LMFDB - Embedded newform 151.2.k.a.39.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [151,2,Mod(5,151)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(151, base_ring=CyclotomicField(150))

chi = DirichletCharacter(H, H._module([112]))

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

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

chi := DirichletCharacter("151.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	151.k (of order $75$, degree $40$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.20574107052$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$12$ over $\Q(\zeta_{75})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{75}]$

Embedding invariants

Embedding label			39.6
Character	$\chi$	$=$	151.39
Dual form			151.2.k.a.31.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0599037 - 0.0127329i) q^{2} +(-0.414095 + 0.163952i) q^{3} +(-1.82366 + 0.811948i) q^{4} +(-3.18220 - 0.960762i) q^{5} +(-0.0227182 + 0.0150940i) q^{6} +(0.0308852 + 1.47445i) q^{7} +(-0.197997 + 0.143853i) q^{8} +(-2.04231 + 1.91786i) q^{9} +O(q^{10})$	\(q+(0.0599037 - 0.0127329i) q^{2} +(-0.414095 + 0.163952i) q^{3} +(-1.82366 + 0.811948i) q^{4} +(-3.18220 - 0.960762i) q^{5} +(-0.0227182 + 0.0150940i) q^{6} +(0.0308852 + 1.47445i) q^{7} +(-0.197997 + 0.143853i) q^{8} +(-2.04231 + 1.91786i) q^{9} +(-0.202859 - 0.0170345i) q^{10} +(0.589333 + 3.99096i) q^{11} +(0.622050 - 0.635217i) q^{12} +(-3.22688 - 6.17245i) q^{13} +(0.0206241 + 0.0879315i) q^{14} +(1.47525 - 0.123880i) q^{15} +(2.66147 - 2.95587i) q^{16} +(2.66664 + 1.61497i) q^{17} +(-0.0979220 + 0.140891i) q^{18} +(-1.85075 - 1.34465i) q^{19} +(6.58335 - 0.831670i) q^{20} +(-0.254528 - 0.605497i) q^{21} +(0.0861198 + 0.231569i) q^{22} +(-0.373711 + 3.55563i) q^{23} +(0.0584047 - 0.0920311i) q^{24} +(5.03870 + 3.34771i) q^{25} +(-0.271895 - 0.328665i) q^{26} +(1.10016 - 2.33797i) q^{27} +(-1.25350 - 2.66382i) q^{28} +(-3.75807 + 4.54272i) q^{29} +(0.0867956 - 0.0262051i) q^{30} +(-0.316804 + 0.273458i) q^{31} +(0.366533 - 0.634855i) q^{32} +(-0.898365 - 1.55601i) q^{33} +(0.180305 + 0.0627888i) q^{34} +(1.31831 - 4.72165i) q^{35} +(2.16729 - 5.15578i) q^{36} +(-1.35414 - 0.0567551i) q^{37} +(-0.127988 - 0.0569839i) q^{38} +(2.34822 + 2.02693i) q^{39} +(0.768275 - 0.267542i) q^{40} +(0.449301 + 7.14143i) q^{41} +(-0.0229569 - 0.0330306i) q^{42} +(-0.0622572 + 2.97213i) q^{43} +(-4.31520 - 6.79966i) q^{44} +(8.34164 - 4.14083i) q^{45} +(0.0228868 + 0.217753i) q^{46} +(-3.23226 - 1.60451i) q^{47} +(-0.617484 + 1.66036i) q^{48} +(4.82082 - 0.202052i) q^{49} +(0.344463 + 0.136383i) q^{50} +(-1.36902 - 0.231553i) q^{51} +(10.8964 + 8.63642i) q^{52} +(-5.40399 + 1.38751i) q^{53} +(0.0361347 - 0.154061i) q^{54} +(1.95898 - 13.2662i) q^{55} +(-0.218219 - 0.287493i) q^{56} +(0.986844 + 0.253379i) q^{57} +(-0.167280 + 0.319977i) q^{58} +(-3.96208 - 12.1940i) q^{59} +(-2.58978 + 1.42374i) q^{60} +(-9.24937 + 7.33096i) q^{61} +(-0.0154958 + 0.0204150i) q^{62} +(-2.89085 - 2.95204i) q^{63} +(-2.44436 + 7.52298i) q^{64} +(4.33831 + 22.7422i) q^{65} +(-0.0736280 - 0.0817722i) q^{66} +(4.66271 + 4.37858i) q^{67} +(-6.17433 - 0.780000i) q^{68} +(-0.428199 - 1.53364i) q^{69} +(0.0188511 - 0.299630i) q^{70} +(-8.19728 + 4.96445i) q^{71} +(0.128482 - 0.673524i) q^{72} +(-7.80250 - 4.28946i) q^{73} +(-0.0818404 + 0.0138423i) q^{74} +(-2.63537 - 0.560164i) q^{75} +(4.46693 + 0.949476i) q^{76} +(-5.86625 + 0.992202i) q^{77} +(0.166476 + 0.0915208i) q^{78} +(2.18781 - 11.4689i) q^{79} +(-11.3092 + 6.84910i) q^{80} +(0.455492 - 7.23983i) q^{81} +(0.117846 + 0.422077i) q^{82} +(15.3806 + 1.94302i) q^{83} +(0.955805 + 0.897561i) q^{84} +(-6.93417 - 7.70117i) q^{85} +(0.0341144 + 0.178834i) q^{86} +(0.811409 - 2.49726i) q^{87} +(-0.690800 - 0.705421i) q^{88} +(-4.16640 + 5.48903i) q^{89} +(0.446970 - 0.354264i) q^{90} +(9.00128 - 4.94849i) q^{91} +(-2.20546 - 6.78770i) q^{92} +(0.0863531 - 0.165178i) q^{93} +(-0.214054 - 0.0549598i) q^{94} +(4.59756 + 6.05707i) q^{95} +(-0.0476941 + 0.322984i) q^{96} +(-1.49562 + 6.37662i) q^{97} +(0.286212 - 0.0734868i) q^{98} +(-8.85769 - 7.02052i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q - 45 q^{2} - 40 q^{3} + 15 q^{4} - 40 q^{5} - 60 q^{6} - 40 q^{7} - 50 q^{8} - 40 q^{9}+O(q^{10}) $ 480 * q - 45 * q^2 - 40 * q^3 + 15 * q^4 - 40 * q^5 - 60 * q^6 - 40 * q^7 - 50 * q^8 - 40 * q^9	\( 480 q - 45 q^{2} - 40 q^{3} + 15 q^{4} - 40 q^{5} - 60 q^{6} - 40 q^{7} - 50 q^{8} - 40 q^{9} - 10 q^{10} - 50 q^{11} - 65 q^{12} - 40 q^{13} - 65 q^{14} + 25 q^{16} - 20 q^{17} - 15 q^{18} - 30 q^{19} + 70 q^{20} - 40 q^{21} - 65 q^{23} + 80 q^{24} + 20 q^{25} - 65 q^{26} + 5 q^{27} - 110 q^{28} - 75 q^{29} - 135 q^{30} - 45 q^{31} + 10 q^{32} + 40 q^{33} + 20 q^{34} - 10 q^{36} - 60 q^{37} - 70 q^{38} + 25 q^{39} - 50 q^{41} + 50 q^{42} - 50 q^{43} - 30 q^{44} + 10 q^{45} - 85 q^{46} + 30 q^{47} + 175 q^{48} - 50 q^{49} + 10 q^{50} + 80 q^{51} - 145 q^{52} + 95 q^{53} + 10 q^{54} + 70 q^{55} + 140 q^{56} - 70 q^{57} + 240 q^{58} - 30 q^{59} - 60 q^{60} - 60 q^{61} + 10 q^{62} + 90 q^{63} - 160 q^{64} + 45 q^{65} - 55 q^{66} - 10 q^{67} + 10 q^{68} - 105 q^{69} + 75 q^{70} - 25 q^{71} + 310 q^{72} + 40 q^{73} + 170 q^{74} - 80 q^{75} - 15 q^{76} + 45 q^{77} - 80 q^{78} + 160 q^{79} - 85 q^{80} + 160 q^{81} - 50 q^{82} - 5 q^{83} + 70 q^{84} - 85 q^{85} + 150 q^{86} + 10 q^{87} + 95 q^{88} - 50 q^{89} - 90 q^{90} + 270 q^{91} + 90 q^{92} + 100 q^{93} - 35 q^{94} + 60 q^{95} + 255 q^{96} + 210 q^{97} - 30 q^{98}+O(q^{100}) \) 480 * q - 45 * q^2 - 40 * q^3 + 15 * q^4 - 40 * q^5 - 60 * q^6 - 40 * q^7 - 50 * q^8 - 40 * q^9 - 10 * q^10 - 50 * q^11 - 65 * q^12 - 40 * q^13 - 65 * q^14 + 25 * q^16 - 20 * q^17 - 15 * q^18 - 30 * q^19 + 70 * q^20 - 40 * q^21 - 65 * q^23 + 80 * q^24 + 20 * q^25 - 65 * q^26 + 5 * q^27 - 110 * q^28 - 75 * q^29 - 135 * q^30 - 45 * q^31 + 10 * q^32 + 40 * q^33 + 20 * q^34 - 10 * q^36 - 60 * q^37 - 70 * q^38 + 25 * q^39 - 50 * q^41 + 50 * q^42 - 50 * q^43 - 30 * q^44 + 10 * q^45 - 85 * q^46 + 30 * q^47 + 175 * q^48 - 50 * q^49 + 10 * q^50 + 80 * q^51 - 145 * q^52 + 95 * q^53 + 10 * q^54 + 70 * q^55 + 140 * q^56 - 70 * q^57 + 240 * q^58 - 30 * q^59 - 60 * q^60 - 60 * q^61 + 10 * q^62 + 90 * q^63 - 160 * q^64 + 45 * q^65 - 55 * q^66 - 10 * q^67 + 10 * q^68 - 105 * q^69 + 75 * q^70 - 25 * q^71 + 310 * q^72 + 40 * q^73 + 170 * q^74 - 80 * q^75 - 15 * q^76 + 45 * q^77 - 80 * q^78 + 160 * q^79 - 85 * q^80 + 160 * q^81 - 50 * q^82 - 5 * q^83 + 70 * q^84 - 85 * q^85 + 150 * q^86 + 10 * q^87 + 95 * q^88 - 50 * q^89 - 90 * q^90 + 270 * q^91 + 90 * q^92 + 100 * q^93 - 35 * q^94 + 60 * q^95 + 255 * q^96 + 210 * q^97 - 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/151\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{61}{75}\right)$

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 $

$2$	0.0599037	−	0.0127329i	0.0423583	−	0.00900353i	−0.186684	−	0.982420i	$-0.559774\pi$
$2$	0.0599037	−	0.0127329i	0.0423583	−	0.00900353i	0.229042	+	0.973417i	$0.426441\pi$
$3$	−0.414095	+	0.163952i	−0.239078	+	0.0946577i	−0.484608	−	0.874731i	$-0.661038\pi$
$3$	−0.414095	+	0.163952i	−0.239078	+	0.0946577i	0.245530	+	0.969389i	$0.421038\pi$
$4$	−1.82366	+	0.811948i	−0.911832	+	0.405974i
$5$	−3.18220	−	0.960762i	−1.42312	−	0.429666i	−0.518206	−	0.855256i	$-0.673400\pi$
$5$	−3.18220	−	0.960762i	−1.42312	−	0.429666i	−0.904916	+	0.425590i	$0.860066\pi$
$6$	−0.0227182	+	0.0150940i	−0.00927468	+	0.00616209i
$7$	0.0308852	+	1.47445i	0.0116735	+	0.557288i	0.966003	+	0.258531i	$0.0832386\pi$
$7$	0.0308852	+	1.47445i	0.0116735	+	0.557288i	−0.954329	+	0.298757i	$0.903428\pi$
$8$	−0.197997	+	0.143853i	−0.0700026	+	0.0508599i
$9$	−2.04231	+	1.91786i	−0.680770	+	0.639286i
$10$	−0.202859	−	0.0170345i	−0.0641495	−	0.00538679i
$11$	0.589333	+	3.99096i	0.177691	+	1.20332i	0.874126	+	0.485699i	$0.161435\pi$
$11$	0.589333	+	3.99096i	0.177691	+	1.20332i	−0.696435	+	0.717620i	$0.745232\pi$
$12$	0.622050	−	0.635217i	0.179570	−	0.183371i
$13$	−3.22688	−	6.17245i	−0.894975	−	1.71193i	−0.677012	−	0.735972i	$-0.736725\pi$
$13$	−3.22688	−	6.17245i	−0.894975	−	1.71193i	−0.217963	−	0.975957i	$-0.569941\pi$
$14$	0.0206241	+	0.0879315i	0.00551203	+	0.0235007i
$15$	1.47525	−	0.123880i	0.380908	−	0.0319858i
$16$	2.66147	−	2.95587i	0.665369	−	0.738967i
$17$	2.66664	+	1.61497i	0.646755	+	0.391689i	0.802958	−	0.596036i	$-0.203259\pi$
$17$	2.66664	+	1.61497i	0.646755	+	0.391689i	−0.156202	+	0.987725i	$0.549925\pi$
$18$	−0.0979220	+	0.140891i	−0.0230804	+	0.0332084i
$19$	−1.85075	−	1.34465i	−0.424591	−	0.308484i	0.354891	−	0.934908i	$-0.384518\pi$
$19$	−1.85075	−	1.34465i	−0.424591	−	0.308484i	−0.779482	+	0.626424i	$0.784518\pi$
$20$	6.58335	−	0.831670i	1.47208	−	0.185967i
$21$	−0.254528	−	0.605497i	−0.0555425	−	0.132130i
$22$	0.0861198	+	0.231569i	0.0183608	+	0.0493707i
$23$	−0.373711	+	3.55563i	−0.0779242	+	0.741399i	0.883890	+	0.467695i	$0.154916\pi$
$23$	−0.373711	+	3.55563i	−0.0779242	+	0.741399i	−0.961814	+	0.273704i	$0.911751\pi$
$24$	0.0584047	−	0.0920311i	0.0119218	−	0.0187858i
$25$	5.03870	+	3.34771i	1.00774	+	0.669541i
$26$	−0.271895	−	0.328665i	−0.0533230	−	0.0644565i
$27$	1.10016	−	2.33797i	0.211727	−	0.449942i
$28$	−1.25350	−	2.66382i	−0.236889	−	0.503414i
$29$	−3.75807	+	4.54272i	−0.697855	+	0.843562i	−0.993747	−	0.111660i	$-0.964383\pi$
$29$	−3.75807	+	4.54272i	−0.697855	+	0.843562i	0.295891	+	0.955222i	$0.404383\pi$
$30$	0.0867956	−	0.0262051i	0.0158466	−	0.00478438i
$31$	−0.316804	+	0.273458i	−0.0568997	+	0.0491145i	−0.681409	−	0.731903i	$-0.738632\pi$
$31$	−0.316804	+	0.273458i	−0.0568997	+	0.0491145i	0.624509	+	0.781018i	$0.285299\pi$
$32$	0.366533	−	0.634855i	0.0647946	−	0.112227i
$33$	−0.898365	−	1.55601i	−0.156385	−	0.270867i
$34$	0.180305	+	0.0627888i	0.0309220	+	0.0107682i
$35$	1.31831	−	4.72165i	0.222835	−	0.798104i
$36$	2.16729	−	5.15578i	0.361215	−	0.859297i
$37$	−1.35414	−	0.0567551i	−0.222619	−	0.00933048i	−0.0696943	−	0.997568i	$-0.522202\pi$
$37$	−1.35414	−	0.0567551i	−0.222619	−	0.00933048i	−0.152924	+	0.988238i	$0.548869\pi$
$38$	−0.127988	−	0.0569839i	−0.0207624	−	0.00924402i
$39$	2.34822	+	2.02693i	0.376016	+	0.324568i
$40$	0.768275	−	0.267542i	0.121475	−	0.0423021i
$41$	0.449301	+	7.14143i	0.0701690	+	1.11530i	0.862781	+	0.505578i	$0.168721\pi$
