LMFDB - Embedded newform 1122.2.l.g.727.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1122,2,Mod(463,1122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1122, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("1122.463");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1122 = 2 \cdot 3 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1122.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.95921510679$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 44 x^{18} + 732 x^{16} + 6050 x^{14} + 27262 x^{12} + 69598 x^{10} + 100205 x^{8} + 77682 x^{6} + \cdots + 289 $ x^20 + 44x^18 + 732x^16 + 6050x^14 + 27262x^12 + 69598x^10 + 100205x^8 + 77682x^6 + 29931x^4 + 5170*x^2 + 289
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			727.7
Root			$-0.320425i$ of defining polynomial
Character	$\chi$	$=$	1122.727
Dual form			1122.2.l.g.463.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.11456 - 2.11456i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-3.02020 + 3.02020i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.11456 - 2.11456i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-3.02020 + 3.02020i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(2.11456 - 2.11456i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(-0.707107 - 0.707107i) q^{12} -1.12124 q^{13} +(-3.02020 - 3.02020i) q^{14} -2.99043i q^{15} +1.00000 q^{16} +(4.12158 + 0.112193i) q^{17} -1.00000 q^{18} -5.98141i q^{19} +(2.11456 + 2.11456i) q^{20} -4.27120 q^{21} +(-0.707107 - 0.707107i) q^{22} +(5.70573 - 5.70573i) q^{23} +(0.707107 - 0.707107i) q^{24} +3.94269i q^{25} -1.12124i q^{26} +(-0.707107 + 0.707107i) q^{27} +(3.02020 - 3.02020i) q^{28} +(-0.420743 - 0.420743i) q^{29} +2.99043 q^{30} +(-2.09392 - 2.09392i) q^{31} +1.00000i q^{32} -1.00000 q^{33} +(-0.112193 + 4.12158i) q^{34} +12.7727 q^{35} -1.00000i q^{36} +(1.97499 + 1.97499i) q^{37} +5.98141 q^{38} +(-0.792834 - 0.792834i) q^{39} +(-2.11456 + 2.11456i) q^{40} +(4.14996 - 4.14996i) q^{41} -4.27120i q^{42} -5.97503i q^{43} +(0.707107 - 0.707107i) q^{44} +(2.11456 - 2.11456i) q^{45} +(5.70573 + 5.70573i) q^{46} -13.2032 q^{47} +(0.707107 + 0.707107i) q^{48} -11.2432i q^{49} -3.94269 q^{50} +(2.83506 + 2.99373i) q^{51} +1.12124 q^{52} -13.7348i q^{53} +(-0.707107 - 0.707107i) q^{54} +2.99043 q^{55} +(3.02020 + 3.02020i) q^{56} +(4.22949 - 4.22949i) q^{57} +(0.420743 - 0.420743i) q^{58} +10.4811i q^{59} +2.99043i q^{60} +(7.71924 - 7.71924i) q^{61} +(2.09392 - 2.09392i) q^{62} +(-3.02020 - 3.02020i) q^{63} -1.00000 q^{64} +(2.37092 + 2.37092i) q^{65} -1.00000i q^{66} -10.0270 q^{67} +(-4.12158 - 0.112193i) q^{68} +8.06912 q^{69} +12.7727i q^{70} +(0.330151 + 0.330151i) q^{71} +1.00000 q^{72} +(-9.32808 - 9.32808i) q^{73} +(-1.97499 + 1.97499i) q^{74} +(-2.78790 + 2.78790i) q^{75} +5.98141i q^{76} -4.27120i