LMFDB - Embedded newform 122.2.i.a.83.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [122,2,Mod(15,122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(122, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([14]))

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

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

chi := DirichletCharacter("122.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 122 = 2 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	122.i (of order $15$, degree $8$, 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:	$0.974174904660$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			83.1
Root			$0.333129i$ of defining polynomial
Character	$\chi$	$=$	122.83
Dual form			122.2.i.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.669131 - 0.743145i) q^{2} +(-0.247563 + 0.761920i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(1.61830 - 0.720515i) q^{5} +(0.731869 - 0.325849i) q^{6} +(0.428042 + 0.0909831i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.90782 + 1.38611i) q^{9} +O(q^{10})$	\(q+(-0.669131 - 0.743145i) q^{2} +(-0.247563 + 0.761920i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(1.61830 - 0.720515i) q^{5} +(0.731869 - 0.325849i) q^{6} +(0.428042 + 0.0909831i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.90782 + 1.38611i) q^{9} +(-1.61830 - 0.720515i) q^{10} +2.54891 q^{11} +(-0.731869 - 0.325849i) q^{12} +(0.937990 - 1.62465i) q^{13} +(-0.218802 - 0.378976i) q^{14} +(0.148343 + 1.41139i) q^{15} +(-0.978148 - 0.207912i) q^{16} +(0.306331 - 2.91455i) q^{17} +(-0.246498 - 2.34527i) q^{18} +(-8.11525 + 1.72495i) q^{19} +(0.547409 + 1.68475i) q^{20} +(-0.175289 + 0.303610i) q^{21} +(-1.70555 - 1.89421i) q^{22} +(-0.194999 - 0.141675i) q^{23} +(0.247563 + 0.761920i) q^{24} +(-1.24589 + 1.38370i) q^{25} +(-1.83498 + 0.390038i) q^{26} +(-3.47279 + 2.52313i) q^{27} +(-0.135227 + 0.416186i) q^{28} +(1.37411 + 2.38003i) q^{29} +(0.949606 - 1.05464i) q^{30} +(-2.62628 + 2.91677i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.631014 + 1.94206i) q^{33} +(-2.37091 + 1.72256i) q^{34} +(0.758255 - 0.161172i) q^{35} +(-1.57794 + 1.75248i) q^{36} +(-1.47193 - 4.53013i) q^{37} +(6.71205 + 4.87659i) q^{38} +(1.00564 + 1.11688i) q^{39} +(0.885726 - 1.53412i) q^{40} +(-1.06120 - 3.26603i) q^{41} +(0.342917 - 0.0728893i) q^{42} +(-0.575123 - 5.47193i) q^{43} +(-0.266433 + 2.53494i) q^{44} +(4.08614 + 0.868535i) q^{45} +(0.0251947 + 0.239711i) q^{46} +(-1.82215 - 3.15605i) q^{47} +(0.400565 - 0.693799i) q^{48} +(-6.21988 - 2.76927i) q^{49} +1.86196 q^{50} +(2.14482 + 0.954933i) q^{51} +(1.51770 + 1.10267i) q^{52} +(0.735495 - 0.534368i) q^{53} +(4.19880 + 0.892483i) q^{54} +(4.12490 - 1.83652i) q^{55} +(0.399771 - 0.177990i) q^{56} +(0.694761 - 6.61021i) q^{57} +(0.849246 - 2.61371i) q^{58} +(4.33207 + 4.81125i) q^{59} -1.41916 q^{60} +(-1.75492 - 7.61054i) q^{61} +3.92491 q^{62} +(0.690512 + 0.766892i) q^{63} +(0.309017 - 0.951057i) q^{64} +(0.347370 - 3.30500i) q^{65} +(1.86546 - 0.830558i) q^{66} +(-5.74046 + 2.55582i) q^{67} +(2.86656 + 0.609306i) q^{68} +(0.156219 - 0.113500i) q^{69} +(-0.627146 - 0.455648i) q^{70} +(7.39569 + 3.29277i) q^{71} +2.35819 q^{72} +(14.5768 + 6.49002i) q^{73} +(-2.38163 + 4.12510i) q^{74} +(-0.745835 - 1.29182i) q^{75} +(-0.867226 - 8.25110i) q^{76} +(1.09104 + 0.231907i) q^{77} +(0.157096 - 1.49467i) q^{78} +(1.10558 + 10.5189i) q^{79} +(-1.73274 + 0.368306i) q^{80} +(1.12347 + 3.45769i) q^{81} +(-1.71705 + 2.97402i) q^{82} +(-9.45931 - 10.5056i) q^{83} +(-0.283624 - 0.206065i) q^{84} +(-1.60424 - 4.93733i) q^{85} +(-3.68160 + 4.08884i) q^{86} +(-2.15357 + 0.457755i) q^{87} +(2.06211 - 1.49821i) q^{88} +(-2.10199 + 6.46927i) q^{89} +(-2.08871 - 3.61775i) q^{90} +(0.549314 - 0.610075i) q^{91} +(0.161282 - 0.179122i) q^{92} +(-1.57218 - 2.72310i) q^{93} +(-1.12615 + 3.46593i) q^{94} +(-11.8901 + 8.63865i) q^{95} +(-0.783624 + 0.166564i) q^{96} +(-7.48873 + 8.31708i) q^{97} +(2.10394 + 6.47527i) q^{98} +(4.86284 + 3.53306i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 6 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} + 3 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 6 * q^5 - q^6 - 10 * q^7 + 4 * q^8 + 3 * q^9	\( 16 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 6 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} + 3 q^{9} - 6 q^{10} - 2 q^{11} + q^{12} - 9 q^{13} - 10 q^{14} - 3 q^{15} + 2 q^{16} + 2 q^{17} + 24 q^{18} + 10 q^{19} - 7 q^{20} - 6 q^{21} - 11 q^{22} - 11 q^{23} - 3 q^{24} - 28 q^{25} + 4 q^{26} - 33 q^{27} + 5 q^{28} + 15 q^{29} - 12 q^{30} - 12 q^{31} + 8 q^{32} + 15 q^{33} - 11 q^{34} + 19 q^{35} + q^{36} + 16 q^{37} - 10 q^{38} + 24 q^{39} + 4 q^{40} - 20 q^{41} - 19 q^{42} - 21 q^{43} - 4 q^{44} + 17 q^{45} + 2 q^{46} - 11 q^{47} + q^{48} - 10 q^{49} + 4 q^{50} - 56 q^{51} - 2 q^{52} - 8 q^{53} + 41 q^{54} + 35 q^{55} + 10 q^{56} + 49 q^{57} - 10 q^{58} + 35 q^{59} + 6 q^{60} + 15 q^{61} + 16 q^{62} - 26 q^{63} - 4 q^{64} + 24 q^{65} + 10 q^{66} + 22 q^{67} + 12 q^{68} + 46 q^{69} + 28 q^{70} + 10 q^{71} + 2 q^{72} + 9 q^{73} - 7 q^{74} - 15 q^{75} - 20 q^{76} + 2 q^{77} + 11 q^{78} + 10 q^{79} - 4 q^{80} - 27 q^{81} + 15 q^{82} - 45 q^{83} + 17 q^{84} + 2 q^{85} + 11 q^{86} - 9 q^{87} - 8 q^{88} - 26 q^{89} + 8 q^{90} - 84 q^{91} - 47 q^{92} - 33 q^{93} - 2 q^{94} + 37 q^{95} + 9 q^{96} - 41 q^{97} - 5 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 6 * q^5 - q^6 - 10 * q^7 + 4 * q^8 + 3 * q^9 - 6 * q^10 - 2 * q^11 + q^12 - 9 * q^13 - 10 * q^14 - 3 * q^15 + 2 * q^16 + 2 * q^17 + 24 * q^18 + 10 * q^19 - 7 * q^20 - 6 * q^21 - 11 * q^22 - 11 * q^23 - 3 * q^24 - 28 * q^25 + 4 * q^26 - 33 * q^27 + 5 * q^28 + 15 * q^29 - 12 * q^30 - 12 * q^31 + 8 * q^32 + 15 * q^33 - 11 * q^34 + 19 * q^35 + q^36 + 16 * q^37 - 10 * q^38 + 24 * q^39 + 4 * q^40 - 20 * q^41 - 19 * q^42 - 21 * q^43 - 4 * q^44 + 17 * q^45 + 2 * q^46 - 11 * q^47 + q^48 - 10 * q^49 + 4 * q^50 - 56 * q^51 - 2 * q^52 - 8 * q^53 + 41 * q^54 + 35 * q^55 + 10 * q^56 + 49 * q^57 - 10 * q^58 + 35 * q^59 + 6 * q^60 + 15 * q^61 + 16 * q^62 - 26 * q^63 - 4 * q^64 + 24 * q^65 + 10 * q^66 + 22 * q^67 + 12 * q^68 + 46 * q^69 + 28 * q^70 + 10 * q^71 + 2 * q^72 + 9 * q^73 - 7 * q^74 - 15 * q^75 - 20 * q^76 + 2 * q^77 + 11 * q^78 + 10 * q^79 - 4 * q^80 - 27 * q^81 + 15 * q^82 - 45 * q^83 + 17 * q^84 + 2 * q^85 + 11 * q^86 - 9 * q^87 - 8 * q^88 - 26 * q^89 + 8 * q^90 - 84 * q^91 - 47 * q^92 - 33 * q^93 - 2 * q^94 + 37 * q^95 + 9 * q^96 - 41 * q^97 - 5 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/122\mathbb{Z}\right)^\times$.

$n$	$63$
$\chi(n)$	$e\left(\frac{4}{15}\right)$

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 $

$2$	−0.669131	−	0.743145i	−0.473147	−	0.525483i
$2$	−0.669131	−	0.743145i	−0.473147	−	0.525483i
$3$	−0.247563	+	0.761920i	−0.142930	+	0.439895i	−0.996739	−	0.0806923i	$-0.974287\pi$
$3$	−0.247563	+	0.761920i	−0.142930	+	0.439895i	0.853809	+	0.520587i	$0.174287\pi$
$4$	−0.104528	+	0.994522i	−0.0522642	+	0.497261i
$5$	1.61830	−	0.720515i	0.723727	−	0.322224i	−0.0116036	−	0.999933i	$-0.503694\pi$
$5$	1.61830	−	0.720515i	0.723727	−	0.322224i	0.735330	+	0.677709i	$0.237027\pi$
$6$	0.731869	−	0.325849i	0.298784	−	0.133027i
$7$	0.428042	+	0.0909831i	0.161785	+	0.0343884i	0.288092	−	0.957603i	$-0.406979\pi$
$7$	0.428042	+	0.0909831i	0.161785	+	0.0343884i	−0.126307	+	0.991991i	$0.540313\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	1.90782	+	1.38611i	0.635939	+	0.462036i
$10$	−1.61830	−	0.720515i	−0.511752	−	0.227847i
$11$	2.54891			0.768524			0.384262	−	0.923224i	$-0.374456\pi$
$11$	2.54891			0.768524			0.384262	+	0.923224i	$0.374456\pi$
$12$	−0.731869	−	0.325849i	−0.211272	−	0.0940645i
$13$	0.937990	−	1.62465i	0.260152	−	0.450596i	−0.706131	−	0.708082i	$-0.749561\pi$
$13$	0.937990	−	1.62465i	0.260152	−	0.450596i	0.966282	+	0.257486i	$0.0828942\pi$
$14$	−0.218802	−	0.378976i	−0.0584773	−	0.101286i
$15$	0.148343	+	1.41139i	0.0383020	+	0.364419i
$16$	−0.978148	−	0.207912i	−0.244537	−	0.0519779i
$17$	0.306331	−	2.91455i	0.0742962	−	0.706881i	−0.892450	−	0.451145i	$-0.851016\pi$
$17$	0.306331	−	2.91455i	0.0742962	−	0.706881i	0.966747	−	0.255736i	$-0.0823178\pi$
$18$	−0.246498	−	2.34527i	−0.0581001	−	0.552786i
$19$	−8.11525	+	1.72495i	−1.86177	+	0.395731i	−0.994731	−	0.102517i	$-0.967310\pi$
$19$	−8.11525	+	1.72495i	−1.86177	+	0.395731i	−0.867035	+	0.498248i	$0.833977\pi$
$20$	0.547409	+	1.68475i	0.122404	+	0.376722i
$21$	−0.175289	+	0.303610i	−0.0382512	+	0.0662530i
$22$	−1.70555	−	1.89421i	−0.363625	−	0.403846i
$23$	−0.194999	−	0.141675i	−0.0406601	−	0.0295413i	0.567270	−	0.823532i	$-0.308000\pi$
$23$	−0.194999	−	0.141675i	−0.0406601	−	0.0295413i	−0.607930	+	0.793991i	$0.708000\pi$
$24$	0.247563	+	0.761920i	0.0505336	+	0.155526i
$25$	−1.24589	+	1.38370i	−0.249178	+	0.276741i
$26$	−1.83498	+	0.390038i	−0.359870	+	0.0764927i
$27$	−3.47279	+	2.52313i	−0.668339	+	0.485577i
$28$	−0.135227	+	0.416186i	−0.0255555	+	0.0786519i
$29$	1.37411	+	2.38003i	0.255166	+	0.441960i	0.964941	−	0.262469i	$-0.0845366\pi$
$29$	1.37411	+	2.38003i	0.255166	+	0.441960i	−0.709775	+	0.704429i	$0.751203\pi$
$30$	0.949606	−	1.05464i	0.173374	−	0.192551i
$31$	−2.62628	+	2.91677i	−0.471693	+	0.523868i	−0.931299	−	0.364255i	$-0.881324\pi$
$31$	−2.62628	+	2.91677i	−0.471693	+	0.523868i	0.459606	+	0.888123i	$0.347990\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.631014	+	1.94206i	−0.109845	+	0.338070i
$34$	−2.37091	+	1.72256i	−0.406607	+	0.295417i
$35$	0.758255	−	0.161172i	0.128169	−	0.0272431i
$36$	−1.57794	+	1.75248i	−0.262990	+	0.292079i
$37$	−1.47193	−	4.53013i	−0.241983	−	0.744748i	−0.996118	−	0.0880284i	$-0.971943\pi$
$37$	−1.47193	−	4.53013i	−0.241983	−	0.744748i	0.754135	−	0.656720i	$-0.228057\pi$
$38$	6.71205	+	4.87659i	1.08884	+	0.791087i
$39$	1.00564	+	1.11688i	0.161031	+	0.178843i
$40$	0.885726	−	1.53412i	0.140046	−	0.242566i
$41$	−1.06120	−	3.26603i	−0.165731	−	0.510068i	0.833358	−	0.552733i	$-0.186415\pi$
