.257986i	−0.566248	+	0.824235i	$0.691606\pi$
$294$	−7.63453	+	0.574721i	−0.445255	+	0.0335184i
$295$	19.9067	+	23.9967i	1.15901	+	1.39714i
$296$		−	3.76147i		−	0.218631i
$297$	3.61328	−	5.76345i	0.209664	−	0.334429i
$298$	7.02692	−	7.02692i	0.407058	−	0.407058i
$299$	14.1151			0.816295
$300$	10.7851	−	8.62825i	0.622679	−	0.498152i
$301$	0.335570			0.0193420
$302$	−8.49975	+	8.49975i	−0.489106	+	0.489106i
$303$	0.932253	+	0.801721i	0.0535565	+	0.0460576i
$304$			11.4884i			0.658904i
$305$	−4.85775	−	5.85583i	−0.278154	−	0.335304i
$306$	2.31051	−	0.349850i	0.132083	−	0.0199996i
$307$	−8.21053	−	8.21053i	−0.468600	−	0.468600i	0.432861	−	0.901461i	$-0.357504\pi$
$307$	−8.21053	−	8.21053i	−0.468600	−	0.468600i	−0.901461	+	0.432861i	$0.857504\pi$
$308$	0.347851	+	0.347851i	0.0198206	+	0.0198206i
$309$	−0.866365	−	11.5087i	−0.0492858	−	0.654707i
$310$	1.41716	+	0.132024i	0.0804890	+	0.00749843i
$311$		−	5.75447i		−	0.326306i	−0.986601	−	0.163153i	$-0.947834\pi$
$311$		−	5.75447i		−	0.326306i	0.986601	−	0.163153i	$-0.0521664\pi$
$312$	−7.37469	+	8.57540i	−0.417510	+	0.485487i
$313$	−1.93373	+	1.93373i	−0.109301	+	0.109301i	−0.759642	−	0.650341i	$-0.774626\pi$
$313$	−1.93373	+	1.93373i	−0.109301	+	0.109301i	0.650341	+	0.759642i	$0.274626\pi$
$314$	−3.73496			−0.210776
$315$	−1.57796	+	0.0906462i	−0.0889081	+	0.00510734i
$316$	16.7688			0.943317
$317$	17.5870	−	17.5870i	0.987786	−	0.987786i	−0.0121400	−	0.999926i	$-0.503864\pi$
$317$	17.5870	−	17.5870i	0.987786	−	0.987786i	0.999926	+	0.0121400i	$0.00386438\pi$
$318$	−5.99135	+	6.96683i	−0.335978	+	0.390680i
$319$		−	10.5292i		−	0.589524i
$320$	0.255860	−	0.212251i	0.0143030	−	0.0118652i
$321$	−0.790692	−	10.5035i	−0.0441321	−	0.586246i
$322$	0.524514	+	0.524514i	0.0292300	+	0.0292300i
$323$	−5.73570	−	5.73570i	−0.319143	−	0.319143i
$324$	−4.24933	−	13.7102i	−0.236074	−	0.761679i
$325$	−8.05235	−	11.7799i	−0.446664	−	0.653430i
$326$			1.87251i			0.103709i
$327$	12.0543	+	10.3665i	0.666603	+	0.573267i
$328$	−11.8014	+	11.8014i	−0.651623	+	0.651623i
$329$	−1.67540			−0.0923680
$330$	2.24116	+	2.32219i	0.123372	+	0.127832i
$331$	−12.4794			−0.685932			−0.342966	−	0.939348i	$-0.611432\pi$
$331$	−12.4794			−0.685932			−0.342966	+	0.939348i	$0.611432\pi$
$332$	17.9618	−	17.9618i	0.985783	−	0.985783i
$333$	2.92582	−	3.96995i	0.160334	−	0.217552i
$334$		−	4.23534i		−	0.231748i
$335$	−1.81628	+	19.4962i	−0.0992341	+	1.06519i
$336$	0.705338	−	0.0530972i	0.0384793	−	0.00289669i
$337$	−13.2583	−	13.2583i	−0.722225	−	0.722225i	0.246833	−	0.969058i	$-0.420610\pi$
$337$	−13.2583	−	13.2583i	−0.722225	−	0.722225i	−0.969058	+	0.246833i	$0.920610\pi$
$338$	−2.18550	−	2.18550i	−0.118876	−	0.118876i
$339$	−1.08199	+	0.0814514i	−0.0587657	+	0.00442383i
$340$	0.404821	−	4.34539i	0.0219545	−	0.235662i
$341$		−	1.30913i		−	0.0708933i
$342$	7.50911	−	10.1889i	0.406046	−	0.550951i
$343$	2.32324	−	2.32324i	0.125443	−	0.125443i
$344$	−3.25887			−0.175707
$345$	−13.3027	−	13.7836i	−0.716191	−	0.742086i
$346$	8.57861			0.461189
$347$	−7.42203	+	7.42203i	−0.398436	+	0.398436i	−0.877681	−	0.479245i	$-0.840910\pi$
$347$	−7.42203	+	7.42203i	−0.398436	+	0.398436i	0.479245	+	0.877681i	$0.340910\pi$
$348$	−16.8451	−	14.4865i	−0.902992	−	0.776557i
$349$		−	2.74731i		−	0.147060i	−0.997293	−	0.0735302i	$-0.976573\pi$
$349$		−	2.74731i		−	0.147060i	0.997293	−	0.0735302i	$-0.0234265\pi$
$350$	0.138515	−	0.736964i	0.00740392	−	0.0393924i
$351$	−14.4537	+	3.31437i	−0.771481	+	0.176908i
$352$	−5.25756	−	5.25756i	−0.280229	−	0.280229i
$353$	23.8825	+	23.8825i	1.27114	+	1.27114i	0.945493	+	0.325642i	$0.105580\pi$
$353$	23.8825	+	23.8825i	1.27114	+	1.27114i	0.325642	+	0.945493i	$0.394420\pi$
$354$	1.15396	+	15.3291i	0.0613324	+	0.814733i
$355$	12.9632	−	10.7537i	0.688014	−	0.570747i
$356$		−	5.40040i		−	0.286220i
$357$	−0.325639	+	0.378657i	−0.0172346	+	0.0200407i
$358$	6.73279	−	6.73279i	0.355839	−	0.355839i
$359$	1.51489			0.0799529			0.0399765	−	0.999201i	$-0.487272\pi$
$359$	1.51489			0.0799529			0.0399765	+	0.999201i	$0.487272\pi$
$360$	15.3243	−	0.880305i	0.807661	−	0.0463962i
$361$	−24.9341			−1.31232
$362$	4.36474	−	4.36474i	0.229405	−	0.229405i
$363$	−10.4874	+	12.1949i	−0.550444	+	0.640064i
$364$		−	1.07238i		−	0.0562082i
$365$	16.1011	+	1.49999i	0.842770	+	0.0785133i
$366$	−0.281597	−	3.74071i	−0.0147193	−	0.195530i
$367$	−9.92553	−	9.92553i	−0.518108	−	0.518108i	0.398890	−	0.916999i	$-0.369395\pi$
$367$	−9.92553	−	9.92553i	−0.518108	−	0.518108i	−0.916999	+	0.398890i	$0.869395\pi$
$368$	6.06178	+	6.06178i	0.315992	+	0.315992i
$369$	−21.6350	+	3.27590i	−1.12627	+	0.170536i
$370$	1.49383	+	1.80076i	0.0776606	+	0.0936169i
$371$		−	1.96378i		−	0.101954i
$372$	−2.09440	−	1.80114i	−0.108589	−	0.0933850i
$373$	0.317045	−	0.317045i	0.0164160	−	0.0164160i	−0.698851	−	0.715267i	$-0.746305\pi$
$373$	0.317045	−	0.317045i	0.0164160	−	0.0164160i	0.715267	+	0.698851i	$0.246305\pi$
$374$	1.01975			0.0527298
$375$	−3.91440	+	18.9652i	−0.202139	+	0.979357i
$376$	16.2706			0.839091
$377$	−16.2302	+	16.2302i	−0.835899	+	0.835899i
$378$	−0.660260	−	0.413937i	−0.0339601	−	0.0212906i
$379$			26.3234i			1.35214i	0.736837	+	0.676071i	$0.236319\pi$
$379$			26.3234i			1.35214i	−0.736837	+	0.676071i	$0.763681\pi$
$380$	−15.0919	−	18.1927i	−0.774198	−	0.933267i
$381$	5.57073	−	0.419360i	0.285397	−	0.0214844i
$382$	−10.2061	−	10.2061i	−0.522190	−	0.522190i
$383$	−10.8811	−	10.8811i	−0.556000	−	0.556000i	0.372166	−	0.928166i	$-0.378615\pi$
$383$	−10.8811	−	10.8811i	−0.556000	−	0.556000i	−0.928166	+	0.372166i	$0.878615\pi$
$384$	−19.4557	+	1.46461i	−0.992845	+	0.0747405i
$385$	−0.686747	−	0.0639780i	−0.0349999	−	0.00326062i
$386$			14.5633i			0.741251i
$387$	−3.43949	−	2.53487i	−0.174839	−	0.128855i
$388$	−7.71633	+	7.71633i	−0.391737	+	0.391737i
$389$	35.9572			1.82310			0.911551	−	0.411186i	$-0.134885\pi$
$389$	35.9572			1.82310			0.911551	+	0.411186i	$0.134885\pi$