q^{77} +(0.792834 - 0.792834i) q^{78} +(3.01568 - 3.01568i) q^{79} +(-2.11456 - 2.11456i) q^{80} -1.00000 q^{81} +(4.14996 + 4.14996i) q^{82} +7.58758i q^{83} +4.27120 q^{84} +(-8.47807 - 8.95254i) q^{85} +5.97503 q^{86} -0.595021i q^{87} +(0.707107 + 0.707107i) q^{88} +11.0720 q^{89} +(2.11456 + 2.11456i) q^{90} +(3.38635 - 3.38635i) q^{91} +(-5.70573 + 5.70573i) q^{92} -2.96124i q^{93} -13.2032i q^{94} +(-12.6480 + 12.6480i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(-1.80211 - 1.80211i) q^{97} +11.2432 q^{98} +(-0.707107 - 0.707107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{4} - 4 q^{5}+O(q^{10}) $ 20 * q - 20 * q^4 - 4 * q^5	$ 20 q - 20 q^{4} - 4 q^{5} + 4 q^{10} + 20 q^{16} - 12 q^{17} - 20 q^{18} + 4 q^{20} + 16 q^{23} + 4 q^{29} - 8 q^{31} - 20 q^{33} + 16 q^{35} - 20 q^{37} + 8 q^{39} - 4 q^{40} + 20 q^{41} + 4 q^{45} + 16 q^{46} - 16 q^{47} - 68 q^{50} + 8 q^{57} - 4 q^{58} - 20 q^{61} + 8 q^{62} - 20 q^{64} + 8 q^{65} - 48 q^{67} + 12 q^{68} - 32 q^{71} + 20 q^{72} + 20 q^{73} + 20 q^{74} - 8 q^{75} - 8 q^{78} - 16 q^{79} - 4 q^{80} - 20 q^{81} + 20 q^{82} - 4 q^{85} - 16 q^{86} + 4 q^{90} + 88 q^{91} - 16 q^{92} - 48 q^{95} + 4 q^{97} + 36 q^{98}+O(q^{100}) $ 20 * q - 20 * q^4 - 4 * q^5 + 4 * q^10 + 20 * q^16 - 12 * q^17 - 20 * q^18 + 4 * q^20 + 16 * q^23 + 4 * q^29 - 8 * q^31 - 20 * q^33 + 16 * q^35 - 20 * q^37 + 8 * q^39 - 4 * q^40 + 20 * q^41 + 4 * q^45 + 16 * q^46 - 16 * q^47 - 68 * q^50 + 8 * q^57 - 4 * q^58 - 20 * q^61 + 8 * q^62 - 20 * q^64 + 8 * q^65 - 48 * q^67 + 12 * q^68 - 32 * q^71 + 20 * q^72 + 20 * q^73 + 20 * q^74 - 8 * q^75 - 8 * q^78 - 16 * q^79 - 4 * q^80 - 20 * q^81 + 20 * q^82 - 4 * q^85 - 16 * q^86 + 4 * q^90 + 88 * q^91 - 16 * q^92 - 48 * q^95 + 4 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1122\mathbb{Z}\right)^\times$.

$n$	$409$	$749$	$1057$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−1.00000			−0.500000
$5$	−2.11456	−	2.11456i	−0.945658	−	0.945658i	0.0529399	−	0.998598i	$-0.483141\pi$
$5$	−2.11456	−	2.11456i	−0.945658	−	0.945658i	−0.998598	+	0.0529399i	$0.983141\pi$
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	−3.02020	+	3.02020i	−1.14153	+	1.14153i	−0.153355	+	0.988171i	$0.549008\pi$
$7$	−3.02020	+	3.02020i	−1.14153	+	1.14153i	−0.988171	+	0.153355i	$0.950992\pi$
$8$		−	1.00000i		−	0.353553i
$9$			1.00000i			0.333333i
$10$	2.11456	−	2.11456i	0.668681	−	0.668681i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	−1.12124			−0.310975			−0.155487	−	0.987838i	$-0.549695\pi$
$13$	−1.12124			−0.310975			−0.155487	+	0.987838i	$0.549695\pi$
$14$	−3.02020	−	3.02020i	−0.807181	−	0.807181i
$15$		−	2.99043i		−	0.772126i
$16$	1.00000			0.250000
$17$	4.12158	+	0.112193i	0.999630	+	0.0272108i
$17$	4.12158	+	0.112193i	0.999630	+	0.0272108i
$18$	−1.00000			−0.235702