$41$	−1.06120	−	3.26603i	−0.165731	−	0.510068i	−0.999089	+	0.0426651i	$0.986415\pi$
$42$	0.342917	−	0.0728893i	0.0529133	−	0.0112471i
$43$	−0.575123	−	5.47193i	−0.0877054	−	0.834461i	−0.946622	−	0.322346i	$-0.895529\pi$
$43$	−0.575123	−	5.47193i	−0.0877054	−	0.834461i	0.858917	−	0.512116i	$-0.171138\pi$
$44$	−0.266433	+	2.53494i	−0.0401663	+	0.382157i
$45$	4.08614	+	0.868535i	0.609125	+	0.129474i
$46$	0.0251947	+	0.239711i	0.00371475	+	0.0353435i
$47$	−1.82215	−	3.15605i	−0.265787	−	0.460357i	0.701982	−	0.712194i	$-0.252299\pi$
$47$	−1.82215	−	3.15605i	−0.265787	−	0.460357i	−0.967770	+	0.251837i	$0.918965\pi$
$48$	0.400565	−	0.693799i	0.0578166	−	0.100141i
$49$	−6.21988	−	2.76927i	−0.888554	−	0.395610i
$50$	1.86196			0.263320
$51$	2.14482	+	0.954933i	0.300334	+	0.133717i
$52$	1.51770	+	1.10267i	0.210467	+	0.152913i
$53$	0.735495	−	0.534368i	0.101028	−	0.0734011i	−0.536124	−	0.844139i	$-0.680112\pi$
$53$	0.735495	−	0.534368i	0.101028	−	0.0734011i	0.637152	+	0.770738i	$0.280112\pi$
$54$	4.19880	+	0.892483i	0.571385	+	0.121452i
$55$	4.12490	−	1.83652i	0.556201	−	0.247637i
$56$	0.399771	−	0.177990i	0.0534217	−	0.0237849i
$57$	0.694761	−	6.61021i	0.0920233	−	0.875543i
$58$	0.849246	−	2.61371i	0.111512	−	0.343197i
$59$	4.33207	+	4.81125i	0.563988	+	0.626372i	0.955922	−	0.293622i	$-0.0948605\pi$
$59$	4.33207	+	4.81125i	0.563988	+	0.626372i	−0.391934	+	0.919993i	$0.628194\pi$
$60$	−1.41916			−0.183213
$61$	−1.75492	−	7.61054i	−0.224694	−	0.974429i
$61$	−1.75492	−	7.61054i	−0.224694	−	0.974429i
$62$	3.92491			0.498464
$63$	0.690512	+	0.766892i	0.0869964	+	0.0966193i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	0.347370	−	3.30500i	0.0430859	−	0.409935i
$66$	1.86546	−	0.830558i	0.229623	−	0.102235i
$67$	−5.74046	+	2.55582i	−0.701309	+	0.312243i	−0.726235	−	0.687446i	$-0.758732\pi$
$67$	−5.74046	+	2.55582i	−0.701309	+	0.312243i	0.0249259	+	0.999689i	$0.492065\pi$
$68$	2.86656	+	0.609306i	0.347621	+	0.0738892i
$69$	0.156219	−	0.113500i	0.0188066	−	0.0136638i
$70$	−0.627146	−	0.455648i	−0.0749583	−	0.0544604i
$71$	7.39569	+	3.29277i	0.877706	+	0.390780i	0.795585	−	0.605842i	$-0.207164\pi$
$71$	7.39569	+	3.29277i	0.877706	+	0.390780i	0.0821216	+	0.996622i	$0.473830\pi$
$72$	2.35819			0.277915
$73$	14.5768	+	6.49002i	1.70609	+	0.759599i	0.998601	+	0.0528711i	$0.0168372\pi$
$73$	14.5768	+	6.49002i	1.70609	+	0.759599i	0.707486	+	0.706728i	$0.249829\pi$
$74$	−2.38163	+	4.12510i	−0.276859	+	0.479533i
$75$	−0.745835	−	1.29182i	−0.0861216	−	0.149167i
$76$	−0.867226	−	8.25110i	−0.0994776	−	0.946466i
$77$	1.09104	+	0.231907i	0.124335	+	0.0264283i
$78$	0.157096	−	1.49467i	0.0177876	−	0.169238i
$79$	1.10558	+	10.5189i	0.124387	+	1.18346i	0.861522	+	0.507720i	$0.169511\pi$
$79$	1.10558	+	10.5189i	0.124387	+	1.18346i	−0.737135	+	0.675745i	$0.763822\pi$
$80$	−1.73274	+	0.368306i	−0.193726	+	0.0411778i
$81$	1.12347	+	3.45769i	0.124830	+	0.384188i
$82$	−1.71705	+	2.97402i	−0.189617	+	0.328426i
$83$	−9.45931	−	10.5056i	−1.03829	−	1.15314i	−0.988007	−	0.154408i	$-0.950653\pi$
$83$	−9.45931	−	10.5056i	−1.03829	−	1.15314i	−0.0502868	−	0.998735i	$-0.516014\pi$
$84$	−0.283624	−	0.206065i	−0.0309459	−	0.0224835i
$85$	−1.60424	−	4.93733i	−0.174004	−	0.535529i
$86$	−3.68160	+	4.08884i	−0.396998	+	0.440910i
$87$	−2.15357	+	0.457755i	−0.230887	+	0.0490765i
$88$	2.06211	−	1.49821i	0.219821	−	0.159710i
$89$	−2.10199	+	6.46927i	−0.222811	+	0.685742i	0.775696	+	0.631107i	$0.217399\pi$
$89$	−2.10199	+	6.46927i	−0.222811	+	0.685742i	−0.998506	+	0.0546342i	$0.982601\pi$
$90$	−2.08871	−	3.61775i	−0.220169	−	0.381345i
$91$	0.549314	−	0.610075i	0.0575837	−	0.0639532i
$92$	0.161282	−	0.179122i	0.0168148	−	0.0186747i
$93$	−1.57218	−	2.72310i	−0.163028	−	0.282372i
$94$	−1.12615	+	3.46593i	−0.116153	+	0.357483i
$95$	−11.8901	+	8.63865i	−1.21990	+	0.886306i
$96$	−0.783624	+	0.166564i	−0.0799783	+	0.0169999i
$97$	−7.48873	+	8.31708i	−0.760366	+	0.844472i	−0.991723	−	0.128397i	$-0.959017\pi$
$97$	−7.48873	+	8.31708i	−0.760366	+	0.844472i	0.231357	+	0.972869i	$0.425683\pi$
$98$	2.10394	+	6.47527i	0.212530	+	0.654101i
$99$	4.86284	+	3.53306i	0.488734	+	0.355086i
$100$	−1.24589	−	1.38370i	−0.124589	−	0.138370i
$101$	6.27220	−	10.8638i	0.624107	−	1.08099i	−0.364606	−	0.931162i	$-0.618796\pi$
$101$	6.27220	−	10.8638i	0.624107	−	1.08099i	0.988713	−	0.149823i	$-0.0478705\pi$
$102$	−0.725508	−	2.23288i	−0.0718360	−	0.221088i
$103$	−3.12575	+	0.664398i	−0.307989	+	0.0654651i	−0.359313	−	0.933217i	$-0.616989\pi$
$103$	−3.12575	+	0.664398i	−0.307989	+	0.0654651i	0.0513244	+	0.998682i	$0.483656\pi$
$104$	−0.196093	−	1.86570i	−0.0192285	−	0.182947i
$105$	−0.0649156	+	0.617630i	−0.00633511	+	0.0602746i
$106$	−0.889255	−	0.189017i	−0.0863721	−	0.0183590i
$107$	−0.875328	−	8.32819i	−0.0846212	−	0.805117i	−0.951717	−	0.306976i	$-0.900683\pi$
$107$	−0.875328	−	8.32819i	−0.0846212	−	0.805117i	0.867096	−	0.498141i	$-0.165984\pi$
$108$	−2.14630	−	3.71751i	−0.206528	−	0.357717i
$109$	−5.72063	+	9.90843i	−0.547937	+	0.949055i	0.450478	+	0.892787i	$0.351253\pi$
$109$	−5.72063	+	9.90843i	−0.547937	+	0.949055i	−0.998416	+	0.0562681i	$0.982080\pi$
$110$	−4.12490	−	1.83652i	−0.393294	−	0.175106i
$111$	3.81599			0.362198
$112$	−0.399771	−	0.177990i	−0.0377749	−	0.0168184i
$113$	1.22513	+	0.890108i	0.115250	+	0.0837343i	0.643918	−	0.765095i	$-0.277308\pi$
$113$	1.22513	+	0.890108i	0.115250	+	0.0837343i	−0.528667	+	0.848829i	$0.677308\pi$
$114$	−5.37723	+	3.90678i	−0.503623	+	0.365904i
$115$	−0.417646	−	0.0887734i	−0.0389457	−	0.00827816i
$116$	−2.51062	+	1.11780i	−0.233106	+	0.103785i
$117$	4.04145	−	1.79937i	0.373632	−	0.166352i
$118$	0.676736	−	6.43871i	0.0622986	−	0.592732i
$119$	0.396297	−	1.21968i	0.0363285	−	0.111808i
$120$	0.949606	+	1.05464i	0.0866868	+	0.0962754i
$121$	−4.50308			−0.409371
$122$	−4.48146	+	6.39660i	−0.405733	+	0.579121i
$123$	2.75117			0.248064
$124$	−2.62628	−	2.91677i	−0.235847	−	0.261934i
$125$	−3.75630	+	11.5607i	−0.335973	+	1.03402i
$126$	0.107869	−	1.02630i	0.00960970	−	0.0914302i
$127$	12.7075	−	5.65776i	1.12761	−	0.502045i	0.243771	−	0.969833i	$-0.421615\pi$
$127$	12.7075	−	5.65776i	1.12761	−	0.502045i	0.883841	+	0.467788i	$0.154949\pi$
$128$	−0.913545	+	0.406737i	−0.0807468	+	0.0359508i
$129$	4.31155	+	0.916449i	0.379611	+	0.0806888i
$130$	−2.68853	+	1.95333i	−0.235800	+	0.171319i
$131$	−7.08304	−	5.14613i	−0.618848	−	0.449620i	0.233671	−	0.972316i	$-0.424926\pi$
$131$	−7.08304	−	5.14613i	−0.618848	−	0.449620i	−0.852519	+	0.522696i	$0.824926\pi$
$132$	−1.86546	−	0.830558i	−0.162368	−	0.0722908i
$133$	−3.63061			−0.314813
$134$	5.74046	+	2.55582i	0.495901	+	0.220789i
$135$	−3.80208	+	6.58539i	−0.327231	+	0.566780i
$136$	−1.46530	−	2.53797i	−0.125648	−	0.217630i
$137$	−1.21309	−	11.5418i	−0.103641	−	0.986079i	−0.915525	−	0.402260i	$-0.868225\pi$
$137$	−1.21309	−	11.5418i	−0.103641	−	0.986079i	0.811884	−	0.583818i	$-0.198442\pi$
$138$	−0.188878	−	0.0401473i	−0.0160784	−	0.00341757i
$139$	1.02238	−	9.72727i	0.0867169	−	0.825056i	−0.861569	−	0.507640i	$-0.830518\pi$
$139$	1.02238	−	9.72727i	0.0867169	−	0.825056i	0.948286	−	0.317416i	$-0.102815\pi$
$140$	0.0810300	+	0.770949i	0.00684828	+	0.0651571i
$141$	2.85575	−	0.607009i	0.240498	−	0.0511194i
$142$	−2.50167	−	7.69936i	−0.209936	−	0.646116i
$143$	2.39085	−	4.14107i	0.199933	−	0.346294i
$144$	−1.57794	−	1.75248i	−0.131495	−	0.146040i
$145$	3.93857	+	2.86154i	0.327080	+	0.237638i
$146$	−4.93077	−	15.1754i	−0.408073	−	1.25592i
$147$	3.64977	−	4.05348i	0.301028	−	0.334326i
$148$	4.65917	−	0.990337i	0.382981	−	0.0814052i
$149$	−15.4928	+	11.2562i	−1.26922	+	0.922140i	−0.999171	−	0.0407075i	$-0.987039\pi$
$149$	−15.4928	+	11.2562i	−1.26922	+	0.922140i	−0.270046	+	0.962848i	$0.587039\pi$
$150$	−0.460951	+	1.41866i	−0.0376365	+	0.115833i
$151$	11.5752	+	20.0488i	0.941974	+	1.63155i	0.761699	+	0.647931i	$0.224366\pi$
$151$	11.5752	+	20.0488i	0.941974	+	1.63155i	0.180276	+	0.983616i	$0.442301\pi$
$152$	−5.55147	+	6.16554i	−0.450284	+	0.500091i
$153$	4.62430	−	5.13581i	0.373853	−	0.415206i
$154$	−0.557706	−	0.965975i	−0.0449412	−	0.0778405i
$155$	−2.14853	+	6.61249i	−0.172574	+	0.531128i
$156$	−1.21587	+	0.883385i	−0.0973479	+	0.0707274i
$157$	19.2026	−	4.08163i	1.53253	−	0.325750i	0.637042	−	0.770829i	$-0.280158\pi$
$157$	19.2026	−	4.08163i	1.53253	−	0.325750i	0.895491	+	0.445080i	$0.146825\pi$
$158$	7.07727	−	7.86010i	0.563037	−	0.625316i
$159$	0.225065	+	0.692678i	0.0178488	+	0.0549329i
$160$	1.43314	+	1.04123i	0.113299	+	0.0823168i
$161$	−0.0705776	−	0.0783844i	−0.00556229	−	0.00617755i
$162$	1.81782	−	3.14855i	0.142821	−	0.247373i
$163$	−1.18178	−	3.63716i	−0.0925645	−	0.284884i	0.894047	−	0.447974i	$-0.147854\pi$
$163$	−1.18178	−	3.63716i	−0.0925645	−	0.284884i	−0.986611	+	0.163089i	$0.947854\pi$
$164$	3.35906	−	0.713991i	0.262299	−	0.0557533i
$165$	0.378112	+	3.59750i	0.0294360	+	0.280065i
$166$	−1.47769	+	14.0593i	−0.114691	+	1.09121i
$167$	15.9382	+	3.38777i	1.23333	+	0.262153i	0.778055	−	0.628196i	$-0.216206\pi$
$167$	15.9382	+	3.38777i	1.23333	+	0.262153i	0.455279	+	0.890349i	$0.349540\pi$
$168$	0.0366454	+	0.348658i	0.00282725	+	0.0268995i
$169$	4.74035	+	8.21053i	0.364642	+	0.631579i
$170$	−2.59571	+	4.49590i	−0.199082	+	0.344820i
$171$	−17.8734	−	7.95774i	−1.36681	−	0.608543i
$172$	5.50207			0.419529
$173$	−14.6008	−	6.50070i	−1.11008	−	0.494239i	−0.231981	−	0.972720i	$-0.574521\pi$
$173$	−14.6008	−	6.50070i	−1.11008	−	0.494239i	−0.878098	+	0.478481i	$0.841187\pi$
$174$	1.78120	+	1.29412i	0.135032	+	0.0981067i
$175$	−0.659187	+	0.478927i	−0.0498299	+	0.0362035i
$176$	−2.49321	−	0.529947i	−0.187932	−	0.0399463i
$177$	−4.73825	+	2.10960i	−0.356149	+	0.158568i
$178$	6.21412	−	2.76670i	0.465768	−	0.207373i
$179$	0.595454	−	5.66536i	0.0445063	−	0.423449i	−0.949470	−	0.313857i	$-0.898379\pi$
$179$	0.595454	−	5.66536i	0.0445063	−	0.423449i	0.993977	−	0.109592i	$-0.0349545\pi$
$180$	−1.29089	+	3.97296i	−0.0962176	+	0.296127i
$181$	16.6660	+	18.5094i	1.23877	+	1.37580i	0.900564	+	0.434724i	$0.143154\pi$
$181$	16.6660	+	18.5094i	1.23877	+	1.37580i	0.338208	+	0.941071i	$0.390179\pi$