$390$	0.124907	−	7.03415i	0.00632492	−	0.356188i
$391$	−6.05283			−0.306105
$392$	−11.2361	+	11.2361i	−0.567507	+	0.567507i
$393$	12.3093	+	10.5858i	0.620921	+	0.533981i
$394$			8.81595i			0.444141i
$395$	−18.0950	+	15.0109i	−0.910461	+	0.755279i
$396$	−0.937721	−	6.19300i	−0.0471222	−	0.311210i
$397$	−2.31541	−	2.31541i	−0.116207	−	0.116207i	0.646612	−	0.762819i	$-0.276185\pi$
$397$	−2.31541	−	2.31541i	−0.116207	−	0.116207i	−0.762819	+	0.646612i	$0.776185\pi$
$398$	1.76190	+	1.76190i	0.0883159	+	0.0883159i
$399$	0.203056	+	2.69737i	0.0101655	+	0.135037i
$400$	1.60081	−	8.51705i	0.0800403	−	0.425852i
$401$			27.7888i			1.38771i	0.720117	+	0.693853i	$0.244088\pi$
$401$			27.7888i			1.38771i	−0.720117	+	0.693853i	$0.755912\pi$
$402$	−6.29476	+	7.31964i	−0.313954	+	0.365070i
$403$	−2.01795	+	2.01795i	−0.100521	+	0.100521i
$404$	1.13217			0.0563278
$405$	16.8584	+	10.9907i	0.837698	+	0.546133i
$406$	−1.20623			−0.0598641
$407$	1.52172	−	1.52172i	0.0754291	−	0.0754291i
$408$	3.16242	−	3.67731i	0.156563	−	0.182054i
$409$			10.3916i			0.513833i	0.966434	+	0.256917i	$0.0827066\pi$
$409$			10.3916i			0.513833i	−0.966434	+	0.256917i	$0.917293\pi$
$410$	0.962964	−	10.3366i	0.0475574	−	0.510486i
$411$	0.365916	+	4.86078i	0.0180493	+	0.239765i
$412$	−7.51445	−	7.51445i	−0.370210	−	0.370210i
$413$	−2.32309	−	2.32309i	−0.114312	−	0.114312i
$414$	−1.41396	−	9.33825i	−0.0694925	−	0.458950i
$415$	−3.30361	+	35.4613i	−0.162168	+	1.74073i
$416$			16.2085i			0.794685i
$417$	−21.4565	−	18.4522i	−1.05073	−	0.903607i
$418$	3.90551	−	3.90551i	0.191025	−	0.191025i
$419$	−24.6777			−1.20558			−0.602792	−	0.797898i	$-0.705945\pi$
$419$	−24.6777			−1.20558			−0.602792	+	0.797898i	$0.705945\pi$
$420$	−1.04720	+	1.01066i	−0.0510984	+	0.0493153i
$421$	40.6295			1.98016			0.990080	−	0.140508i	$-0.0448737\pi$
$421$	40.6295			1.98016			0.990080	+	0.140508i	$0.0448737\pi$
$422$	6.47619	−	6.47619i	0.315256	−	0.315256i
$423$	17.1724	+	12.6559i	0.834949	+	0.615350i
$424$			19.0711i			0.926175i
$425$	3.45301	+	5.05146i	0.167496	+	0.245032i
$426$	8.28088	−	0.623378i	0.401210	−	0.0302027i
$427$	0.566894	+	0.566894i	0.0274339	+	0.0274339i
$428$	−6.85809	−	6.85809i	−0.331498	−	0.331498i
$429$	−6.45270	+	0.485753i	−0.311539	+	0.0234524i
$430$	1.56014	−	1.29423i	0.0752368	−	0.0624132i
$431$			26.6096i			1.28174i	0.767650	+	0.640869i	$0.221426\pi$
$431$			26.6096i			1.28174i	−0.767650	+	0.640869i	$0.778574\pi$
$432$	−7.63058	−	4.78384i	−0.367127	−	0.230163i
$433$	16.3242	−	16.3242i	0.784490	−	0.784490i	−0.196095	−	0.980585i	$-0.562826\pi$
$433$	16.3242	−	16.3242i	0.784490	−	0.784490i	0.980585	+	0.196095i	$0.0628260\pi$
$434$	−0.149974			−0.00719896
$435$	31.1452	+	0.553054i	1.49330	+	0.0265169i
$436$	14.6393			0.701096
$437$	−23.1816	+	23.1816i	−1.10893	+	1.10893i
$438$	6.04499	+	5.19859i	0.288841	+	0.248398i
$439$			9.60942i			0.458632i	0.973352	+	0.229316i	$0.0736490\pi$
$439$			9.60942i			0.458632i	−0.973352	+	0.229316i	$0.926351\pi$
$440$	6.66930	+	0.621319i	0.317947	+	0.0296202i
$441$	−20.5987	+	3.11897i	−0.980889	+	0.148523i
$442$	−1.57188	−	1.57188i	−0.0747668	−	0.0747668i
$443$	−1.46051	−	1.46051i	−0.0693909	−	0.0693909i	0.671560	−	0.740951i	$-0.265625\pi$
$443$	−1.46051	−	1.46051i	−0.0693909	−	0.0693909i	−0.740951	+	0.671560i	$0.765625\pi$
$444$	−0.340876	−	4.52816i	−0.0161772	−	0.214897i
$445$	4.83426	+	5.82752i	0.229166	+	0.276251i
$446$			16.5664i			0.784444i
$447$	17.6319	−	20.5027i	0.833962	−	0.969743i
$448$	−0.0247694	+	0.0247694i	−0.00117025	+	0.00117025i
$449$	−4.84829			−0.228805			−0.114402	−	0.993434i	$-0.536495\pi$
$449$	−4.84829			−0.228805			−0.114402	+	0.993434i	$0.536495\pi$
$450$	−6.98670	+	6.50732i	−0.329356	+	0.306758i
$451$	−9.54863			−0.449627
$452$	−0.706472	+	0.706472i	−0.0332296	+	0.0332296i
$453$	−21.3276	+	24.8000i	−1.00206	+	1.16521i
$454$			14.1718i			0.665115i
$455$	0.959964	+	1.15720i	0.0450038	+	0.0542504i
$456$	−1.97196	−	26.1953i	−0.0923456	−	1.22671i
$457$	−6.22154	−	6.22154i	−0.291031	−	0.291031i	0.546456	−	0.837488i	$-0.315976\pi$
$457$	−6.22154	−	6.22154i	−0.291031	−	0.291031i	−0.837488	+	0.546456i	$0.815976\pi$
$458$	4.82245	+	4.82245i	0.225338	+	0.225338i
$459$	6.19804	−	1.42127i	0.289300	−	0.0663392i
$460$	−17.5625	−	1.63614i	−0.818854	−	0.0762852i
$461$		−	33.8943i		−	1.57862i	−0.613997	−	0.789309i	$-0.710439\pi$
$461$		−	33.8943i		−	1.57862i	0.613997	−	0.789309i	$-0.289561\pi$
$462$	−0.257832	−	0.221731i	−0.0119954	−	0.0103159i
$463$	19.4407	−	19.4407i	0.903486	−	0.903486i	−0.0922496	−	0.995736i	$-0.529406\pi$
$463$	19.4407	−	19.4407i	0.903486	−	0.903486i	0.995736	+	0.0922496i	$0.0294058\pi$
$464$	−13.9403			−0.647162
$465$	3.87237	+	0.0687627i	0.179577	+	0.00318880i
$466$	−8.09623			−0.375051
$467$	−28.2835	+	28.2835i	−1.30880	+	1.30880i	−0.386523	+	0.922280i	$0.626324\pi$
$467$	−28.2835	+	28.2835i	−1.30880	+	1.30880i	−0.922280	+	0.386523i	$0.873676\pi$
$468$	−8.10071	+	10.9916i	−0.374456	+	0.508087i
$469$		−	2.06323i		−	0.0952709i
$470$	−7.78933	+	6.46169i	−0.359295	+	0.298056i
$471$	−10.1347	+	0.762930i	−0.466981	+	0.0351540i
$472$	22.5605	+	22.5605i	1.03843	+	1.03843i
$473$	−1.31839	−	1.31839i	−0.0606198	−	0.0606198i
$474$	−11.5591	+	0.870160i	−0.530928	+	0.0399678i
$475$	32.5711	+	6.12184i	1.49446	+	0.280889i
$476$			0.459860i			0.0210777i
$477$	−14.8342	+	20.1281i	−0.679213	+	0.921602i
$478$	−9.53672	+	9.53672i	−0.436199	+	0.436199i
$479$	−4.12664			−0.188551			−0.0942756	−	0.995546i	$-0.530053\pi$
$479$	−4.12664			−0.188551			−0.0942756	+	0.995546i	$0.530053\pi$
$480$	15.8279	−	15.2756i	0.722441	−	0.697231i
$481$	−4.69131			−0.213905
$482$	4.63814	−	4.63814i	0.211261	−	0.211261i
$483$	1.53039	+	1.31611i	0.0696353	+	0.0598851i
$484$			14.8100i			0.673184i
$485$	1.41922	−	15.2340i	0.0644434	−	0.691742i
$486$	3.64061	+	9.23027i	0.165141	+	0.418694i