$19$		−	5.98141i		−	1.37223i	−0.727494	−	0.686114i	$-0.759315\pi$
$19$		−	5.98141i		−	1.37223i	0.727494	−	0.686114i	$-0.240685\pi$
$20$	2.11456	+	2.11456i	0.472829	+	0.472829i
$21$	−4.27120			−0.932052
$22$	−0.707107	−	0.707107i	−0.150756	−	0.150756i
$23$	5.70573	−	5.70573i	1.18973	−	1.18973i	0.212584	−	0.977143i	$-0.431812\pi$
$23$	5.70573	−	5.70573i	1.18973	−	1.18973i	0.977143	−	0.212584i	$-0.0681879\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$			3.94269i			0.788537i
$26$		−	1.12124i		−	0.219893i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	3.02020	−	3.02020i	0.570763	−	0.570763i
$29$	−0.420743	−	0.420743i	−0.0781300	−	0.0781300i	0.666962	−	0.745092i	$-0.267594\pi$
$29$	−0.420743	−	0.420743i	−0.0781300	−	0.0781300i	−0.745092	+	0.666962i	$0.767594\pi$
$30$	2.99043			0.545976
$31$	−2.09392	−	2.09392i	−0.376078	−	0.376078i	0.493607	−	0.869685i	$-0.335678\pi$
$31$	−2.09392	−	2.09392i	−0.376078	−	0.376078i	−0.869685	+	0.493607i	$0.835678\pi$
$32$			1.00000i			0.176777i
$33$	−1.00000			−0.174078
$34$	−0.112193	+	4.12158i	−0.0192410	+	0.706845i
$35$	12.7727			2.15899
$36$		−	1.00000i		−	0.166667i
$37$	1.97499	+	1.97499i	0.324687	+	0.324687i	0.850562	−	0.525875i	$-0.176262\pi$
$37$	1.97499	+	1.97499i	0.324687	+	0.324687i	−0.525875	+	0.850562i	$0.676262\pi$
$38$	5.98141			0.970312
$39$	−0.792834	−	0.792834i	−0.126955	−	0.126955i
$40$	−2.11456	+	2.11456i	−0.334341	+	0.334341i
$41$	4.14996	−	4.14996i	0.648116	−	0.648116i	−0.304422	−	0.952537i	$-0.598463\pi$
$41$	4.14996	−	4.14996i	0.648116	−	0.648116i	0.952537	+	0.304422i	$0.0984632\pi$
$42$		−	4.27120i		−	0.659061i
$43$		−	5.97503i		−	0.911183i	−0.890189	−	0.455592i	$-0.849428\pi$
$43$		−	5.97503i		−	0.911183i	0.890189	−	0.455592i	$-0.150572\pi$
$44$	0.707107	−	0.707107i	0.106600	−	0.106600i
$45$	2.11456	−	2.11456i	0.315219	−	0.315219i
$46$	5.70573	+	5.70573i	0.841264	+	0.841264i
$47$	−13.2032			−1.92589			−0.962943	−	0.269704i	$-0.913074\pi$
$47$	−13.2032			−1.92589			−0.962943	+	0.269704i	$0.913074\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$		−	11.2432i		−	1.60617i
$50$	−3.94269			−0.557580
$51$	2.83506	+	2.99373i	0.396988	+	0.419206i
$52$	1.12124			0.155487
$53$		−	13.7348i		−	1.88662i	−0.331908	−	0.943312i	$-0.607692\pi$
$53$		−	13.7348i		−	1.88662i	0.331908	−	0.943312i	$-0.392308\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	2.99043			0.403230
$56$	3.02020	+	3.02020i	0.403591	+	0.403591i
$57$	4.22949	−	4.22949i	0.560210	−	0.560210i
$58$	0.420743	−	0.420743i	0.0552463	−	0.0552463i
$59$			10.4811i			1.36452i	0.731110	+	0.682260i	$0.239003\pi$
$59$			10.4811i			1.36452i	−0.731110	+	0.682260i	$0.760997\pi$
$60$			2.99043i			0.386063i
$61$	7.71924	−	7.71924i	0.988348	−	0.988348i	−0.0115851	−	0.999933i	$-0.503688\pi$
$61$	7.71924	−	7.71924i	0.988348	−	0.988348i	0.999933	+	0.0115851i	$0.00368774\pi$