$182$	−0.820937			−0.0608519
$183$	6.23307	+	0.546980i	0.460762	+	0.0404339i
$184$	−0.241032			−0.0177691
$185$	−5.64605	−	6.27057i	−0.415106	−	0.461022i
$186$	−0.971661	+	2.99047i	−0.0712457	+	0.219272i
$187$	0.780809	−	7.42890i	0.0570984	−	0.543255i
$188$	3.32922	−	1.48227i	0.242809	−	0.108105i
$189$	−1.71606	+	0.764040i	−0.124825	+	0.0555757i
$190$	14.3758	+	3.05567i	1.04293	+	0.221681i
$191$	18.5008	−	13.4416i	1.33867	−	0.972600i	0.339178	−	0.940722i	$-0.389851\pi$
$191$	18.5008	−	13.4416i	1.33867	−	0.972600i	0.999492	−	0.0318782i	$-0.0101489\pi$
$192$	0.648128	+	0.470893i	0.0467746	+	0.0339837i
$193$	−12.0949	−	5.38498i	−0.870607	−	0.387619i	−0.0777109	−	0.996976i	$-0.524761\pi$
$193$	−12.0949	−	5.38498i	−0.870607	−	0.387619i	−0.792896	+	0.609357i	$0.791428\pi$
$194$	11.1917			0.803520
$195$	2.43215	+	1.08286i	0.174170	+	0.0775455i
$196$	3.40425	−	5.89634i	0.243161	−	0.421167i
$197$	11.3841	+	19.7179i	0.811084	+	1.40484i	0.912106	+	0.409955i	$0.134456\pi$
$197$	11.3841	+	19.7179i	0.811084	+	1.40484i	−0.101022	+	0.994884i	$0.532211\pi$
$198$	−0.628300	−	5.97788i	−0.0446513	−	0.424829i
$199$	−0.503149	−	0.106948i	−0.0356673	−	0.00758132i	0.190043	−	0.981776i	$-0.439137\pi$
$199$	−0.503149	−	0.106948i	−0.0356673	−	0.00758132i	−0.225711	+	0.974194i	$0.572470\pi$
$200$	−0.194627	+	1.85176i	−0.0137622	+	0.130939i
$201$	−0.526204	−	5.00650i	−0.0371156	−	0.353131i
$202$	−12.2703	+	2.60813i	−0.863334	+	0.183507i
$203$	0.371634	+	1.14377i	0.0260836	+	0.0802770i
$204$	−1.17390	+	2.03325i	−0.0821892	+	0.142356i
$205$	−4.07056	−	4.52082i	−0.284300	−	0.315747i
$206$	2.58528	+	1.87831i	0.180125	+	0.130868i
$207$	−0.175645	−	0.540580i	−0.0122082	−	0.0375729i
$208$	−1.25528	+	1.39412i	−0.0870377	+	0.0966651i
$209$	−20.6850	+	4.39673i	−1.43081	+	0.304128i
$210$	0.502426	−	0.365034i	0.0346707	−	0.0251897i
$211$	7.13412	−	21.9566i	0.491133	−	1.51155i	−0.331764	−	0.943362i	$-0.607644\pi$
$211$	7.13412	−	21.9566i	0.491133	−	1.51155i	0.822897	−	0.568190i	$-0.192356\pi$
$212$	0.454561	+	0.787322i	0.0312194	+	0.0540735i
$213$	−4.33973	+	4.81975i	−0.297353	+	0.330244i
$214$	−5.60334	+	6.22314i	−0.383037	+	0.425405i
$215$	−4.87333	−	8.44085i	−0.332358	−	0.575661i
$216$	−1.32649	+	4.08251i	−0.0902561	+	0.277780i
$217$	−1.38953	+	1.00955i	−0.0943276	+	0.0685330i
$218$	11.1913	−	2.37877i	0.757967	−	0.161111i
$219$	−8.55355	+	9.49968i	−0.577995	+	0.641929i
$220$	1.39529	+	4.29427i	0.0940707	+	0.289520i
$221$	−4.44777	−	3.23149i	−0.299189	−	0.217374i
$222$	−2.55340	−	2.83583i	−0.171373	−	0.190329i
$223$	−1.78665	+	3.09456i	−0.119643	+	0.207227i	−0.919626	−	0.392795i	$-0.871508\pi$
$223$	−1.78665	+	3.09456i	−0.119643	+	0.207227i	0.799983	+	0.600022i	$0.204842\pi$
$224$	0.135227	+	0.416186i	0.00903525	+	0.0278076i
$225$	−4.29490	+	0.912908i	−0.286326	+	0.0608605i
$226$	−0.158292	−	1.50605i	−0.0105294	−	0.100181i
$227$	1.58998	−	15.1276i	0.105531	−	1.00406i	−0.805746	−	0.592262i	$-0.798235\pi$
$227$	1.58998	−	15.1276i	0.105531	−	1.00406i	0.911276	−	0.411796i	$-0.135098\pi$
$228$	6.50137	+	1.38191i	0.430564	+	0.0915192i
$229$	−1.13351	−	10.7846i	−0.0749045	−	0.712669i	−0.965945	−	0.258746i	$-0.916691\pi$
$229$	−1.13351	−	10.7846i	−0.0749045	−	0.712669i	0.891041	−	0.453923i	$-0.149976\pi$
$230$	0.213488	+	0.369772i	0.0140770	+	0.0243821i
$231$	−0.446795	+	0.773872i	−0.0293970	+	0.0509170i
$232$	2.51062	+	1.11780i	0.164830	+	0.0733873i
$233$	13.2963			0.871072			0.435536	−	0.900171i	$-0.356559\pi$
$233$	13.2963			0.871072			0.435536	+	0.900171i	$0.356559\pi$
$234$	−4.04145	−	1.79937i	−0.264198	−	0.117628i
$235$	−5.22276	−	3.79456i	−0.340695	−	0.247530i
$236$	−5.23772	+	3.80543i	−0.340947	+	0.247712i
$237$	−8.28824	−	1.76172i	−0.538379	−	0.114436i
$238$	−1.17157	+	0.521617i	−0.0759416	+	0.0338114i
$239$	15.8260	−	7.04621i	1.02370	−	0.455781i	0.174952	−	0.984577i	$-0.444023\pi$
$239$	15.8260	−	7.04621i	1.02370	−	0.455781i	0.848749	+	0.528796i	$0.177356\pi$
$240$	0.148343	−	1.41139i	0.00957550	−	0.0911048i
$241$	1.60148	−	4.92884i	0.103160	−	0.317495i	−0.886134	−	0.463429i	$-0.846619\pi$
$241$	1.60148	−	4.92884i	0.103160	−	0.317495i	0.989294	+	0.145934i	$0.0466189\pi$
$242$	3.01315	+	3.34644i	0.193693	+	0.215117i
$243$	−15.7904			−1.01296
$244$	7.75228	−	0.949785i	0.496289	−	0.0608038i
$245$	−12.0609			−0.770545
$246$	−1.84089	−	2.04452i	−0.117371	−	0.130354i
$247$	−4.80959	+	14.8024i	−0.306027	+	0.941853i
$248$	−0.410265	+	3.90341i	−0.0260518	+	0.247867i
$249$	10.3462	−	4.60644i	0.655665	−	0.291921i
$250$	11.1047	−	4.94414i	0.702324	−	0.312695i
$251$	8.32769	+	1.77010i	0.525639	+	0.111728i	0.463086	−	0.886314i	$-0.346742\pi$
$251$	8.32769	+	1.77010i	0.525639	+	0.111728i	0.0625534	+	0.998042i	$0.480076\pi$
$252$	−0.834869	+	0.606568i	−0.0525918	+	0.0382102i
$253$	−0.497034	−	0.361116i	−0.0312482	−	0.0227032i
$254$	−12.7075	−	5.65776i	−0.797342	−	0.355000i
$255$	4.15900			0.260447
$256$	0.913545	+	0.406737i	0.0570966	+	0.0254210i
$257$	−12.4206	+	21.5131i	−0.774776	+	1.34195i	0.160144	+	0.987094i	$0.448804\pi$
$257$	−12.4206	+	21.5131i	−0.774776	+	1.34195i	−0.934920	+	0.354858i	$0.884529\pi$
$258$	−2.20394	−	3.81733i	−0.137211	−	0.237657i
$259$	−0.217881	−	2.07300i	−0.0135385	−	0.128810i
$260$	3.25059	+	0.690934i	0.201593	+	0.0428499i
$261$	−0.677431	+	6.44532i	−0.0419319	+	0.398955i
$262$	0.915159	+	8.70716i	0.0565387	+	0.537930i
$263$	−10.0364	+	2.13331i	−0.618872	+	0.131545i	−0.506670	−	0.862140i	$-0.669124\pi$
$263$	−10.0364	+	2.13331i	−0.618872	+	0.131545i	−0.112202	+	0.993685i	$0.535790\pi$
$264$	0.631014	+	1.94206i	0.0388362	+	0.119526i
$265$	0.805233	−	1.39470i	0.0494651	−	0.0856760i
$266$	2.42935	+	2.69807i	0.148953	+	0.165429i
$267$	−4.40869	−	3.20310i	−0.269808	−	0.196027i
$268$	−1.94178	−	5.97617i	−0.118613	−	0.365053i
$269$	2.40993	−	2.67650i	0.146936	−	0.163189i	−0.665184	−	0.746680i	$-0.731647\pi$
$269$	2.40993	−	2.67650i	0.146936	−	0.163189i	0.812120	+	0.583490i	$0.198313\pi$
$270$	7.43798	−	1.58099i	0.452661	−	0.0962161i
$271$	−3.97652	+	2.88911i	−0.241556	+	0.175501i	−0.701976	−	0.712200i	$-0.747699\pi$
$271$	−3.97652	+	2.88911i	−0.241556	+	0.175501i	0.460420	+	0.887701i	$0.347699\pi$
$272$	−0.905605	+	2.78717i	−0.0549104	+	0.168997i
$273$	0.328839	+	0.569565i	0.0199022	+	0.0344717i
$274$	−7.76548	+	8.62444i	−0.469130	+	0.521022i
$275$	−3.17566	+	3.52693i	−0.191499	+	0.212682i
$276$	0.0965489	+	0.167228i	0.00581156	+	0.0100659i
$277$	−5.22674	+	16.0862i	−0.314044	+	0.966528i	0.662102	+	0.749414i	$0.269665\pi$
$277$	−5.22674	+	16.0862i	−0.314044	+	0.966528i	−0.976146	+	0.217115i	$0.930335\pi$
$278$	−7.91287	+	5.74904i	−0.474582	+	0.344804i
$279$	−9.05342	+	1.92436i	−0.542014	+	0.115209i
$280$	0.518707	−	0.576082i	0.0309987	−	0.0344275i
$281$	1.45601	+	4.48114i	0.0868583	+	0.267322i	0.985046	−	0.172289i	$-0.0551162\pi$
$281$	1.45601	+	4.48114i	0.0868583	+	0.267322i	−0.898188	+	0.439611i	$0.855116\pi$
$282$	−2.36197	−	1.71607i	−0.140653	−	0.102190i
$283$	−5.88787	−	6.53914i	−0.349998	−	0.388712i	0.542281	−	0.840197i	$-0.317561\pi$
$283$	−5.88787	−	6.53914i	−0.349998	−	0.388712i	−0.892278	+	0.451486i	$0.850894\pi$
$284$	−4.04779	+	7.01098i	−0.240192	+	0.416025i
$285$	−3.63842	−	11.1979i	−0.215521	−	0.663306i
$286$	−4.67720	+	0.994170i	−0.276569	+	0.0587865i
$287$	−0.157083	−	1.49455i	−0.00927233	−	0.0882204i
$288$	−0.246498	+	2.34527i	−0.0145250	+	0.138196i
$289$	8.22777	+	1.74887i	0.483986	+	0.102874i
$290$	−0.508880	−	4.84167i	−0.0298825	−	0.284313i
$291$	−4.48302	−	7.76482i	−0.262799	−	0.455182i
$292$	−7.97815	+	13.8186i	−0.466886	+	0.808671i
$293$	−28.3833	−	12.6371i	−1.65817	−	0.738266i	−0.658277	−	0.752776i	$-0.728714\pi$
$293$	−28.3833	−	12.6371i	−1.65817	−	0.738266i	−0.999895	+	0.0145105i	$0.995381\pi$
$294$	−5.45450			−0.318113
$295$	10.4772	+	4.66474i	0.610005	+	0.271592i
$296$	−3.85356	−	2.79977i	−0.223983	−	0.162733i
$297$	−8.85182	+	6.43122i	−0.513635	+	0.373177i
$298$	18.7316	+	3.98153i	1.08509	+	0.230644i
$299$	−0.413078	+	0.183914i	−0.0238889	+	0.0106360i
$300$	1.36271	−	0.606716i	0.0786760	−	0.0350288i
$301$	0.251676	−	2.39454i	0.0145064	−	0.138019i
$302$	7.15385	−	22.0173i	0.411658	−	1.26695i
$303$	6.72456	+	7.46838i	0.386316	+	0.429047i
$304$	8.29655			0.475840
$305$	−8.32349	−	11.0517i	−0.476602	−	0.632819i
$306$	−6.91091			−0.395071
$307$	4.10736	+	4.56169i	0.234420	+	0.260349i	0.848865	−	0.528610i	$-0.177287\pi$
$307$	4.10736	+	4.56169i	0.234420	+	0.260349i	−0.614445	+	0.788960i	$0.710620\pi$
$308$	−0.344681	+	1.06082i	−0.0196400	+	0.0604458i
$309$	0.267601	−	2.54605i	0.0152233	−	0.144840i
$310$	6.35169	−	2.82795i	0.360752	−	0.160617i
$311$	13.0621	−	5.81560i	0.740681	−	0.329772i	−0.00147561	−	0.999999i	$-0.500470\pi$
$311$	13.0621	−	5.81560i	0.740681	−	0.329772i	0.742157	+	0.670226i	$0.233803\pi$
$312$	1.47006	+	0.312471i	0.0832258	+	0.0176902i
$313$	6.59675	−	4.79282i	0.372870	−	0.270906i	−0.385530	−	0.922695i	$-0.625981\pi$
$313$	6.59675	−	4.79282i	0.372870	−	0.270906i	0.758400	+	0.651789i	$0.225981\pi$
$314$	−15.8823	−	11.5392i	−0.896289	−	0.651192i
$315$	1.67001	+	0.743538i	0.0940946	+	0.0418936i
$316$	−10.5768			−0.594992
$317$	14.0189	+	6.24163i	0.787382	+	0.350565i	0.760721	−	0.649079i	$-0.224846\pi$
$317$	14.0189	+	6.24163i	0.787382	+	0.350565i	0.0266614	+	0.999645i	$0.491512\pi$
$318$	0.364162	−	0.630748i	0.0204212	−	0.0353706i
$319$	3.50248	+	6.06647i	0.196101	+	0.339657i
$320$	−0.185167	−	1.76175i	−0.0103512	−	0.0984847i
$321$	6.56212	+	1.39482i	0.366262	+	0.0778513i
$322$	−0.0110253	+	0.104899i	−0.000614416	+	0.00584578i
$323$	2.54149	+	24.1807i	0.141412	+	1.34545i
$324$	−3.55619	+	0.755891i	−0.197566	+	0.0419939i
$325$	1.07939	+	3.32203i	0.0598740	+	0.184273i
$326$	−1.91217	+	3.31197i	−0.105905	+	0.183433i
$327$	−6.13322	−	6.81163i	−0.339168	−	0.376684i
$328$	−2.77825	−	2.01852i	−0.153403	−	0.111454i
$329$	−0.492807	−	1.51670i	−0.0271693	−	0.0836186i
$330$	2.42046	−	2.68819i	0.133242	−	0.147980i
$331$	−12.6705	+	2.69319i	−0.696432	+	0.148031i	−0.542507	−	0.840051i	$-0.682525\pi$