$487$	−25.9558	−	25.9558i	−1.17617	−	1.17617i	−0.980712	−	0.195458i	$-0.937381\pi$
$487$	−25.9558	−	25.9558i	−1.17617	−	1.17617i	−0.195458	−	0.980712i	$-0.562619\pi$
$488$	−5.50536	−	5.50536i	−0.249216	−	0.249216i
$489$	0.382493	+	5.08099i	0.0172969	+	0.229770i
$490$	0.916835	−	9.84141i	0.0414184	−	0.444590i
$491$		−	24.4228i		−	1.10219i	−0.834444	−	0.551093i	$-0.814211\pi$
$491$		−	24.4228i		−	1.10219i	0.834444	−	0.551093i	$-0.185789\pi$
$492$	−13.1373	+	15.2763i	−0.592276	+	0.688708i
$493$	6.95986	−	6.95986i	0.313456	−	0.313456i
$494$	−12.0402			−0.541716
$495$	6.55566	+	5.84339i	0.294655	+	0.262641i
$496$	−1.73324			−0.0778246
$497$	−1.25495	+	1.25495i	−0.0562920	+	0.0562920i
$498$	−11.4494	+	13.3136i	−0.513062	+	0.596596i
$499$		−	25.4810i		−	1.14068i	−0.821407	−	0.570342i	$-0.806811\pi$
$499$		−	25.4810i		−	1.14068i	0.821407	−	0.570342i	$-0.193189\pi$
$500$	8.65357	+	15.5903i	0.386999	+	0.697221i
$501$	−0.865143	−	11.4925i	−0.0386517	−	0.513445i
$502$	−3.04595	−	3.04595i	−0.135947	−	0.135947i
$503$	−3.10337	−	3.10337i	−0.138373	−	0.138373i	0.634528	−	0.772900i	$-0.281195\pi$
$503$	−3.10337	−	3.10337i	−0.138373	−	0.138373i	−0.772900	+	0.634528i	$0.781195\pi$
$504$	−1.59917	+	0.242140i	−0.0712326	+	0.0107858i
$505$	−1.22172	+	1.01349i	−0.0543658	+	0.0450995i
$506$		−	4.12144i		−	0.183220i
$507$	−6.37672	−	5.48386i	−0.283200	−	0.243547i
$508$	3.63733	−	3.63733i	0.161380	−	0.161380i
$509$	−20.1600			−0.893575			−0.446788	−	0.894640i	$-0.647432\pi$
$509$	−20.1600			−0.893575			−0.446788	+	0.894640i	$0.647432\pi$
$510$	−0.0535628	+	3.01639i	−0.00237180	+	0.133568i
$511$	−1.70393			−0.0753776
$512$	−12.5695	+	12.5695i	−0.555499	+	0.555499i
$513$	18.2945	−	29.1810i	0.807721	−	1.28837i
$514$		−	3.08618i		−	0.136126i
$515$	14.8355	+	1.38209i	0.653729	+	0.0609020i
$516$	−3.92311	+	0.295328i	−0.172705	+	0.0130011i
$517$	6.58235	+	6.58235i	0.289492	+	0.289492i
$518$	−0.174329	−	0.174329i	−0.00765956	−	0.00765956i
$519$	23.2778	−	1.75233i	1.02178	−	0.0769188i
$520$	−9.32263	−	11.2381i	−0.408824	−	0.492823i
$521$			33.7108i			1.47690i	0.674309	+	0.738449i	$0.264442\pi$
$521$			33.7108i			1.47690i	−0.674309	+	0.738449i	$0.735558\pi$
$522$	12.3635	+	9.11175i	0.541134	+	0.398811i
$523$	−8.91031	+	8.91031i	−0.389620	+	0.389620i	−0.874552	−	0.484932i	$-0.838844\pi$
$523$	−8.91031	+	8.91031i	−0.389620	+	0.389620i	0.484932	+	0.874552i	$0.338844\pi$
$524$	14.9490			0.653050
$525$	0.225317	−	2.02802i	0.00983365	−	0.0885101i
$526$	−13.6892			−0.596878
$527$	0.865338	−	0.865338i	0.0376947	−	0.0376947i
$528$	−2.97975	−	2.56253i	−0.129677	−	0.111520i
$529$			1.46329i			0.0636215i
$530$	−7.57389	−	9.13005i	−0.328989	−	0.396584i
$531$	6.26248	+	41.3593i	0.271768	+	1.79484i
$532$	1.76121	+	1.76121i	0.0763581	+	0.0763581i
$533$	14.7187	+	14.7187i	0.637537	+	0.637537i
$534$	0.280236	+	3.72262i	0.0121270	+	0.161094i
$535$	13.5396	+	1.26137i	0.585370	+	0.0545336i
$536$			20.0369i			0.865462i
$537$	16.8939	−	19.6445i	0.729026	−	0.847722i
$538$	−1.73504	+	1.73504i	−0.0748029	+	0.0748029i
$539$	−9.09123			−0.391587
$540$	18.3680	−	2.44847i	0.790432	−	0.105365i
$541$	9.50247			0.408543			0.204272	−	0.978914i	$-0.434517\pi$
$541$	9.50247			0.408543			0.204272	+	0.978914i	$0.434517\pi$
$542$	3.71841	−	3.71841i	0.159719	−	0.159719i
$543$	10.9520	−	12.7351i	0.469995	−	0.546517i
$544$		−	6.95052i		−	0.298001i
$545$	−15.7972	+	13.1046i	−0.676676	+	0.561341i
$546$	0.0556478	+	0.739220i	0.00238151	+	0.0316357i
$547$	−17.9418	−	17.9418i	−0.767136	−	0.767136i	0.210465	−	0.977601i	$-0.432502\pi$
$547$	−17.9418	−	17.9418i	−0.767136	−	0.767136i	−0.977601	+	0.210465i	$0.932502\pi$
$548$	3.17378	+	3.17378i	0.135577	+	0.135577i
$549$	−1.52821	−	10.0928i	−0.0652224	−	0.430749i
$550$	−3.43959	+	2.35120i	−0.146665	+	0.100255i
$551$		−	53.3108i		−	2.27112i
$552$	−14.8623	−	12.7813i	−0.632583	−	0.544010i
$553$	1.75175	−	1.75175i	0.0744921	−	0.0744921i
$554$	2.20305			0.0935988
$555$	4.42130	+	4.58116i	0.187674	+	0.194459i
$556$	−26.0578			−1.10510
$557$	19.6562	−	19.6562i	0.832862	−	0.832862i	−0.155046	−	0.987907i	$-0.549552\pi$
$557$	19.6562	−	19.6562i	0.832862	−	0.832862i	0.987907	+	0.155046i	$0.0495525\pi$
$558$	1.53718	+	1.13289i	0.0650741	+	0.0479590i
$559$			4.06446i			0.171908i
$560$	−0.0847044	+	0.909227i	−0.00357942	+	0.0384218i
$561$	2.76705	−	0.208301i	0.116825	−	0.00879448i
$562$	−9.01092	−	9.01092i	−0.380103	−	0.380103i
$563$	21.1380	+	21.1380i	0.890861	+	0.890861i	0.994604	−	0.103743i	$-0.0330821\pi$
$563$	21.1380	+	21.1380i	0.890861	+	0.890861i	−0.103743	+	0.994604i	$0.533082\pi$
$564$	19.5869	−	1.47449i	0.824759	−	0.0620871i
$565$	0.129937	−	1.39476i	0.00546649	−	0.0586779i
$566$		−	16.3195i		−	0.685959i
$567$	−1.87615	−	0.988334i	−0.0787908	−	0.0415061i
$568$	12.1873	−	12.1873i	0.511369	−	0.511369i
$569$	35.0904			1.47107			0.735533	−	0.677489i	$-0.236932\pi$
$569$	35.0904			1.47107			0.735533	+	0.677489i	$0.236932\pi$
$570$	11.3473	+	11.7575i	0.475284	+	0.492469i
$571$	26.3361			1.10213			0.551067	−	0.834461i	$-0.314221\pi$
$571$	26.3361			1.10213			0.551067	+	0.834461i	$0.314221\pi$
$572$	−4.21320	+	4.21320i	−0.176163	+	0.176163i
$573$	−29.7787	−	25.6092i	−1.24402	−	1.06984i
$574$			1.09389i			0.0456581i
$575$	20.4161	−	13.9558i	0.851411	−	0.581997i
$576$	0.440985	−	0.0667724i	0.0183744	−	0.00278218i
$577$	30.2874	+	30.2874i	1.26088	+	1.26088i	0.950667	+	0.310213i	$0.100400\pi$
$577$	30.2874	+	30.2874i	1.26088	+	1.26088i	0.310213	+	0.950667i	$0.399600\pi$
$578$	−6.97738	−	6.97738i	−0.290221	−	0.290221i
$579$	2.97480	+	39.5170i	0.123629	+	1.64227i
$580$	22.0755	−	18.3129i	0.916637	−	0.760402i
$581$		−	3.75277i		−	0.155691i
$582$	4.91864	−	5.71947i	0.203884	−	0.237079i
$583$	−7.71532	+	7.71532i	−0.319536	+	0.319536i
$584$	16.5477			0.684747
$585$	−1.09792	−	19.1124i	−0.0453932	−	0.790202i
$586$	−3.97516			−0.164212
$587$	−13.8884	+	13.8884i	−0.573236	+	0.573236i	−0.933031	−	0.359795i	$-0.882847\pi$