$62$	2.09392	−	2.09392i	0.265928	−	0.265928i
$63$	−3.02020	−	3.02020i	−0.380509	−	0.380509i
$64$	−1.00000			−0.125000
$65$	2.37092	+	2.37092i	0.294076	+	0.294076i
$66$		−	1.00000i		−	0.123091i
$67$	−10.0270			−1.22500			−0.612498	−	0.790472i	$-0.709835\pi$
$67$	−10.0270			−1.22500			−0.612498	+	0.790472i	$0.709835\pi$
$68$	−4.12158	−	0.112193i	−0.499815	−	0.0136054i
$69$	8.06912			0.971408
$70$			12.7727i			1.52663i
$71$	0.330151	+	0.330151i	0.0391818	+	0.0391818i	0.726426	−	0.687244i	$-0.241180\pi$
$71$	0.330151	+	0.330151i	0.0391818	+	0.0391818i	−0.687244	+	0.726426i	$0.741180\pi$
$72$	1.00000			0.117851
$73$	−9.32808	−	9.32808i	−1.09177	−	1.09177i	−0.995340	−	0.0964294i	$-0.969258\pi$
$73$	−9.32808	−	9.32808i	−1.09177	−	1.09177i	−0.0964294	−	0.995340i	$-0.530742\pi$
$74$	−1.97499	+	1.97499i	−0.229588	+	0.229588i
$75$	−2.78790	+	2.78790i	−0.321919	+	0.321919i
$76$			5.98141i			0.686114i
$77$		−	4.27120i		−	0.486749i
$78$	0.792834	−	0.792834i	0.0897707	−	0.0897707i
$79$	3.01568	−	3.01568i	0.339291	−	0.339291i	−0.516809	−	0.856100i	$-0.672880\pi$
$79$	3.01568	−	3.01568i	0.339291	−	0.339291i	0.856100	+	0.516809i	$0.172880\pi$
$80$	−2.11456	−	2.11456i	−0.236414	−	0.236414i
$81$	−1.00000			−0.111111
$82$	4.14996	+	4.14996i	0.458287	+	0.458287i
$83$			7.58758i			0.832845i	0.909171	+	0.416423i	$0.136716\pi$
$83$			7.58758i			0.832845i	−0.909171	+	0.416423i	$0.863284\pi$
$84$	4.27120			0.466026
$85$	−8.47807	−	8.95254i	−0.919576	−	0.971040i
$86$	5.97503			0.644304
$87$		−	0.595021i		−	0.0637929i
$88$	0.707107	+	0.707107i	0.0753778	+	0.0753778i
$89$	11.0720			1.17363			0.586814	−	0.809722i	$-0.300382\pi$
$89$	11.0720			1.17363			0.586814	+	0.809722i	$0.300382\pi$
$90$	2.11456	+	2.11456i	0.222894	+	0.222894i
$91$	3.38635	−	3.38635i	0.354986	−	0.354986i
$92$	−5.70573	+	5.70573i	−0.594863	+	0.594863i
$93$		−	2.96124i		−	0.307067i
$94$		−	13.2032i		−	1.36181i
$95$	−12.6480	+	12.6480i	−1.29766	+	1.29766i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$	−1.80211	−	1.80211i	−0.182976	−	0.182976i	0.609675	−	0.792651i	$-0.291300\pi$
$97$	−1.80211	−	1.80211i	−0.182976	−	0.182976i	−0.792651	+	0.609675i	$0.791300\pi$
$98$	11.2432			1.13573
$99$	−0.707107	−	0.707107i	−0.0710669	−	0.0710669i
$100$		−	3.94269i		−	0.394269i
$101$	−3.12301			−0.310751			−0.155376	−	0.987855i	$-0.549659\pi$
$101$	−3.12301			−0.310751			−0.155376	+	0.987855i	$0.549659\pi$
$102$	−2.99373	+	2.83506i	−0.296423	+	0.280713i
$103$	−17.0156			−1.67660			−0.838298	−	0.545212i	$-0.816449\pi$
$103$	−17.0156			−1.67660			−0.838298	+	0.545212i	$0.816449\pi$
$104$			1.12124i			0.109946i
$105$	9.03169	+	9.03169i	0.881403	+	0.881403i
$106$	13.7348			1.33404
$107$	12.9421	+	12.9421i	1.25116	+	1.25116i	0.955200	+	0.295961i	$0.0956398\pi$