$41$	0.449301	+	7.14143i	0.0701690	+	1.11530i	−0.792612	+	0.609727i	$0.791279\pi$
$42$	−0.0229569	−	0.0330306i	−0.00354232	−	0.00509674i
$43$	−0.0622572	+	2.97213i	−0.00949414	+	0.453245i	0.969010	+	0.247020i	$0.0794513\pi$
$43$	−0.0622572	+	2.97213i	−0.00949414	+	0.453245i	−0.978505	+	0.206225i	$0.933882\pi$
$44$	−4.31520	−	6.79966i	−0.650540	−	1.02509i
$45$	8.34164	−	4.14083i	1.24350	−	0.617278i
$46$	0.0228868	+	0.217753i	0.00337448	+	0.0321060i
$47$	−3.23226	−	1.60451i	−0.471474	−	0.234042i	0.193223	−	0.981155i	$-0.438106\pi$
$47$	−3.23226	−	1.60451i	−0.471474	−	0.234042i	−0.664697	+	0.747113i	$0.731439\pi$
$48$	−0.617484	+	1.66036i	−0.0891261	+	0.239653i
$49$	4.82082	−	0.202052i	0.688689	−	0.0288646i
$50$	0.344463	+	0.136383i	0.0487144	+	0.0192874i
$51$	−1.36902	−	0.231553i	−0.191701	−	0.0324239i
$52$	10.8964	+	8.63642i	1.51107	+	1.19766i
$53$	−5.40399	+	1.38751i	−0.742296	+	0.190589i	−0.600855	−	0.799358i	$-0.705173\pi$
$53$	−5.40399	+	1.38751i	−0.742296	+	0.190589i	−0.141440	+	0.989947i	$0.545173\pi$
$54$	0.0361347	−	0.154061i	0.00491731	−	0.0209651i
$55$	1.95898	−	13.2662i	0.264149	−	1.78882i
$56$	−0.218219	−	0.287493i	−0.0291608	−	0.0384179i
$57$	0.986844	+	0.253379i	0.130711	+	0.0335608i
$58$	−0.167280	+	0.319977i	−0.0219649	+	0.0420150i
$59$	−3.96208	−	12.1940i	−0.515819	−	1.58753i	−0.781786	−	0.623546i	$-0.785691\pi$
$59$	−3.96208	−	12.1940i	−0.515819	−	1.58753i	0.265967	−	0.963982i	$-0.414309\pi$
$60$	−2.58978	+	1.42374i	−0.334339	+	0.183804i
$61$	−9.24937	+	7.33096i	−1.18426	+	0.938634i	−0.999029	−	0.0440612i	$-0.985970\pi$
$61$	−9.24937	+	7.33096i	−1.18426	+	0.938634i	−0.185232	+	0.982695i	$0.559304\pi$
$62$	−0.0154958	+	0.0204150i	−0.00196797	+	0.00259271i
$63$	−2.89085	−	2.95204i	−0.364213	−	0.371923i
$64$	−2.44436	+	7.52298i	−0.305545	+	0.940372i
$65$	4.33831	+	22.7422i	0.538101	+	2.82082i
$66$	−0.0736280	−	0.0817722i	−0.00906298	−	0.0100655i
$67$	4.66271	+	4.37858i	0.569641	+	0.534929i	0.914954	−	0.403559i	$-0.132227\pi$
$67$	4.66271	+	4.37858i	0.569641	+	0.534929i	−0.345312	+	0.938488i	$0.612227\pi$
$68$	−6.17433	−	0.780000i	−0.748748	−	0.0945888i
$69$	−0.428199	−	1.53364i	−0.0515492	−	0.184628i
$70$	0.0188511	−	0.299630i	0.00225314	−	0.0358126i
$71$	−8.19728	+	4.96445i	−0.972838	+	0.589171i	−0.912531	−	0.409008i	$-0.865875\pi$
$71$	−8.19728	+	4.96445i	−0.972838	+	0.589171i	−0.0603071	+	0.998180i	$0.519208\pi$
$72$	0.128482	−	0.673524i	0.0151417	−	0.0793756i
$73$	−7.80250	−	4.28946i	−0.913213	−	0.502043i	−0.0454197	−	0.998968i	$-0.514463\pi$
$73$	−7.80250	−	4.28946i	−0.913213	−	0.502043i	−0.867794	+	0.496925i	$0.834463\pi$
$74$	−0.0818404	+	0.0138423i	−0.00951375	+	0.00160913i
$75$	−2.63537	−	0.560164i	−0.304306	−	0.0646822i
$76$	4.46693	+	0.949476i	0.512392	+	0.108912i
$77$	−5.86625	+	0.992202i	−0.668521	+	0.113072i
$78$	0.166476	+	0.0915208i	0.0188497	+	0.0103627i
$79$	2.18781	−	11.4689i	0.246148	−	1.29035i	−0.617626	−	0.786472i	$-0.711906\pi$
$79$	2.18781	−	11.4689i	0.246148	−	1.29035i	0.863774	−	0.503880i	$-0.168094\pi$
$80$	−11.3092	+	6.84910i	−1.26441	+	0.765753i
$81$	0.455492	−	7.23983i	0.0506102	−	0.804426i
$82$	0.117846	+	0.422077i	0.0130139	+	0.0466106i
$83$	15.3806	+	1.94302i	1.68824	+	0.213275i	0.909976	−	0.414661i	$-0.136100\pi$
$83$	15.3806	+	1.94302i	1.68824	+	0.213275i	0.778266	+	0.627935i	$0.216100\pi$
$84$	0.955805	+	0.897561i	0.104287	+	0.0979319i
$85$	−6.93417	−	7.70117i	−0.752116	−	0.835309i
$86$	0.0341144	+	0.178834i	0.00367865	+	0.0192842i
$87$	0.811409	−	2.49726i	0.0869922	−	0.267734i
$88$	−0.690800	−	0.705421i	−0.0736395	−	0.0751982i
$89$	−4.16640	+	5.48903i	−0.441638	+	0.581836i	−0.962322	−	0.271913i	$-0.912344\pi$
$89$	−4.16640	+	5.48903i	−0.441638	+	0.581836i	0.520684	+	0.853749i	$0.325677\pi$
$90$	0.446970	−	0.354264i	0.0471148	−	0.0373427i
$91$	9.00128	−	4.94849i	0.943590	−	0.518743i
$92$	−2.20546	−	6.78770i	−0.229935	−	0.707667i
$93$	0.0863531	−	0.165178i	0.00895440	−	0.0171282i
$94$	−0.214054	−	0.0549598i	−0.0220780	−	0.00566867i
$95$	4.59756	+	6.05707i	0.471700	+	0.621442i
$96$	−0.0476941	+	0.322984i	−0.00486776	+	0.0329644i
$97$	−1.49562	+	6.37662i	−0.151857	+	0.647448i	0.842254	+	0.539081i	$0.181229\pi$
$97$	−1.49562	+	6.37662i	−0.151857	+	0.647448i	−0.994111	+	0.108366i	$0.965438\pi$
$98$	0.286212	−	0.0734868i	0.0289118	−	0.00742329i
$99$	−8.85769	−	7.02052i	−0.890232	−	0.705589i
$100$	−11.9071	−	2.01393i	−1.19071	−	0.201393i
$101$	9.37176	+	3.71054i	0.932525	+	0.369213i	0.784753	−	0.619809i	$-0.212790\pi$
$101$	9.37176	+	3.71054i	0.932525	+	0.369213i	0.147772	+	0.989021i	$0.452790\pi$
$102$	−0.0849578	+	0.00356078i	−0.00841207	+	0.000352570i
$103$	−5.45319	+	14.6632i	−0.537319	+	1.44481i	0.328525	+	0.944495i	$0.393448\pi$
$103$	−5.45319	+	14.6632i	−0.537319	+	1.44481i	−0.865845	+	0.500313i	$0.833218\pi$
$104$	1.52684	+	0.757931i	0.149719	+	0.0743212i
$105$	0.228218	+	2.17135i	0.0222718	+	0.211902i
$106$	−0.306052	+	0.151926i	−0.0297264	+	0.0147563i
$107$	3.31011	+	5.21590i	0.320000	+	0.504240i	0.965807	−	0.259261i	$-0.0834790\pi$
$107$	3.31011	+	5.21590i	0.320000	+	0.504240i	−0.645807	+	0.763501i	$0.723479\pi$
$108$	−0.108023	+	5.15694i	−0.0103945	+	0.496227i
$109$	−4.46276	−	6.42108i	−0.427455	−	0.615028i	0.547667	−	0.836697i	$-0.315516\pi$
$109$	−4.46276	−	6.42108i	−0.427455	−	0.615028i	−0.975122	+	0.221669i	$0.928850\pi$
$110$	−0.0515673	−	0.819639i	−0.00491675	−	0.0781495i
$111$	0.570046	−	0.198511i	0.0541064	−	0.0188418i
$112$	4.44046	+	3.83291i	0.419584	+	0.362176i
$113$	3.35172	+	1.49228i	0.315303	+	0.140382i	0.558286	−	0.829649i	$-0.311459\pi$
$113$	3.35172	+	1.49228i	0.315303	+	0.140382i	−0.242983	+	0.970031i	$0.578126\pi$
$114$	0.0623419	+	0.00261290i	0.00583885	+	0.000244720i
$115$	4.60533	−	10.9557i	0.429449	−	1.02162i
$116$	3.16500	−	11.3358i	0.293863	−	1.05250i
$117$	18.4282	+	6.41737i	1.70368	+	0.593286i
$118$	−0.392609	−	0.680019i	−0.0361426	−	0.0626008i
$119$	−2.29883	+	3.98170i	−0.210734	+	0.365001i
$120$	−0.274275	+	0.236748i	−0.0250378	+	0.0216120i
$121$	−5.04992	+	1.52466i	−0.459083	+	0.138605i
$122$	−0.460727	+	0.556923i	−0.0417123	+	0.0504215i
$123$	−1.35691	−	2.88357i	−0.122348	−	0.260003i
$124$	0.355711	−	0.755924i	0.0319438	−	0.0678840i
$125$	−2.22359	−	2.68786i	−0.198884	−	0.240409i
$126$	−0.210761	−	0.140029i	−0.0187761	−	0.0124748i
$127$	11.9565	−	18.8404i	1.06097	−	1.67182i	0.411537	−	0.911393i	$-0.364992\pi$
$127$	11.9565	−	18.8404i	1.06097	−	1.67182i	0.649430	−	0.760422i	$-0.275008\pi$
$128$	−0.203890	+	1.93988i	−0.0180215	+	0.171463i
$129$	−0.461506	−	1.24095i	−0.0406333	−	0.109260i
$130$	0.549455	+	1.30710i	0.0481904	+	0.114640i
$131$	−12.8617	+	1.62481i	−1.12373	+	0.141960i	−0.665161	−	0.746700i	$-0.731637\pi$
$131$	−12.8617	+	1.62481i	−1.12373	+	0.141960i	−0.458567	+	0.888660i	$0.651637\pi$
$132$	2.90172	+	2.10822i	0.252562	+	0.183497i
$133$	1.92545	−	2.77036i	0.166958	−	0.240221i
$134$	0.335066	+	0.202923i	0.0289453	+	0.0175299i
$135$	−5.74717	+	6.38287i	−0.494637	+	0.549350i
$136$	−0.760307	+	0.0638448i	−0.0651958	+	0.00547465i
$137$	0.235651	+	1.00470i	0.0201330	+	0.0858376i	0.982699	−	0.185210i	$-0.0592966\pi$
$137$	0.235651	+	1.00470i	0.0201330	+	0.0858376i	−0.962566	+	0.271048i	$0.912630\pi$
$138$	−0.0451784	−	0.0864183i	−0.00384584	−	0.00735642i
$139$	−2.77083	+	2.82948i	−0.235019	+	0.239993i	−0.821833	−	0.569728i	$-0.807049\pi$
$139$	−2.77083	+	2.82948i	−0.235019	+	0.239993i	0.586814	+	0.809722i	$0.300382\pi$
$140$	1.42958	+	9.68110i	0.120822	+	0.818202i
$141$	1.60153	+	0.134484i	0.134873	+	0.0113256i
$142$	−0.427835	+	0.401764i	−0.0359031	+	0.0337153i
$143$	22.7323	−	16.5160i	1.90097	−	1.38113i
$144$	0.233373	+	11.1411i	0.0194478	+	0.928427i
$145$	16.3234	−	10.8452i	1.35558	−	0.900647i
$146$	−0.522016	−	0.157606i	−0.0432023	−	0.0130436i
$147$	−1.96315	+	0.874052i	−0.161918	+	0.0720906i
$148$	2.51557	−	0.995985i	0.206779	−	0.0818695i
$149$	−1.60065	+	0.340229i	−0.131130	+	0.0278726i	−0.273009	−	0.962011i	$-0.588019\pi$
$149$	−1.60065	+	0.340229i	−0.131130	+	0.0278726i	0.141879	+	0.989884i	$0.454686\pi$
$150$	−0.165001			−0.0134722
$151$	9.52199	−	7.76735i	0.774888	−	0.632098i
$151$	9.52199	−	7.76735i	0.774888	−	0.632098i
$152$	0.559876			0.0454119
$153$	−8.54340	+	1.81596i	−0.690693	+	0.146811i
$154$	−0.338776	+	0.134131i	−0.0272994	+	0.0108086i
$155$	1.27086	−	0.565824i	0.102078	−	0.0454481i
$156$	−5.92813	−	1.78981i	−0.474630	−	0.143299i
$157$	12.6539	−	8.40726i	1.00989	−	0.670972i	0.0648433	−	0.997895i	$-0.479345\pi$
$157$	12.6539	−	8.40726i	1.00989	−	0.670972i	0.945051	+	0.326923i	$0.106012\pi$
$158$	−0.0149747	−	0.714886i	−0.00119133	−	0.0568733i
$159$	2.01028	−	1.46056i	0.159426	−	0.115830i
$160$	−1.77633	+	1.66808i	−0.140431	+	0.131873i
$161$	−5.25412	−	0.441201i	−0.414083	−	0.0347715i
$162$	−0.0648986	−	0.439492i	−0.00509892	−	0.0345298i
$163$	4.44427	−	4.53834i	0.348102	−	0.355470i	−0.517961	−	0.855404i	$-0.673309\pi$
$163$	4.44427	−	4.53834i	0.348102	−	0.355470i	0.866064	+	0.499934i	$0.166642\pi$
$164$	−6.61785	−	12.6588i	−0.516767	−	0.988484i
$165$	1.36382	+	5.81466i	0.106173	+	0.452670i
$166$	0.946096	−	0.0794459i	0.0734313	−	0.00616620i
$167$	11.6848	−	12.9773i	0.904198	−	1.00421i	−0.0957628	−	0.995404i	$-0.530529\pi$
$167$	11.6848	−	12.9773i	0.904198	−	1.00421i	0.999961	−	0.00880990i	$-0.00280432\pi$
$168$	0.137499	+	0.0832722i	0.0106083	+	0.00642459i
$169$	−20.2671	+	29.1605i	−1.55901	+	2.24312i
$170$	−0.513441	−	0.373036i	−0.0393791	−	0.0286106i
$171$	6.35865	−	0.803285i	0.486258	−	0.0614287i
$172$	−2.29968	−	5.47071i	−0.175349	−	0.417138i
$173$	−2.64998	−	7.12558i	−0.201474	−	0.541748i	0.796550	−	0.604572i	$-0.206656\pi$
$173$	−2.64998	−	7.12558i	−0.201474	−	0.541748i	−0.998025	+	0.0628245i	$0.979989\pi$
$174$	0.0168090	−	0.159927i	0.00127429	−	0.0121240i
$175$	−4.78039	+	7.53269i	−0.361364	+	0.569418i
$176$	13.3652	+	8.87984i	1.00744	+	0.669343i
$177$	3.63991	+	4.39990i	0.273593	+	0.330717i
$178$	−0.179691	+	0.381864i	−0.0134684	+	0.0286219i
$179$	−3.34970	−	7.11847i	−0.250368	−	0.532060i	0.739651	−	0.672990i	$-0.234991\pi$
$179$	−3.34970	−	7.11847i	−0.250368	−	0.532060i	−0.990019	+	0.140931i	$0.954991\pi$
$180$	−11.8502	+	14.3245i	−0.883263	+	1.06768i
$181$	8.97871	−	2.71083i	0.667382	−	0.201495i	0.0627863	−	0.998027i	$-0.480001\pi$