$587$	−13.8884	+	13.8884i	−0.573236	+	0.573236i	0.359795	+	0.933031i	$0.382847\pi$
$588$	−12.5080	+	14.5445i	−0.515822	+	0.599806i
$589$		−	6.62828i		−	0.273114i
$590$	−19.7602	−	1.84088i	−0.813516	−	0.0757879i
$591$	1.80081	+	23.9218i	0.0740755	+	0.984010i
$592$	−2.01470	−	2.01470i	−0.0828039	−	0.0828039i
$593$	−31.1997	−	31.1997i	−1.28122	−	1.28122i	−0.939974	−	0.341245i	$-0.889151\pi$
$593$	−31.1997	−	31.1997i	−1.28122	−	1.28122i	−0.341245	−	0.939974i	$-0.610849\pi$
$594$	0.967758	+	4.22032i	0.0397076	+	0.173162i
$595$	−0.411652	−	0.496232i	−0.0168761	−	0.0203435i
$596$		−	24.8995i		−	1.01992i
$597$	5.14075	+	4.42095i	0.210397	+	0.180937i
$598$	−6.35297	+	6.35297i	−0.259792	+	0.259792i
$599$	−8.01039			−0.327296			−0.163648	−	0.986519i	$-0.552326\pi$
$599$	−8.01039			−0.327296			−0.163648	+	0.986519i	$0.552326\pi$
$600$	−2.18815	+	19.6950i	−0.0893310	+	0.804045i
$601$	−15.4940			−0.632012			−0.316006	−	0.948757i	$-0.602342\pi$
$601$	−15.4940			−0.632012			−0.316006	+	0.948757i	$0.602342\pi$
$602$	−0.151035	+	0.151035i	−0.00615573	+	0.00615573i
$603$	−15.5855	+	21.1474i	−0.634689	+	0.861189i
$604$			30.1184i			1.22550i
$605$	−13.2575	−	15.9814i	−0.538993	−	0.649736i
$606$	−0.780434	+	0.0587504i	−0.0317030	+	0.00238657i
$607$	−21.2326	−	21.2326i	−0.861806	−	0.861806i	0.129742	−	0.991548i	$-0.458585\pi$
$607$	−21.2326	−	21.2326i	−0.861806	−	0.861806i	−0.991548	+	0.129742i	$0.958585\pi$
$608$	−26.6197	−	26.6197i	−1.07957	−	1.07957i
$609$	−3.27306	+	0.246393i	−0.132631	+	0.00998435i
$610$	4.82202	+	0.449223i	0.195238	+	0.0181885i
$611$		−	20.2927i		−	0.820953i
$612$	3.47375	−	4.71342i	0.140418	−	0.190529i
$613$	28.9411	−	28.9411i	1.16892	−	1.16892i	0.186456	−	0.982463i	$-0.440300\pi$
$613$	28.9411	−	28.9411i	1.16892	−	1.16892i	0.982463	−	0.186456i	$-0.0597003\pi$
$614$	7.39086			0.298271
$615$	0.501547	−	28.2446i	0.0202243	−	1.13893i
$616$	−0.705794			−0.0284372
$617$	−1.87095	+	1.87095i	−0.0753217	+	0.0753217i	−0.743764	−	0.668442i	$-0.766961\pi$
$617$	−1.87095	+	1.87095i	−0.0753217	+	0.0753217i	0.668442	+	0.743764i	$0.266961\pi$
$618$	5.56983	+	4.78995i	0.224051	+	0.192680i
$619$		−	2.01941i		−	0.0811669i	−0.999176	−	0.0405835i	$-0.987078\pi$
$619$		−	2.01941i		−	0.0811669i	0.999176	−	0.0405835i	$-0.0129217\pi$
$620$	2.74471	−	2.27690i	0.110230	−	0.0914423i
$621$	−5.74424	−	25.0502i	−0.230509	−	1.00523i
$622$	2.59000	+	2.59000i	0.103849	+	0.103849i
$623$	−0.564153	−	0.564153i	−0.0226023	−	0.0226023i
$624$	0.643119	+	8.54312i	0.0257454	+	0.341999i
$625$	−23.2939	−	9.07700i	−0.931758	−	0.363080i
$626$		−	1.74068i		−	0.0695716i
$627$	9.79970	−	11.3952i	0.391362	−	0.455082i
$628$	−6.61730	+	6.61730i	−0.264059	+	0.264059i
$629$	2.01173			0.0802129
$630$	0.669418	−	0.751015i	0.0266703	−	0.0299212i
$631$	9.12584			0.363294			0.181647	−	0.983364i	$-0.441857\pi$
$631$	9.12584			0.363294			0.181647	+	0.983364i	$0.441857\pi$
$632$	−17.0120	+	17.0120i	−0.676703	+	0.676703i
$633$	16.2501	−	18.8958i	0.645882	−	0.751041i
$634$			15.8313i			0.628741i
$635$	−0.668992	+	7.18103i	−0.0265481	+	0.284971i
$636$	1.72828	+	22.9583i	0.0685307	+	0.910355i
$637$	14.0136	+	14.0136i	0.555240	+	0.555240i
$638$	4.73905	+	4.73905i	0.187621	+	0.187621i
$639$	22.3426	−	3.38303i	0.883858	−	0.133831i
$640$	2.33645	−	25.0797i	0.0923561	−	0.991361i
$641$		−	44.3028i		−	1.74985i	−0.484255	−	0.874927i	$-0.660909\pi$
$641$		−	44.3028i		−	1.74985i	0.484255	−	0.874927i	$-0.339091\pi$
$642$	5.08332	+	4.37157i	0.200623	+	0.172532i
$643$	15.2507	−	15.2507i	0.601430	−	0.601430i	−0.339262	−	0.940692i	$-0.610177\pi$
$643$	15.2507	−	15.2507i	0.601430	−	0.601430i	0.940692	+	0.339262i	$0.110177\pi$
$644$	1.85859			0.0732386
$645$	3.96903	−	3.83053i	0.156280	−	0.150827i
$646$	5.16310			0.203140
$647$	30.2415	−	30.2415i	1.18892	−	1.18892i	0.211547	−	0.977368i	$-0.432150\pi$
$647$	30.2415	−	30.2415i	1.18892	−	1.18892i	0.977368	−	0.211547i	$-0.0678502\pi$
$648$	18.2201	+	9.59814i	0.715753	+	0.377051i
$649$			18.2540i			0.716531i
$650$	8.92618	+	1.67770i	0.350114	+	0.0658049i
$651$	−0.406948	+	0.0306347i	−0.0159496	+	0.00120067i
$652$	3.31756	+	3.31756i	0.129926	+	0.129926i
$653$	0.275708	+	0.275708i	0.0107893	+	0.0107893i	0.712481	−	0.701692i	$-0.247572\pi$
$653$	0.275708	+	0.275708i	0.0107893	+	0.0107893i	−0.701692	+	0.712481i	$0.747572\pi$
$654$	−10.0912	+	0.759659i	−0.394598	+	0.0297050i
$655$	−16.1313	+	13.3819i	−0.630303	+	0.522872i
$656$			12.6420i			0.493588i
$657$	17.4648	+	12.8714i	0.681367	+	0.502161i
$658$	0.754073	−	0.754073i	0.0293968	−	0.0293968i
$659$	29.1198			1.13435			0.567174	−	0.823598i	$-0.308037\pi$
$659$	29.1198			1.13435			0.567174	+	0.823598i	$0.308037\pi$
$660$	8.08498	+	0.143567i	0.314707	+	0.00558834i
$661$	−34.6100			−1.34617			−0.673086	−	0.739564i	$-0.735032\pi$
$661$	−34.6100			−1.34617			−0.673086	+	0.739564i	$0.735032\pi$
$662$	5.61680	−	5.61680i	0.218303	−	0.218303i
$663$	−4.58634	−	3.94417i	−0.178119	−	0.153179i
$664$			36.4448i			1.41433i
$665$	−3.47709	−	0.323929i	−0.134836	−	0.0125614i
$666$	0.469948	+	3.10368i	0.0182101	+	0.120265i
$667$	−28.1292	−	28.1292i	−1.08917	−	1.08917i
$668$	−7.50385	−	7.50385i	−0.290333	−	0.290333i
$669$	3.38399	+	44.9525i	0.130833	+	1.73796i
$670$	−7.95744	−	9.59240i	−0.307423	−	0.370587i
$671$		−	4.45444i		−	0.171962i
$672$	−1.51130	+	1.75737i	−0.0582998	+	0.0677919i
$673$	−20.3105	+	20.3105i	−0.782911	+	0.782911i	−0.980321	−	0.197410i	$-0.936747\pi$
$673$	−20.3105	+	20.3105i	−0.782911	+	0.782911i	0.197410	+	0.980321i	$0.436747\pi$
$674$	11.9347			0.459708
$675$	−17.6290	+	19.0845i	−0.678539	+	0.734565i
$676$	−7.74420			−0.297854
$677$	16.8878	−	16.8878i	0.649050	−	0.649050i	−0.303713	−	0.952763i	$-0.598227\pi$
$677$	16.8878	−	16.8878i	0.649050	−	0.649050i	0.952763	+	0.303713i	$0.0982265\pi$
$678$	0.450328	−	0.523648i	0.0172947	−	0.0201106i
$679$			1.61218i			0.0618697i