$107$	12.9421	+	12.9421i	1.25116	+	1.25116i	0.295961	+	0.955200i	$0.404360\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	−5.74231	+	5.74231i	−0.550014	+	0.550014i	−0.926445	−	0.376431i	$-0.877151\pi$
$109$	−5.74231	+	5.74231i	−0.550014	+	0.550014i	0.376431	+	0.926445i	$0.377151\pi$
$110$			2.99043i			0.285127i
$111$			2.79306i			0.265106i
$112$	−3.02020	+	3.02020i	−0.285382	+	0.285382i
$113$	−0.814913	+	0.814913i	−0.0766606	+	0.0766606i	−0.744397	−	0.667737i	$-0.767263\pi$
$113$	−0.814913	+	0.814913i	−0.0766606	+	0.0766606i	0.667737	+	0.744397i	$0.267263\pi$
$114$	4.22949	+	4.22949i	0.396128	+	0.396128i
$115$	−24.1302			−2.25015
$116$	0.420743	+	0.420743i	0.0390650	+	0.0390650i
$117$		−	1.12124i		−	0.103658i
$118$	−10.4811			−0.964861
$119$	−12.7868	+	12.1091i	−1.17217	+	1.11004i
$120$	−2.99043			−0.272988
$121$		−	1.00000i		−	0.0909091i
$122$	7.71924	+	7.71924i	0.698867	+	0.698867i
$123$	5.86894			0.529184
$124$	2.09392	+	2.09392i	0.188039	+	0.188039i
$125$	−2.23575	+	2.23575i	−0.199971	+	0.199971i
$126$	3.02020	−	3.02020i	0.269060	−	0.269060i
$127$			7.28710i			0.646626i	0.946292	+	0.323313i	$0.104797\pi$
$127$			7.28710i			0.646626i	−0.946292	+	0.323313i	$0.895203\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	4.22498	−	4.22498i	0.371989	−	0.371989i
$130$	−2.37092	+	2.37092i	−0.207943	+	0.207943i
$131$	9.81947	+	9.81947i	0.857931	+	0.857931i	0.991094	−	0.133163i	$-0.0425135\pi$
$131$	9.81947	+	9.81947i	0.857931	+	0.857931i	−0.133163	+	0.991094i	$0.542513\pi$
$132$	1.00000			0.0870388
$133$	18.0650	+	18.0650i	1.56644	+	1.56644i
$134$		−	10.0270i		−	0.866203i
$135$	2.99043			0.257375
$136$	0.112193	−	4.12158i	0.00962048	−	0.353422i
$137$	−11.1312			−0.951003			−0.475502	−	0.879715i	$-0.657733\pi$
$137$	−11.1312			−0.951003			−0.475502	+	0.879715i	$0.657733\pi$
$138$			8.06912i			0.686889i
$139$	6.70219	+	6.70219i	0.568472	+	0.568472i	0.931700	−	0.363228i	$-0.118325\pi$
$139$	6.70219	+	6.70219i	0.568472	+	0.568472i	−0.363228	+	0.931700i	$0.618325\pi$
$140$	−12.7727			−1.07949
$141$	−9.33608	−	9.33608i	−0.786240	−	0.786240i
$142$	−0.330151	+	0.330151i	−0.0277057	+	0.0277057i
$143$	0.792834	−	0.792834i	0.0663001	−	0.0663001i
$144$			1.00000i			0.0833333i
$145$			1.77937i			0.147769i
$146$	9.32808	−	9.32808i	0.771997	−	0.771997i
$147$	7.95011	−	7.95011i	0.655714	−	0.655714i
$148$	−1.97499	−	1.97499i	−0.162344	−	0.162344i
$149$	18.6201			1.52542			0.762709	−	0.646742i	$-0.223869\pi$
$149$	18.6201			1.52542			0.762709	+	0.646742i	$0.223869\pi$
$150$	−2.78790	−	2.78790i	−0.227631	−	0.227631i
$151$		−	19.5530i		−	1.59120i	−0.605821	−	0.795601i	$-0.707155\pi$
$151$		−	19.5530i		−	1.59120i	0.605821	−	0.795601i	$-0.292845\pi$
$152$	−5.98141			−0.485156
$153$	−0.112193	+	4.12158i	−0.00907028	+	0.333210i
$154$	4.27120			0.344183
$155$			8.85540i			0.711283i
$156$	0.792834	+	0.792834i	0.0634775	+	0.0634775i
$157$	−10.1767			−0.812189			−0.406094	−	0.913831i	$-0.633110\pi$