$181$	8.97871	−	2.71083i	0.667382	−	0.201495i	0.604596	+	0.796532i	$0.293335\pi$
$182$	0.476201	−	0.411046i	0.0352984	−	0.0304687i
$183$	2.62820	−	4.55217i	0.194282	−	0.336506i
$184$	−0.437495	−	0.757764i	−0.0322526	−	0.0558631i
$185$	4.25460	+	1.48161i	0.312804	+	0.108930i
$186$	0.00306967	−	0.0109943i	0.000225079	−	0.000806142i
$187$	−4.87376	+	11.5942i	−0.356404	+	0.847852i
$188$	7.19734	+	0.301658i	0.524920	+	0.0220007i
$189$	3.48118	+	1.54992i	0.253219	+	0.112740i
$190$	0.352535	+	0.304300i	0.0255756	+	0.0220763i
$191$	−21.1421	+	7.36245i	−1.52979	+	0.532728i	−0.957776	−	0.287517i	$-0.907170\pi$
$191$	−21.1421	+	7.36245i	−1.52979	+	0.532728i	−0.572012	+	0.820245i	$0.693837\pi$
$192$	−0.221207	−	3.51599i	−0.0159643	−	0.253745i
$193$	6.73034	+	9.68369i	0.484460	+	0.697047i	0.985747	−	0.168234i	$-0.0538065\pi$
$193$	6.73034	+	9.68369i	0.484460	+	0.697047i	−0.501287	+	0.865281i	$0.667140\pi$
$194$	−0.00840031	+	0.401027i	−0.000603107	+	0.0287920i
$195$	−5.52510	−	8.70616i	−0.395661	−	0.623461i
$196$	−8.62751	+	4.28273i	−0.616251	+	0.305909i
$197$	0.711501	+	6.76948i	0.0506923	+	0.482305i	0.990188	+	0.139744i	$0.0446279\pi$
$197$	0.711501	+	6.76948i	0.0506923	+	0.482305i	−0.939495	+	0.342562i	$0.888705\pi$
$198$	−0.620000	−	0.307771i	−0.0440615	−	0.0218723i
$199$	−7.33395	+	19.7204i	−0.519890	+	1.39794i	0.364505	+	0.931202i	$0.381238\pi$
$199$	−7.33395	+	19.7204i	−0.519890	+	1.39794i	−0.884394	+	0.466740i	$0.845428\pi$
$200$	−1.47923	+	0.0619981i	−0.104597	+	0.00438393i
$201$	−2.64868	−	1.04869i	−0.186824	−	0.0739688i
$202$	0.608649	+	0.102945i	0.0428244	+	0.00724321i
$203$	−6.81406	−	5.40076i	−0.478253	−	0.379059i
$204$	2.68464	−	0.689299i	0.187963	−	0.0482606i
$205$	5.43145	−	23.1571i	0.379349	−	1.61736i
$206$	−0.139961	+	0.947815i	−0.00975155	+	0.0660374i
$207$	−6.05595	−	7.97842i	−0.420918	−	0.554538i
$208$	−26.8332	−	6.88959i	−1.86055	−	0.477707i
$209$	4.27573	−	8.17871i	0.295758	−	0.565733i
$210$	0.0413188	+	0.127166i	0.00285127	+	0.00877529i
$211$	−10.3063	+	5.66594i	−0.709515	+	0.390059i	−0.795269	−	0.606257i	$-0.792670\pi$
$211$	−10.3063	+	5.66594i	−0.709515	+	0.390059i	0.0857536	+	0.996316i	$0.472670\pi$
$212$	8.72849	−	6.91811i	0.599475	−	0.475138i
$213$	2.58052	−	3.39971i	0.176814	−	0.232944i
$214$	0.264701	+	0.270304i	0.0180946	+	0.0184776i
$215$	3.05362	−	9.39808i	0.208255	−	0.640944i
$216$	0.118495	+	0.621174i	0.00806258	+	0.0422655i
$217$	−0.412984	−	0.458665i	−0.0280352	−	0.0311362i
$218$	−0.349095	−	0.327822i	−0.0236437	−	0.0222029i
$219$	3.93424	+	0.497010i	0.265851	+	0.0335849i
$220$	7.19895	+	25.7837i	0.485353	+	1.73834i
$221$	1.36343	−	21.6710i	0.0917139	−	1.45775i
$222$	0.0316202	−	0.0191499i	0.00212221	−	0.00128526i
$223$	−2.84982	+	14.9393i	−0.190838	+	1.00041i	0.749971	+	0.661471i	$0.230068\pi$
$223$	−2.84982	+	14.9393i	−0.190838	+	1.00041i	−0.940809	+	0.338938i	$0.889932\pi$
$224$	0.947379	+	0.520826i	0.0632994	+	0.0347992i
$225$	−16.7110	+	2.82646i	−1.11407	+	0.188431i
$226$	0.219782	+	0.0467160i	0.0146196	+	0.00310750i
$227$	−7.16576	−	1.52313i	−0.475608	−	0.101094i	−0.0361303	−	0.999347i	$-0.511503\pi$
$227$	−7.16576	−	1.52313i	−0.475608	−	0.101094i	−0.439478	+	0.898253i	$0.644836\pi$
$228$	−2.00540	+	0.339189i	−0.132811	+	0.0224633i
$229$	−10.2571	−	5.63891i	−0.677811	−	0.372630i	0.105362	−	0.994434i	$-0.466400\pi$
$229$	−10.2571	−	5.63891i	−0.677811	−	0.372630i	−0.783173	+	0.621804i	$0.786400\pi$
$230$	0.136379	−	0.714923i	0.00899256	−	0.0471406i
$231$	2.26651	−	1.37265i	0.149126	−	0.0903137i
$232$	0.0906007	−	1.44006i	0.00594823	−	0.0945444i
$233$	3.83000	+	13.7175i	0.250912	+	0.898664i	0.977385	+	0.211469i	$0.0678249\pi$
$233$	3.83000	+	13.7175i	0.250912	+	0.898664i	−0.726473	+	0.687195i	$0.758842\pi$
$234$	1.18563	+	0.149780i	0.0775069	+	0.00979139i
$235$	8.74414	+	8.21129i	0.570405	+	0.535646i
$236$	17.1264	+	19.0208i	1.11484	+	1.23815i
$237$	0.974386	+	5.10791i	0.0632932	+	0.331794i
$238$	−0.0870099	+	0.267789i	−0.00564002	+	0.0173582i
$239$	−4.54979	−	4.64609i	−0.294302	−	0.300531i	0.551342	−	0.834280i	$-0.314116\pi$
$239$	−4.54979	−	4.64609i	−0.294302	−	0.300531i	−0.845643	+	0.533749i	$0.820783\pi$
$240$	3.56017	−	4.69035i	0.229808	−	0.302761i
$241$	−20.7105	+	16.4150i	−1.33408	+	1.05738i	−0.340989	+	0.940067i	$0.610762\pi$
$241$	−20.7105	+	16.4150i	−1.33408	+	1.05738i	−0.993095	+	0.117314i	$0.962571\pi$
$242$	−0.283095	+	0.155633i	−0.0181981	+	0.0100045i
$243$	3.39376	+	10.4449i	0.217710	+	0.670042i
$244$	10.9154	−	20.8792i	0.698787	−	1.33666i
$245$	−15.5349	−	3.98869i	−0.992490	−	0.254828i
$246$	−0.118000	−	0.155459i	−0.00752340	−	0.00991171i
$247$	−2.32763	+	15.7627i	−0.148104	+	1.00296i
$248$	0.0233885	−	0.0997174i	0.00148517	−	0.00633206i
$249$	−6.68760	+	1.71708i	−0.423810	+	0.108816i
$250$	−0.167425	−	0.132700i	−0.0105889	−	0.00839267i
$251$	−12.1240	−	2.05062i	−0.765258	−	0.129434i	−0.228929	−	0.973443i	$-0.573522\pi$
$251$	−12.1240	−	2.05062i	−0.765258	−	0.129434i	−0.536328	+	0.844009i	$0.680189\pi$
$252$	7.66885	+	3.03631i	0.483092	+	0.191270i
$253$	−14.4106	+	0.603983i	−0.905986	+	0.0379721i
$254$	0.476344	−	1.28085i	0.0298885	−	0.0803677i
$255$	4.13403	+	2.05215i	0.258883	+	0.128511i
$256$	−1.64118	−	15.6148i	−0.102574	−	0.975924i
$257$	−3.31135	+	1.64377i	−0.206556	+	0.102535i	−0.544948	−	0.838470i	$-0.683451\pi$
$257$	−3.31135	+	1.64377i	−0.206556	+	0.102535i	0.338391	+	0.941005i	$0.390117\pi$
$258$	−0.0434468	−	0.0684612i	−0.00270488	−	0.00426221i
$259$	0.0418595	−	1.99835i	0.00260102	−	0.124172i
$260$	−26.3771	−	37.9517i	−1.63584	−	2.35366i
$261$	−1.03715	−	16.4851i	−0.0641982	−	1.02040i
$262$	−0.749773	+	0.261098i	−0.0463211	+	0.0161307i
$263$	19.8527	+	17.1364i	1.22417	+	1.05667i	0.996556	+	0.0829225i	$0.0264254\pi$
$263$	19.8527	+	17.1364i	1.22417	+	1.05667i	0.227613	+	0.973752i	$0.426908\pi$
$264$	0.401712	+	0.178854i	0.0247237	+	0.0110077i
$265$	18.5296	+	0.776622i	1.13827	+	0.0477075i
$266$	0.0800668	−	0.190471i	0.00490921	−	0.0116786i
$267$	0.825350	−	2.95607i	0.0505106	−	0.180909i
$268$	−12.0584	−	4.19918i	−0.736584	−	0.256506i
$269$	10.9642	+	18.9906i	0.668499	+	1.15787i	0.978324	+	0.207081i	$0.0663963\pi$
$269$	10.9642	+	18.9906i	0.668499	+	1.15787i	−0.309825	+	0.950794i	$0.600270\pi$
$270$	−0.263004	+	0.455536i	−0.0160059	+	0.0277230i
$271$	4.46688	−	3.85571i	0.271344	−	0.234218i	−0.507169	−	0.861847i	$-0.669308\pi$
$271$	4.46688	−	3.85571i	0.271344	−	0.234218i	0.778513	+	0.627629i	$0.215975\pi$
$272$	11.8708	−	3.58402i	0.719776	−	0.217313i
$273$	−2.91607	+	3.52492i	−0.176489	+	0.213338i
$274$	0.0269092	+	0.0571849i	0.00162564	+	0.00345467i
$275$	−10.3911	+	22.0822i	−0.626606	+	1.33160i
$276$	2.02613	+	2.44917i	0.121958	+	0.147422i
$277$	3.57475	+	2.37506i	0.214786	+	0.142703i	0.656165	−	0.754617i	$-0.272177\pi$
$277$	3.57475	+	2.37506i	0.214786	+	0.142703i	−0.441379	+	0.897321i	$0.645511\pi$
$278$	−0.129955	+	0.204777i	−0.00779421	+	0.0122817i
$279$	0.122559	−	1.16607i	0.00733742	−	0.0698109i
$280$	0.418204	+	1.12452i	0.0249925	+	0.0672028i
$281$	−1.05395	−	2.50724i	−0.0628733	−	0.149570i	0.887388	−	0.461023i	$-0.152517\pi$
$281$	−1.05395	−	2.50724i	−0.0628733	−	0.149570i	−0.950261	+	0.311454i	$0.899184\pi$
$282$	0.0976497	−	0.0123360i	0.00581495	−	0.000734600i
$283$	1.06484	+	0.773649i	0.0632980	+	0.0459887i	0.618984	−	0.785403i	$-0.287544\pi$
$283$	1.06484	+	0.773649i	0.0632980	+	0.0459887i	−0.555686	+	0.831392i	$0.687544\pi$
$284$	10.9182	−	15.7092i	0.647877	−	0.932172i
$285$	−2.89690	−	1.75442i	−0.171597	−	0.103923i
$286$	1.15145	−	1.27882i	0.0680867	−	0.0756179i
$287$	−10.5158	+	0.883035i	−0.620727	+	0.0521239i
$288$	0.468985	+	1.99953i	0.0276352	+	0.117823i
$289$	−3.37321	−	6.45235i	−0.198424	−	0.379550i
$290$	0.839739	−	0.857513i	0.0493112	−	0.0503549i
$291$	−0.426129	−	2.88574i	−0.0249801	−	0.169165i
$292$	17.7120	+	1.48731i	1.03651	+	0.0870385i
$293$	−6.81736	+	6.40193i	−0.398275	+	0.374005i	−0.857647	−	0.514239i	$-0.828074\pi$
$293$	−6.81736	+	6.40193i	−0.398275	+	0.374005i	0.459372	+	0.888244i	$0.348074\pi$
$294$	−0.106471	+	0.0773556i	−0.00620951	+	0.00451147i
$295$	0.892561	+	42.6104i	0.0519669	+	2.48088i
$296$	0.276280	−	0.183560i	0.0160584	−	0.0106692i
$297$	9.97909	+	3.01287i	0.579046	+	0.174824i
$298$	−0.0915528	+	0.0407619i	−0.00530351	+	0.00236127i
$299$	23.1528	−	9.16686i	1.33896	−	0.530133i
$300$	5.26085	−	1.11823i	0.303735	−	0.0645609i
$301$	−4.38416			−0.252699
$302$	0.471501	−	0.586536i	0.0271318	−	0.0337513i
$303$	−4.48915			−0.257895
$304$	−8.90032	+	1.89182i	−0.510469	+	0.108503i
$305$	36.4766	−	14.4421i	2.08865	−	0.826953i
$306$	−0.488659	+	0.217565i	−0.0279348	+	0.0124374i
$307$	15.1122	+	4.56265i	0.862500	+	0.260404i	0.689294	−	0.724482i	$-0.257921\pi$
$307$	15.1122	+	4.56265i	0.862500	+	0.260404i	0.173206	+	0.984886i	$0.444588\pi$
$308$	9.89245	−	6.57253i	0.563675	−	0.374505i
$309$	−0.145917	−	6.96602i	−0.00830095	−	0.396283i
$310$	0.0689247	−	0.0500767i	0.00391466	−	0.00284417i
$311$	11.4580	−	10.7598i	0.649722	−	0.610130i	−0.287952	−	0.957645i	$-0.592974\pi$
$311$	11.4580	−	10.7598i	0.649722	−	0.610130i	0.937674	+	0.347515i	$0.112974\pi$
$312$	−0.756522	−	0.0635269i	−0.0428296	−	0.00359650i
$313$	−4.18715	−	28.3553i	−0.236672	−	1.60274i	−0.698394	−	0.715714i	$-0.746102\pi$
$313$	−4.18715	−	28.3553i	−0.236672	−	1.60274i	0.461722	−	0.887025i	$-0.347232\pi$
$314$	0.650968	−	0.664747i	0.0367363	−	0.0375139i
$315$	6.36306	+	12.1714i	0.358518	+	0.685781i
$316$	5.32231	+	22.6918i	0.299404	+	1.27651i
$317$	−16.9892	+	1.42663i	−0.954210	+	0.0801273i	−0.550569	−	0.834790i	$-0.685589\pi$
$317$	−16.9892	+	1.42663i	−0.954210	+	0.0801273i	−0.403642	+	0.914917i	$0.632256\pi$
$318$	0.101826	−	0.113089i	0.00571013	−	0.00634174i
$319$	−20.3446	−	12.3211i	−1.13908	−	0.689849i
$320$	15.0062	−	21.5911i	0.838874	−	1.20698i
$321$	−2.22586	−	1.61718i	−0.124235	−	0.0902621i
$322$	−0.320359	+	0.0404707i	−0.0178529	+	0.00225535i
$323$	−2.76371	−	6.57461i	−0.153777	−	0.365821i
$324$	5.04770	+	13.5729i	0.280428	+	0.754048i
$325$	4.40426	−	41.9038i	0.244305	−	2.32440i
$326$	0.208442	−	0.328452i	0.0115445	−	0.0181913i
$327$	2.90076	+	1.92726i	0.160412	+	0.106578i
$328$	−1.11628	−	1.34935i	−0.0616363	−	0.0745055i
$329$	2.26593	−	4.81535i	0.124925	−	0.265479i
$330$	0.155735	+	0.330954i	0.00857294	+	0.0182184i