$680$	3.99774	+	4.81912i	0.153306	+	0.184805i
$681$	2.89484	+	38.4547i	0.110930	+	1.47359i
$682$	0.589219	+	0.589219i	0.0225623	+	0.0225623i
$683$	−33.0111	−	33.0111i	−1.26314	−	1.26314i	−0.949565	−	0.313571i	$-0.898475\pi$
$683$	−33.0111	−	33.0111i	−1.26314	−	1.26314i	−0.313571	−	0.949565i	$-0.601525\pi$
$684$	−4.74780	−	31.3559i	−0.181536	−	1.19892i
$685$	−6.26587	−	0.583734i	−0.239407	−	0.0223033i
$686$			2.09130i			0.0798464i
$687$	14.0706	+	12.1005i	0.536828	+	0.461662i
$688$	−1.74550	+	1.74550i	−0.0665467	+	0.0665467i
$689$	23.7855			0.906154
$690$	12.1911	+	0.216481i	0.464108	+	0.00824129i
$691$	22.9945			0.874753			0.437377	−	0.899278i	$-0.355908\pi$
$691$	22.9945			0.874753			0.437377	+	0.899278i	$0.355908\pi$
$692$	15.1989	−	15.1989i	0.577776	−	0.577776i
$693$	−0.744912	−	0.548993i	−0.0282969	−	0.0208545i
$694$		−	6.68108i		−	0.253610i
$695$	28.1188	−	23.3261i	1.06661	−	0.884810i
$696$	31.7861	−	2.39283i	1.20485	−	0.0907001i
$697$	−6.31167	−	6.31167i	−0.239072	−	0.239072i
$698$	1.23652	+	1.23652i	0.0468031	+	0.0468031i
$699$	−21.9689	+	1.65380i	−0.830939	+	0.0625523i
$700$	−1.06029	−	1.55110i	−0.0400750	−	0.0586262i
$701$		−	3.95998i		−	0.149566i	−0.997200	−	0.0747831i	$-0.976174\pi$
$701$		−	3.95998i		−	0.149566i	0.997200	−	0.0747831i	$-0.0238265\pi$
$702$	5.01364	−	7.99713i	0.189228	−	0.301832i
$703$	7.70468	−	7.70468i	0.290587	−	0.290587i
$704$	0.194629			0.00733536
$705$	−19.8162	+	19.1247i	−0.746321	+	0.720278i
$706$	−21.4982			−0.809097
$707$	0.118273	−	0.118273i	0.00444811	−	0.00444811i
$708$	29.2034	+	25.1144i	1.09753	+	0.943858i
$709$		−	34.2787i		−	1.28736i	−0.765294	−	0.643681i	$-0.777406\pi$
$709$		−	34.2787i		−	1.28736i	0.765294	−	0.643681i	$-0.222594\pi$
$710$	−0.994456	+	10.6746i	−0.0373213	+	0.400611i
$711$	−31.1875	+	4.72230i	−1.16962	+	0.177100i
$712$	5.47874	+	5.47874i	0.205324	+	0.205324i
$713$	−3.49738	−	3.49738i	−0.130978	−	0.130978i
$714$	−0.0238629	−	0.316993i	−0.000893048	−	0.0118632i
$715$	0.774908	−	8.31795i	0.0289799	−	0.311074i
$716$		−	23.8572i		−	0.891587i
$717$	−23.9295	+	27.8256i	−0.893665	+	1.03917i
$718$	−0.681829	+	0.681829i	−0.0254456	+	0.0254456i
$719$	−15.3242			−0.571495			−0.285747	−	0.958305i	$-0.592242\pi$
$719$	−15.3242			−0.571495			−0.285747	+	0.958305i	$0.592242\pi$
$720$	7.73643	−	8.67944i	0.288320	−	0.323463i
$721$	−1.57000			−0.0584697
$722$	11.2225	−	11.2225i	0.417656	−	0.417656i
$723$	11.6380	−	13.5329i	0.432822	−	0.503292i
$724$		−	15.4662i		−	0.574796i
$725$	−7.42840	+	39.5226i	−0.275884	+	1.46783i
$726$	−0.768519	−	10.2089i	−0.0285224	−	0.378888i
$727$	−18.2934	−	18.2934i	−0.678465	−	0.678465i	0.281188	−	0.959653i	$-0.409272\pi$
$727$	−18.2934	−	18.2934i	−0.678465	−	0.678465i	−0.959653	+	0.281188i	$0.909272\pi$
$728$	1.08794	+	1.08794i	0.0403218	+	0.0403218i
$729$	11.7641	+	24.3024i	0.435708	+	0.900088i
$730$	−7.92198	+	6.57173i	−0.293206	+	0.243231i
$731$		−	1.74292i		−	0.0644644i
$732$	−7.12640	−	6.12858i	−0.263399	−	0.226519i
$733$	31.7157	−	31.7157i	1.17145	−	1.17145i	0.189582	−	0.981865i	$-0.439287\pi$
$733$	31.7157	−	31.7157i	1.17145	−	1.17145i	0.981865	−	0.189582i	$-0.0607132\pi$
$734$	8.93465			0.329784
$735$	0.477522	−	26.8916i	0.0176137	−	0.991913i
$736$	−28.0914			−1.03546
$737$	−8.10603	+	8.10603i	−0.298589	+	0.298589i
$738$	8.26316	−	11.2120i	0.304171	−	0.412720i
$739$			27.0980i			0.996816i	0.866943	+	0.498408i	$0.166082\pi$
$739$			27.0980i			0.996816i	−0.866943	+	0.498408i	$0.833918\pi$
$740$	5.83709	+	0.543789i	0.214576	+	0.0199901i
$741$	−32.6708	+	2.45943i	−1.20019	+	0.0903494i
$742$	0.883866	+	0.883866i	0.0324477	+	0.0324477i
$743$	37.1102	+	37.1102i	1.36144	+	1.36144i	0.872083	+	0.489359i	$0.162769\pi$
$743$	37.1102	+	37.1102i	1.36144	+	1.36144i	0.489359	+	0.872083i	$0.337231\pi$
$744$	3.95206	−	0.297507i	0.144889	−	0.0109071i
$745$	22.2892	+	26.8688i	0.816613	+	0.984397i
$746$			0.285394i			0.0104490i
$747$	−28.3481	+	38.4647i	−1.03720	+	1.40735i
$748$	1.80671	−	1.80671i	0.0660597	−	0.0660597i
$749$	−1.43286			−0.0523557
$750$	−6.77412	−	10.2977i	−0.247356	−	0.376020i
$751$	10.6689			0.389314			0.194657	−	0.980871i	$-0.437641\pi$
$751$	10.6689			0.389314			0.194657	+	0.980871i	$0.437641\pi$
$752$	8.71478	−	8.71478i	0.317795	−	0.317795i
$753$	−8.88728	−	7.64290i	−0.323870	−	0.278523i
$754$		−	14.6099i		−	0.532063i
$755$	−26.9610	−	32.5005i	−0.981211	−	1.18281i
$756$	−1.90318	+	0.436416i	−0.0692178	+	0.0158723i
$757$	21.9224	+	21.9224i	0.796782	+	0.796782i	0.982587	−	0.185805i	$-0.0594891\pi$
$757$	21.9224	+	21.9224i	0.796782	+	0.796782i	−0.185805	+	0.982587i	$0.559489\pi$
$758$	−11.8477	−	11.8477i	−0.430329	−	0.430329i
$759$	−0.841876	−	11.1834i	−0.0305582	−	0.405931i
$760$	33.7675	+	3.14581i	1.22488	+	0.114111i
$761$		−	31.4581i		−	1.14035i	−0.821522	−	0.570177i	$-0.806875\pi$
$761$		−	31.4581i		−	1.14035i	0.821522	−	0.570177i	$-0.193125\pi$
$762$	−2.31855	+	2.69604i	−0.0839922	+	0.0976674i
$763$	1.52930	−	1.52930i	0.0553643	−	0.0553643i
$764$	−36.1648			−1.30840
$765$	0.470809	+	8.19581i	0.0170221	+	0.296320i
$766$	9.79486			0.353903
$767$	28.1375	−	28.1375i	1.01598	−	1.01598i
$768$	8.43331	−	9.80638i	0.304311	−	0.353857i
$769$			24.8293i			0.895368i	0.894192	+	0.447684i	$0.147751\pi$
$769$			24.8293i			0.895368i	−0.894192	+	0.447684i	$0.852249\pi$
$770$	0.337890	−	0.280299i	0.0121767	−	0.0101013i
$771$	−0.630406	−	8.37425i	−0.0227035	−	0.301591i
$772$	25.8021	+	25.8021i	0.928636	+	0.928636i
$773$	−2.78989	−	2.78989i	−0.100345	−	0.100345i	0.655152	−	0.755497i	$-0.272605\pi$
$773$	−2.78989	−	2.78989i	−0.100345	−	0.100345i	−0.755497	+	0.655152i	$0.772605\pi$
$774$	2.68897	−	0.407154i	0.0966530	−	0.0146348i
$775$	−0.923594	+	4.91396i	−0.0331765	+	0.176515i
$776$		−	15.6566i		−	0.562038i
$777$	−0.508644	−	0.437425i	−0.0182475	−	0.0156925i
$778$	−16.1838	+	16.1838i	−0.580217	+	0.580217i
$779$	−48.3459			−1.73217
$780$	−12.2412	−	12.6838i	−0.438307	−	0.454154i