$157$	−10.1767			−0.812189			−0.406094	+	0.913831i	$0.633110\pi$
$158$	3.01568	+	3.01568i	0.239915	+	0.239915i
$159$	9.71199	−	9.71199i	0.770211	−	0.770211i
$160$	2.11456	−	2.11456i	0.167170	−	0.167170i
$161$			34.4648i			2.71621i
$162$		−	1.00000i		−	0.0785674i
$163$	6.76244	−	6.76244i	0.529675	−	0.529675i	−0.390801	−	0.920475i	$-0.627802\pi$
$163$	6.76244	−	6.76244i	0.529675	−	0.529675i	0.920475	+	0.390801i	$0.127802\pi$
$164$	−4.14996	+	4.14996i	−0.324058	+	0.324058i
$165$	2.11456	+	2.11456i	0.164618	+	0.164618i
$166$	−7.58758			−0.588910
$167$	−15.0285	−	15.0285i	−1.16294	−	1.16294i	−0.983829	−	0.179112i	$-0.942678\pi$
$167$	−15.0285	−	15.0285i	−1.16294	−	1.16294i	−0.179112	−	0.983829i	$-0.557322\pi$
$168$			4.27120i			0.329530i
$169$	−11.7428			−0.903295
$170$	8.95254	−	8.47807i	0.686629	−	0.650238i
$171$	5.98141			0.457409
$172$			5.97503i			0.455592i
$173$	6.29902	+	6.29902i	0.478905	+	0.478905i	0.904781	−	0.425876i	$-0.140034\pi$
$173$	6.29902	+	6.29902i	0.478905	+	0.478905i	−0.425876	+	0.904781i	$0.640034\pi$
$174$	0.595021			0.0451084
$175$	−11.9077	−	11.9077i	−0.900136	−	0.900136i
$176$	−0.707107	+	0.707107i	−0.0533002	+	0.0533002i
$177$	−7.41124	+	7.41124i	−0.557063	+	0.557063i
$178$			11.0720i			0.829880i
$179$		−	15.9031i		−	1.18866i	−0.804223	−	0.594328i	$-0.797418\pi$
$179$		−	15.9031i		−	1.18866i	0.804223	−	0.594328i	$-0.202582\pi$
$180$	−2.11456	+	2.11456i	−0.157610	+	0.157610i
$181$	−3.98836	+	3.98836i	−0.296452	+	0.296452i	−0.839623	−	0.543170i	$-0.817224\pi$
$181$	−3.98836	+	3.98836i	−0.296452	+	0.296452i	0.543170	+	0.839623i	$0.317224\pi$
$182$	3.38635	+	3.38635i	0.251013	+	0.251013i
$183$	10.9167			0.806983
$184$	−5.70573	−	5.70573i	−0.420632	−	0.420632i
$185$		−	8.35247i		−	0.614086i
$186$	2.96124			0.217129
$187$	−2.99373	+	2.83506i	−0.218923	+	0.207320i
$188$	13.2032			0.962943
$189$		−	4.27120i		−	0.310684i
$190$	−12.6480	−	12.6480i	−0.917583	−	0.917583i
$191$	0.138993			0.0100572			0.00502859	−	0.999987i	$-0.498399\pi$
$191$	0.138993			0.0100572			0.00502859	+	0.999987i	$0.498399\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	10.6849	−	10.6849i	0.769113	−	0.769113i	−0.208837	−	0.977950i	$-0.566968\pi$
$193$	10.6849	−	10.6849i	0.769113	−	0.769113i	0.977950	+	0.208837i	$0.0669679\pi$
$194$	1.80211	−	1.80211i	0.129384	−	0.129384i
$195$			3.35298i			0.240112i
$196$			11.2432i			0.803083i
$197$	14.6643	−	14.6643i	1.04479	−	1.04479i	0.0458381	−	0.998949i	$-0.485404\pi$
$197$	14.6643	−	14.6643i	1.04479	−	1.04479i	0.998949	−	0.0458381i	$-0.0145958\pi$
$198$	0.707107	−	0.707107i	0.0502519	−	0.0502519i
$199$	0.962297	+	0.962297i	0.0682155	+	0.0682155i	0.740391	−	0.672176i	$-0.234640\pi$
$199$	0.962297	+	0.962297i	0.0682155	+	0.0682155i	−0.672176	+	0.740391i	$0.734640\pi$
$200$	3.94269			0.278790
$201$	−7.09018	−	7.09018i	−0.500103	−	0.500103i