$331$	12.8199	−	15.4966i	0.704644	−	0.851769i	−0.289794	−	0.957089i	$-0.593587\pi$
$331$	12.8199	−	15.4966i	0.704644	−	0.851769i	0.994438	+	0.105320i	$0.0335868\pi$
$332$	−29.6267	+	8.94483i	−1.62598	+	0.490911i
$333$	2.87441	−	2.48113i	0.157517	−	0.135965i
$334$	0.534725	−	0.926170i	0.0292588	−	0.0506778i
$335$	−10.6309	−	18.4133i	−0.580828	−	1.00602i
$336$	−2.46719	−	0.859166i	−0.134596	−	0.0468713i
$337$	−9.42795	+	33.7671i	−0.513573	+	1.83941i	0.0292614	+	0.999572i	$0.490684\pi$
$337$	−9.42795	+	33.7671i	−0.513573	+	1.83941i	−0.542834	+	0.839840i	$0.682649\pi$
$338$	−0.842775	+	2.00488i	−0.0458409	+	0.109051i
$339$	−1.63259	−	0.0684260i	−0.0886703	−	0.00371639i
$340$	18.8985	+	8.41417i	1.02492	+	0.456323i
$341$	−1.27806	−	1.10319i	−0.0692110	−	0.0597413i
$342$	0.370679	−	0.129084i	0.0200440	−	0.00698006i
$343$	1.09502	+	17.4048i	0.0591254	+	0.939772i
$344$	−0.415224	−	0.597429i	−0.0223874	−	0.0322112i
$345$	−0.110846	+	5.29174i	−0.00596775	+	0.284897i
$346$	−0.249473	−	0.393106i	−0.0134117	−	0.0211335i
$347$	−10.9926	+	5.45678i	−0.590114	+	0.292935i	−0.714876	−	0.699252i	$-0.753517\pi$
$347$	−10.9926	+	5.45678i	−0.590114	+	0.292935i	0.124762	+	0.992187i	$0.460183\pi$
$348$	0.547907	+	5.21299i	0.0293709	+	0.279445i
$349$	3.75293	+	1.86297i	0.200890	+	0.0997227i	0.542276	−	0.840201i	$-0.317563\pi$
$349$	3.75293	+	1.86297i	0.200890	+	0.0997227i	−0.341386	+	0.939923i	$0.610896\pi$
$350$	−0.190450	+	0.512104i	−0.0101800	+	0.0273731i
$351$	−17.9811	+	0.753630i	−0.959759	+	0.0402258i
$352$	2.74969	+	1.08868i	0.146559	+	0.0580268i
$353$	−24.4425	−	4.13415i	−1.30095	−	0.220038i	−0.525143	−	0.851014i	$-0.675988\pi$
$353$	−24.4425	−	4.13415i	−1.30095	−	0.220038i	−0.775802	+	0.630976i	$0.782655\pi$
$354$	0.274068	+	0.217224i	0.0145665	+	0.0115453i
$355$	30.8550	−	7.92222i	1.63761	−	0.420468i
$356$	3.14131	−	13.3930i	0.166489	−	0.709830i
$357$	0.299129	−	2.02570i	0.0158316	−	0.107211i
$358$	−0.291298	−	0.383771i	−0.0153956	−	0.0202829i
$359$	3.35321	+	0.860958i	0.176976	+	0.0454396i	0.336138	−	0.941813i	$-0.390879\pi$
$359$	3.35321	+	0.860958i	0.176976	+	0.0454396i	−0.159162	+	0.987252i	$0.550879\pi$
$360$	−1.05595	+	2.01985i	−0.0556535	+	0.106455i
$361$	−4.25413	−	13.0929i	−0.223901	−	0.689098i
$362$	0.503341	−	0.276714i	0.0264550	−	0.0145438i
$363$	1.84118	−	1.45930i	0.0966367	−	0.0765933i
$364$	−12.3974	+	16.3330i	−0.649800	+	0.856080i
$365$	20.7079	+	21.1462i	1.08390	+	1.10685i
$366$	0.0994762	−	0.306156i	0.00519970	−	0.0160030i
$367$	2.45350	+	12.8617i	0.128072	+	0.671376i	0.987184	+	0.159588i	$0.0510166\pi$
$367$	2.45350	+	12.8617i	0.128072	+	0.671376i	−0.859112	+	0.511788i	$0.828983\pi$
$368$	9.51533	+	10.5678i	0.496021	+	0.550887i
$369$	−14.6139	−	13.7233i	−0.760768	−	0.714408i
$370$	0.273731	+	0.0345803i	0.0142306	+	0.00179774i
$371$	−2.21271	−	7.92504i	−0.114878	−	0.411448i
$372$	−0.0233630	+	0.371344i	−0.00121131	+	0.0192533i
$373$	3.19559	−	1.93532i	0.165462	−	0.100207i	−0.432868	−	0.901458i	$-0.642498\pi$
$373$	3.19559	−	1.93532i	0.165462	−	0.100207i	0.598329	+	0.801250i	$0.295832\pi$
$374$	−0.144328	+	0.756593i	−0.00746301	+	0.0391225i
$375$	1.36146	+	0.748467i	0.0703053	+	0.0386507i
$376$	0.870793	−	0.147284i	0.0449077	−	0.00759558i
$377$	40.1665	+	8.53766i	2.06868	+	0.439712i
$378$	0.228271	+	0.0485205i	0.0117410	+	0.00249562i
$379$	−0.348346	+	0.0589184i	−0.0178933	+	0.00302643i	−0.175709	−	0.984442i	$-0.556222\pi$
$379$	−0.348346	+	0.0589184i	−0.0178933	+	0.00302643i	0.157815	+	0.987469i	$0.449555\pi$
$380$	−13.3024	−	7.31307i	−0.682400	−	0.375153i
$381$	−1.86220	+	9.76201i	−0.0954035	+	0.500123i
$382$	−1.17274	+	0.710239i	−0.0600028	+	0.0363390i
$383$	1.68594	−	26.7972i	0.0861474	−	1.36927i	−0.683101	−	0.730324i	$-0.739369\pi$
$383$	1.68594	−	26.7972i	0.0861474	−	1.36927i	0.769249	−	0.638950i	$-0.220631\pi$
$384$	−0.233617	−	0.836723i	−0.0119217	−	0.0426989i
$385$	19.6208	+	2.47869i	0.999970	+	0.126326i
$386$	0.526474	+	0.494392i	0.0267968	+	0.0251639i
$387$	−5.57297	−	6.18941i	−0.283290	−	0.314625i
$388$	−2.44997	−	12.8432i	−0.124378	−	0.652014i
$389$	−7.60104	+	23.3936i	−0.385388	+	1.18610i	0.550811	+	0.834630i	$0.314319\pi$
$389$	−7.60104	+	23.3936i	−0.385388	+	1.18610i	−0.936199	+	0.351472i	$0.885681\pi$
$390$	−0.441829	−	0.451181i	−0.0223729	−	0.0228464i
$391$	−6.73880	+	8.87804i	−0.340796	+	0.448982i
$392$	−0.925444	+	0.733498i	−0.0467420	+	0.0370473i
$393$	5.05956	−	2.78152i	0.255221	−	0.140309i
$394$	0.128817	+	0.396457i	0.00648969	+	0.0199732i
$395$	−17.9809	+	34.3943i	−0.904718	+	1.73057i
$396$	21.8538	+	5.61109i	1.09819	+	0.281968i
$397$	−15.7615	−	20.7650i	−0.791047	−	1.04217i	−0.997962	−	0.0638067i	$-0.979676\pi$
$397$	−15.7615	−	20.7650i	−0.791047	−	1.04217i	0.206916	−	0.978359i	$-0.433657\pi$
$398$	−0.188232	+	1.27471i	−0.00943524	+	0.0638953i
$399$	−0.343114	+	1.46287i	−0.0171772	+	0.0732353i
$400$	23.3058	−	5.98390i	1.16529	−	0.299195i
$401$	18.3858	+	14.5724i	0.918145	+	0.727713i	0.962494	−	0.271303i	$-0.0874546\pi$
$401$	18.3858	+	14.5724i	0.918145	+	0.727713i	−0.0443486	+	0.999016i	$0.514121\pi$
$402$	−0.172019	−	0.0290948i	−0.00857952	−	0.00145112i
$403$	2.71019	+	1.07304i	0.135004	+	0.0534520i
$404$	−20.1037	+	0.842595i	−1.00020	+	0.0419207i
$405$	−8.40522	+	22.6010i	−0.417659	+	1.12305i
$406$	−0.476955	−	0.236762i	−0.0236709	−	0.0117503i
$407$	−0.571530	−	5.43775i	−0.0283297	−	0.269539i
$408$	0.304372	−	0.151092i	0.0150687	−	0.00748015i
$409$	−6.73234	−	10.6085i	−0.332893	−	0.524555i	0.636112	−	0.771597i	$-0.280542\pi$
$409$	−6.73234	−	10.6085i	−0.332893	−	0.524555i	−0.969005	+	0.247042i	$0.920542\pi$
$410$	0.0305063	−	1.45635i	0.00150660	−	0.0719242i
$411$	−0.262305	−	0.377408i	−0.0129386	−	0.0186161i
$412$	−1.96095	−	31.1685i	−0.0966093	−	1.53556i
$413$	17.8571	−	6.21849i	0.878689	−	0.305992i
$414$	−0.464362	−	0.400827i	−0.0228222	−	0.0196996i
$415$	−47.0774	−	20.9602i	−2.31094	−	1.02890i
$416$	−5.10137	−	0.213811i	−0.250115	−	0.0104829i
$417$	0.683490	−	1.62596i	0.0334706	−	0.0796235i
$418$	0.151993	−	0.544377i	0.00743422	−	0.0266264i
$419$	12.4295	+	4.32841i	0.607221	+	0.211457i	0.615018	−	0.788513i	$-0.289149\pi$
$419$	12.4295	+	4.32841i	0.607221	+	0.211457i	−0.00779722	+	0.999970i	$0.502482\pi$
$420$	−2.17922	−	3.77452i	−0.106335	−	0.184177i
$421$	−6.11436	+	10.5904i	−0.297996	+	0.516144i	−0.975677	−	0.219212i	$-0.929651\pi$
$421$	−6.11436	+	10.5904i	−0.297996	+	0.516144i	0.677682	+	0.735355i	$0.262985\pi$
$422$	−0.545241	+	0.470640i	−0.0265419	+	0.0229104i
$423$	9.67850	−	2.92211i	0.470585	−	0.142078i
$424$	0.870378	−	1.05211i	0.0422693	−	0.0510948i
$425$	8.02995	+	17.0645i	0.389510	+	0.827750i
$426$	0.111295	−	0.236513i	0.00539224	−	0.0114591i
$427$	−11.0948	−	13.4113i	−0.536914	−	0.649017i
$428$	−10.2716	−	6.82441i	−0.496495	−	0.329870i
$429$	−6.70550	+	10.5662i	−0.323745	+	0.510140i
$430$	0.0632582	−	0.601861i	0.00305058	−	0.0290243i
$431$	−6.46296	−	17.3784i	−0.311310	−	0.837087i	−0.994296	−	0.106656i	$-0.965986\pi$
$431$	−6.46296	−	17.3784i	−0.311310	−	0.837087i	0.682986	−	0.730431i	$-0.260681\pi$
$432$	−3.98266	−	9.47438i	−0.191616	−	0.455836i
$433$	1.24299	−	0.157026i	0.0597342	−	0.00754618i	−0.0954094	−	0.995438i	$-0.530416\pi$
$433$	1.24299	−	0.157026i	0.0597342	−	0.00754618i	0.155144	+	0.987892i	$0.450416\pi$
$434$	−0.0305794	−	0.0222172i	−0.00146786	−	0.00106646i
$435$	−4.98134	+	7.16720i	−0.238837	+	0.343641i
$436$	13.3522	+	8.08636i	0.639453	+	0.387266i
$437$	5.47271	−	6.07806i	0.261795	−	0.290753i
$438$	0.242004	−	0.0203216i	0.0115634	−	0.000971006i
$439$	4.13086	+	17.6120i	0.197155	+	0.840576i	0.976766	+	0.214311i	$0.0687505\pi$
$439$	4.13086	+	17.6120i	0.197155	+	0.840576i	−0.779610	+	0.626265i	$0.784583\pi$
$440$	1.52052	+	2.90848i	0.0724879	+	0.138656i
$441$	−9.45811	+	9.65831i	−0.450386	+	0.459919i
$442$	−0.194261	−	1.31553i	−0.00924007	−	0.0625736i
$443$	−29.4737	−	2.47498i	−1.40034	−	0.117590i	−0.640628	−	0.767852i	$-0.721326\pi$
$443$	−29.4737	−	2.47498i	−1.40034	−	0.117590i	−0.759710	+	0.650262i	$0.774659\pi$
$444$	−0.878392	+	0.824865i	−0.0416867	+	0.0391464i
$445$	18.5320	−	13.4643i	0.878499	−	0.638267i
$446$	0.0195060	+	0.931205i	0.000923634	+	0.0440938i
$447$	0.607041	−	0.403317i	0.0287120	−	0.0190762i
$448$	−11.1677	−	3.37173i	−0.527625	−	0.159299i
$449$	4.02661	−	1.79276i	0.190028	−	0.0846057i	−0.309517	−	0.950894i	$-0.600167\pi$
$449$	4.02661	−	1.79276i	0.190028	−	0.0846057i	0.499545	+	0.866288i	$0.333501\pi$
$450$	−0.965063	+	0.382095i	−0.0454935	+	0.0180122i
$451$	−28.2364	+	6.00183i	−1.32960	+	0.282615i
$452$	−7.32407			−0.344495
$453$	−2.66954	+	4.77757i	−0.125426	+	0.224470i
$454$	−0.448649			−0.0210562
$455$	−33.3982	+	7.09900i	−1.56573	+	0.332806i
$456$	−0.231842	+	0.0917927i	−0.0108570	+	0.00429859i
$457$	−7.64840	+	3.40529i	−0.357777	+	0.159293i	−0.577751	−	0.816213i	$-0.696069\pi$
$457$	−7.64840	+	3.40529i	−0.357777	+	0.159293i	0.219974	+	0.975506i	$0.429403\pi$
$458$	−0.686241	−	0.207188i	−0.0320659	−	0.00968127i
$459$	6.70950	−	4.45778i	0.313173	−	0.208071i
$460$	0.496836	+	23.7187i	0.0231651	+	1.10589i
$461$	−8.16032	+	5.92882i	−0.380064	+	0.276133i	−0.761372	−	0.648315i	$-0.775474\pi$
$461$	−8.16032	+	5.92882i	−0.380064	+	0.276133i	0.381308	+	0.924448i	$0.375474\pi$
$462$	0.118295	−	0.111086i	0.00550356	−	0.00516819i
$463$	26.8522	+	2.25485i	1.24793	+	0.104792i	0.689208	−	0.724564i	$-0.257959\pi$
$463$	26.8522	+	2.25485i	1.24793	+	0.104792i	0.558722	+	0.829355i	$0.311292\pi$
$464$	3.42568	+	23.1987i	0.159033	+	1.07697i
$465$	−0.433490	+	0.442665i	−0.0201026	+	0.0205281i
$466$	0.404095	+	0.772963i	0.0187193	+	0.0358068i
$467$	5.49342	+	23.4213i	0.254205	+	1.08381i	0.935926	+	0.352197i	$0.114565\pi$
$467$	5.49342	+	23.4213i	0.254205	+	1.08381i	−0.681720	+	0.731613i	$0.738768\pi$
$468$	−38.8174	+	3.25959i	−1.79433	+	0.150674i
$469$	−6.31197	+	7.01015i	−0.291460	+	0.323699i
$470$	0.628360	+	0.380548i	0.0289841	+	0.0175534i
$471$	−3.86155	+	5.55604i	−0.177931	+	0.256009i
$472$	2.53864	+	1.84443i	0.116850	+	0.0848967i
$473$	−11.8983	+	1.50311i	−0.547086	+	0.0691130i
$474$	0.123408	+	0.293576i	0.00566831	+	0.0134844i
$475$	−4.82389	−	12.9711i	−0.221335	−	0.595153i
$476$	0.959371	−	9.12781i	0.0439727	−	0.418372i
$477$	8.37559	−	13.1978i	0.383492	−	0.604287i
$478$	−0.331708	−	0.220386i	−0.0151720	−	0.0100802i