$781$	9.86090			0.352851
$782$	2.72428	−	2.72428i	0.0974202	−	0.0974202i
$783$	35.4091	+	22.1990i	1.26542	+	0.793327i
$784$			12.0364i			0.429873i
$785$	1.21708	−	13.0643i	0.0434394	−	0.466284i
$786$	−10.3047	+	0.775729i	−0.367556	+	0.0276693i
$787$	0.0357071	+	0.0357071i	0.00127282	+	0.00127282i	0.707743	−	0.706470i	$-0.249714\pi$
$787$	0.0357071	+	0.0357071i	0.00127282	+	0.00127282i	−0.706470	+	0.707743i	$0.749714\pi$
$788$	15.6194	+	15.6194i	0.556418	+	0.556418i
$789$	−37.1452	+	2.79626i	−1.32240	+	0.0995495i
$790$	1.38814	−	14.9005i	0.0493878	−	0.530134i
$791$			0.147603i			0.00524817i
$792$	7.23416	+	5.33151i	0.257055	+	0.189447i
$793$	−6.86628	+	6.86628i	−0.243829	+	0.243829i
$794$	2.08426			0.0739677
$795$	−22.4165	−	23.2270i	−0.795031	−	0.823776i
$796$	6.24318			0.221284
$797$	−14.3367	+	14.3367i	−0.507831	+	0.507831i	−0.913860	−	0.406029i	$-0.866913\pi$
$797$	−14.3367	+	14.3367i	−0.507831	+	0.507831i	0.406029	+	0.913860i	$0.366913\pi$
$798$	−1.30544	−	1.12265i	−0.0462119	−	0.0397414i
$799$			8.70191i			0.307851i
$800$	16.0256	+	23.4440i	0.566590	+	0.828872i
$801$	1.52082	+	10.0440i	0.0537356	+	0.354886i
$802$	−12.5073	−	12.5073i	−0.441648	−	0.441648i
$803$	6.69445	+	6.69445i	0.236242	+	0.236242i
$804$	1.81580	+	24.1209i	0.0640384	+	0.850679i
$805$	−2.00558	+	1.66375i	−0.0706876	+	0.0586394i
$806$		−	1.81649i		−	0.0639833i
$807$	−4.35356	+	5.06239i	−0.153253	+	0.178204i
$808$	−1.14860	+	1.14860i	−0.0404076	+	0.0404076i
$809$	−19.3637			−0.680791			−0.340396	−	0.940282i	$-0.610561\pi$
$809$	−19.3637			−0.680791			−0.340396	+	0.940282i	$0.610561\pi$
$810$	−12.5344	+	2.64093i	−0.440415	+	0.0927929i
$811$	−15.0639			−0.528964			−0.264482	−	0.964391i	$-0.585201\pi$
$811$	−15.0639			−0.528964			−0.264482	+	0.964391i	$0.585201\pi$
$812$	−2.13710	+	2.13710i	−0.0749975	+	0.0749975i
$813$	9.33023	−	10.8493i	0.327226	−	0.380503i
$814$			1.36981i			0.0480118i
$815$	−6.54973	−	0.610179i	−0.229427	−	0.0213736i
$816$	−0.275783	−	3.66347i	−0.00965432	−	0.128247i
$817$	−6.67519	−	6.67519i	−0.233535	−	0.233535i
$818$	−4.67711	−	4.67711i	−0.163531	−	0.163531i
$819$	0.301997	+	1.99448i	0.0105526	+	0.0696928i
$820$	−16.6074	−	20.0196i	−0.579955	−	0.699115i
$821$			21.1683i			0.738778i	0.929275	+	0.369389i	$0.120433\pi$
$821$			21.1683i			0.738778i	−0.929275	+	0.369389i	$0.879567\pi$
$822$	−2.35246	−	2.02307i	−0.0820513	−	0.0705627i
$823$	−10.9885	+	10.9885i	−0.383034	+	0.383034i	−0.872194	−	0.489160i	$-0.837303\pi$
$823$	−10.9885	+	10.9885i	−0.383034	+	0.383034i	0.489160	+	0.872194i	$0.337303\pi$
$824$	15.2469			0.531152
$825$	−8.85295	+	7.08249i	−0.308220	+	0.246581i
$826$	2.09117			0.0727611
$827$	2.34893	−	2.34893i	0.0816804	−	0.0816804i	−0.665086	−	0.746767i	$-0.731605\pi$
$827$	2.34893	−	2.34893i	0.0816804	−	0.0816804i	0.746767	+	0.665086i	$0.231605\pi$
$828$	−19.0499	−	14.0396i	−0.662030	−	0.487911i
$829$		−	44.1285i		−	1.53265i	−0.642455	−	0.766324i	$-0.722084\pi$
$829$		−	44.1285i		−	1.53265i	0.642455	−	0.766324i	$-0.277916\pi$
$830$	−14.4737	−	17.4475i	−0.502389	−	0.605611i
$831$	5.97792	−	0.450012i	0.207372	−	0.0156108i
$832$	−0.300010	−	0.300010i	−0.0104010	−	0.0104010i
$833$	−6.00933	−	6.00933i	−0.208211	−	0.208211i
$834$	17.9623	−	1.35218i	0.621982	−	0.0468223i
$835$	14.8145	+	1.38014i	0.512678	+	0.0477616i
$836$		−	13.8389i		−	0.478630i
$837$	4.40251	+	2.76006i	0.152173	+	0.0954017i
$838$	11.1070	−	11.1070i	0.383686	−	0.383686i
$839$	−15.8930			−0.548686			−0.274343	−	0.961632i	$-0.588460\pi$
$839$	−15.8930			−0.548686			−0.274343	+	0.961632i	$0.588460\pi$
$840$	0.0370722	−	2.08772i	0.00127911	−	0.0720332i
$841$	35.6888			1.23065
$842$	−18.2867	+	18.2867i	−0.630201	+	0.630201i
$843$	−26.2915	−	22.6102i	−0.905527	−	0.778737i
$844$		−	22.9480i		−	0.789903i
$845$	8.35670	−	6.93236i	0.287479	−	0.238480i
$846$	−13.4252	+	2.03280i	−0.461569	+	0.0698891i
$847$	1.54713	+	1.54713i	0.0531602	+	0.0531602i
$848$	10.2148	+	10.2148i	0.350777	+	0.350777i
$849$	−3.33354	−	44.2824i	−0.114407	−	1.51977i
$850$	−3.82773	−	0.719434i	−0.131290	−	0.0246764i
$851$		−	8.13067i		−	0.278716i
$852$	13.5670	−	15.7759i	0.464796	−	0.540472i
$853$	−20.4813	+	20.4813i	−0.701266	+	0.701266i	−0.964682	−	0.263416i	$-0.915151\pi$
$853$	−20.4813	+	20.4813i	−0.701266	+	0.701266i	0.263416	+	0.964682i	$0.415151\pi$
$854$	−0.510300			−0.0174621
$855$	33.1921	+	29.5858i	1.13515	+	1.01181i
$856$	13.9152			0.475611
$857$	−11.5920	+	11.5920i	−0.395975	+	0.395975i	−0.876811	−	0.480836i	$-0.840333\pi$
$857$	−11.5920	+	11.5920i	−0.395975	+	0.395975i	0.480836	+	0.876811i	$0.340333\pi$
$858$	2.68563	−	3.12289i	0.0916858	−	0.106614i
$859$		−	32.8645i		−	1.12132i	−0.828046	−	0.560661i	$-0.810547\pi$
$859$		−	32.8645i		−	1.12132i	0.828046	−	0.560661i	$-0.189453\pi$
$860$	0.471129	−	5.05715i	0.0160654	−	0.172447i
$861$	0.223446	+	2.96823i	0.00761502	+	0.101157i
$862$	−11.9766	−	11.9766i	−0.407923	−	0.407923i
$863$	−26.3572	−	26.3572i	−0.897209	−	0.897209i	0.0979791	−	0.995188i	$-0.468762\pi$
$863$	−26.3572	−	26.3572i	−0.897209	−	0.897209i	−0.995188	+	0.0979791i	$0.968762\pi$
$864$	28.7654	−	6.59617i	0.978619	−	0.224406i
$865$	−2.79544	+	30.0066i	−0.0950479	+	1.02025i
$866$			14.6945i			0.499340i
$867$	−20.3581	−	17.5076i	−0.691399	−	0.594591i
$868$	−0.265711	+	0.265711i	−0.00901883	+	0.00901883i
$869$	−13.7646			−0.466933
$870$	−14.2669	+	13.7691i	−0.483693	+	0.466815i
$871$	24.9900			0.846753
$872$	−14.8517	+	14.8517i	−0.502942	+	0.502942i
$873$	12.1783	−	16.5243i	0.412172	−	0.559263i
$874$		−	20.8674i		−	0.705849i
$875$	2.53264	+	0.724650i	0.0856190	+	0.0244976i
$876$	19.9205	−	1.49960i	0.673051	−	0.0506667i
$877$	16.9959	+	16.9959i	0.573911	+	0.573911i	0.933219	−	0.359308i	$-0.116987\pi$
$877$	16.9959	+	16.9959i	0.573911	+	0.573911i	−0.359308	+	0.933219i	$0.616987\pi$
$878$	−4.32505	−	4.32505i	−0.145963	−	0.145963i
$879$	−10.7865	+	0.811996i	−0.363818	+	0.0273879i