$331$	−12.6705	+	2.69319i	−0.696432	+	0.148031i	−0.153925	+	0.988082i	$0.549191\pi$
$332$	11.4368	−	8.30935i	0.627678	−	0.456035i
$333$	3.47109	−	10.6829i	0.190214	−	0.585419i
$334$	−8.14713	−	14.1112i	−0.445791	−	0.772133i
$335$	−7.44830	+	8.27218i	−0.406944	+	0.451957i
$336$	0.234583	−	0.260530i	0.0127975	−	0.0142131i
$337$	11.5706	+	20.0408i	0.630289	+	1.09169i	0.987492	+	0.157666i	$0.0503970\pi$
$337$	11.5706	+	20.0408i	0.630289	+	1.09169i	−0.357203	+	0.934027i	$0.616270\pi$
$338$	2.92970	−	9.01668i	0.159355	−	0.490443i
$339$	−0.981488	+	0.713093i	−0.0533071	+	0.0387299i
$340$	5.07797	−	1.07936i	0.275392	−	0.0585363i
$341$	−6.69413	+	7.43458i	−0.362507	+	0.402605i
$342$	6.04587	+	18.6073i	0.326923	+	1.00617i
$343$	−4.88862	−	3.55179i	−0.263960	−	0.191778i
$344$	−3.68160	−	4.08884i	−0.198499	−	0.220455i
$345$	0.171032	−	0.296236i	0.00920805	−	0.0159488i
$346$	4.93889	+	15.2003i	0.265516	+	0.817175i
$347$	36.3232	−	7.72074i	1.94993	−	0.414471i	0.958212	−	0.286060i	$-0.0923455\pi$
$347$	36.3232	−	7.72074i	1.94993	−	0.414471i	0.991721	−	0.128411i	$-0.0409878\pi$
$348$	−0.230138	−	2.18962i	−0.0123367	−	0.117376i
$349$	1.38030	−	13.1327i	0.0738857	−	0.702976i	−0.893396	−	0.449271i	$-0.851684\pi$
$349$	1.38030	−	13.1327i	0.0738857	−	0.702976i	0.967282	−	0.253705i	$-0.0816494\pi$
$350$	0.796995	+	0.169406i	0.0426012	+	0.00905515i
$351$	0.841751	+	8.00873i	0.0449294	+	0.427474i
$352$	1.27445	+	2.20742i	0.0679286	+	0.117656i
$353$	−0.554227	+	0.959949i	−0.0294985	+	0.0510929i	−0.880398	−	0.474236i	$-0.842724\pi$
$353$	−0.554227	+	0.959949i	−0.0294985	+	0.0510929i	0.850899	+	0.525329i	$0.176058\pi$
$354$	4.73825	+	2.10960i	0.251835	+	0.112124i
$355$	14.3409			0.761138
$356$	−6.21412	−	2.76670i	−0.329347	−	0.146635i
$357$	0.831188	+	0.603893i	0.0439911	+	0.0319614i
$358$	−4.60862	+	3.34836i	−0.243573	+	0.176966i
$359$	30.9898	+	6.58709i	1.63558	+	0.347653i	0.931858	−	0.362823i	$-0.118187\pi$
$359$	30.9898	+	6.58709i	1.63558	+	0.347653i	0.703721	+	0.710476i	$0.251520\pi$
$360$	3.81627	−	1.69911i	0.201135	−	0.0895510i
$361$	45.5245	−	20.2688i	2.39602	−	1.06678i
$362$	2.60348	−	24.7705i	0.136836	−	1.30191i
$363$	1.11480	−	3.43099i	0.0585116	−	0.180080i
$364$	0.549314	+	0.610075i	0.0287919	+	0.0319766i
$365$	28.2658			1.47950
$366$	−3.76425	−	4.99808i	−0.196761	−	0.261254i
$367$	−16.6322			−0.868193			−0.434096	−	0.900866i	$-0.642932\pi$
$367$	−16.6322			−0.868193			−0.434096	+	0.900866i	$0.642932\pi$
$368$	0.161282	+	0.179122i	0.00840739	+	0.00933736i
$369$	2.50251	−	7.70192i	0.130275	−	0.400946i
$370$	−0.881999	+	8.39166i	−0.0458530	+	0.436262i
$371$	0.363441	−	0.161814i	0.0188689	−	0.00840098i
$372$	2.87252	−	1.27893i	0.148933	−	0.0663093i
$373$	13.4869	+	2.86673i	0.698326	+	0.148434i	0.543377	−	0.839489i	$-0.317145\pi$
$373$	13.4869	+	2.86673i	0.698326	+	0.148434i	0.154949	+	0.987922i	$0.450479\pi$
$374$	−6.04321	+	4.39065i	−0.312487	+	0.227035i
$375$	−7.87840	−	5.72400i	−0.406839	−	0.295586i
$376$	−3.32922	−	1.48227i	−0.171692	−	0.0764421i
$377$	5.15560			0.265527
$378$	1.71606	+	0.764040i	0.0882647	+	0.0392980i
$379$	−8.56877	+	14.8415i	−0.440148	+	0.762359i	−0.997700	−	0.0677833i	$-0.978407\pi$
$379$	−8.56877	+	14.8415i	−0.440148	+	0.762359i	0.557552	+	0.830142i	$0.311741\pi$
$380$	−7.34847	−	12.7279i	−0.376969	−	0.652929i
$381$	1.16485	+	11.0828i	0.0596769	+	0.567788i
$382$	−22.3685	−	4.75457i	−1.14447	−	0.243265i
$383$	−0.371653	+	3.53605i	−0.0189906	+	0.180683i	−0.999905	−	0.0137546i	$-0.995622\pi$
$383$	−0.371653	+	3.53605i	−0.0189906	+	0.180683i	0.980915	+	0.194438i	$0.0622883\pi$
$384$	−0.0837409	−	0.796742i	−0.00427339	−	0.0406585i
$385$	1.93272	−	0.410813i	0.0985006	−	0.0209370i
$386$	4.09122	+	12.5915i	0.208238	+	0.640890i
$387$	6.48746	−	11.2366i	0.329776	−	0.571189i
$388$	−7.48873	−	8.31708i	−0.380183	−	0.422236i
$389$	−17.2148	−	12.5073i	−0.872823	−	0.634143i	0.0585198	−	0.998286i	$-0.481362\pi$
$389$	−17.2148	−	12.5073i	−0.872823	−	0.634143i	−0.931343	+	0.364143i	$0.881362\pi$
$390$	−0.822703	−	2.53202i	−0.0416592	−	0.128214i
$391$	−0.472652	+	0.524934i	−0.0239031	+	0.0265470i
$392$	−6.65972	+	1.41557i	−0.336367	+	0.0714969i
$393$	5.67444	−	4.12272i	0.286238	−	0.207964i
$394$	7.03577	−	21.6539i	0.354457	−	1.09091i
$395$	9.36816	+	16.2261i	0.471363	+	0.816425i
$396$	−4.02201	+	4.46690i	−0.202114	+	0.224470i
$397$	−2.28182	+	2.53421i	−0.114521	+	0.127188i	−0.797679	−	0.603082i	$-0.793939\pi$
$397$	−2.28182	+	2.53421i	−0.114521	+	0.127188i	0.683158	+	0.730270i	$0.260606\pi$
$398$	0.257195	+	0.445475i	0.0128920	+	0.0223296i
$399$	0.898803	−	2.76623i	0.0449964	−	0.138485i
$400$	1.50635	−	1.09443i	0.0753177	−	0.0547215i
$401$	−29.3062	+	6.22922i	−1.46348	+	0.311073i	−0.869711	−	0.493562i	$-0.835695\pi$
$401$	−29.3062	+	6.22922i	−1.46348	+	0.311073i	−0.593771	+	0.804634i	$0.702361\pi$
$402$	−3.36846	+	3.74105i	−0.168003	+	0.186587i
$403$	2.27531	+	7.00267i	0.113341	+	0.348828i
$404$	10.1486	+	7.37341i	0.504913	+	0.366841i
$405$	4.30944	+	4.78611i	0.214138	+	0.237824i
$406$	0.601316	−	1.04151i	0.0298428	−	0.0516893i
$407$	−3.75180	−	11.5469i	−0.185970	−	0.572357i
$408$	2.29649	−	0.488134i	0.113693	−	0.0241662i
$409$	−2.35363	−	22.3933i	−0.116379	−	1.10728i	−0.884361	−	0.466803i	$-0.845406\pi$
$409$	−2.35363	−	22.3933i	−0.116379	−	1.10728i	0.767982	−	0.640472i	$-0.221261\pi$
$410$	−0.635884	+	6.05003i	−0.0314041	+	0.298790i
$411$	9.09421	+	1.93303i	0.448584	+	0.0953495i
$412$	−0.334029	−	3.17807i	−0.0164564	−	0.156572i
$413$	1.41656	+	2.45356i	0.0697046	+	0.120732i
$414$	−0.284199	+	0.492248i	−0.0139676	+	0.0241927i
$415$	−22.8775	−	10.1857i	−1.12301	−	0.499997i
$416$	1.87598			0.0919774
$417$	7.15830	+	3.18708i	0.350543	+	0.156072i
$418$	17.1084	+	12.4300i	0.836798	+	0.607969i
$419$	−5.13165	+	3.72836i	−0.250698	+	0.182142i	−0.706036	−	0.708176i	$-0.749518\pi$
$419$	−5.13165	+	3.72836i	−0.250698	+	0.182142i	0.455338	+	0.890318i	$0.349518\pi$
$420$	−0.607461	−	0.129120i	−0.0296411	−	0.00630041i
$421$	0.233180	−	0.103818i	0.0113645	−	0.00505980i	−0.401047	−	0.916058i	$-0.631353\pi$
$421$	0.233180	−	0.103818i	0.0113645	−	0.00505980i	0.412411	+	0.910998i	$0.364687\pi$
$422$	−21.0906	+	9.39012i	−1.02667	+	0.457104i
$423$	0.898310	−	8.54685i	0.0436773	−	0.415562i
$424$	0.280934	−	0.864626i	0.0136434	−	0.0419900i
$425$	3.65121	+	4.05508i	0.177110	+	0.196700i
$426$	6.48562			0.314229
$427$	−0.0587476	−	3.41729i	−0.00284299	−	0.165374i
$428$	8.37407			0.404776
$429$	2.56328	+	2.84681i	0.123756	+	0.137445i
$430$	−3.01188	+	9.26962i	−0.145246	+	0.447021i
$431$	1.99933	−	19.0223i	0.0963043	−	0.916274i	−0.834562	−	0.550914i	$-0.814279\pi$
$431$	1.99933	−	19.0223i	0.0963043	−	0.916274i	0.930866	−	0.365360i	$-0.119054\pi$
$432$	3.92149	−	1.74596i	0.188673	−	0.0840026i
$433$	−23.4274	+	10.4305i	−1.12585	+	0.501260i	−0.883266	−	0.468872i	$-0.844661\pi$
$433$	−23.4274	+	10.4305i	−1.12585	+	0.501260i	−0.242581	+	0.970131i	$0.577994\pi$
$434$	1.68002	+	0.357100i	0.0806437	+	0.0171414i
$435$	−3.15531	+	2.29247i	−0.151285	+	0.109915i
$436$	−9.25618	−	6.72501i	−0.443291	−	0.322070i
$437$	1.82685	+	0.813364i	0.0873899	+	0.0389085i
$438$	12.7831			0.610799
$439$	−4.49971	−	2.00340i	−0.214759	−	0.0956171i	0.296537	−	0.955021i	$-0.404168\pi$
$439$	−4.49971	−	2.00340i	−0.214759	−	0.0956171i	−0.511297	+	0.859404i	$0.670835\pi$
$440$	2.25763	−	3.91033i	0.107628	−	0.186418i
$441$	−8.02787	−	13.9047i	−0.382280	−	0.662128i
$442$	0.574671	+	5.46763i	0.0273343	+	0.260069i
$443$	0.568150	+	0.120764i	0.0269936	+	0.00573767i	0.221389	−	0.975186i	$-0.428941\pi$
$443$	0.568150	+	0.120764i	0.0269936	+	0.00573767i	−0.194395	+	0.980923i	$0.562274\pi$
$444$	−0.398880	+	3.79509i	−0.0189300	+	0.180107i
$445$	1.25954	+	11.9838i	0.0597081	+	0.568085i
$446$	3.49521	−	0.742929i	0.165503	−	0.0351787i
$447$	−4.74086	−	14.5909i	−0.224235	−	0.690124i
$448$	0.218802	−	0.378976i	0.0103374	−	0.0179050i
$449$	9.68709	+	10.7586i	0.457162	+	0.507730i	0.927020	−	0.375012i	$-0.122361\pi$
$449$	9.68709	+	10.7586i	0.457162	+	0.507730i	−0.469858	+	0.882742i	$0.655695\pi$
$450$	3.55227	+	2.58087i	0.167456	+	0.121664i
$451$	−2.70489	−	8.32480i	−0.127368	−	0.392000i
$452$	−1.01329	+	1.12538i	−0.0476613	+	0.0529332i
$453$	−18.1412	+	3.85602i	−0.852346	+	0.181172i
$454$	−12.3059	+	8.94079i	−0.577546	+	0.419612i
$455$	0.449388	−	1.38307i	0.0210676	−	0.0648395i
$456$	−3.32331	−	5.75614i	−0.155628	−	0.269556i
$457$	−17.9840	+	19.9733i	−0.841256	+	0.934310i	−0.998582	−	0.0532370i	$-0.983046\pi$
$457$	−17.9840	+	19.9733i	−0.841256	+	0.934310i	0.157326	+	0.987547i	$0.449713\pi$
$458$	−7.25608	+	8.05869i	−0.339054	+	0.376558i
$459$	6.28996	+	10.8945i	0.293590	+	0.508513i
$460$	0.131943	−	0.406079i	0.00615187	−	0.0189335i
$461$	9.63267	−	6.99854i	0.448638	−	0.325955i	−0.340420	−	0.940274i	$-0.610569\pi$
$461$	9.63267	−	6.99854i	0.448638	−	0.325955i	0.789058	+	0.614319i	$0.210569\pi$
$462$	0.874063	−	0.185788i	0.0406651	−	0.00864363i
$463$	−17.2984	+	19.2118i	−0.803923	+	0.892847i	−0.996075	−	0.0885182i	$-0.971787\pi$
$463$	−17.2984	+	19.2118i	−0.803923	+	0.892847i	0.192151	+	0.981365i	$0.438454\pi$
$464$	−0.849246	−	2.61371i	−0.0394253	−	0.121339i
$465$	−4.50630	−	3.27402i	−0.208974	−	0.151829i
$466$	−8.89699	−	9.88111i	−0.412145	−	0.457733i
$467$	−16.8916	+	29.2571i	−0.781650	+	1.35386i	0.149330	+	0.988787i	$0.452288\pi$
$467$	−16.8916	+	29.2571i	−0.781650	+	1.35386i	−0.930980	+	0.365070i	$0.881045\pi$
$468$	1.36707	+	4.20739i	0.0631926	+	0.194487i
$469$	−2.68969	+	0.571712i	−0.124199	+	0.0263992i
$470$	0.674803	+	6.42032i	0.0311263	+	0.296147i
$471$	−1.64397	+	15.6413i	−0.0757500	+	0.720713i
$472$	6.33270	+	1.34606i	0.291486	+	0.0619573i
$473$	−1.46593	−	13.9474i	−0.0674037	−	0.641304i
$474$	4.23670	+	7.33818i	0.194598	+	0.337054i
$475$	7.72390	−	13.3782i	0.354397	−	0.613834i
$476$	1.17157	+	0.521617i	0.0536988	+	0.0239083i
$477$	2.14388			0.0981616
$478$	−15.8260	−	7.04621i	−0.723866	−	0.322286i
$479$	−18.8712	−	13.7107i	−0.862247	−	0.626459i	0.0662483	−	0.997803i	$-0.478897\pi$
$479$	−18.8712	−	13.7107i	−0.862247	−	0.626459i	−0.928495	+	0.371344i	$0.878897\pi$