$479$	−9.18843	−	11.1069i	−0.419830	−	0.507487i	0.517618	−	0.855612i	$-0.326819\pi$
$479$	−9.18843	−	11.1069i	−0.419830	−	0.507487i	−0.937448	+	0.348124i	$0.886819\pi$
$480$	0.462083	−	0.981976i	0.0210911	−	0.0448209i
$481$	4.01931	+	8.54147i	0.183265	+	0.389458i
$482$	−1.03163	+	1.24702i	−0.0469893	+	0.0568004i
$483$	2.24804	−	0.678724i	0.102289	−	0.0308830i
$484$	7.97141	−	6.88074i	0.362337	−	0.312761i
$485$	10.8858	−	18.8547i	0.494298	−	0.856149i
$486$	0.336293	+	0.582476i	0.0152546	+	0.0264217i
$487$	−25.5441	−	8.89540i	−1.15751	−	0.403089i	−0.318886	−	0.947793i	$-0.603309\pi$
$487$	−25.5441	−	8.89540i	−1.15751	−	0.403089i	−0.838629	+	0.544704i	$0.816642\pi$
$488$	0.776767	−	2.78207i	0.0351626	−	0.125938i
$489$	−1.09628	+	2.60795i	−0.0495756	+	0.117936i
$490$	−0.981387	−	0.0411323i	−0.0443346	−	0.00185817i
$491$	−11.3977	−	5.07458i	−0.514371	−	0.229013i	0.133100	−	0.991103i	$-0.457507\pi$
$491$	−11.3977	−	5.07458i	−0.514371	−	0.229013i	−0.647471	+	0.762090i	$0.724173\pi$
$492$	4.81585	+	4.15693i	0.217115	+	0.187409i
$493$	−17.3578	+	6.04462i	−0.781755	+	0.272236i
$494$	0.0612713	+	0.973880i	0.00275673	+	0.0438169i
$495$	21.4419	+	30.8508i	0.963740	+	1.38664i
$496$	−0.0348607	+	1.66423i	−0.00156529	+	0.0747262i
$497$	−7.57298	−	11.9331i	−0.339695	−	0.535273i
$498$	−0.378748	+	0.188012i	−0.0169721	+	0.00842504i
$499$	3.13480	+	29.8256i	0.140333	+	1.33518i	0.807322	+	0.590111i	$0.200916\pi$
$499$	3.13480	+	29.8256i	0.140333	+	1.33518i	−0.666989	+	0.745067i	$0.732417\pi$
$500$	6.23748	+	3.09631i	0.278949	+	0.138471i
$501$	−2.71097	+	7.28959i	−0.121117	+	0.325675i
$502$	−0.752380	+	0.0315341i	−0.0335804	+	0.00140744i
$503$	39.0883	+	15.4761i	1.74286	+	0.690047i	0.999783	+	0.0208410i	$0.00663438\pi$
$503$	39.0883	+	15.4761i	1.74286	+	0.690047i	0.743077	+	0.669206i	$0.233366\pi$
$504$	0.997043	+	0.168637i	0.0444118	+	0.00751170i
$505$	−26.2578	−	20.8117i	−1.16846	−	0.926109i
$506$	−0.855557	+	0.219670i	−0.0380342	+	0.00976551i
$507$	3.61158	−	15.3981i	0.160396	−	0.683852i
$508$	−6.50719	+	44.0666i	−0.288710	+	1.95514i
$509$	−14.6562	−	19.3088i	−0.649624	−	0.855848i	0.347007	−	0.937862i	$-0.387198\pi$
$509$	−14.6562	−	19.3088i	−0.649624	−	0.855848i	−0.996631	+	0.0820148i	$0.973865\pi$
$510$	0.273773	+	0.0702930i	0.0121229	+	0.00311263i
$511$	6.08359	−	11.6368i	0.269122	−	0.514784i
$512$	−1.50265	−	4.62468i	−0.0664084	−	0.204384i
$513$	−5.17987	+	2.84766i	−0.228697	+	0.125727i
$514$	−0.177432	+	0.140631i	−0.00782619	+	0.00620296i
$515$	31.4410	−	41.4220i	1.38545	−	1.82527i
$516$	1.84922	+	1.88836i	0.0814073	+	0.0831304i
$517$	4.49865	−	13.8454i	0.197850	−	0.608920i
$518$	−0.0229373	−	0.120242i	−0.00100781	−	0.00528311i
$519$	2.26560	+	2.51620i	0.0994486	+	0.110449i
$520$	−4.13052	−	3.87882i	−0.181135	−	0.170097i
$521$	2.99319	+	0.378127i	0.131134	+	0.0165661i	0.190626	−	0.981663i	$-0.438948\pi$
$521$	2.99319	+	0.378127i	0.131134	+	0.0165661i	−0.0594923	+	0.998229i	$0.518948\pi$
$522$	−0.272033	−	0.974311i	−0.0119065	−	0.0426444i
$523$	0.299761	−	4.76456i	0.0131076	−	0.208340i	−0.986022	−	0.166617i	$-0.946716\pi$
$523$	0.299761	−	4.76456i	0.0131076	−	0.208340i	0.999129	−	0.0417222i	$-0.0132845\pi$
$524$	22.1361	−	13.4061i	0.967020	−	0.585648i
$525$	0.744538	−	3.90300i	0.0324943	−	0.170341i
$526$	1.40744	+	0.773749i	0.0613675	+	0.0337371i
$527$	−1.28643	+	0.217583i	−0.0560378	+	0.00947808i
$528$	−6.99035	−	1.48584i	−0.304216	−	0.0646631i
$529$	9.99458	+	2.12441i	0.434547	+	0.0923658i
$530$	1.11988	−	0.189414i	0.0486446	−	0.00822761i
$531$	31.4782	+	17.3053i	1.36604	+	0.750986i
$532$	−1.26199	+	6.61557i	−0.0547141	+	0.286821i
$533$	42.6303	−	25.8178i	1.84652	−	1.11829i
$534$	0.0118021	−	0.187589i	0.000510726	−	0.00811775i
$535$	−5.52218	−	19.7782i	−0.238745	−	0.855087i
$536$	−1.55308	−	0.196199i	−0.0670828	−	0.00847453i
$537$	2.55418	+	2.39854i	0.110221	+	0.103504i
$538$	0.898601	+	0.997998i	0.0387415	+	0.0430267i
$539$	3.64745	+	19.1206i	0.157107	+	0.823584i
$540$	5.29834	−	16.3066i	0.228004	−	0.701725i
$541$	14.2003	+	14.5008i	0.610518	+	0.623440i	0.948144	−	0.317840i	$-0.102957\pi$
$541$	14.2003	+	14.5008i	0.610518	+	0.623440i	−0.337627	+	0.941280i	$0.609624\pi$
$542$	0.218488	−	0.287848i	0.00938488	−	0.0123641i
$543$	−3.27359	+	2.59462i	−0.140483	+	0.111346i
$544$	2.00269	−	1.10099i	0.0858645	−	0.0472044i
$545$	8.03227	+	24.7208i	0.344065	+	1.05892i
$546$	−0.129801	+	0.248286i	−0.00555496	+	0.0106257i
$547$	24.2397	+	6.22370i	1.03641	+	0.266106i	0.728311	−	0.685247i	$-0.240306\pi$
$547$	24.2397	+	6.22370i	1.03641	+	0.266106i	0.308104	+	0.951353i	$0.400306\pi$
$548$	−1.24552	−	1.64091i	−0.0532058	−	0.0700960i
$549$	4.83035	−	32.7111i	0.206154	−	1.39608i
$550$	−0.341293	+	1.45511i	−0.0145528	+	0.0620462i
$551$	13.0636	−	3.35416i	0.556528	−	0.142892i
$552$	0.305402	+	0.242058i	0.0129988	+	0.0103027i
$553$	16.9778	+	2.87159i	0.721971	+	0.122112i
$554$	0.244382	+	0.0967578i	0.0103828	+	0.00411084i
$555$	−2.00472	+	0.0840227i	−0.0850956	+	0.00356656i
$556$	2.75568	−	7.40979i	0.116867	−	0.314245i
$557$	−13.3097	−	6.60702i	−0.563952	−	0.279948i	0.140052	−	0.990144i	$-0.455273\pi$
$557$	−13.3097	−	6.60702i	−0.563952	−	0.279948i	−0.704004	+	0.710196i	$0.748606\pi$
$558$	−0.00750576	−	0.0714125i	−0.000317744	−	0.00302313i
$559$	18.5462	−	9.20642i	0.784421	−	0.389390i
$560$	−10.4479	−	16.4633i	−0.441505	−	0.695701i
$561$	0.117307	−	5.60017i	0.00495270	−	0.236439i
$562$	−0.0950599	−	0.136773i	−0.00400986	−	0.00576943i
$563$	−0.359348	−	5.71168i	−0.0151447	−	0.240718i	−0.998315	−	0.0580270i	$-0.981519\pi$
$563$	−0.359348	−	5.71168i	−0.0151447	−	0.240718i	0.983170	−	0.182691i	$-0.0584810\pi$
$564$	−3.02984	+	1.05510i	−0.127579	+	0.0444278i
$565$	−9.23210	−	7.96894i	−0.388398	−	0.335256i
$566$	0.0736385	+	0.0327860i	0.00309526	+	0.00137810i
$567$	10.6888	+	0.447994i	0.448888	+	0.0188140i
$568$	0.908886	−	2.16215i	0.0381360	−	0.0907220i
$569$	−1.99662	+	7.15110i	−0.0837028	+	0.299790i	−0.993279	−	0.115748i	$-0.963073\pi$
$569$	−1.99662	+	7.15110i	−0.0837028	+	0.299790i	0.909576	+	0.415538i	$0.136407\pi$
$570$	−0.195874	−	0.0682104i	−0.00820425	−	0.00285702i
$571$	15.1490	+	26.2389i	0.633968	+	1.09806i	0.986733	+	0.162352i	$0.0519081\pi$
$571$	15.1490	+	26.2389i	0.633968	+	1.09806i	−0.352765	+	0.935712i	$0.614759\pi$
$572$	−28.0459	+	48.5770i	−1.17266	+	2.03111i
$573$	7.54775	−	6.51504i	0.315312	−	0.272170i
$574$	−0.618690	+	0.186794i	−0.0258236	+	0.00779662i
$575$	−13.7862	+	16.6647i	−0.574925	+	0.694965i
$576$	−9.43585	−	20.0522i	−0.393160	−	0.835508i
$577$	5.32028	−	11.3062i	0.221486	−	0.470682i	−0.762943	−	0.646466i	$-0.776246\pi$
$577$	5.32028	−	11.3062i	0.221486	−	0.470682i	0.984429	+	0.175784i	$0.0562461\pi$
$578$	−0.284225	−	0.343569i	−0.0118222	−	0.0142906i
$579$	−4.37466	−	2.90652i	−0.181805	−	0.120791i
$580$	−20.9626	+	33.0318i	−0.870425	+	1.37157i
$581$	−2.38985	+	22.7379i	−0.0991476	+	0.943327i
$582$	−0.0622705	−	0.167440i	−0.00258120	−	0.00694063i
$583$	−8.72225	−	20.7494i	−0.361239	−	0.859353i
$584$	2.16193	−	0.273115i	0.0894612	−	0.0113016i
$585$	−52.4765	−	38.1264i	−2.16964	−	1.57633i
$586$	−0.326870	+	0.470304i	−0.0135029	+	0.0194281i
$587$	7.02166	+	4.25247i	0.289815	+	0.175518i	0.655447	−	0.755241i	$-0.272480\pi$
$587$	7.02166	+	4.25247i	0.289815	+	0.175518i	−0.365632	+	0.930760i	$0.619147\pi$
$588$	2.87045	−	3.18796i	0.118375	−	0.131469i
$589$	0.954030	−	0.0801122i	0.0393101	−	0.00330096i
$590$	0.596023	+	2.54116i	0.0245379	+	0.104618i
$591$	−1.40450	−	2.68656i	−0.0577733	−	0.110510i
$592$	−3.77176	+	3.85159i	−0.155018	+	0.158299i
$593$	−4.36549	−	29.5630i	−0.179269	−	1.21401i	−0.870791	−	0.491653i	$-0.836393\pi$
$593$	−4.36549	−	29.5630i	−0.179269	−	1.21401i	0.691522	−	0.722356i	$-0.256941\pi$
$594$	0.636147	+	0.0534187i	0.0261014	+	0.00219180i
$595$	11.1408	−	10.4619i	0.456728	−	0.428896i
$596$	2.64280	−	1.92011i	0.108253	−	0.0786507i
$597$	−0.196243	−	9.36854i	−0.00803169	−	0.383429i
$598$	1.27022	−	0.843932i	0.0519431	−	0.0345109i
$599$	22.1864	+	6.69848i	0.906513	+	0.273692i	0.707839	−	0.706373i	$-0.249670\pi$
$599$	22.1864	+	6.69848i	0.906513	+	0.273692i	0.198673	+	0.980066i	$0.436337\pi$
$600$	0.602377	−	0.268196i	0.0245919	−	0.0109490i
$601$	29.0567	−	11.5044i	1.18525	−	0.469273i	0.308966	−	0.951073i	$-0.400017\pi$
$601$	29.0567	−	11.5044i	1.18525	−	0.469273i	0.876281	+	0.481800i	$0.160017\pi$
$602$	−0.262628	+	0.0558232i	−0.0107039	+	0.00227518i
$603$	−17.9202			−0.729767
$604$	−11.0582	+	21.8964i	−0.449953	+	0.890952i
$605$	17.5347			0.712885
$606$	−0.268917	+	0.0571600i	−0.0109240	+	0.00232197i
$607$	−9.48307	+	3.75461i	−0.384906	+	0.152395i	−0.552605	−	0.833443i	$-0.686366\pi$
$607$	−9.48307	+	3.75461i	−0.384906	+	0.152395i	0.167699	+	0.985838i	$0.446366\pi$
$608$	−1.53202	+	0.682098i	−0.0621315	+	0.0276627i
$609$	3.70714	+	1.11925i	0.150221	+	0.0453543i
$610$	2.00119	−	1.32959i	0.0810260	−	0.0538335i
$611$	0.526367	+	25.1285i	0.0212945	+	1.01659i
$612$	14.1058	−	10.2485i	0.570195	−	0.414271i
$613$	−21.5669	+	20.2526i	−0.871077	+	0.817996i	−0.984470	−	0.175554i	$-0.943828\pi$
$613$	−21.5669	+	20.2526i	−0.871077	+	0.817996i	0.113393	+	0.993550i	$0.463828\pi$
$614$	0.963373	+	0.0808967i	0.0388786	+	0.00326472i
$615$	1.54751	+	10.4797i	0.0624018	+	0.422584i
$616$	1.01877	−	1.04033i	0.0410474	−	0.0419162i
$617$	−11.4295	−	21.8626i	−0.460135	−	0.880157i	−0.999280	−	0.0379437i	$-0.987919\pi$
$617$	−11.4295	−	21.8626i	−0.460135	−	0.880157i	0.539145	−	0.842213i	$-0.318747\pi$
$618$	−0.0974388	−	0.415432i	−0.00391956	−	0.0167111i
$619$	43.7835	−	3.67660i	1.75981	−	0.147775i	0.840627	−	0.541614i	$-0.182187\pi$
$619$	43.7835	−	3.67660i	1.75981	−	0.147775i	0.919179	+	0.393839i	$0.128853\pi$
$620$	−1.85821	+	2.06375i	−0.0746273	+	0.0828820i
$621$	7.90179	+	4.78549i	0.317088	+	0.192035i
$622$	0.549372	−	0.790443i	0.0220278	−	0.0316939i
$623$	−8.22196	−	5.97360i	−0.329406	−	0.239327i
$624$	12.2411	−	1.54641i	0.490034	−	0.0619057i
$625$	−7.22775	−	17.1941i	−0.289110	−	0.687765i
$626$	−0.611872	−	1.64527i	−0.0244553	−	0.0657584i
$627$	−0.429643	+	4.08778i	−0.0171583	+	0.163250i
$628$	−16.2503	+	25.6064i	−0.648457	+	1.02180i
$629$	−3.51933	−	2.33824i	−0.140325	−	0.0932317i
$630$	0.536148	+	0.648092i	0.0213606	+	0.0258206i
$631$	−3.40931	+	7.24515i	−0.135722	+	0.288425i	−0.961122	−	0.276124i	$-0.910950\pi$