$880$	3.90497	−	3.23940i	0.131637	−	0.109200i
$881$		−	37.2462i		−	1.25486i	−0.778674	−	0.627428i	$-0.784107\pi$
$881$		−	37.2462i		−	1.25486i	0.778674	−	0.627428i	$-0.215893\pi$
$882$	7.86733	−	10.6749i	0.264907	−	0.359444i
$883$	1.99607	−	1.99607i	0.0671730	−	0.0671730i	−0.672722	−	0.739895i	$-0.734875\pi$
$883$	1.99607	−	1.99607i	0.0671730	−	0.0671730i	0.739895	+	0.672722i	$0.234875\pi$
$884$	−5.56987			−0.187335
$885$	−53.9948	−	0.958799i	−1.81501	−	0.0322297i
$886$	1.31470			0.0441684
$887$	32.6707	−	32.6707i	1.09698	−	1.09698i	0.102214	−	0.994762i	$-0.467407\pi$
$887$	32.6707	−	32.6707i	1.09698	−	1.09698i	0.994762	−	0.102214i	$-0.0325925\pi$
$888$	4.93967	+	4.24803i	0.165764	+	0.142554i
$889$		−	0.759949i		−	0.0254879i
$890$	−4.79870	−	0.447052i	−0.160853	−	0.0149852i
$891$	3.48805	+	11.2540i	0.116854	+	0.377024i
$892$	29.3511	+	29.3511i	0.982748	+	0.982748i
$893$	33.3273	+	33.3273i	1.11525	+	1.11525i
$894$	1.29208	+	17.1638i	0.0432135	+	0.574043i
$895$	21.3562	+	25.7441i	0.713860	+	0.860532i
$896$			2.65411i			0.0886677i
$897$	−15.9409	+	18.5363i	−0.532250	+	0.618908i
$898$	2.18214	−	2.18214i	0.0728189	−	0.0728189i
$899$	8.04293			0.268247
$900$	−0.849336	+	23.9076i	−0.0283112	+	0.796921i
$901$	−10.1997			−0.339801
$902$	4.29769	−	4.29769i	0.143097	−	0.143097i
$903$	−0.378977	+	0.440680i	−0.0126116	+	0.0146649i
$904$		−	1.43344i		−	0.0476756i
$905$	13.8448	+	16.6894i	0.460218	+	0.554776i
$906$	−1.56289	−	20.7613i	−0.0519237	−	0.689748i
$907$	−13.9528	−	13.9528i	−0.463295	−	0.463295i	0.436439	−	0.899734i	$-0.356239\pi$
$907$	−13.9528	−	13.9528i	−0.463295	−	0.463295i	−0.899734	+	0.436439i	$0.856239\pi$
$908$	25.1085	+	25.1085i	0.833254	+	0.833254i
$909$	−2.10568	+	0.318835i	−0.0698411	+	0.0105751i
$910$	−0.952903	−	0.0887733i	−0.0315884	−	0.00294281i
$911$			37.6574i			1.24764i	0.781566	+	0.623822i	$0.214421\pi$
$911$			37.6574i			1.24764i	−0.781566	+	0.623822i	$0.785579\pi$
$912$	−15.0868	−	12.9744i	−0.499575	−	0.429626i
$913$	−14.7439	+	14.7439i	−0.487953	+	0.487953i
$914$	5.60043			0.185246
$915$	13.1761	+	0.233972i	0.435590	+	0.00773488i
$916$	17.0881			0.564606
$917$	1.56165	−	1.56165i	0.0515702	−	0.0515702i
$918$	−2.14995	+	3.42933i	−0.0709590	+	0.113185i
$919$			51.9181i			1.71262i	0.516463	+	0.856309i	$0.327248\pi$
$919$			51.9181i			1.71262i	−0.516463	+	0.856309i	$0.672752\pi$
$920$	19.4771	−	16.1574i	0.642141	−	0.532693i
$921$	20.0549	−	1.50971i	0.660830	−	0.0497467i
$922$	15.2553	+	15.2553i	0.502407	+	0.502407i
$923$	−15.2000	−	15.2000i	−0.500315	−	0.500315i
$924$	−0.849652	+	0.0639611i	−0.0279515	+	0.00210417i
$925$	−6.78554	+	4.63838i	−0.223107	+	0.152509i
$926$			17.4999i			0.575083i
$927$	16.0920	+	11.8596i	0.528530	+	0.389522i
$928$	32.3010	−	32.3010i	1.06033	−	1.06033i
$929$	−27.4276			−0.899872			−0.449936	−	0.893061i	$-0.648553\pi$
$929$	−27.4276			−0.899872			−0.449936	+	0.893061i	$0.648553\pi$
$930$	−1.77384	+	1.71195i	−0.0581666	+	0.0561369i
$931$	−46.0300			−1.50857
$932$	−14.3443	+	14.3443i	−0.469862	+	0.469862i
$933$	7.55692	+	6.49882i	0.247403	+	0.212762i
$934$		−	25.4599i		−	0.833073i
$935$	−0.332296	+	3.56691i	−0.0108673	+	0.116650i
$936$	−2.93283	−	19.3693i	−0.0958625	−	0.633105i
$937$	−7.28597	−	7.28597i	−0.238022	−	0.238022i	0.578009	−	0.816031i	$-0.303830\pi$
$937$	−7.28597	−	7.28597i	−0.238022	−	0.238022i	−0.816031	+	0.578009i	$0.803830\pi$
$938$	0.928626	+	0.928626i	0.0303207	+	0.0303207i
$939$	−0.355564	−	4.72328i	−0.0116034	−	0.154138i
$940$	−2.35221	+	25.2488i	−0.0767205	+	0.823526i
$941$			19.7263i			0.643060i	0.946899	+	0.321530i	$0.104197\pi$
$941$			19.7263i			0.643060i	−0.946899	+	0.321530i	$0.895803\pi$
$942$	4.21808	−	4.90484i	0.137432	−	0.159808i
$943$	−25.5094	+	25.5094i	−0.830702	+	0.830702i
$944$	24.1675			0.786586
$945$	1.66304	−	2.17459i	0.0540986	−	0.0707396i
$946$	1.18678			0.0385855
$947$	−2.56738	+	2.56738i	−0.0834285	+	0.0834285i	−0.747590	−	0.664161i	$-0.768789\pi$
$947$	−2.56738	+	2.56738i	−0.0834285	+	0.0834285i	0.664161	+	0.747590i	$0.268789\pi$
$948$	−18.9378	+	22.0212i	−0.615073	+	0.715216i
$949$		−	20.6382i		−	0.669945i
$950$	−17.4151	+	11.9044i	−0.565020	+	0.386230i
$951$	3.23382	+	42.9577i	0.104864	+	1.39300i
$952$	−0.466532	−	0.466532i	−0.0151204	−	0.0151204i
$953$	24.3113	+	24.3113i	0.787520	+	0.787520i	0.981087	−	0.193567i	$-0.0620057\pi$
$953$	24.3113	+	24.3113i	0.787520	+	0.787520i	−0.193567	+	0.981087i	$0.562006\pi$
$954$	−2.38269	−	15.7360i	−0.0771424	−	0.509472i
$955$	39.0251	−	32.3735i	1.26282	−	1.04758i
$956$			33.7928i			1.09294i
$957$	13.8273	+	11.8912i	0.446972	+	0.384388i
$958$	1.85734	−	1.85734i	0.0600079	−	0.0600079i
$959$	0.663100			0.0214126
$960$	−0.0102230	+	0.575708i	−0.000329946	+	0.0185809i
$961$	1.00000			0.0322581
$962$	2.11148	−	2.11148i	0.0680770	−	0.0680770i
$963$	14.6864	+	10.8237i	0.473262	+	0.348790i
$964$		−	16.4350i		−	0.529335i
$965$	−50.9399	−	4.74561i	−1.63981	−	0.152767i
$966$	−1.28117	+	0.0964452i	−0.0412209	+	0.00310307i
$967$	7.55155	+	7.55155i	0.242842	+	0.242842i	0.818025	−	0.575183i	$-0.195069\pi$
$967$	7.55155	+	7.55155i	0.242842	+	0.242842i	−0.575183	+	0.818025i	$0.695069\pi$
$968$	−15.0249	−	15.0249i	−0.482919	−	0.482919i
$969$	14.0099	−	1.05465i	0.450063	−	0.0338804i
$970$	6.21784	+	7.49537i	0.199643	+	0.240662i
$971$		−	32.7293i		−	1.05033i	−0.851000	−	0.525166i	$-0.824003\pi$
$971$		−	32.7293i		−	1.05033i	0.851000	−	0.525166i	$-0.175997\pi$
$972$	22.8036	+	9.90333i	0.731426	+	0.317649i
$973$	−2.72213	+	2.72213i	−0.0872676	+	0.0872676i
$974$	23.3646			0.748650
$975$	24.5636	+	2.72906i	0.786665	+	0.0874000i
$976$	−5.89751			−0.188775
$977$	11.9717	−	11.9717i	0.383009	−	0.383009i	−0.489176	−	0.872185i	$-0.662703\pi$
$977$	11.9717	−	11.9717i	0.383009	−	0.383009i	0.872185	+	0.489176i	$0.162703\pi$
$978$	−2.45903	−	2.11472i	−0.0786310	−	0.0676213i
$979$			4.43291i			0.141676i