$480$	−1.14813	+	0.834164i	−0.0524046	+	0.0380742i
$481$	−8.74050	−	1.85785i	−0.398533	−	0.0847107i
$482$	−4.73444	+	2.10791i	−0.215648	+	0.0960127i
$483$	0.0771950	−	0.0343694i	0.00351250	−	0.00156386i
$484$	0.470700	−	4.47841i	0.0213955	−	0.203564i
$485$	−6.12646	+	18.8553i	−0.278188	+	0.856175i
$486$	10.5659	+	11.7346i	0.479277	+	0.532292i
$487$	−16.4580			−0.745785			−0.372892	−	0.927875i	$-0.621634\pi$
$487$	−16.4580			−0.745785			−0.372892	+	0.927875i	$0.621634\pi$
$488$	−5.89312	−	5.12554i	−0.266769	−	0.232022i
$489$	3.06379			0.138549
$490$	8.07034	+	8.96302i	0.364581	+	0.404908i
$491$	−11.4636	+	35.2813i	−0.517345	+	1.59222i	0.261629	+	0.965168i	$0.415740\pi$
$491$	−11.4636	+	35.2813i	−0.517345	+	1.59222i	−0.778974	+	0.627056i	$0.784260\pi$
$492$	−0.287575	+	2.73610i	−0.0129649	+	0.123353i
$493$	7.35763	−	3.27583i	0.331371	−	0.147536i
$494$	14.2186	−	6.33051i	0.639723	−	0.284823i
$495$	10.4152	+	2.21381i	0.468127	+	0.0995035i
$496$	3.17532	−	2.30700i	0.142576	−	0.103587i
$497$	2.86608	+	2.08233i	0.128561	+	0.0934051i
$498$	−10.3462	−	4.60644i	−0.463625	−	0.206419i
$499$	−24.5094			−1.09719			−0.548597	−	0.836087i	$-0.684838\pi$
$499$	−24.5094			−1.09719			−0.548597	+	0.836087i	$0.684838\pi$
$500$	−11.1047	−	4.94414i	−0.496618	−	0.221109i
$501$	−6.52691	+	11.3049i	−0.291601	+	0.505067i
$502$	−4.25687	−	7.37311i	−0.189993	−	0.329078i
$503$	1.66860	+	15.8757i	0.0743994	+	0.707863i	0.966611	+	0.256246i	$0.0824859\pi$
$503$	1.66860	+	15.8757i	0.0743994	+	0.707863i	−0.892212	+	0.451617i	$0.850847\pi$
$504$	1.00940	+	0.214555i	0.0449624	+	0.00955706i
$505$	2.32281	−	22.1001i	0.103364	−	0.983441i
$506$	0.0642189	+	0.611002i	0.00285488	+	0.0271623i
$507$	−7.42930	+	1.57915i	−0.329947	+	0.0701324i
$508$	4.29847	+	13.2293i	0.190714	+	0.586956i
$509$	19.2460	−	33.3350i	0.853063	−	1.47755i	−0.0253674	−	0.999678i	$-0.508076\pi$
$509$	19.2460	−	33.3350i	0.853063	−	1.47755i	0.878430	−	0.477870i	$-0.158591\pi$
$510$	−2.78292	−	3.09074i	−0.123230	−	0.136860i
$511$	5.64900	+	4.10424i	0.249897	+	0.181561i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	23.8303	−	26.4662i	1.05213	−	1.16851i
$514$	24.2984	−	5.16478i	1.07176	−	0.227809i
$515$	−4.57970	+	3.32734i	−0.201806	+	0.146620i
$516$	−1.36211	+	4.19214i	−0.0599635	+	0.184549i
$517$	−4.64448	−	8.04447i	−0.204264	−	0.353795i
$518$	−1.39475	+	1.54903i	−0.0612818	+	0.0680604i
$519$	8.56763	−	9.51532i	0.376077	−	0.417676i
$520$	−1.66160	−	2.87798i	−0.0728662	−	0.126208i
$521$	−3.91569	+	12.0512i	−0.171549	+	0.527975i	−0.999459	−	0.0328867i	$-0.989530\pi$
$521$	−3.91569	+	12.0512i	−0.171549	+	0.527975i	0.827910	+	0.560861i	$0.189530\pi$
$522$	5.24310	−	3.80933i	0.229484	−	0.166730i
$523$	−6.62018	+	1.40716i	−0.289480	+	0.0615309i	−0.350363	−	0.936614i	$-0.613942\pi$
$523$	−6.62018	+	1.40716i	−0.289480	+	0.0615309i	0.0608828	+	0.998145i	$0.480608\pi$
$524$	5.85832	−	6.50632i	0.255922	−	0.284230i
$525$	−0.201714	−	0.620812i	−0.00880353	−	0.0270945i
$526$	8.30103	+	6.03105i	0.361942	+	0.262966i
$527$	7.69656	+	8.54790i	0.335268	+	0.372352i
$528$	1.02100	−	1.76843i	0.0444334	−	0.0769610i
$529$	−7.08944	−	21.8190i	−0.308236	−	0.948654i
$530$	−1.57527	+	0.334835i	−0.0684255	+	0.0145443i
$531$	1.59587	+	15.1837i	0.0692550	+	0.658917i
$532$	0.379502	−	3.61072i	0.0164535	−	0.156544i
$533$	−6.30153	−	1.33943i	−0.272950	−	0.0580172i
$534$	0.569622	+	5.41959i	0.0246500	+	0.234529i
$535$	−7.41713	−	12.8468i	−0.320671	−	0.555418i
$536$	−3.14186	+	5.44186i	−0.135708	+	0.235053i
$537$	4.16914	+	1.85622i	0.179912	+	0.0801019i
$538$	−3.60159			−0.155276
$539$	−15.8539	−	7.05860i	−0.682875	−	0.304035i
$540$	−6.15189	−	4.46961i	−0.264735	−	0.192341i
$541$	22.5401	−	16.3764i	0.969076	−	0.704075i	0.0138353	−	0.999904i	$-0.495596\pi$
$541$	22.5401	−	16.3764i	0.969076	−	0.704075i	0.955241	+	0.295829i	$0.0955959\pi$
$542$	4.80783	+	1.02194i	0.206514	+	0.0438959i
$543$	−18.2286	+	8.11589i	−0.782264	+	0.348286i
$544$	2.67724	−	1.19198i	0.114786	−	0.0511058i
$545$	−2.11855	+	20.1566i	−0.0907486	+	0.863416i
$546$	0.203233	−	0.625488i	0.00869759	−	0.0267684i
$547$	−18.7103	−	20.7799i	−0.799995	−	0.888484i	0.195748	−	0.980654i	$-0.437286\pi$
$547$	−18.7103	−	20.7799i	−0.799995	−	0.888484i	−0.995743	+	0.0921697i	$0.970620\pi$
$548$	11.6053			0.495755
$549$	7.20098	−	16.9520i	0.307330	−	0.723494i
$550$	4.74595			0.202368
$551$	−15.2567	−	16.9442i	−0.649956	−	0.721849i
$552$	0.0596705	−	0.183647i	0.00253975	−	0.00781654i
$553$	−0.483805	+	4.60310i	−0.0205735	+	0.195744i
$554$	15.4518	−	6.87957i	0.656483	−	0.292285i
$555$	6.17543	−	2.74948i	0.262132	−	0.116709i
$556$	9.56711	+	2.03355i	0.405736	+	0.0862418i
$557$	29.6649	−	21.5528i	1.25694	−	0.913221i	0.258337	−	0.966055i	$-0.416826\pi$
$557$	29.6649	−	21.5528i	1.25694	−	0.913221i	0.998603	+	0.0528343i	$0.0168255\pi$
$558$	7.48800	+	5.44035i	0.316992	+	0.230308i
$559$	−9.42941	−	4.19824i	−0.398821	−	0.177567i
$560$	−0.775195			−0.0327580
$561$	5.46693	+	2.43403i	0.230814	+	0.102765i
$562$	2.35588	−	4.08050i	0.0993766	−	0.172125i
$563$	19.7773	+	34.2553i	0.833515	+	1.44369i	0.895234	+	0.445597i	$0.147009\pi$
$563$	19.7773	+	34.2553i	0.833515	+	1.44369i	−0.0617184	+	0.998094i	$0.519658\pi$
$564$	0.305176	+	2.90356i	0.0128502	+	0.122262i
$565$	2.62397	+	0.557741i	0.110391	+	0.0234643i
$566$	−0.919776	+	8.75108i	−0.0386611	+	0.367835i
$567$	0.166302	+	1.58225i	0.00698401	+	0.0664484i
$568$	7.91868	−	1.68317i	0.332260	−	0.0706241i
$569$	−4.66681	−	14.3630i	−0.195643	−	0.602126i	−0.999968	−	0.00793774i	$-0.997473\pi$
$569$	−4.66681	−	14.3630i	−0.195643	−	0.602126i	0.804326	−	0.594189i	$-0.202527\pi$
$570$	−5.88708	+	10.1967i	−0.246583	+	0.427094i
$571$	−5.45267	−	6.05580i	−0.228187	−	0.253428i	0.618169	−	0.786046i	$-0.287875\pi$
$571$	−5.45267	−	6.05580i	−0.228187	−	0.253428i	−0.846356	+	0.532618i	$0.821208\pi$
$572$	3.86847	+	2.81061i	0.161749	+	0.117517i
$573$	5.66132	+	17.4238i	0.236505	+	0.727888i
$574$	−1.00556	+	1.11678i	−0.0419711	+	0.0466136i
$575$	0.438983	−	0.0933088i	0.0183069	−	0.00389125i
$576$	1.90782	−	1.38611i	0.0794923	−	0.0577546i
$577$	12.7318	−	39.1844i	0.530031	−	1.63127i	−0.224117	−	0.974562i	$-0.571950\pi$
$577$	12.7318	−	39.1844i	0.530031	−	1.63127i	0.754148	−	0.656705i	$-0.228050\pi$
$578$	−4.20579	−	7.28464i	−0.174938	−	0.303001i
$579$	7.09716	−	7.88220i	0.294948	−	0.327573i
$580$	−3.25756	+	3.61788i	−0.135263	+	0.150224i
$581$	−3.09314	−	5.35748i	−0.128325	−	0.222266i
$582$	−2.77066	+	8.52721i	−0.114847	+	0.353464i
$583$	1.87471	−	1.36205i	0.0776424	−	0.0564105i
$584$	15.6076	−	3.31750i	0.645848	−	0.137279i
$585$	5.24381	−	5.82385i	0.216805	−	0.240786i
$586$	9.60098	+	29.5488i	0.396613	+	1.22065i
$587$	5.45328	+	3.96204i	0.225081	+	0.163531i	0.694611	−	0.719386i	$-0.255577\pi$
$587$	5.45328	+	3.96204i	0.225081	+	0.163531i	−0.469530	+	0.882917i	$0.655577\pi$
$588$	3.64977	+	4.05348i	0.150514	+	0.167163i
$589$	16.2816	−	28.2005i	0.670871	−	1.16198i
$590$	−3.54402	−	10.9074i	−0.145905	−	0.449050i
$591$	−17.8417	+	3.79237i	−0.733910	+	0.155997i
$592$	0.497896	+	4.73716i	0.0204634	+	0.194696i
$593$	−3.96330	+	37.7082i	−0.162753	+	1.54849i	0.542817	+	0.839851i	$0.317358\pi$
$593$	−3.96330	+	37.7082i	−0.162753	+	1.54849i	−0.705570	+	0.708641i	$0.749309\pi$
$594$	10.7024	+	2.27486i	0.439123	+	0.0933385i
$595$	−0.237466	−	2.25934i	−0.00973518	−	0.0926240i
$596$	−9.57506	−	16.5845i	−0.392210	−	0.679327i
$597$	0.206047	−	0.356883i	0.00843293	−	0.0146063i
$598$	0.413078	+	0.183914i	0.0168920	+	0.00752082i
$599$	36.7292			1.50072			0.750358	−	0.661032i	$-0.229881\pi$
$599$	36.7292			1.50072			0.750358	+	0.661032i	$0.229881\pi$
$600$	−1.36271	−	0.606716i	−0.0556323	−	0.0247691i
$601$	−11.8591	−	8.61618i	−0.483745	−	0.351461i	0.319029	−	0.947745i	$-0.396643\pi$
$601$	−11.8591	−	8.61618i	−0.483745	−	0.351461i	−0.802774	+	0.596284i	$0.796643\pi$
$602$	−1.94789	+	1.41523i	−0.0793903	+	0.0576804i
$603$	−14.4944	−	3.08088i	−0.590257	−	0.125463i
$604$	−21.1489	+	9.41610i	−0.860536	+	0.383136i
$605$	−7.28735	+	3.24454i	−0.296273	+	0.131909i
$606$	1.05048	−	9.99465i	0.0426728	−	0.406005i
$607$	0.861947	−	2.65280i	0.0349854	−	0.107674i	−0.932039	−	0.362358i	$-0.881972\pi$
$607$	0.861947	−	2.65280i	0.0349854	−	0.107674i	0.967024	+	0.254685i	$0.0819716\pi$
$608$	−5.55147	−	6.16554i	−0.225142	−	0.250046i
$609$	−0.963465			−0.0390416
$610$	−2.64352	+	13.5806i	−0.107033	+	0.549862i
$611$	−6.83661			−0.276580
$612$	4.62430	+	5.13581i	0.186926	+	0.207603i
$613$	−2.03413	+	6.26039i	−0.0821575	+	0.252855i	−0.983695	−	0.179847i	$-0.942440\pi$
$613$	−2.03413	+	6.26039i	−0.0821575	+	0.252855i	0.901537	+	0.432702i	$0.142440\pi$
$614$	0.641633	−	6.10473i	0.0258942	−	0.246367i
$615$	4.45222	−	1.98226i	0.179531	−	0.0799323i
$616$	1.01898	−	0.453679i	0.0410559	−	0.0182792i
$617$	14.7566	+	3.13661i	0.594078	+	0.126275i	0.495132	−	0.868818i	$-0.335120\pi$
$617$	14.7566	+	3.13661i	0.594078	+	0.126275i	0.0989456	+	0.995093i	$0.468453\pi$
$618$	−2.07114	+	1.50477i	−0.0833136	+	0.0605309i
$619$	37.2997	+	27.0998i	1.49920	+	1.08923i	0.970697	+	0.240305i	$0.0772475\pi$
$619$	37.2997	+	27.0998i	1.49920	+	1.08923i	0.528506	+	0.848930i	$0.322752\pi$
$620$	−6.35169	−	2.82795i	−0.255090	−	0.113573i
$621$	1.03466			0.0415193
$622$	−13.0621	−	5.81560i	−0.523741	−	0.233184i
$623$	−1.48834	+	2.57787i	−0.0596289	+	0.103280i
$624$	−0.751452	−	1.30155i	−0.0300821	−	0.0521038i
$625$	1.27769	+	12.1564i	0.0511075	+	0.486255i
$626$	−7.97584	−	1.69532i	−0.318779	−	0.0677585i
$627$	1.77088	−	16.8488i	0.0707221	−	0.672876i
$628$	2.05206	+	19.5240i	0.0818860	+	0.779094i
$629$	−13.6542	+	2.90228i	−0.544427	+	0.115722i
$630$	−0.564901	−	1.73859i	−0.0225062	−	0.0692670i
$631$	−10.4056	+	18.0230i	−0.414239	+	0.717483i	−0.995348	−	0.0963426i	$-0.969286\pi$
$631$	−10.4056	+	18.0230i	−0.414239	+	0.717483i	0.581109	+	0.813826i	$0.302619\pi$
$632$	7.07727	+	7.86010i	0.281519	+	0.312658i
$633$	14.9630	+	10.8713i	0.594726	+	0.432094i
$634$	−4.74206	−	14.5946i	−0.188331	−	0.579624i
$635$	16.4881	−	18.3119i	0.654312	−	0.726687i