$631$	−3.40931	+	7.24515i	−0.135722	+	0.288425i	0.825400	+	0.564549i	$0.190950\pi$
$632$	1.21666	+	2.58553i	0.0483961	+	0.102847i
$633$	3.33885	−	4.03598i	0.132707	−	0.160416i
$634$	−0.999552	+	0.301783i	−0.0396973	+	0.0119853i
$635$	−56.1490	+	48.4665i	−2.22821	+	1.92334i
$636$	−2.48019	+	4.29581i	−0.0983458	+	0.170340i
$637$	−16.8034	−	29.1043i	−0.665774	−	1.15315i
$638$	−1.37560	−	0.479034i	−0.0544604	−	0.0189651i
$639$	7.22029	−	25.8602i	0.285630	−	1.02301i
$640$	2.51258	−	5.97719i	0.0993184	−	0.236269i
$641$	−12.4639	−	0.522393i	−0.492295	−	0.0206333i	−0.205563	−	0.978644i	$-0.565902\pi$
$641$	−12.4639	−	0.522393i	−0.492295	−	0.0206333i	−0.286733	+	0.958011i	$0.592569\pi$
$642$	−0.153928	−	0.0685333i	−0.00607507	−	0.00270479i
$643$	−8.97720	−	7.74891i	−0.354026	−	0.305587i	0.458292	−	0.888802i	$-0.348461\pi$
$643$	−8.97720	−	7.74891i	−0.354026	−	0.305587i	−0.812318	+	0.583214i	$0.801795\pi$
$644$	9.93998	−	3.46147i	0.391690	−	0.136401i
$645$	0.276343	+	4.39235i	0.0108810	+	0.172949i
$646$	−0.249270	−	0.358653i	−0.00980741	−	0.0141110i
$647$	−0.326115	+	15.5686i	−0.0128209	+	0.612063i	0.945381	+	0.325969i	$0.105690\pi$
$647$	−0.326115	+	15.5686i	−0.0128209	+	0.612063i	−0.958201	+	0.286094i	$0.907643\pi$
$648$	0.951289	+	1.49899i	0.0373702	+	0.0588860i
$649$	46.3309	−	22.9989i	1.81865	−	0.902784i
$650$	−0.269726	−	2.56627i	−0.0105795	−	0.100657i
$651$	0.246214	+	0.122221i	0.00964987	+	0.00479024i
$652$	−4.41997	+	11.8849i	−0.173099	+	0.465450i
$653$	31.8896	−	1.33657i	1.24793	−	0.0523040i	0.591262	−	0.806479i	$-0.298630\pi$
$653$	31.8896	−	1.33657i	1.24793	−	0.0523040i	0.656673	+	0.754176i	$0.271963\pi$
$654$	0.198306	+	0.0785148i	0.00775437	+	0.00307017i
$655$	42.4894	+	7.18654i	1.66020	+	0.280801i
$656$	22.3049	+	17.6787i	0.870861	+	0.690236i
$657$	24.1617	−	6.20367i	0.942638	−	0.242028i
$658$	0.0744242	−	0.317309i	0.00290136	−	0.0123700i
$659$	3.07974	−	20.8560i	0.119970	−	0.812433i	−0.842039	−	0.539416i	$-0.818645\pi$
$659$	3.07974	−	20.8560i	0.119970	−	0.812433i	0.962009	−	0.273017i	$-0.0880216\pi$
$660$	−7.20834	−	9.49664i	−0.280584	−	0.369656i
$661$	29.5017	+	7.57475i	1.14748	+	0.294624i	0.774106	−	0.633056i	$-0.218200\pi$
$661$	29.5017	+	7.57475i	1.14748	+	0.294624i	0.373377	+	0.927680i	$0.378200\pi$
$662$	0.570641	−	1.09154i	0.0221786	−	0.0424238i
$663$	2.98842	+	9.19741i	0.116061	+	0.357198i
$664$	−3.32483	+	1.82784i	−0.129028	+	0.0709340i
$665$	−8.78882	+	6.96593i	−0.340816	+	0.270127i
$666$	0.140596	−	0.185228i	0.00544798	−	0.00717745i
$667$	−14.7478	−	15.0599i	−0.571036	−	0.583123i
$668$	−10.7723	+	33.1537i	−0.416793	+	1.28276i
$669$	−1.26923	−	6.65352i	−0.0490711	−	0.257240i
$670$	−0.871285	−	0.967659i	−0.0336607	−	0.0373839i
$671$	−34.7085	−	32.5935i	−1.33991	−	1.25826i
$672$	−0.477696	−	0.0603470i	−0.0184275	−	0.00232794i
$673$	5.48527	+	19.6460i	0.211442	+	0.757299i	0.991332	+	0.131383i	$0.0419417\pi$
$673$	5.48527	+	19.6460i	0.211442	+	0.757299i	−0.779890	+	0.625917i	$0.784725\pi$
$674$	−0.134815	+	2.14282i	−0.00519287	+	0.0825383i
$675$	13.3702	−	8.09730i	0.514620	−	0.311665i
$676$	13.2836	−	69.6349i	0.510906	−	2.67826i
$677$	−9.18099	−	5.04729i	−0.352854	−	0.193983i	0.295462	−	0.955354i	$-0.404526\pi$
$677$	−9.18099	−	5.04729i	−0.352854	−	0.193983i	−0.648316	+	0.761371i	$0.724526\pi$
$678$	−0.0986696	+	0.0166887i	−0.00378939	+	0.000640927i
$679$	−9.44817	−	2.00827i	−0.362588	−	0.0770704i
$680$	2.48079	+	0.527308i	0.0951338	+	0.0202213i
$681$	3.21703	−	0.544119i	0.123277	−	0.0208507i
$682$	−0.0906076	−	0.0498119i	−0.00346954	−	0.00190740i
$683$	3.73569	−	19.5831i	0.142942	−	0.749328i	−0.836557	−	0.547880i	$-0.815435\pi$
$683$	3.73569	−	19.5831i	0.142942	−	0.749328i	0.979499	−	0.201449i	$-0.0645649\pi$
$684$	−10.9438	+	6.62782i	−0.418448	+	0.253421i
$685$	0.215393	−	3.42357i	0.00822973	−	0.130808i
$686$	0.287210	+	1.02867i	0.0109657	+	0.0392748i
$687$	5.17195	+	0.653369i	0.197322	+	0.0249276i
$688$	8.61952	+	8.09427i	0.328616	+	0.308591i
$689$	26.0024	+	28.8785i	0.990611	+	1.10019i
$690$	0.0607392	+	0.318406i	0.00231230	+	0.0121215i
$691$	0.0572153	−	0.176091i	0.00217657	−	0.00669880i	−0.949962	−	0.312364i	$-0.898879\pi$
$691$	0.0572153	−	0.176091i	0.00217657	−	0.00669880i	0.952139	+	0.305666i	$0.0988790\pi$
$692$	10.6183	+	10.8430i	0.403646	+	0.412190i
$693$	10.0778	−	13.2770i	0.382824	−	0.504352i
$694$	−0.589017	+	0.466849i	−0.0223588	+	0.0177214i
$695$	11.5358	−	6.34185i	0.437577	−	0.240560i
$696$	0.198583	+	0.611175i	0.00752726	+	0.0231665i
$697$	−10.3351	+	19.7692i	−0.391470	+	0.748814i
$698$	0.248536	+	0.0638131i	0.00940722	+	0.00241536i
$699$	−3.83500	−	5.05242i	−0.145053	−	0.191100i
$700$	2.60168	−	17.6185i	0.0983342	−	0.665918i
$701$	−6.46550	+	27.5658i	−0.244199	+	1.04115i	0.700616	+	0.713539i	$0.252909\pi$
$701$	−6.46550	+	27.5658i	−0.244199	+	1.04115i	−0.944814	+	0.327607i	$0.893758\pi$
$702$	−1.06754	+	0.274097i	−0.0402916	+	0.0103451i
$703$	2.42985	+	1.92588i	0.0916436	+	0.0726358i
$704$	−31.4644	−	5.32181i	−1.18586	−	0.200573i
$705$	−4.96716	−	1.96664i	−0.187074	−	0.0740679i
$706$	−1.51684	+	0.0635743i	−0.0570869	+	0.00239265i
$707$	−5.18155	+	13.9328i	−0.194872	+	0.523995i
$708$	−10.2105	−	5.06852i	−0.383733	−	0.190487i
$709$	−2.51601	−	23.9382i	−0.0944908	−	0.899019i	−0.934384	−	0.356268i	$-0.884049\pi$
$709$	−2.51601	−	23.9382i	−0.0944908	−	0.899019i	0.839893	−	0.542752i	$-0.182618\pi$
$710$	1.74745	−	0.867444i	0.0655808	−	0.0325546i
$711$	17.5275	+	27.6190i	0.657333	+	1.03579i
$712$	0.0353201	−	1.68616i	0.00132368	−	0.0631917i
$713$	−0.853921	−	1.22863i	−0.0319796	−	0.0460126i
$714$	−0.00787412	−	0.125156i	−0.000294682	−	0.00468383i
$715$	−88.2065	+	30.7167i	−3.29873	+	1.14874i
$716$	11.8886	+	10.2619i	0.444296	+	0.383506i
$717$	2.64578	+	1.17798i	0.0988086	+	0.0439924i
$718$	0.211832	+	0.00887840i	0.00790550	+	0.000331339i
$719$	−12.2332	+	29.1016i	−0.456220	+	1.08531i	0.517114	+	0.855916i	$0.327006\pi$
$719$	−12.2332	+	29.1016i	−0.456220	+	1.08531i	−0.973335	+	0.229389i	$0.926327\pi$
$720$	9.96133	−	35.6775i	0.371237	−	1.32962i
$721$	−21.7885	−	7.58756i	−0.811447	−	0.282576i
$722$	−0.421548	−	0.730143i	−0.0156884	−	0.0271731i
$723$	5.88487	−	10.1929i	0.218861	−	0.379078i
$724$	−14.1731	+	12.2339i	−0.526739	+	0.454669i
$725$	−34.1435	+	10.3085i	−1.26806	+	0.382849i
$726$	0.0917121	−	0.110861i	0.00340375	−	0.00411443i
$727$	2.41248	+	5.12678i	0.0894738	+	0.190142i	0.944556	−	0.328352i	$-0.106493\pi$
$727$	2.41248	+	5.12678i	0.0894738	+	0.190142i	−0.855082	+	0.518493i	$0.826493\pi$
$728$	−1.07037	+	2.27465i	−0.0396706	+	0.0843043i
$729$	10.7541	+	12.9995i	0.398300	+	0.481462i
$730$	1.50973	+	1.00307i	0.0558778	+	0.0371251i
$731$	−4.96593	+	7.82505i	−0.183672	+	0.289420i
$732$	−1.09682	+	10.4356i	−0.0405398	+	0.385710i
$733$	7.40694	+	19.9167i	0.273581	+	0.735638i	0.998885	+	0.0472092i	$0.0150328\pi$
$733$	7.40694	+	19.9167i	0.273581	+	0.735638i	−0.725304	+	0.688429i	$0.758301\pi$
$734$	0.310741	+	0.739224i	0.0114697	+	0.0272852i
$735$	7.08689	−	0.895283i	0.261404	−	0.0330230i
$736$	2.12033	+	1.54051i	0.0781563	+	0.0567839i
$737$	−14.7268	+	21.1891i	−0.542470	+	0.780512i
$738$	−1.05016	−	0.636001i	−0.0386570	−	0.0234115i
$739$	−17.0955	+	18.9864i	−0.628867	+	0.698427i	−0.970417	−	0.241436i	$-0.922382\pi$
$739$	−17.0955	+	18.9864i	−0.628867	+	0.698427i	0.341550	+	0.939864i	$0.389048\pi$
$740$	−8.96195	+	0.752556i	−0.329448	+	0.0276645i
$741$	−1.62046	−	6.90887i	−0.0595291	−	0.253804i
$742$	−0.233458	−	0.446565i	−0.00857053	−	0.0163939i
$743$	37.4900	−	38.2835i	1.37537	−	1.40449i	0.556061	−	0.831142i	$-0.312312\pi$
$743$	37.4900	−	38.2835i	1.37537	−	1.40449i	0.819314	−	0.573345i	$-0.194354\pi$
$744$	0.00666379	+	0.0451271i	0.000244306	+	0.00165444i
$745$	5.42046	+	0.455169i	0.198590	+	0.0166761i
$746$	0.166785	−	0.156622i	0.00610645	−	0.00573434i
$747$	−35.1384	+	25.5296i	−1.28565	+	0.934078i
$748$	−0.525795	−	25.1012i	−0.0192250	−	0.917790i
$749$	−7.58832	+	5.04167i	−0.277271	+	0.184219i
$750$	0.0910864	+	0.0275006i	0.00332601	+	0.00100418i
$751$	−7.47263	+	3.32703i	−0.272680	+	0.121405i	−0.538521	−	0.842612i	$-0.681017\pi$
$751$	−7.47263	+	3.32703i	−0.272680	+	0.121405i	0.265841	+	0.964017i	$0.414350\pi$
$752$	−13.3453	+	5.28378i	−0.486653	+	0.192679i
$753$	5.35668	−	1.13860i	0.195208	−	0.0414928i
$754$	2.51483			0.0915848
$755$	−37.7634	+	15.5689i	−1.37435	+	0.566610i
$756$	−7.60697			−0.276663
$757$	−27.6531	+	5.87786i	−1.00507	+	0.213634i	−0.680909	−	0.732368i	$-0.738415\pi$
$757$	−27.6531	+	5.87786i	−1.00507	+	0.213634i	−0.324161	+	0.946002i	$0.605082\pi$
$758$	−0.0201170	+	0.00796489i	−0.000730683	+	0.000289298i
$759$	5.86833	−	2.61275i	0.213007	−	0.0948368i
$760$	−1.78164	−	0.537907i	−0.0646267	−	0.0195120i
$761$	−7.51963	+	4.99603i	−0.272586	+	0.181106i	−0.682226	−	0.731142i	$-0.738988\pi$
$761$	−7.51963	+	4.99603i	−0.272586	+	0.181106i	0.409639	+	0.912248i	$0.365655\pi$
$762$	0.0127461	+	0.608491i	0.000461742	+	0.0220433i
$763$	9.32970	−	6.77842i	0.337758	−	0.245395i
$764$	32.5781	−	30.5929i	1.17864	−	1.10681i
$765$	28.9315	+	2.42944i	1.04602	+	0.0878367i
$766$	−0.240213	−	1.62672i	−0.00867924	−	0.0587757i
$767$	−62.4819	+	63.8044i	−2.25609	+	2.30384i
$768$	3.23968	+	6.19693i	0.116902	+	0.223613i
$769$	−10.4766	−	44.6672i	−0.377796	−	1.61074i	−0.735921	−	0.677068i	$-0.763250\pi$
$769$	−10.4766	−	44.6672i	−0.377796	−	1.61074i	0.358125	−	0.933674i	$-0.383416\pi$
$770$	1.20692	−	0.101348i	0.0434944	−	0.00365233i
$771$	1.10171	−	1.22358i	0.0396773	−	0.0440661i
$772$	−20.1365	−	12.1951i	−0.724729	−	0.438912i
$773$	−23.1790	+	33.3503i	−0.833692	+	1.19953i	0.144020	+	0.989575i	$0.453997\pi$
$773$	−23.1790	+	33.3503i	−0.833692	+	1.19953i	−0.977712	+	0.209951i	$0.932670\pi$
$774$	−0.412651	−	0.299808i	−0.0148324	−	0.0107764i
$775$	−2.51174	+	0.317307i	−0.0902244	+	0.0113980i
$776$	−0.621170	−	1.47770i	−0.0222987	−	0.0530465i
$777$	0.310300	+	0.834371i	0.0111319	+	0.0299329i
$778$	−0.157461	+	1.49815i	−0.00564527	+	0.0537111i
$779$	8.77118	−	13.8212i	0.314260	−	0.495194i
$780$	17.1449	+	11.3910i	0.613885	+	0.407864i
$781$	−24.6438	−	29.7893i	−0.881826	−	1.06594i
$782$	−0.290635	+	0.617632i	−0.0103931	+	0.0220865i
$783$	6.48624	+	13.7840i	0.231799	+	0.492599i
$784$	12.2333	−	14.7875i	0.436902	−	0.528124i