$202$		−	3.12301i		−	0.219734i
$203$	2.54145			0.178375
$204$	−2.83506	−	2.99373i	−0.198494	−	0.209603i
$205$	−17.5507			−1.22579
$206$		−	17.0156i		−	1.18553i
$207$	5.70573	+	5.70573i	0.396576	+	0.396576i
$208$	−1.12124			−0.0777437
$209$	4.22949	+	4.22949i	0.292560	+	0.292560i
$210$	−9.03169	+	9.03169i	−0.623246	+	0.623246i
$211$	0.689718	−	0.689718i	0.0474821	−	0.0474821i	−0.682967	−	0.730449i	$-0.739311\pi$
$211$	0.689718	−	0.689718i	0.0474821	−	0.0474821i	0.730449	+	0.682967i	$0.239311\pi$
$212$			13.7348i			0.943312i
$213$			0.466904i			0.0319918i
$214$	−12.9421	+	12.9421i	−0.884704	+	0.884704i
$215$	−12.6345	+	12.6345i	−0.861667	+	0.861667i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	12.6481			0.858607
$218$	−5.74231	−	5.74231i	−0.388919	−	0.388919i
$219$		−	13.1919i		−	0.891426i
$220$	−2.99043			−0.201615
$221$	−4.62126	−	0.125795i	−0.310860	−	0.00846189i
$222$	−2.79306			−0.187458
$223$			0.0302217i			0.00202379i	0.999999	+	0.00101190i	$0.000322097\pi$
$223$			0.0302217i			0.00202379i	−0.999999	+	0.00101190i	$0.999678\pi$
$224$	−3.02020	−	3.02020i	−0.201795	−	0.201795i
$225$	−3.94269			−0.262846
$226$	−0.814913	−	0.814913i	−0.0542072	−	0.0542072i
$227$	3.47082	−	3.47082i	0.230366	−	0.230366i	−0.582479	−	0.812846i	$-0.697917\pi$
$227$	3.47082	−	3.47082i	0.230366	−	0.230366i	0.812846	+	0.582479i	$0.197917\pi$
$228$	−4.22949	+	4.22949i	−0.280105	+	0.280105i
$229$		−	18.0229i		−	1.19099i	−0.803359	−	0.595494i	$-0.796956\pi$
$229$		−	18.0229i		−	1.19099i	0.803359	−	0.595494i	$-0.203044\pi$
$230$		−	24.1302i		−	1.59110i
$231$	3.02020	−	3.02020i	0.198714	−	0.198714i
$232$	−0.420743	+	0.420743i	−0.0276231	+	0.0276231i
$233$	−16.9619	−	16.9619i	−1.11121	−	1.11121i	−0.992987	−	0.118222i	$-0.962281\pi$
$233$	−16.9619	−	16.9619i	−1.11121	−	1.11121i	−0.118222	−	0.992987i	$-0.537719\pi$
$234$	1.12124			0.0732975
$235$	27.9189	+	27.9189i	1.82123	+	1.82123i
$236$		−	10.4811i		−	0.682260i
$237$	4.26482			0.277030
$238$	−12.1091	−	12.7868i	−0.784918	−	0.828846i
$239$	−29.4171			−1.90283			−0.951416	−	0.307908i	$-0.900371\pi$
$239$	−29.4171			−1.90283			−0.951416	+	0.307908i	$0.900371\pi$
$240$		−	2.99043i		−	0.193032i
$241$	−4.18761	−	4.18761i	−0.269748	−	0.269748i	0.559251	−	0.828998i	$-0.311089\pi$
$241$	−4.18761	−	4.18761i	−0.269748	−	0.269748i	−0.828998	+	0.559251i	$0.811089\pi$
$242$	1.00000			0.0642824
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−7.71924	+	7.71924i	−0.494174	+	0.494174i
$245$	−23.7743	+	23.7743i	−1.51888	+	1.51888i
$246$			5.86894i			0.374190i
$247$			6.70657i			0.426729i
$248$	−2.09392	+	2.09392i	−0.132964	+	0.132964i
$249$	−5.36523	+	5.36523i	−0.340008	+	0.340008i
$250$	−2.23575	−	2.23575i	−0.141401	−	0.141401i
$251$	14.8831			0.939415			0.469708	−	0.882822i	$-0.344359\pi$
$251$	14.8831			0.939415			0.469708	+	0.882822i	$0.344359\pi$