$636$	−0.712409	+	0.151427i	−0.0282489	+	0.00600448i
$637$	−10.3333	+	7.50755i	−0.409419	+	0.297460i
$638$	2.16465	−	6.66210i	0.0856993	−	0.263755i
$639$	9.54547	+	16.5332i	0.377613	+	0.654045i
$640$	−1.18533	+	1.31645i	−0.0468544	+	0.0520371i
$641$	−14.6838	+	16.3080i	−0.579975	+	0.644127i	−0.959718	−	0.280965i	$-0.909346\pi$
$641$	−14.6838	+	16.3080i	−0.579975	+	0.644127i	0.379743	+	0.925092i	$0.376012\pi$
$642$	−3.35436	−	5.80992i	−0.132386	−	0.229299i
$643$	5.03823	−	15.5061i	0.198688	−	0.611500i	−0.801225	−	0.598363i	$-0.795818\pi$
$643$	5.03823	−	15.5061i	0.198688	−	0.611500i	0.999914	−	0.0131374i	$-0.00418187\pi$
$644$	0.0853323	−	0.0619976i	0.00336257	−	0.00244305i
$645$	7.63771	−	1.62345i	0.300735	−	0.0639231i
$646$	16.2692	−	18.0687i	0.640101	−	0.710905i
$647$	−1.74467	−	5.36955i	−0.0685901	−	0.211099i	0.910886	−	0.412657i	$-0.135399\pi$
$647$	−1.74467	−	5.36955i	−0.0685901	−	0.211099i	−0.979476	+	0.201559i	$0.935399\pi$
$648$	2.94129	+	2.13697i	0.115545	+	0.0839482i
$649$	11.0420	+	12.2634i	0.433438	+	0.481382i
$650$	1.74650	−	3.02502i	0.0685032	−	0.118651i
$651$	−0.425203	−	1.30864i	−0.0166650	−	0.0512897i
$652$	3.74076	−	0.795124i	0.146500	−	0.0311395i
$653$	1.45471	+	13.8407i	0.0569273	+	0.541627i	0.985403	+	0.170235i	$0.0544527\pi$
$653$	1.45471	+	13.8407i	0.0569273	+	0.541627i	−0.928476	+	0.371392i	$0.878881\pi$
$654$	−0.958102	+	9.11574i	−0.0374648	+	0.356453i
$655$	−15.1704	−	3.22456i	−0.592755	−	0.125994i
$656$	0.358962	+	3.41529i	0.0140151	+	0.133345i
$657$	18.8140	+	32.5868i	0.734004	+	1.27133i
$658$	−0.797379	+	1.38110i	−0.0310851	+	0.0538409i
$659$	29.8569	+	13.2932i	1.16306	+	0.517828i	0.895215	−	0.445634i	$-0.147022\pi$
$659$	29.8569	+	13.2932i	1.16306	+	0.517828i	0.267846	+	0.963462i	$0.413688\pi$
$660$	−3.61732			−0.140804
$661$	−4.63652	−	2.06431i	−0.180340	−	0.0802924i	0.314581	−	0.949231i	$-0.398136\pi$
$661$	−4.63652	−	2.06431i	−0.180340	−	0.0802924i	−0.494920	+	0.868938i	$0.664803\pi$
$662$	10.4796	+	7.61390i	0.407303	+	0.295923i
$663$	3.56324	−	2.58885i	0.138385	−	0.100542i
$664$	−13.8278	−	2.93919i	−0.536623	−	0.114063i
$665$	−5.87542	+	2.61590i	−0.227839	+	0.101440i
$666$	−10.2616	+	4.56874i	−0.397627	+	0.177035i
$667$	0.0692405	−	0.658780i	0.00268100	−	0.0255080i
$668$	−5.03520	+	15.4968i	−0.194818	+	0.599588i
$669$	−1.91550	−	2.12738i	−0.0740576	−	0.0822493i
$670$	11.1313			0.430040
$671$	−4.47312	−	19.3985i	−0.172683	−	0.748872i
$672$	−0.350578			−0.0135238
$673$	−26.1237	−	29.0134i	−1.00700	−	1.11838i	−0.992956	−	0.118481i	$-0.962197\pi$
$673$	−26.1237	−	29.0134i	−1.00700	−	1.11838i	−0.0140400	−	0.999901i	$-0.504469\pi$
$674$	7.15101	−	22.0085i	0.275446	−	0.847737i
$675$	0.835459	−	7.94886i	0.0321568	−	0.305952i
$676$	−8.66105	+	3.85615i	−0.333117	+	0.148313i
$677$	−17.0797	+	7.60438i	−0.656427	+	0.292260i	−0.707793	−	0.706420i	$-0.750309\pi$
$677$	−17.0797	+	7.60438i	−0.656427	+	0.292260i	0.0513661	+	0.998680i	$0.483642\pi$
$678$	1.18667	+	0.252235i	0.0455740	+	0.00968705i
$679$	−3.96220	+	2.87871i	−0.152055	+	0.110475i
$680$	−4.19995	−	3.05144i	−0.161061	−	0.117017i
$681$	11.1324	+	4.95648i	0.426596	+	0.189933i
$682$	10.0042			0.383081
$683$	8.62877	+	3.84178i	0.330171	+	0.147002i	0.565126	−	0.825005i	$-0.308828\pi$
$683$	8.62877	+	3.84178i	0.330171	+	0.147002i	−0.234955	+	0.972006i	$0.575494\pi$
$684$	9.78242	−	16.9437i	0.374040	−	0.647857i
$685$	−10.2791	−	17.8040i	−0.392746	−	0.680256i
$686$	0.631630	+	6.00956i	0.0241157	+	0.229446i
$687$	8.49765	+	1.80623i	0.324205	+	0.0689120i
$688$	−0.575123	+	5.47193i	−0.0219264	+	0.208615i
$689$	−0.178273	−	1.69615i	−0.00679164	−	0.0646182i
$690$	−0.334589	+	0.0711191i	−0.0127376	+	0.00270746i
$691$	2.63707	+	8.11607i	0.100319	+	0.308750i	0.988603	−	0.150544i	$-0.0481025\pi$
$691$	2.63707	+	8.11607i	0.100319	+	0.308750i	−0.888284	+	0.459294i	$0.848103\pi$
$692$	7.99129	−	13.8413i	0.303783	−	0.526168i
$693$	1.76005	+	1.95473i	0.0668588	+	0.0742542i
$694$	−30.0426	−	21.8272i	−1.14040	−	0.828550i
$695$	−5.35412	−	16.4783i	−0.203093	−	0.625057i
$696$	−1.47321	+	1.63617i	−0.0558420	+	0.0620188i
$697$	−9.84407	+	2.09242i	−0.372871	+	0.0792561i
$698$	−10.6831	+	7.76171i	−0.404361	+	0.293785i
$699$	−3.29168	+	10.1307i	−0.124503	+	0.383180i
$700$	−0.407400	−	0.705637i	−0.0153983	−	0.0266706i
$701$	9.70998	−	10.7840i	0.366741	−	0.407307i	−0.531325	−	0.847168i	$-0.678306\pi$
$701$	9.70998	−	10.7840i	0.366741	−	0.407307i	0.898066	+	0.439861i	$0.144972\pi$
$702$	5.38840	−	5.98443i	0.203372	−	0.225868i
$703$	19.7593	+	34.2241i	0.745236	+	1.29079i
$704$	0.787655	−	2.42415i	0.0296859	−	0.0913637i
$705$	4.18411	−	3.03994i	0.157583	−	0.114491i
$706$	1.08423	−	0.230461i	0.0408056	−	0.00867350i
$707$	3.67318	−	4.07948i	0.138144	−	0.153425i
$708$	−1.60277	−	4.93281i	−0.0602356	−	0.185386i
$709$	0.537236	+	0.390325i	0.0201763	+	0.0146590i	0.597828	−	0.801625i	$-0.296031\pi$
$709$	0.537236	+	0.390325i	0.0201763	+	0.0146590i	−0.577651	+	0.816284i	$0.696031\pi$
$710$	−9.59597	−	10.6574i	−0.360130	−	0.399965i
$711$	−12.4711	+	21.6005i	−0.467701	+	0.810083i
$712$	2.10199	+	6.46927i	0.0787756	+	0.242446i
$713$	0.925355	−	0.196690i	0.0346548	−	0.00736611i
$714$	−0.107393	−	1.02178i	−0.00401908	−	0.0382390i
$715$	0.885413	−	8.42414i	0.0331126	−	0.315045i
$716$	5.57209	+	1.18438i	0.208239	+	0.0442625i
$717$	1.45071	+	13.8026i	0.0541777	+	0.515466i
$718$	−15.8411	−	27.4375i	−0.591183	−	1.02396i
$719$	6.10767	−	10.5788i	0.227778	−	0.394522i	−0.729372	−	0.684118i	$-0.760187\pi$
$719$	6.10767	−	10.5788i	0.227778	−	0.394522i	0.957149	+	0.289595i	$0.0935208\pi$
$720$	−3.81627	−	1.69911i	−0.142224	−	0.0633221i
$721$	−1.39840			−0.0520791
$722$	−45.5245	−	20.2688i	−1.69425	−	0.754326i
$723$	3.35892	+	2.44040i	0.124920	+	0.0907594i
$724$	−20.1501	+	14.6399i	−0.748873	+	0.544088i
$725$	−5.00524	−	1.06390i	−0.185890	−	0.0395121i
$726$	−3.29566	+	1.46732i	−0.122314	+	0.0544575i
$727$	−8.66544	+	3.85810i	−0.321384	+	0.143089i	−0.561087	−	0.827757i	$-0.689617\pi$
$727$	−8.66544	+	3.85810i	−0.321384	+	0.143089i	0.239703	+	0.970846i	$0.422950\pi$
$728$	0.0858112	−	0.816439i	0.00318038	−	0.0302593i
$729$	0.538710	−	1.65798i	0.0199522	−	0.0614066i
$730$	−18.9135	−	21.0056i	−0.700022	−	0.777453i
$731$	−16.1244			−0.596381
$732$	−1.19552	+	6.14175i	−0.0441876	+	0.227006i
$733$	−2.49577			−0.0921833			−0.0460917	−	0.998937i	$-0.514677\pi$
$733$	−2.49577			−0.0921833			−0.0460917	+	0.998937i	$0.514677\pi$
$734$	11.1291	+	12.3601i	0.410783	+	0.456220i
$735$	2.98584	−	9.18947i	0.110134	−	0.338959i
$736$	0.0251947	−	0.239711i	0.000928688	−	0.00883588i
$737$	−14.6319	+	6.51454i	−0.538973	+	0.239966i
$738$	−7.39814	+	3.29387i	−0.272329	+	0.121249i
$739$	−13.4744	−	2.86406i	−0.495662	−	0.105356i	−0.0467035	−	0.998909i	$-0.514872\pi$
$739$	−13.4744	−	2.86406i	−0.495662	−	0.105356i	−0.448959	+	0.893553i	$0.648205\pi$
$740$	6.82639	−	4.95966i	0.250943	−	0.182321i
$741$	−10.0876	−	7.32904i	−0.370576	−	0.269239i
$742$	−0.363441	−	0.161814i	−0.0133423	−	0.00594039i
$743$	−47.1781			−1.73080			−0.865398	−	0.501084i	$-0.832935\pi$
$743$	−47.1781			−1.73080			−0.865398	+	0.501084i	$0.832935\pi$
$744$	−2.87252	−	1.27893i	−0.105312	−	0.0468877i
$745$	−16.9618	+	29.3786i	−0.621431	+	1.07635i
$746$	−6.89411	−	11.9409i	−0.252411	−	0.437189i
$747$	−3.48467	−	33.1544i	−0.127497	−	1.21306i
$748$	7.30659	+	1.55306i	0.267155	+	0.0567856i
$749$	0.383047	−	3.64445i	0.0139962	−	0.133165i
$750$	1.01792	+	9.68490i	0.0371693	+	0.353642i
$751$	52.9761	−	11.2604i	1.93313	−	0.410899i	0.934659	−	0.355544i	$-0.115704\pi$
$751$	52.9761	−	11.2604i	1.93313	−	0.410899i	0.998467	−	0.0553543i	$-0.0176288\pi$
$752$	1.12615	+	3.46593i	0.0410664	+	0.126389i
$753$	−3.41030	+	5.90682i	−0.124278	+	0.215257i
$754$	−3.44977	−	3.83136i	−0.125633	−	0.139530i
$755$	33.1776	+	24.1049i	1.20746	+	0.877268i
$756$	−0.580477	−	1.78653i	−0.0211118	−	0.0649753i
$757$	−28.9960	+	32.2033i	−1.05388	+	1.17045i	−0.0689252	+	0.997622i	$0.521957\pi$
$757$	−28.9960	+	32.2033i	−1.05388	+	1.17045i	−0.984952	+	0.172827i	$0.944710\pi$
$758$	16.7630	−	3.56309i	0.608861	−	0.129417i
$759$	0.398189	−	0.289301i	0.0144533	−	0.0105010i
$760$	−4.54161	+	13.9776i	−0.164741	+	0.507022i
$761$	−10.9880	−	19.0318i	−0.398315	−	0.689901i	0.595204	−	0.803575i	$-0.297071\pi$
$761$	−10.9880	−	19.0318i	−0.398315	−	0.689901i	−0.993518	+	0.113674i	$0.963738\pi$
$762$	7.45668	−	8.28148i	0.270127	−	0.300006i
$763$	−3.35017	+	3.72074i	−0.121284	+	0.134700i
$764$	11.4341	+	19.8045i	0.413672	+	0.716500i
$765$	3.78310	−	11.6432i	0.136778	−	0.420960i
$766$	2.87648	−	2.08988i	0.103931	−	0.0755106i
$767$	11.8800	−	2.52518i	0.428963	−	0.0911788i
$768$	−0.536061	+	0.595356i	−0.0193434	+	0.0214831i
$769$	5.22958	+	16.0950i	0.188583	+	0.580400i	0.999992	−	0.00407974i	$-0.00129862\pi$
$769$	5.22958	+	16.0950i	0.188583	+	0.580400i	−0.811408	+	0.584480i	$0.801299\pi$
$770$	−1.59854	−	1.16140i	−0.0576073	−	0.0418541i
$771$	−13.3164	−	14.7894i	−0.479579	−	0.532626i
$772$	6.61974	−	11.4657i	0.238250	−	0.412660i
$773$	−4.44349	−	13.6757i	−0.159821	−	0.491879i	0.838796	−	0.544446i	$-0.183260\pi$
$773$	−4.44349	−	13.6757i	−0.159821	−	0.491879i	−0.998617	+	0.0525663i	$0.983260\pi$
$774$	−12.6914	+	2.69764i	−0.456183	+	0.0969647i
$775$	−0.763894	−	7.26797i	−0.0274399	−	0.261073i
$776$	−1.16985	+	11.1304i	−0.0419953	+	0.399559i
$777$	1.63340	+	0.347190i	0.0585980	+	0.0124554i
$778$	2.22422	+	21.1621i	0.0797422	+	0.758696i
$779$	14.2456	+	24.6741i	0.510402	+	0.884043i
$780$	−1.33116	+	2.30564i	−0.0476632	+	0.0825551i
$781$	18.8509	+	8.39296i	0.674538	+	0.300324i
$782$	0.706368			0.0252597
$783$	−10.7771	−	4.79828i	−0.385143	−	0.171477i
$784$	5.50819	+	4.00194i	0.196721	+	0.142926i
$785$	28.1347	−	20.4411i	1.00417	−	0.729573i
$786$	−6.86072	−	1.45829i	−0.244714	−	0.0520155i
$787$	−16.4325	+	7.31624i	−0.585757	+	0.260796i	−0.678146	−	0.734927i	$-0.737216\pi$
$787$	−16.4325	+	7.31624i	−0.585757	+	0.260796i	0.0923890	+	0.995723i	$0.470550\pi$
$788$	−20.7998	+	9.26067i	−0.740962	+	0.329898i
$789$	0.859235	−	8.17507i	0.0305896	−	0.291040i