$785$	−48.3447	+	14.5961i	−1.72550	+	0.520958i
$786$	0.267670	−	0.231046i	0.00954746	−	0.00824115i
$787$	16.5359	−	28.6409i	0.589439	−	1.02094i	−0.404866	−	0.914376i	$-0.632682\pi$
$787$	16.5359	−	28.6409i	0.589439	−	1.02094i	0.994306	−	0.106563i	$-0.0339847\pi$
$788$	−6.79400	−	11.7676i	−0.242026	−	0.419202i
$789$	−11.0304	−	3.84121i	−0.392694	−	0.136751i
$790$	−0.639183	+	2.28930i	−0.0227411	+	0.0814495i
$791$	−2.09677	+	4.98802i	−0.0745526	+	0.177354i
$792$	2.76373	+	0.115834i	0.0982047	+	0.00411600i
$793$	75.0966	+	33.4352i	2.66676	+	1.18732i
$794$	−1.20857	−	1.04321i	−0.0428906	−	0.0370221i
$795$	−7.80036	+	2.71637i	−0.276650	+	0.0963398i
$796$	−2.63727	−	41.9182i	−0.0934755	−	1.48575i
$797$	−29.8309	−	42.9210i	−1.05666	−	1.52034i	−0.838859	−	0.544348i	$-0.816777\pi$
$797$	−29.8309	−	42.9210i	−1.05666	−	1.52034i	−0.217805	−	0.975992i	$-0.569890\pi$
$798$	−0.00192713	+	0.0920004i	−6.82198e−5	+	0.00325678i
$799$	−6.02804	−	9.49867i	−0.213257	−	0.336039i
$800$	3.97216	−	1.97180i	0.140437	−	0.0697136i
$801$	−2.01809	−	19.2009i	−0.0713058	−	0.678429i
$802$	1.28693	+	0.638837i	0.0454431	+	0.0225581i
$803$	12.5208	−	33.6674i	0.441849	−	1.18810i
$804$	5.68179	−	0.238138i	0.200381	−	0.00839847i
$805$	16.2957	+	6.45194i	0.574350	+	0.227401i
$806$	0.176014	+	0.0297705i	0.00619981	+	0.00104862i
$807$	−7.65376	−	6.06630i	−0.269425	−	0.213544i
$808$	−2.38936	+	0.613483i	−0.0840573	+	0.0215823i
$809$	−7.95670	+	33.9236i	−0.279743	+	1.19269i	0.629693	+	0.776844i	$0.283181\pi$
$809$	−7.95670	+	33.9236i	−0.279743	+	1.19269i	−0.909436	+	0.415845i	$0.863486\pi$
$810$	−0.215727	+	1.46090i	−0.00757989	+	0.0513309i
$811$	1.96693	+	2.59133i	0.0690681	+	0.0909939i	0.829764	−	0.558115i	$-0.188475\pi$
$811$	1.96693	+	2.59133i	0.0690681	+	0.0909939i	−0.760695	+	0.649109i	$0.775142\pi$
$812$	16.8117	+	4.31651i	0.589975	+	0.151480i
$813$	−1.21756	+	2.32899i	−0.0427018	+	0.0816811i
$814$	−0.103475	−	0.318464i	−0.00362680	−	0.0111621i
$815$	−18.5028	+	10.1720i	−0.648125	+	0.356310i
$816$	−4.32805	+	3.43037i	−0.151512	+	0.120087i
$817$	4.11169	−	5.41695i	0.143850	−	0.189515i
$818$	−0.538369	−	0.549764i	−0.0188236	−	0.0192220i
$819$	−8.89290	+	27.3695i	−0.310743	+	0.956369i
$820$	8.89722	+	46.6409i	0.310704	+	1.62877i
$821$	−3.52736	−	3.91753i	−0.123106	−	0.136723i	0.678441	−	0.734655i	$-0.262656\pi$
$821$	−3.52736	−	3.91753i	−0.123106	−	0.136723i	−0.801547	+	0.597932i	$0.795989\pi$
$822$	−0.0205185	−	0.0192682i	−0.000715666	−	0.000672055i
$823$	34.0446	+	4.30083i	1.18672	+	0.149917i	0.693806	−	0.720162i	$-0.255932\pi$
$823$	34.0446	+	4.30083i	1.18672	+	0.149917i	0.492912	+	0.870079i	$0.335932\pi$
$824$	−1.02963	−	3.68774i	−0.0358690	−	0.128468i
$825$	0.682483	−	10.8478i	0.0237610	−	0.377670i
$826$	0.990525	−	0.599883i	0.0344648	−	0.0208726i
$827$	−0.853408	+	4.47372i	−0.0296759	+	0.155567i	−0.994041	−	0.109010i	$-0.965232\pi$
$827$	−0.853408	+	4.47372i	−0.0296759	+	0.155567i	0.964365	+	0.264576i	$0.0852321\pi$
$828$	17.5221	+	9.63285i	0.608934	+	0.334765i
$829$	18.8864	−	3.19439i	0.655950	−	0.110946i	0.170703	−	0.985323i	$-0.445396\pi$
$829$	18.8864	−	3.19439i	0.655950	−	0.110946i	0.485247	+	0.874377i	$0.338730\pi$
$830$	−3.08699	−	0.656160i	−0.107151	−	0.0227757i
$831$	−1.86968	−	0.397413i	−0.0648586	−	0.0137861i
$832$	54.3229	−	9.18802i	1.88331	−	0.318537i
$833$	13.1817	+	7.24671i	0.456719	+	0.251084i
$834$	0.0202404	−	0.106104i	0.000700866	−	0.00367407i
$835$	−49.6515	+	30.0700i	−1.71826	+	1.04062i
$836$	−1.15681	+	18.3869i	−0.0400089	+	0.635924i
$837$	0.290799	+	1.04153i	0.0100515	+	0.0360004i
$838$	0.799686	+	0.101024i	0.0276247	+	0.00348981i
$839$	25.0987	+	23.5693i	0.866504	+	0.813701i	0.983777	−	0.179398i	$-0.0574151\pi$
$839$	25.0987	+	23.5693i	0.866504	+	0.813701i	−0.117272	+	0.993100i	$0.537415\pi$
$840$	−0.357543	−	0.397092i	−0.0123364	−	0.0137010i
$841$	−1.07920	−	5.65735i	−0.0372137	−	0.195081i
$842$	−0.231426	+	0.712257i	−0.00797547	+	0.0245460i
$843$	0.847502	+	0.865440i	0.0291895	+	0.0298074i
$844$	14.1948	−	18.7009i	0.488605	−	0.643713i
$845$	92.5102	−	73.3227i	3.18245	−	2.52238i
$846$	0.542571	−	0.298281i	0.0186540	−	0.0102551i
$847$	−2.40400	−	7.39874i	−0.0826023	−	0.254224i
$848$	−10.2813	+	19.6663i	−0.353061	+	0.675344i
$849$	−0.567785	−	0.145782i	−0.0194863	−	0.00500324i
$850$	0.698305	+	0.919982i	0.0239516	+	0.0315551i
$851$	0.707856	−	4.79359i	0.0242650	−	0.164322i
$852$	−1.94562	+	8.29519i	−0.0666558	+	0.284188i
$853$	0.173912	−	0.0446531i	0.00595465	−	0.00152889i	−0.245711	−	0.969343i	$-0.579022\pi$
$853$	0.173912	−	0.0446531i	0.00595465	−	0.00152889i	0.251666	+	0.967814i	$0.419022\pi$
$854$	−0.835383	−	0.662116i	−0.0285862	−	0.0226571i
$855$	−21.0062	−	3.55294i	−0.718398	−	0.121508i
$856$	−1.40572	−	0.556563i	−0.0480464	−	0.0190229i
$857$	−22.6649	+	0.949940i	−0.774217	+	0.0324493i	−0.425713	−	0.904858i	$-0.639977\pi$
$857$	−22.6649	+	0.949940i	−0.774217	+	0.0324493i	−0.348504	+	0.937307i	$0.613310\pi$
$858$	−0.267146	+	0.718334i	−0.00912021	+	0.0245235i
$859$	−4.96191	−	2.46311i	−0.169298	−	0.0840404i	0.357996	−	0.933723i	$-0.383460\pi$
$859$	−4.96191	−	2.46311i	−0.169298	−	0.0840404i	−0.527294	+	0.849683i	$0.676793\pi$
$860$	2.06197	+	19.6183i	0.0703126	+	0.668979i
$861$	4.20976	−	2.08974i	0.143468	−	0.0712182i
$862$	−0.608433	−	0.958736i	−0.0207233	−	0.0326547i
$863$	−0.167016	+	7.97326i	−0.00568529	+	0.271413i	0.987685	+	0.156455i	$0.0500066\pi$
$863$	−0.167016	+	7.97326i	−0.00568529	+	0.271413i	−0.993370	+	0.114958i	$0.963327\pi$
$864$	−1.08102	−	1.55539i	−0.0367771	−	0.0529153i
$865$	1.58677	+	25.2210i	0.0539518	+	0.857539i
$866$	0.0724601	−	0.0252333i	0.00246229	−	0.000857462i
$867$	2.45470	+	2.11884i	0.0833661	+	0.0719597i
$868$	1.12556	+	0.501130i	0.0382038	+	0.0170094i
$869$	47.0612	+	1.97245i	1.59644	+	0.0669108i
$870$	−0.207141	+	0.492769i	−0.00702274	+	0.0167064i
$871$	11.9805	−	42.9095i	0.405945	−	1.45393i
$872$	1.80731	+	0.629372i	0.0612032	+	0.0213132i
$873$	−9.17492	−	15.8914i	−0.310524	−	0.537843i
$874$	0.250444	−	0.433782i	0.00847140	−	0.0146729i
$875$	3.89442	−	3.36158i	0.131656	−	0.113642i
$876$	−7.57829	+	2.28802i	−0.256047	+	0.0773050i
$877$	25.2205	−	30.4864i	0.851637	−	1.02945i	−0.147547	−	0.989055i	$-0.547138\pi$
$877$	25.2205	−	30.4864i	0.851637	−	1.02945i	0.999184	−	0.0403970i	$-0.0128623\pi$
$878$	0.471706	+	1.00243i	0.0159193	+	0.0338303i
$879$	1.77343	−	3.76873i	0.0598163	−	0.127116i
$880$	−33.9994	−	41.0982i	−1.14612	−	1.38542i
$881$	−34.7982	−	23.1198i	−1.17238	−	0.778927i	−0.193048	−	0.981189i	$-0.561837\pi$
$881$	−34.7982	−	23.1198i	−1.17238	−	0.778927i	−0.979331	+	0.202262i	$0.935171\pi$
$882$	−0.443597	+	0.698998i	−0.0149367	+	0.0235365i
$883$	2.11857	−	20.1568i	0.0712955	−	0.678331i	−0.899254	−	0.437428i	$-0.855890\pi$
$883$	2.11857	−	20.1568i	0.0712955	−	0.678331i	0.970549	−	0.240904i	$-0.0774438\pi$
$884$	15.1093	+	40.6277i	0.508181	+	1.36646i
$885$	−7.35567	−	17.4984i	−0.247258	−	0.588204i
$886$	−1.79710	+	0.227026i	−0.0603746	+	0.00762709i
$887$	−6.60488	−	4.79873i	−0.221770	−	0.161125i	0.471353	−	0.881945i	$-0.343766\pi$
$887$	−6.60488	−	4.79873i	−0.221770	−	0.161125i	−0.693123	+	0.720819i	$0.743766\pi$
$888$	−0.0843111	+	0.121308i	−0.00282930	+	0.00407082i
$889$	28.1484	+	17.0473i	0.944068	+	0.571748i
$890$	0.938693	−	1.04252i	0.0314651	−	0.0349455i
$891$	29.1623	−	2.44883i	0.976974	−	0.0820388i
$892$	−6.93280	−	29.5581i	−0.232127	−	0.989680i
$893$	3.82461	+	7.31580i	0.127986	+	0.244814i
$894$	0.0312286	−	0.0318896i	0.00104444	−	0.00106655i
$895$	3.82024	+	25.8706i	0.127697	+	0.864760i
$896$	−2.86655	−	0.240711i	−0.0957646	−	0.00804157i
$897$	−8.08456	+	7.59190i	−0.269935	+	0.253486i
$898$	0.218382	−	0.158664i	0.00728750	−	0.00529468i
$899$	−0.0516726	−	2.46683i	−0.00172338	−	0.0822733i
$900$	28.1804	−	18.7230i	0.939346	−	0.624100i
$901$	−16.6513	−	5.02732i	−0.554735	−	0.167484i
$902$	−1.61504	+	0.719063i	−0.0537750	+	0.0239422i
$903$	1.81546	−	0.718792i	0.0604148	−	0.0239199i
$904$	−0.878302	+	0.186689i	−0.0292119	+	0.00620918i
$905$	−31.1765			−1.03634
$906$	−0.0990827	+	0.320185i	−0.00329180	+	0.0106374i
$907$	−1.26762			−0.0420907			−0.0210453	−	0.999779i	$-0.506699\pi$
$907$	−1.26762			−0.0420907			−0.0210453	+	0.999779i	$0.506699\pi$
$908$	14.3046	−	3.04055i	0.474716	−	0.100904i
$909$	−26.2563	+	10.3956i	−0.870868	+	0.344801i
$910$	−1.91028	+	0.850512i	−0.0633252	+	0.0281942i
$911$	27.5741	+	8.32512i	0.913572	+	0.275824i	0.710793	−	0.703401i	$-0.248336\pi$
$911$	27.5741	+	8.32512i	0.913572	+	0.275824i	0.202779	+	0.979225i	$0.435003\pi$
$912$	3.37541	−	2.24262i	0.111771	−	0.0742606i
$913$	1.30978	+	62.5285i	0.0433476	+	2.06939i
$914$	−0.414808	+	0.301376i	−0.0137206	+	0.00996862i
$915$	−12.7370	+	11.9608i	−0.421072	+	0.395413i
$916$	23.2841	+	1.95522i	0.769328	+	0.0646023i
$917$	−2.79292	−	18.9136i	−0.0922305	−	0.624583i
$918$	0.345163	−	0.352469i	0.0113921	−	0.0116332i
$919$	3.31069	+	6.33277i	0.109210	+	0.208899i	0.934632	−	0.355617i	$-0.115729\pi$
$919$	3.31069	+	6.33277i	0.109210	+	0.208899i	−0.825422	+	0.564516i	$0.809063\pi$
$920$	0.664165	+	2.83168i	0.0218969	+	0.0933578i
$921$	−7.00595	+	0.588306i	−0.230854	+	0.0193853i
$922$	−0.413342	+	0.459063i	−0.0136127	+	0.0151184i
$923$	57.0944	+	34.5776i	1.87929	+	1.13814i
$924$	−3.01884	+	4.34354i	−0.0993125	+	0.142892i
$925$	−6.63309	−	4.81922i	−0.218095	−	0.158455i
$926$	1.63726	−	0.206834i	0.0538037	−	0.00679698i
$927$	−16.9848	−	40.4053i	−0.557854	−	1.32708i
$928$	1.50651	+	4.05088i	0.0494536	+	0.132977i
$929$	−5.03084	+	47.8653i	−0.165057	+	1.57041i	0.527823	+	0.849354i	$0.323008\pi$
$929$	−5.03084	+	47.8653i	−0.165057	+	1.57041i	−0.692879	+	0.721053i	$0.743658\pi$
$930$	−0.0203312	+	0.0320369i	−0.000666687	+	0.00105053i
$931$	−9.19383	−	6.10837i	−0.301316	−	0.200194i
$932$	−18.1225	−	21.9064i	−0.593624	−	0.717568i
$933$	−2.98061	+	6.33412i	−0.0975808	+	0.207370i
$934$	0.627298	+	1.33308i	0.0205258	+	0.0436196i
$935$	26.6485	−	32.2125i	0.871500	−	1.05346i
$936$	−4.57189	+	1.38033i	−0.149437	+	0.0451177i
$937$	−19.4226	+	16.7652i	−0.634510	+	0.547694i	−0.910522	−	0.413460i	$-0.864320\pi$
$937$	−19.4226	+	16.7652i	−0.634510	+	0.547694i	0.276012	+	0.961154i	$0.410987\pi$
$938$	−0.288850	+	0.500304i	−0.00943130	+	0.0163355i
$939$	6.38279	+	11.0553i	0.208294	+	0.360777i