$980$	−15.8119	−	19.0606i	−0.505091	−	0.608869i
$981$	−27.2270	+	4.12262i	−0.869293	+	0.131625i
$982$	10.9923	+	10.9923i	0.350779	+	0.350779i
$983$	6.61966	+	6.61966i	0.211134	+	0.211134i	0.804749	−	0.593615i	$-0.202300\pi$
$983$	6.61966	+	6.61966i	0.211134	+	0.211134i	−0.593615	+	0.804749i	$0.702300\pi$
$984$	−2.16998	−	28.8258i	−0.0691765	−	0.918933i
$985$	−30.8367	−	2.87278i	−0.982540	−	0.0915344i
$986$			6.26505i			0.199520i
$987$	1.89212	−	2.20019i	0.0602269	−	0.0700327i
$988$	−21.3319	+	21.3319i	−0.678660	+	0.678660i
$989$	−7.04426			−0.223994
$990$	−5.58062	+	0.320579i	−0.177364	+	0.0101887i
$991$	−19.7920			−0.628714			−0.314357	−	0.949305i	$-0.601789\pi$
$991$	−19.7920			−0.628714			−0.314357	+	0.949305i	$0.601789\pi$
$992$	4.01607	−	4.01607i	0.127510	−	0.127510i
$993$	14.0937	−	16.3883i	0.447249	−	0.520068i
$994$		−	1.12966i		−	0.0358307i
$995$	−6.73696	+	5.58869i	−0.213576	+	0.177173i
$996$	3.30273	+	43.8732i	0.104651	+	1.39017i
$997$	37.5376	+	37.5376i	1.18883	+	1.18883i	0.977392	+	0.211435i	$0.0678136\pi$
$997$	37.5376	+	37.5376i	1.18883	+	1.18883i	0.211435	+	0.977392i	$0.432186\pi$
$998$	11.4686	+	11.4686i	0.363032	+	0.363032i
$999$	1.90917	+	8.32573i	0.0604034	+	0.263414i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.k.a.32.14	✓	60
3.2	odd	2	inner	465.2.k.a.32.17	yes	60
5.3	odd	4	inner	465.2.k.a.218.17	yes	60
15.8	even	4	inner	465.2.k.a.218.14	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.k.a.32.14	✓	60	1.1	even	1	trivial
465.2.k.a.32.17	yes	60	3.2	odd	2	inner
465.2.k.a.218.14	yes	60	15.8	even	4	inner
465.2.k.a.218.17	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)

\(f(q)\)	\(=\)	\(q+(-0.450084 + 0.450084i) q^{2} +(-1.12935 + 1.31323i) q^{3} +1.59485i q^{4} +(-1.42766 - 1.72099i) q^{5} +(-0.0827594 - 1.09937i) q^{6} +(0.166606 + 0.166606i) q^{7} +(-1.61799 - 1.61799i) q^{8} +(-0.449130 - 2.96619i) q^{9} +O(q^{10})\)	\(q+(-0.450084 + 0.450084i) q^{2} +(-1.12935 + 1.31323i) q^{3} +1.59485i q^{4} +(-1.42766 - 1.72099i) q^{5} +(-0.0827594 - 1.09937i) q^{6} +(0.166606 + 0.166606i) q^{7} +(-1.61799 - 1.61799i) q^{8} +(-0.449130 - 2.96619i) q^{9} +(1.41716 + 0.132024i) q^{10} -1.30913i q^{11} +(-2.09440 - 1.80114i) q^{12} +(-2.01795 + 2.01795i) q^{13} -0.149974 q^{14} +(3.87237 + 0.0687627i) q^{15} -1.73324 q^{16} +(0.865338 - 0.865338i) q^{17} +(1.53718 + 1.13289i) q^{18} -6.62828i q^{19} +(2.74471 - 2.27690i) q^{20} +(-0.406948 + 0.0306347i) q^{21} +(0.589219 + 0.589219i) q^{22} +(-3.49738 - 3.49738i) q^{23} +(3.95206 - 0.297507i) q^{24} +(-0.923594 + 4.91396i) q^{25} -1.81649i q^{26} +(4.40251 + 2.76006i) q^{27} +(-0.265711 + 0.265711i) q^{28} +8.04293 q^{29} +(-1.77384 + 1.71195i) q^{30} +1.00000 q^{31} +(4.01607 - 4.01607i) q^{32} +(1.71918 + 1.47847i) q^{33} +0.778950i q^{34} +(0.0488707 - 0.524583i) q^{35} +(4.73062 - 0.716294i) q^{36} +(1.16239 + 1.16239i) q^{37} +(2.98329 + 2.98329i) q^{38} +(-0.371051 - 4.92900i) q^{39} +(-0.474605 + 5.09446i) q^{40} -7.29388i q^{41} +(0.169373 - 0.196949i) q^{42} +(1.00708 - 1.00708i) q^{43} +2.08786 q^{44} +(-4.46357 + 5.00765i) q^{45} +3.14823 q^{46} +(-5.02804 + 5.02804i) q^{47} +(1.95743 - 2.27613i) q^{48} -6.94448i q^{49} +(-1.79600 - 2.62739i) q^{50} +(0.159114 + 2.11366i) q^{51} +(-3.21832 - 3.21832i) q^{52} +(-5.89347 - 5.89347i) q^{53} +(-3.22376 + 0.739238i) q^{54} +(-2.25299 + 1.86899i) q^{55} -0.539132i q^{56} +(8.70444 + 7.48566i) q^{57} +(-3.62000 + 3.62000i) q^{58} -13.9436 q^{59} +(-0.109666 + 6.17585i) q^{60} +3.40260 q^{61} +(-0.450084 + 0.450084i) q^{62} +(0.419358 - 0.569013i) q^{63} +0.148671i q^{64} +(6.35380 + 0.591926i) q^{65} +(-1.43921 + 0.108343i) q^{66} +(-6.19193 - 6.19193i) q^{67} +(1.38008 + 1.38008i) q^{68} +(8.54262 - 0.643081i) q^{69} +(0.214111 + 0.258103i) q^{70} +7.53241i q^{71} +(-4.07257 + 5.52594i) q^{72} +(-5.11366 + 5.11366i) q^{73} -1.04635 q^{74} +(-5.41008 - 6.76247i) q^{75} +10.5711 q^{76} +(0.218109 - 0.218109i) q^{77} +(2.38547 + 2.05146i) q^{78} -10.5143i q^{79} +(2.47447 + 2.98288i) q^{80} +(-8.59657 + 2.66441i) q^{81} +(3.28286 + 3.28286i) q^{82} +(-11.2624 - 11.2624i) q^{83} +(-0.0488577 - 0.649021i) q^{84} +(-2.72464 - 0.253830i) q^{85} +0.906540i q^{86} +(-9.08330 + 10.5622i) q^{87} +(-2.11815 + 2.11815i) q^{88} -3.38615 q^{89} +(-0.244880 - 4.26285i) q^{90} -0.672405 q^{91} +(5.57779 - 5.57779i) q^{92} +(-1.12935 + 1.31323i) q^{93} -4.52608i q^{94} +(-11.4072 + 9.46291i) q^{95} +(0.738456 + 9.80957i) q^{96} +(4.83829 + 4.83829i) q^{97} +(3.12560 + 3.12560i) q^{98} +(-3.88313 + 0.587969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 4 q^{6}+O(q^{10}) \) 60 * q - 4 * q^6	\( 60 q - 4 q^{6} - 32 q^{10} + 4 q^{13} + 20 q^{15} - 60 q^{16} - 46 q^{18} - 4 q^{21} + 8 q^{22} - 8 q^{25} - 6 q^{27} + 112 q^{28} + 54 q^{30} + 60 q^{31} - 30 q^{33} - 4 q^{36} - 36 q^{37} - 36 q^{40} + 44 q^{42} + 16 q^{43} + 14 q^{45} + 40 q^{46} - 104 q^{48} - 48 q^{51} - 12 q^{52} - 48 q^{55} + 42 q^{57} + 80 q^{58} + 60 q^{60} - 8 q^{61} - 10 q^{63} - 24 q^{66} - 88 q^{67} - 84 q^{70} + 84 q^{72} + 60 q^{73} + 14 q^{75} + 72 q^{76} - 152 q^{78} - 132 q^{81} - 60 q^{82} - 16 q^{85} + 34 q^{87} + 124 q^{88} + 190 q^{90} + 64 q^{91} - 88 q^{96} - 8 q^{97}+O(q^{100}) \) 60 * q - 4 * q^6 - 32 * q^10 + 4 * q^13 + 20 * q^15 - 60 * q^16 - 46 * q^18 - 4 * q^21 + 8 * q^22 - 8 * q^25 - 6 * q^27 + 112 * q^28 + 54 * q^30 + 60 * q^31 - 30 * q^33 - 4 * q^36 - 36 * q^37 - 36 * q^40 + 44 * q^42 + 16 * q^43 + 14 * q^45 + 40 * q^46 - 104 * q^48 - 48 * q^51 - 12 * q^52 - 48 * q^55 + 42 * q^57 + 80 * q^58 + 60 * q^60 - 8 * q^61 - 10 * q^63 - 24 * q^66 - 88 * q^67 - 84 * q^70 + 84 * q^72 + 60 * q^73 + 14 * q^75 + 72 * q^76 - 152 * q^78 - 132 * q^81 - 60 * q^82 - 16 * q^85 + 34 * q^87 + 124 * q^88 + 190 * q^90 + 64 * q^91 - 88 * q^96 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

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