$790$	5.78984	−	17.8193i	0.205993	−	0.633982i
$791$	0.443421	+	0.492469i	0.0157663	+	0.0175102i
$792$	6.01080			0.213585
$793$	−14.0105	−	4.28749i	−0.497528	−	0.152253i
$794$	3.41012			0.121021
$795$	0.863308	+	0.958800i	0.0306184	+	0.0340051i
$796$	0.158955	−	0.489214i	0.00563402	−	0.0173397i
$797$	2.27040	−	21.6014i	0.0804218	−	0.765162i	−0.877779	−	0.479066i	$-0.840976\pi$
$797$	2.27040	−	21.6014i	0.0804218	−	0.765162i	0.958201	−	0.286096i	$-0.0923578\pi$
$798$	−2.65713	+	1.18303i	−0.0940613	+	0.0418788i
$799$	−9.75663	+	4.34393i	−0.345165	+	0.153677i
$800$	−1.82127	−	0.387122i	−0.0643915	−	0.0136868i
$801$	−12.9773	+	9.42859i	−0.458532	+	0.333143i
$802$	24.2389	+	17.6106i	0.855905	+	0.621851i
$803$	37.1549	+	16.5424i	1.31117	+	0.583770i
$804$	5.03408			0.177538
$805$	−0.170693	−	0.0759974i	−0.00601614	−	0.00267856i
$806$	3.68152	−	6.37658i	0.129676	−	0.224606i
$807$	1.44267	+	2.49878i	0.0507844	+	0.0879612i
$808$	−1.31125	−	12.4757i	−0.0461295	−	0.438893i
$809$	−16.1311	−	3.42877i	−0.567139	−	0.120549i	−0.0845866	−	0.996416i	$-0.526957\pi$
$809$	−16.1311	−	3.42877i	−0.567139	−	0.120549i	−0.482553	+	0.875867i	$0.660290\pi$
$810$	0.673200	−	6.40507i	0.0236538	−	0.225051i
$811$	0.343330	+	3.26657i	0.0120560	+	0.114705i	0.998895	−	0.0470021i	$-0.0149667\pi$
$811$	0.343330	+	3.26657i	0.0120560	+	0.114705i	−0.986839	+	0.161707i	$0.948300\pi$
$812$	−1.17635	+	0.250041i	−0.0412819	+	0.00877473i
$813$	−1.21683	−	3.74502i	−0.0426762	−	0.131344i
$814$	−6.07055	+	10.5145i	−0.212773	+	0.368533i
$815$	−4.53311	−	5.03453i	−0.158788	−	0.176352i
$816$	−1.89940	−	1.38000i	−0.0664924	−	0.0483096i
$817$	14.1061	+	43.4140i	0.493509	+	1.51886i
$818$	−15.0665	+	16.7331i	−0.526789	+	0.585059i
$819$	1.89362	−	0.402501i	0.0661684	−	0.0140645i
$820$	4.92154	−	3.57571i	0.171868	−	0.124869i
$821$	−12.0643	+	37.1302i	−0.421048	+	1.29585i	0.485680	+	0.874137i	$0.338572\pi$
$821$	−12.0643	+	37.1302i	−0.421048	+	1.29585i	−0.906728	+	0.421716i	$0.861428\pi$
$822$	−4.64869	−	8.05177i	−0.162142	−	0.280838i
$823$	24.7273	−	27.4624i	0.861938	−	0.957279i	−0.137510	−	0.990500i	$-0.543910\pi$
$823$	24.7273	−	27.4624i	0.861938	−	0.957279i	0.999448	+	0.0332209i	$0.0105765\pi$
$824$	−2.13826	+	2.37478i	−0.0744898	+	0.0827293i
$825$	−1.90106	−	3.29274i	−0.0661865	−	0.114638i
$826$	0.875485	−	2.69447i	0.0304620	−	0.0937525i
$827$	−0.0324040	+	0.0235429i	−0.00112680	+	0.000818666i	−0.588349	−	0.808607i	$-0.700222\pi$
$827$	−0.0324040	+	0.0235429i	−0.00112680	+	0.000818666i	0.587222	+	0.809426i	$0.300222\pi$
$828$	0.555978	−	0.118177i	0.0193216	−	0.00410693i
$829$	−23.6420	+	26.2571i	−0.821121	+	0.911947i	−0.997376	−	0.0723976i	$-0.976935\pi$
$829$	−23.6420	+	26.2571i	−0.821121	+	0.911947i	0.176255	+	0.984345i	$0.443602\pi$
$830$	7.73856	+	23.8169i	0.268610	+	0.826695i
$831$	−10.9625	−	7.96471i	−0.380284	−	0.276293i
$832$	−1.25528	−	1.39412i	−0.0435188	−	0.0483326i
$833$	−9.97650	+	17.2798i	−0.345665	+	0.598710i
$834$	−2.42137	−	7.45222i	−0.0838453	−	0.258049i
$835$	28.2337	−	6.00127i	0.977069	−	0.207682i
$836$	−2.21048	−	21.0313i	−0.0764509	−	0.727382i
$837$	1.76110	−	16.7558i	0.0608727	−	0.579165i
$838$	6.20446	+	1.31880i	0.214329	+	0.0455571i
$839$	−2.48380	−	23.6318i	−0.0857504	−	0.815860i	−0.949885	−	0.312600i	$-0.898800\pi$
$839$	−2.48380	−	23.6318i	−0.0857504	−	0.815860i	0.864135	−	0.503261i	$-0.167866\pi$
$840$	0.310516	+	0.537830i	0.0107138	+	0.0185569i
$841$	10.7236	−	18.5739i	0.369781	−	0.640479i
$842$	−0.233180	−	0.103818i	−0.00803592	−	0.00357782i
$843$	−3.77473			−0.130008
$844$	21.0906	+	9.39012i	0.725967	+	0.323221i
$845$	13.5871	+	9.87163i	0.467411	+	0.339594i
$846$	−6.95264	+	5.05139i	−0.239037	+	0.173670i
$847$	−1.92751	−	0.409704i	−0.0662299	−	0.0140776i
$848$	−0.830524	+	0.369773i	−0.0285203	+	0.0126981i
$849$	6.43992	−	2.86724i	0.221018	−	0.0984034i
$850$	0.570375	−	5.42676i	0.0195637	−	0.186136i
$851$	−0.354781	+	1.09190i	−0.0121618	+	0.0374300i
$852$	−4.33973	−	4.81975i	−0.148677	−	0.165122i
$853$	11.7167			0.401171			0.200586	−	0.979676i	$-0.435715\pi$
$853$	11.7167			0.401171			0.200586	+	0.979676i	$0.435715\pi$
$854$	−2.50023	+	2.33027i	−0.0855563	+	0.0797403i
$855$	−34.6582			−1.18529
$856$	−5.60334	−	6.22314i	−0.191518	−	0.212703i
$857$	10.5964	−	32.6123i	0.361965	−	1.11401i	−0.589894	−	0.807480i	$-0.700831\pi$
$857$	10.5964	−	32.6123i	0.361965	−	1.11401i	0.951860	−	0.306534i	$-0.0991694\pi$
$858$	0.400423	−	3.80977i	0.0136702	−	0.130064i
$859$	−5.18791	+	2.30981i	−0.177009	+	0.0788096i	−0.493328	−	0.869843i	$-0.664220\pi$
$859$	−5.18791	+	2.30981i	−0.177009	+	0.0788096i	0.316319	+	0.948653i	$0.397553\pi$
$860$	8.90401	−	3.96432i	0.303624	−	0.135182i
$861$	1.17761	+	0.250310i	0.0401330	+	0.00853053i
$862$	−15.4742	+	11.2426i	−0.527052	+	0.382926i
$863$	3.59992	+	2.61550i	0.122543	+	0.0890326i	0.647369	−	0.762177i	$-0.275869\pi$
$863$	3.59992	+	2.61550i	0.122543	+	0.0890326i	−0.524826	+	0.851210i	$0.675869\pi$
$864$	−3.92149	−	1.74596i	−0.133412	−	0.0593988i
$865$	−28.3124			−0.962649
$866$	23.4274	+	10.4305i	0.796094	+	0.354444i
$867$	−3.36939	+	5.83595i	−0.114430	+	0.198199i
$868$	−0.858778	−	1.48745i	−0.0291488	−	0.0504873i
$869$	2.81801	+	26.8116i	0.0955945	+	0.909521i
$870$	3.81495	+	0.810892i	0.129339	+	0.0274918i
$871$	−1.23219	+	11.7236i	−0.0417513	+	0.397237i
$872$	1.19594	+	11.3786i	0.0404996	+	0.385328i
$873$	−25.8155	+	5.48726i	−0.873723	+	0.185715i
$874$	−0.617951	−	1.90186i	−0.0209025	−	0.0643313i
$875$	−2.65968	+	4.60670i	−0.0899135	+	0.155735i
$876$	−8.55355	−	9.49968i	−0.288998	−	0.320964i
$877$	−16.8851	−	12.2677i	−0.570168	−	0.414251i	0.264998	−	0.964249i	$-0.414629\pi$
$877$	−16.8851	−	12.2677i	−0.570168	−	0.414251i	−0.835166	+	0.549998i	$0.814629\pi$
$878$	1.52208	+	4.68447i	0.0513676	+	0.158093i
$879$	16.6551	−	18.4974i	0.561762	−	0.623900i
$880$	−4.41660	+	0.938776i	−0.148883	+	0.0316461i
$881$	9.16555	−	6.65916i	0.308795	−	0.224353i	−0.422584	−	0.906324i	$-0.638877\pi$
$881$	9.16555	−	6.65916i	0.308795	−	0.224353i	0.731379	+	0.681971i	$0.238877\pi$
$882$	−4.96150	+	15.2699i	−0.167062	+	0.514165i
$883$	16.2370	+	28.1234i	0.546420	+	0.946427i	0.998516	+	0.0544578i	$0.0173430\pi$
$883$	16.2370	+	28.1234i	0.546420	+	0.946427i	−0.452096	+	0.891969i	$0.649324\pi$
$884$	3.67871	−	4.08562i	0.123728	−	0.137414i
$885$	−6.14792	+	6.82796i	−0.206660	+	0.229519i
$886$	−0.290422	−	0.503025i	−0.00975690	−	0.0168995i
$887$	18.3675	−	56.5292i	0.616719	−	1.89807i	0.246345	−	0.969182i	$-0.420770\pi$
$887$	18.3675	−	56.5292i	0.616719	−	1.89807i	0.370374	−	0.928883i	$-0.379230\pi$
$888$	3.08720	−	2.24298i	0.103600	−	0.0752696i
$889$	5.95412	−	1.26559i	0.199695	−	0.0424464i
$890$	8.06287	−	8.95472i	0.270268	−	0.300163i
$891$	2.86362	+	8.81333i	0.0959350	+	0.295258i
$892$	−2.89085	−	2.10033i	−0.0967930	−	0.0703242i
$893$	20.2312	+	22.4690i	0.677011	+	0.751897i
$894$	−7.67087	+	13.2863i	−0.256552	+	0.444361i
$895$	−3.11835	−	9.59731i	−0.104235	−	0.320803i
$896$	−0.428042	+	0.0909831i	−0.0142999	+	0.00303953i
$897$	−0.0378652	−	0.360263i	−0.00126428	−	0.0120288i
$898$	1.51327	−	14.3978i	0.0504986	−	0.480462i
$899$	−10.5508	−	2.24264i	−0.351889	−	0.0747963i
$900$	−0.458968	−	4.36679i	−0.0152989	−	0.145560i
$901$	−1.33214	−	2.30733i	−0.0443799	−	0.0768682i
$902$	−4.37661	+	7.58051i	−0.145725	+	0.252403i
$903$	1.76214	+	0.784556i	0.0586404	+	0.0261084i
$904$	1.51434			0.0503663
$905$	40.3069	+	17.9458i	1.33985	+	0.596538i
$906$	15.0044	+	10.9013i	0.498487	+	0.362172i
$907$	6.35127	−	4.61447i	0.210890	−	0.153221i	−0.477326	−	0.878726i	$-0.658394\pi$
$907$	6.35127	−	4.61447i	0.210890	−	0.153221i	0.688216	+	0.725505i	$0.258394\pi$
$908$	14.8786	+	3.16254i	0.493763	+	0.104953i
$909$	27.0246	−	12.0321i	0.896349	−	0.399080i
$910$	−1.32852	+	0.591497i	−0.0440401	+	0.0196079i
$911$	1.35945	−	12.9343i	0.0450405	−	0.428532i	−0.948646	−	0.316339i	$-0.897546\pi$
$911$	1.35945	−	12.9343i	0.0450405	−	0.428532i	0.993687	−	0.112192i	$-0.0357872\pi$
$912$	−2.05392	+	6.32131i	−0.0680120	+	0.209319i
$913$	−24.1109	−	26.7779i	−0.797954	−	0.886217i
$914$	26.8767			0.889001
$915$	10.4811	−	3.60584i	0.346495	−	0.119205i
$916$	10.8440			0.358297
$917$	−2.56363	−	2.84720i	−0.0846584	−	0.0940227i
$918$	3.88741	−	11.9642i	0.128304	−	0.394878i
$919$	0.00135873	−	0.0129274i	4.48202e−5	−	0.000426436i	−0.994499	−	0.104742i	$-0.966598\pi$
$919$	0.00135873	−	0.0129274i	4.48202e−5	−	0.000426436i	0.994544	+	0.104315i	$0.0332651\pi$
$920$	−0.390062	+	0.173667i	−0.0128600	+	0.00572563i
$921$	−4.49247	+	2.00018i	−0.148032	+	0.0659081i
$922$	−11.6464	−	2.47553i	−0.383555	−	0.0815272i
$923$	12.2867	−	8.92678i	0.404420	−	0.293829i
$924$	−0.722930	−	0.525239i	−0.0237826	−	0.0172791i
$925$	8.10221	+	3.60734i	0.266399	+	0.118609i
$926$	25.8520			0.849549
$927$	−6.88428	−	3.06508i	−0.226109	−	0.100670i
$928$	−1.37411	+	2.38003i	−0.0451074	+	0.0781282i
$929$	−19.2950	−	33.4199i	−0.633048	−	1.09647i	−0.986925	−	0.161180i	$-0.948470\pi$
$929$	−19.2950	−	33.4199i	−0.633048	−	1.09647i	0.353877	−	0.935292i	$-0.384863\pi$
$930$	0.582233	+	5.53957i	0.0190922	+	0.181650i
$931$	55.2527	+	11.7443i	1.81083	+	0.384905i
$932$	−1.38985	+	13.2235i	−0.0455259	+	0.433150i
$933$	1.19734	+	11.3920i	0.0391993	+	0.372956i
$934$	33.0449	−	7.02392i	1.08126	−	0.229830i
$935$	−4.08905	−	12.5848i	−0.133726	−	0.411567i
$936$	2.21196	−	3.83122i	0.0723001	−	0.125227i
$937$	13.7877	+	15.3128i	0.450424	+	0.500246i	0.924999	−	0.379968i	$-0.124065\pi$
$937$	13.7877	+	15.3128i	0.450424	+	0.500246i	−0.474576	+	0.880215i	$0.657398\pi$
$938$	2.22462	+	1.61628i	0.0726365	+	0.0527735i
$939$	2.01863	+	6.21272i	0.0658757	+	0.202744i
$940$	4.31970	−	4.79751i	0.140893	−	0.156478i
$941$	−19.9878	+	4.24854i	−0.651585	+	0.138499i	−0.521833	−	0.853048i	$-0.674751\pi$
$941$	−19.9878	+	4.24854i	−0.651585	+	0.138499i	−0.129752	+	0.991546i	$0.541418\pi$
$942$	12.7238	−	9.24436i	0.414563	−	0.301198i
$943$	−0.255782	+	0.787217i	−0.00832942	+	0.0256353i
$944$	−3.23709	−	5.60680i	−0.105358	−	0.182486i
$945$	−2.22661	+	2.47290i	−0.0724315	+	0.0804433i