$940$	−22.6135	−	7.87486i	−0.737572	−	0.256850i
$941$	1.41390	−	5.06403i	0.0460919	−	0.165083i	−0.936573	−	0.350472i	$-0.886021\pi$
$941$	1.41390	−	5.06403i	0.0460919	−	0.165083i	0.982665	+	0.185389i	$0.0593546\pi$
$942$	−0.160576	+	0.381996i	−0.00523186	+	0.0124461i
$943$	−25.5602	−	1.07129i	−0.832354	−	0.0348860i
$944$	−46.5889	−	20.7427i	−1.51634	−	0.675118i
$945$	−9.58870	−	8.27675i	−0.311921	−	0.269243i
$946$	−0.693615	+	0.241542i	−0.0225514	+	0.00785321i
$947$	−2.09847	−	33.3541i	−0.0681910	−	1.08386i	−0.872169	−	0.489205i	$-0.837287\pi$
$947$	−2.09847	−	33.3541i	−0.0681910	−	1.08386i	0.803978	−	0.594659i	$-0.202713\pi$
$948$	−5.92431	−	8.52396i	−0.192413	−	0.276845i
$949$	−1.29876	+	62.0021i	−0.0421595	+	2.01267i
$950$	−0.454128	−	0.715592i	−0.0147339	−	0.0232169i
$951$	6.80126	−	3.37618i	0.220546	−	0.109480i
$952$	−0.117618	−	1.11906i	−0.00381202	−	0.0362689i
$953$	26.2310	+	13.0212i	0.849705	+	0.421797i	0.816288	−	0.577644i	$-0.196028\pi$
$953$	26.2310	+	13.0212i	0.849705	+	0.421797i	0.0334162	+	0.999442i	$0.489361\pi$
$954$	0.333682	−	0.897244i	0.0108034	−	0.0290493i
$955$	74.3518	−	3.11627i	2.40597	−	0.100840i
$956$	12.0697	+	4.77872i	0.390361	+	0.154555i
$957$	10.4447	+	1.76658i	0.337628	+	0.0571054i
$958$	−0.691844	−	0.548349i	−0.0223525	−	0.0177163i
$959$	−1.47410	+	0.378485i	−0.0476013	+	0.0122219i
$960$	−2.67410	+	11.4011i	−0.0863062	+	0.367969i
$961$	−4.50299	+	30.4942i	−0.145258	+	0.983683i
$962$	0.349530	+	0.460488i	0.0112693	+	0.0148467i
$963$	−16.7636	−	4.30417i	−0.540200	−	0.138700i
$964$	24.4410	−	46.7513i	0.787191	−	1.50576i
$965$	−12.1135	−	37.2816i	−0.389949	−	1.20014i
$966$	0.126024	−	0.0692822i	0.00405475	−	0.00222912i
$967$	−26.4254	+	20.9445i	−0.849782	+	0.673529i	−0.946824	−	0.321751i	$-0.895729\pi$
$967$	−26.4254	+	20.9445i	−0.849782	+	0.673529i	0.0970419	+	0.995280i	$0.469062\pi$
$968$	0.780542	−	1.02833i	0.0250876	−	0.0330517i
$969$	2.22236	+	2.26940i	0.0713925	+	0.0729036i
$970$	0.412022	−	1.26807i	0.0132292	−	0.0407154i
$971$	−3.97236	−	20.8238i	−0.127479	−	0.668268i	−0.987451	−	0.157927i	$-0.949519\pi$
$971$	−3.97236	−	20.8238i	−0.127479	−	0.668268i	0.859972	−	0.510342i	$-0.170481\pi$
$972$	−14.6698	−	16.2925i	−0.470534	−	0.522581i
$973$	−4.25749	−	3.99805i	−0.136489	−	0.128172i
$974$	−1.64345	−	0.207616i	−0.0526596	−	0.00665245i
$975$	5.04642	+	18.0742i	0.161615	+	0.578839i
$976$	−2.94762	+	46.8511i	−0.0943510	+	1.49967i
$977$	28.8416	−	17.4671i	0.922725	−	0.558822i	0.0251497	−	0.999684i	$-0.491994\pi$
$977$	28.8416	−	17.4671i	0.922725	−	0.558822i	0.897575	+	0.440862i	$0.145327\pi$
$978$	−0.0324645	+	0.170185i	−0.00103810	+	0.00544191i
$979$	−24.3619	−	13.3931i	−0.778609	−	0.428044i
$980$	31.5691	−	5.33952i	1.00844	−	0.170565i
$981$	21.4291	+	4.55489i	0.684177	+	0.145426i
$982$	−0.747379	−	0.158860i	−0.0238498	−	0.00506943i
$983$	52.3411	−	8.85284i	1.66942	−	0.282362i	0.745943	−	0.666010i	$-0.231999\pi$
$983$	52.3411	−	8.85284i	1.66942	−	0.282362i	0.923479	+	0.383648i	$0.125333\pi$
$984$	0.683475	+	0.375744i	0.0217884	+	0.0119783i
$985$	4.23972	−	22.2254i	0.135089	−	0.708160i
$986$	−0.962830	+	0.583110i	−0.0306627	+	0.0185700i
$987$	−0.148826	+	2.36552i	−0.00473717	+	0.0752952i
$988$	−8.55365	−	30.6357i	−0.272128	−	0.974653i
$989$	−10.5445	−	1.33208i	−0.335296	−	0.0423577i
$990$	1.67727	+	1.57506i	0.0533071	+	0.0500587i
$991$	−17.9090	−	19.8900i	−0.568898	−	0.631825i	0.388205	−	0.921573i	$-0.373095\pi$
$991$	−17.9090	−	19.8900i	−0.568898	−	0.631825i	−0.957103	+	0.289748i	$0.906429\pi$
$992$	0.0574868	+	0.301356i	0.00182521	+	0.00956807i
$993$	−2.76796	+	8.51890i	−0.0878385	+	0.270339i
$994$	−0.605593	−	0.618411i	−0.0192082	−	0.0196148i
$995$	42.2847	−	55.7080i	1.34051	−	1.76606i
$996$	10.8018	−	8.56137i	0.342267	−	0.271277i
$997$	7.06722	−	3.88524i	0.223821	−	0.123047i	−0.365898	−	0.930655i	$-0.619238\pi$
$997$	7.06722	−	3.88524i	0.223821	−	0.123047i	0.589720	+	0.807608i	$0.299238\pi$
$998$	0.567553	+	1.74675i	0.0179656	+	0.0552924i
$999$	−1.62246	+	3.10348i	−0.0513324	+	0.0981899i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.2.k.a.39.6	yes	480
151.31	even	75	inner	151.2.k.a.31.6	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.2.k.a.31.6	✓	480	151.31	even	75	inner
151.2.k.a.39.6	yes	480	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	151.k (of order \(75\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0599037 - 0.0127329i) q^{2} +(-0.414095 + 0.163952i) q^{3} +(-1.82366 + 0.811948i) q^{4} +(-3.18220 - 0.960762i) q^{5} +(-0.0227182 + 0.0150940i) q^{6} +(0.0308852 + 1.47445i) q^{7} +(-0.197997 + 0.143853i) q^{8} +(-2.04231 + 1.91786i) q^{9} +O(q^{10})\)	\(q+(0.0599037 - 0.0127329i) q^{2} +(-0.414095 + 0.163952i) q^{3} +(-1.82366 + 0.811948i) q^{4} +(-3.18220 - 0.960762i) q^{5} +(-0.0227182 + 0.0150940i) q^{6} +(0.0308852 + 1.47445i) q^{7} +(-0.197997 + 0.143853i) q^{8} +(-2.04231 + 1.91786i) q^{9} +(-0.202859 - 0.0170345i) q^{10} +(0.589333 + 3.99096i) q^{11} +(0.622050 - 0.635217i) q^{12} +(-3.22688 - 6.17245i) q^{13} +(0.0206241 + 0.0879315i) q^{14} +(1.47525 - 0.123880i) q^{15} +(2.66147 - 2.95587i) q^{16} +(2.66664 + 1.61497i) q^{17} +(-0.0979220 + 0.140891i) q^{18} +(-1.85075 - 1.34465i) q^{19} +(6.58335 - 0.831670i) q^{20} +(-0.254528 - 0.605497i) q^{21} +(0.0861198 + 0.231569i) q^{22} +(-0.373711 + 3.55563i) q^{23} +(0.0584047 - 0.0920311i) q^{24} +(5.03870 + 3.34771i) q^{25} +(-0.271895 - 0.328665i) q^{26} +(1.10016 - 2.33797i) q^{27} +(-1.25350 - 2.66382i) q^{28} +(-3.75807 + 4.54272i) q^{29} +(0.0867956 - 0.0262051i) q^{30} +(-0.316804 + 0.273458i) q^{31} +(0.366533 - 0.634855i) q^{32} +(-0.898365 - 1.55601i) q^{33} +(0.180305 + 0.0627888i) q^{34} +(1.31831 - 4.72165i) q^{35} +(2.16729 - 5.15578i) q^{36} +(-1.35414 - 0.0567551i) q^{37} +(-0.127988 - 0.0569839i) q^{38} +(2.34822 + 2.02693i) q^{39} +(0.768275 - 0.267542i) q^{40} +(0.449301 + 7.14143i) q^{41} +(-0.0229569 - 0.0330306i) q^{42} +(-0.0622572 + 2.97213i) q^{43} +(-4.31520 - 6.79966i) q^{44} +(8.34164 - 4.14083i) q^{45} +(0.0228868 + 0.217753i) q^{46} +(-3.23226 - 1.60451i) q^{47} +(-0.617484 + 1.66036i) q^{48} +(4.82082 - 0.202052i) q^{49} +(0.344463 + 0.136383i) q^{50} +(-1.36902 - 0.231553i) q^{51} +(10.8964 + 8.63642i) q^{52} +(-5.40399 + 1.38751i) q^{53} +(0.0361347 - 0.154061i) q^{54} +(1.95898 - 13.2662i) q^{55} +(-0.218219 - 0.287493i) q^{56} +(0.986844 + 0.253379i) q^{57} +(-0.167280 + 0.319977i) q^{58} +(-3.96208 - 12.1940i) q^{59} +(-2.58978 + 1.42374i) q^{60} +(-9.24937 + 7.33096i) q^{61} +(-0.0154958 + 0.0204150i) q^{62} +(-2.89085 - 2.95204i) q^{63} +(-2.44436 + 7.52298i) q^{64} +(4.33831 + 22.7422i) q^{65} +(-0.0736280 - 0.0817722i) q^{66} +(4.66271 + 4.37858i) q^{67} +(-6.17433 - 0.780000i) q^{68} +(-0.428199 - 1.53364i) q^{69} +(0.0188511 - 0.299630i) q^{70} +(-8.19728 + 4.96445i) q^{71} +(0.128482 - 0.673524i) q^{72} +(-7.80250 - 4.28946i) q^{73} +(-0.0818404 + 0.0138423i) q^{74} +(-2.63537 - 0.560164i) q^{75} +(4.46693 + 0.949476i) q^{76} +(-5.86625 + 0.992202i) q^{77} +(0.166476 + 0.0915208i) q^{78} +(2.18781 - 11.4689i) q^{79} +(-11.3092 + 6.84910i) q^{80} +(0.455492 - 7.23983i) q^{81} +(0.117846 + 0.422077i) q^{82} +(15.3806 + 1.94302i) q^{83} +(0.955805 + 0.897561i) q^{84} +(-6.93417 - 7.70117i) q^{85} +(0.0341144 + 0.178834i) q^{86} +(0.811409 - 2.49726i) q^{87} +(-0.690800 - 0.705421i) q^{88} +(-4.16640 + 5.48903i) q^{89} +(0.446970 - 0.354264i) q^{90} +(9.00128 - 4.94849i) q^{91} +(-2.20546 - 6.78770i) q^{92} +(0.0863531 - 0.165178i) q^{93} +(-0.214054 - 0.0549598i) q^{94} +(4.59756 + 6.05707i) q^{95} +(-0.0476941 + 0.322984i) q^{96} +(-1.49562 + 6.37662i) q^{97} +(0.286212 - 0.0734868i) q^{98} +(-8.85769 - 7.02052i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 45 q^{2} - 40 q^{3} + 15 q^{4} - 40 q^{5} - 60 q^{6} - 40 q^{7} - 50 q^{8} - 40 q^{9}+O(q^{10}) \) 480 * q - 45 * q^2 - 40 * q^3 + 15 * q^4 - 40 * q^5 - 60 * q^6 - 40 * q^7 - 50 * q^8 - 40 * q^9	\( 480 q - 45 q^{2} - 40 q^{3} + 15 q^{4} - 40 q^{5} - 60 q^{6} - 40 q^{7} - 50 q^{8} - 40 q^{9} - 10 q^{10} - 50 q^{11} - 65 q^{12} - 40 q^{13} - 65 q^{14} + 25 q^{16} - 20 q^{17} - 15 q^{18} - 30 q^{19} + 70 q^{20} - 40 q^{21} - 65 q^{23} + 80 q^{24} + 20 q^{25} - 65 q^{26} + 5 q^{27} - 110 q^{28} - 75 q^{29} - 135 q^{30} - 45 q^{31} + 10 q^{32} + 40 q^{33} + 20 q^{34} - 10 q^{36} - 60 q^{37} - 70 q^{38} + 25 q^{39} - 50 q^{41} + 50 q^{42} - 50 q^{43} - 30 q^{44} + 10 q^{45} - 85 q^{46} + 30 q^{47} + 175 q^{48} - 50 q^{49} + 10 q^{50} + 80 q^{51} - 145 q^{52} + 95 q^{53} + 10 q^{54} + 70 q^{55} + 140 q^{56} - 70 q^{57} + 240 q^{58} - 30 q^{59} - 60 q^{60} - 60 q^{61} + 10 q^{62} + 90 q^{63} - 160 q^{64} + 45 q^{65} - 55 q^{66} - 10 q^{67} + 10 q^{68} - 105 q^{69} + 75 q^{70} - 25 q^{71} + 310 q^{72} + 40 q^{73} + 170 q^{74} - 80 q^{75} - 15 q^{76} + 45 q^{77} - 80 q^{78} + 160 q^{79} - 85 q^{80} + 160 q^{81} - 50 q^{82} - 5 q^{83} + 70 q^{84} - 85 q^{85} + 150 q^{86} + 10 q^{87} + 95 q^{88} - 50 q^{89} - 90 q^{90} + 270 q^{91} + 90 q^{92} + 100 q^{93} - 35 q^{94} + 60 q^{95} + 255 q^{96} + 210 q^{97} - 30 q^{98}+O(q^{100}) \) 480 * q - 45 * q^2 - 40 * q^3 + 15 * q^4 - 40 * q^5 - 60 * q^6 - 40 * q^7 - 50 * q^8 - 40 * q^9 - 10 * q^10 - 50 * q^11 - 65 * q^12 - 40 * q^13 - 65 * q^14 + 25 * q^16 - 20 * q^17 - 15 * q^18 - 30 * q^19 + 70 * q^20 - 40 * q^21 - 65 * q^23 + 80 * q^24 + 20 * q^25 - 65 * q^26 + 5 * q^27 - 110 * q^28 - 75 * q^29 - 135 * q^30 - 45 * q^31 + 10 * q^32 + 40 * q^33 + 20 * q^34 - 10 * q^36 - 60 * q^37 - 70 * q^38 + 25 * q^39 - 50 * q^41 + 50 * q^42 - 50 * q^43 - 30 * q^44 + 10 * q^45 - 85 * q^46 + 30 * q^47 + 175 * q^48 - 50 * q^49 + 10 * q^50 + 80 * q^51 - 145 * q^52 + 95 * q^53 + 10 * q^54 + 70 * q^55 + 140 * q^56 - 70 * q^57 + 240 * q^58 - 30 * q^59 - 60 * q^60 - 60 * q^61 + 10 * q^62 + 90 * q^63 - 160 * q^64 + 45 * q^65 - 55 * q^66 - 10 * q^67 + 10 * q^68 - 105 * q^69 + 75 * q^70 - 25 * q^71 + 310 * q^72 + 40 * q^73 + 170 * q^74 - 80 * q^75 - 15 * q^76 + 45 * q^77 - 80 * q^78 + 160 * q^79 - 85 * q^80 + 160 * q^81 - 50 * q^82 - 5 * q^83 + 70 * q^84 - 85 * q^85 + 150 * q^86 + 10 * q^87 + 95 * q^88 - 50 * q^89 - 90 * q^90 + 270 * q^91 + 90 * q^92 + 100 * q^93 - 35 * q^94 + 60 * q^95 + 255 * q^96 + 210 * q^97 - 30 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more