$946$	−9.38406	+	10.4221i	−0.305102	+	0.338850i
$947$	−17.7618	−	30.7643i	−0.577180	−	0.999705i	−0.995801	−	0.0915442i	$-0.970820\pi$
$947$	−17.7618	−	30.7643i	−0.577180	−	0.999705i	0.418621	−	0.908161i	$-0.362514\pi$
$948$	2.61842	−	8.05868i	0.0850425	−	0.261734i
$949$	24.2169	−	17.5946i	0.786113	−	0.571145i
$950$	−15.1102	+	3.21178i	−0.490241	+	0.104204i
$951$	−8.22620	+	9.13612i	−0.266753	+	0.296259i
$952$	−0.396297	−	1.21968i	−0.0128441	−	0.0395299i
$953$	8.77516	+	6.37553i	0.284255	+	0.206524i	0.720771	−	0.693173i	$-0.243788\pi$
$953$	8.77516	+	6.37553i	0.284255	+	0.206524i	−0.436516	+	0.899697i	$0.643788\pi$
$954$	−1.43454	−	1.59321i	−0.0464448	−	0.0515822i
$955$	20.2550	−	35.0827i	0.655436	−	1.13525i
$956$	5.35334	+	16.4759i	0.173139	+	0.532868i
$957$	−5.48925	+	1.16678i	−0.177442	+	0.0377165i
$958$	2.43824	+	23.1983i	0.0787760	+	0.749503i
$959$	0.530852	−	5.05072i	0.0171421	−	0.163096i
$960$	1.38815	+	0.295061i	0.0448024	+	0.00952305i
$961$	1.63013	+	15.5097i	0.0525849	+	0.500312i
$962$	4.46789	+	7.73861i	0.144050	+	0.249503i
$963$	9.87382	−	17.1020i	0.318179	−	0.551103i
$964$	4.73444	+	2.10791i	0.152486	+	0.0678912i
$965$	−23.4531			−0.754982
$966$	−0.0771950	−	0.0343694i	−0.00248371	−	0.00110582i
$967$	−31.4332	−	22.8376i	−1.01082	−	0.734407i	−0.0464429	−	0.998921i	$-0.514789\pi$
$967$	−31.4332	−	22.8376i	−1.01082	−	0.734407i	−0.964382	+	0.264514i	$0.914789\pi$
$968$	−3.64307	+	2.64684i	−0.117093	+	0.0850728i
$969$	−19.0529	−	4.04982i	−0.612068	−	0.130099i
$970$	18.1116	−	8.06381i	0.581529	−	0.258913i
$971$	−38.2067	+	17.0107i	−1.22611	+	0.545900i	−0.914607	−	0.404344i	$-0.867500\pi$
$971$	−38.2067	+	17.0107i	−1.22611	+	0.545900i	−0.311505	+	0.950244i	$0.600833\pi$
$972$	1.65055	−	15.7039i	0.0529414	−	0.503704i
$973$	1.32264	−	4.07066i	0.0424018	−	0.130499i
$974$	11.0126	+	12.2307i	0.352866	+	0.391897i
$975$	−2.79834			−0.0896186
$976$	0.134248	+	7.80910i	0.00429718	+	0.249963i
$977$	17.2254			0.551088			0.275544	−	0.961288i	$-0.411142\pi$
$977$	17.2254			0.551088			0.275544	+	0.961288i	$0.411142\pi$
$978$	−2.05008	−	2.27684i	−0.0655542	−	0.0728053i
$979$	−5.35778	+	16.4896i	−0.171236	+	0.527009i
$980$	1.26071	−	11.9949i	0.0402719	−	0.383162i
$981$	−24.6481	+	10.9740i	−0.786953	+	0.350374i
$982$	33.8898	−	15.0887i	1.08147	−	0.481500i
$983$	−48.6298	−	10.3366i	−1.55105	−	0.329686i	−0.648820	−	0.760942i	$-0.724737\pi$
$983$	−48.6298	−	10.3366i	−1.55105	−	0.329686i	−0.902230	+	0.431256i	$0.858071\pi$
$984$	2.22574	−	1.61710i	0.0709540	−	0.0515511i
$985$	32.6299	+	23.7070i	1.03968	+	0.755369i
$986$	−7.35763	−	3.27583i	−0.234315	−	0.104324i
$987$	1.27761			0.0406667
$988$	−14.2186	−	6.33051i	−0.452353	−	0.201400i
$989$	−0.663087	+	1.14850i	−0.0210849	+	0.0365202i
$990$	−5.32393	−	9.22131i	−0.169206	−	0.293073i
$991$	0.670785	+	6.38209i	0.0213082	+	0.202734i	0.999997	−	0.00261722i	$-0.000833089\pi$
$991$	0.670785	+	6.38209i	0.0213082	+	0.202734i	−0.978688	+	0.205351i	$0.934166\pi$
$992$	−3.83914	−	0.816034i	−0.121893	−	0.0259091i
$993$	1.08474	−	10.3206i	0.0344232	−	0.327515i
$994$	−0.370309	−	3.52326i	−0.0117455	−	0.111751i
$995$	−0.891305	+	0.189453i	−0.0282563	+	0.00600606i
$996$	3.49973	+	10.7710i	0.110893	+	0.341294i
$997$	−0.161096	+	0.279027i	−0.00510197	+	0.00883688i	−0.868565	−	0.495575i	$-0.834957\pi$
$997$	−0.161096	+	0.279027i	−0.00510197	+	0.00883688i	0.863463	+	0.504412i	$0.168291\pi$
$998$	16.4000	+	18.2141i	0.519133	+	0.576556i
$999$	16.5418	+	12.0183i	0.523360	+	0.380243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	122.2.i.a.83.1	yes	16
4.3	odd	2		976.2.bw.a.449.2		16
61.5	even	30		7442.2.a.r.1.3		8
61.25	even	15	inner	122.2.i.a.25.1	✓	16
61.56	even	15		7442.2.a.p.1.3		8
244.147	odd	30		976.2.bw.a.513.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
122.2.i.a.25.1	✓	16	61.25	even	15	inner
122.2.i.a.83.1	yes	16	1.1	even	1	trivial
976.2.bw.a.449.2		16	4.3	odd	2
976.2.bw.a.513.2		16	244.147	odd	30
7442.2.a.p.1.3		8	61.56	even	15
7442.2.a.r.1.3		8	61.5	even	30

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:	\( N \)	\(=\)	\( 122 = 2 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	122.i (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.669131 - 0.743145i) q^{2} +(-0.247563 + 0.761920i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(1.61830 - 0.720515i) q^{5} +(0.731869 - 0.325849i) q^{6} +(0.428042 + 0.0909831i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.90782 + 1.38611i) q^{9} +O(q^{10})\)	\(q+(-0.669131 - 0.743145i) q^{2} +(-0.247563 + 0.761920i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(1.61830 - 0.720515i) q^{5} +(0.731869 - 0.325849i) q^{6} +(0.428042 + 0.0909831i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.90782 + 1.38611i) q^{9} +(-1.61830 - 0.720515i) q^{10} +2.54891 q^{11} +(-0.731869 - 0.325849i) q^{12} +(0.937990 - 1.62465i) q^{13} +(-0.218802 - 0.378976i) q^{14} +(0.148343 + 1.41139i) q^{15} +(-0.978148 - 0.207912i) q^{16} +(0.306331 - 2.91455i) q^{17} +(-0.246498 - 2.34527i) q^{18} +(-8.11525 + 1.72495i) q^{19} +(0.547409 + 1.68475i) q^{20} +(-0.175289 + 0.303610i) q^{21} +(-1.70555 - 1.89421i) q^{22} +(-0.194999 - 0.141675i) q^{23} +(0.247563 + 0.761920i) q^{24} +(-1.24589 + 1.38370i) q^{25} +(-1.83498 + 0.390038i) q^{26} +(-3.47279 + 2.52313i) q^{27} +(-0.135227 + 0.416186i) q^{28} +(1.37411 + 2.38003i) q^{29} +(0.949606 - 1.05464i) q^{30} +(-2.62628 + 2.91677i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.631014 + 1.94206i) q^{33} +(-2.37091 + 1.72256i) q^{34} +(0.758255 - 0.161172i) q^{35} +(-1.57794 + 1.75248i) q^{36} +(-1.47193 - 4.53013i) q^{37} +(6.71205 + 4.87659i) q^{38} +(1.00564 + 1.11688i) q^{39} +(0.885726 - 1.53412i) q^{40} +(-1.06120 - 3.26603i) q^{41} +(0.342917 - 0.0728893i) q^{42} +(-0.575123 - 5.47193i) q^{43} +(-0.266433 + 2.53494i) q^{44} +(4.08614 + 0.868535i) q^{45} +(0.0251947 + 0.239711i) q^{46} +(-1.82215 - 3.15605i) q^{47} +(0.400565 - 0.693799i) q^{48} +(-6.21988 - 2.76927i) q^{49} +1.86196 q^{50} +(2.14482 + 0.954933i) q^{51} +(1.51770 + 1.10267i) q^{52} +(0.735495 - 0.534368i) q^{53} +(4.19880 + 0.892483i) q^{54} +(4.12490 - 1.83652i) q^{55} +(0.399771 - 0.177990i) q^{56} +(0.694761 - 6.61021i) q^{57} +(0.849246 - 2.61371i) q^{58} +(4.33207 + 4.81125i) q^{59} -1.41916 q^{60} +(-1.75492 - 7.61054i) q^{61} +3.92491 q^{62} +(0.690512 + 0.766892i) q^{63} +(0.309017 - 0.951057i) q^{64} +(0.347370 - 3.30500i) q^{65} +(1.86546 - 0.830558i) q^{66} +(-5.74046 + 2.55582i) q^{67} +(2.86656 + 0.609306i) q^{68} +(0.156219 - 0.113500i) q^{69} +(-0.627146 - 0.455648i) q^{70} +(7.39569 + 3.29277i) q^{71} +2.35819 q^{72} +(14.5768 + 6.49002i) q^{73} +(-2.38163 + 4.12510i) q^{74} +(-0.745835 - 1.29182i) q^{75} +(-0.867226 - 8.25110i) q^{76} +(1.09104 + 0.231907i) q^{77} +(0.157096 - 1.49467i) q^{78} +(1.10558 + 10.5189i) q^{79} +(-1.73274 + 0.368306i) q^{80} +(1.12347 + 3.45769i) q^{81} +(-1.71705 + 2.97402i) q^{82} +(-9.45931 - 10.5056i) q^{83} +(-0.283624 - 0.206065i) q^{84} +(-1.60424 - 4.93733i) q^{85} +(-3.68160 + 4.08884i) q^{86} +(-2.15357 + 0.457755i) q^{87} +(2.06211 - 1.49821i) q^{88} +(-2.10199 + 6.46927i) q^{89} +(-2.08871 - 3.61775i) q^{90} +(0.549314 - 0.610075i) q^{91} +(0.161282 - 0.179122i) q^{92} +(-1.57218 - 2.72310i) q^{93} +(-1.12615 + 3.46593i) q^{94} +(-11.8901 + 8.63865i) q^{95} +(-0.783624 + 0.166564i) q^{96} +(-7.48873 + 8.31708i) q^{97} +(2.10394 + 6.47527i) q^{98} +(4.86284 + 3.53306i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 6 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} + 3 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 6 * q^5 - q^6 - 10 * q^7 + 4 * q^8 + 3 * q^9	\( 16 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 6 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} + 3 q^{9} - 6 q^{10} - 2 q^{11} + q^{12} - 9 q^{13} - 10 q^{14} - 3 q^{15} + 2 q^{16} + 2 q^{17} + 24 q^{18} + 10 q^{19} - 7 q^{20} - 6 q^{21} - 11 q^{22} - 11 q^{23} - 3 q^{24} - 28 q^{25} + 4 q^{26} - 33 q^{27} + 5 q^{28} + 15 q^{29} - 12 q^{30} - 12 q^{31} + 8 q^{32} + 15 q^{33} - 11 q^{34} + 19 q^{35} + q^{36} + 16 q^{37} - 10 q^{38} + 24 q^{39} + 4 q^{40} - 20 q^{41} - 19 q^{42} - 21 q^{43} - 4 q^{44} + 17 q^{45} + 2 q^{46} - 11 q^{47} + q^{48} - 10 q^{49} + 4 q^{50} - 56 q^{51} - 2 q^{52} - 8 q^{53} + 41 q^{54} + 35 q^{55} + 10 q^{56} + 49 q^{57} - 10 q^{58} + 35 q^{59} + 6 q^{60} + 15 q^{61} + 16 q^{62} - 26 q^{63} - 4 q^{64} + 24 q^{65} + 10 q^{66} + 22 q^{67} + 12 q^{68} + 46 q^{69} + 28 q^{70} + 10 q^{71} + 2 q^{72} + 9 q^{73} - 7 q^{74} - 15 q^{75} - 20 q^{76} + 2 q^{77} + 11 q^{78} + 10 q^{79} - 4 q^{80} - 27 q^{81} + 15 q^{82} - 45 q^{83} + 17 q^{84} + 2 q^{85} + 11 q^{86} - 9 q^{87} - 8 q^{88} - 26 q^{89} + 8 q^{90} - 84 q^{91} - 47 q^{92} - 33 q^{93} - 2 q^{94} + 37 q^{95} + 9 q^{96} - 41 q^{97} - 5 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 6 * q^5 - q^6 - 10 * q^7 + 4 * q^8 + 3 * q^9 - 6 * q^10 - 2 * q^11 + q^12 - 9 * q^13 - 10 * q^14 - 3 * q^15 + 2 * q^16 + 2 * q^17 + 24 * q^18 + 10 * q^19 - 7 * q^20 - 6 * q^21 - 11 * q^22 - 11 * q^23 - 3 * q^24 - 28 * q^25 + 4 * q^26 - 33 * q^27 + 5 * q^28 + 15 * q^29 - 12 * q^30 - 12 * q^31 + 8 * q^32 + 15 * q^33 - 11 * q^34 + 19 * q^35 + q^36 + 16 * q^37 - 10 * q^38 + 24 * q^39 + 4 * q^40 - 20 * q^41 - 19 * q^42 - 21 * q^43 - 4 * q^44 + 17 * q^45 + 2 * q^46 - 11 * q^47 + q^48 - 10 * q^49 + 4 * q^50 - 56 * q^51 - 2 * q^52 - 8 * q^53 + 41 * q^54 + 35 * q^55 + 10 * q^56 + 49 * q^57 - 10 * q^58 + 35 * q^59 + 6 * q^60 + 15 * q^61 + 16 * q^62 - 26 * q^63 - 4 * q^64 + 24 * q^65 + 10 * q^66 + 22 * q^67 + 12 * q^68 + 46 * q^69 + 28 * q^70 + 10 * q^71 + 2 * q^72 + 9 * q^73 - 7 * q^74 - 15 * q^75 - 20 * q^76 + 2 * q^77 + 11 * q^78 + 10 * q^79 - 4 * q^80 - 27 * q^81 + 15 * q^82 - 45 * q^83 + 17 * q^84 + 2 * q^85 + 11 * q^86 - 9 * q^87 - 8 * q^88 - 26 * q^89 + 8 * q^90 - 84 * q^91 - 47 * q^92 - 33 * q^93 - 2 * q^94 + 37 * q^95 + 9 * q^96 - 41 * q^97 - 5 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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