$252$	3.02020	+	3.02020i	0.190254	+	0.190254i
$253$			8.06912i			0.507301i
$254$	−7.28710			−0.457233
$255$	0.335506	−	12.3253i	0.0210102	−	0.771840i
$256$	1.00000			0.0625000
$257$		−	4.23710i		−	0.264303i	−0.991230	−	0.132151i	$-0.957811\pi$
$257$		−	4.23710i		−	0.264303i	0.991230	−	0.132151i	$-0.0421885\pi$
$258$	4.22498	+	4.22498i	0.263036	+	0.263036i
$259$	−11.9297			−0.741278
$260$	−2.37092	−	2.37092i	−0.147038	−	0.147038i
$261$	0.420743	−	0.420743i	0.0260433	−	0.0260433i
$262$	−9.81947	+	9.81947i	−0.606649	+	0.606649i
$263$			3.40613i			0.210031i	0.994471	+	0.105016i	$0.0334893\pi$
$263$			3.40613i			0.210031i	−0.994471	+	0.105016i	$0.966511\pi$
$264$			1.00000i			0.0615457i
$265$	−29.0430	+	29.0430i	−1.78410	+	1.78410i
$266$	−18.0650	+	18.0650i	−1.10764	+	1.10764i
$267$	7.82907	+	7.82907i	0.479132	+	0.479132i
$268$	10.0270			0.612498
$269$	−20.6282	−	20.6282i	−1.25773	−	1.25773i	−0.952176	−	0.305550i	$-0.901160\pi$
$269$	−20.6282	−	20.6282i	−1.25773	−	1.25773i	−0.305550	−	0.952176i	$-0.598840\pi$
$270$			2.99043i			0.181992i
$271$	−5.75280			−0.349458			−0.174729	−	0.984617i	$-0.555905\pi$
$271$	−5.75280			−0.349458			−0.174729	+	0.984617i	$0.555905\pi$
$272$	4.12158	+	0.112193i	0.249907	+	0.00680271i
$273$	4.78903			0.289845
$274$		−	11.1312i		−	0.672461i
$275$	−2.78790	−	2.78790i	−0.168117	−	0.168117i
$276$	−8.06912			−0.485704
$277$	0.791792	+	0.791792i	0.0475742	+	0.0475742i	0.730494	−	0.682919i	$-0.239290\pi$
$277$	0.791792	+	0.791792i	0.0475742	+	0.0475742i	−0.682919	+	0.730494i	$0.739290\pi$
$278$	−6.70219	+	6.70219i	−0.401971	+	0.401971i
$279$	2.09392	−	2.09392i	0.125359	−	0.125359i
$280$		−	12.7727i		−	0.763317i
$281$		−	11.5402i		−	0.688428i	−0.938891	−	0.344214i	$-0.888145\pi$
$281$		−	11.5402i		−	0.688428i	0.938891	−	0.344214i	$-0.111855\pi$
$282$	9.33608	−	9.33608i	0.555955	−	0.555955i
$283$	6.51371	−	6.51371i	0.387200	−	0.387200i	−0.486488	−	0.873687i	$-0.661722\pi$
$283$	6.51371	−	6.51371i	0.387200	−	0.387200i	0.873687	+	0.486488i	$0.161722\pi$
$284$	−0.330151	−	0.330151i	−0.0195909	−	0.0195909i
$285$	−17.8870			−1.05953
$286$	0.792834	+	0.792834i	0.0468812	+	0.0468812i
$287$			25.0674i			1.47968i
$288$	−1.00000			−0.0589256
$289$	16.9748	+	0.924826i	0.998519	+	0.0544015i
$290$	−1.77937			−0.104488
$291$		−	2.54857i		−	0.149400i
$292$	9.32808	+	9.32808i	0.545885	+	0.545885i
$293$	−4.11555			−0.240433			−0.120217	−	0.992748i	$-0.538359\pi$
$293$	−4.11555			−0.240433			−0.120217	+	0.992748i	$0.538359\pi$
$294$	7.95011	+	7.95011i	0.463660	+	0.463660i
$295$	22.1628	−	22.1628i	1.29037	−	1.29037i
$296$	1.97499	−	1.97499i	0.114794	−	0.114794i
$297$		−	1.00000i		−	0.0580259i
$298$			18.6201i			1.07863i
$299$	−6.39747	+	6.39747i	−0.369975	+	0.369975i
$300$	2.78790	−	2.78790i	0.160960	−	0.160960i
$301$	18.0457	+	18.0457i	1.04014	+	1.04014i
$302$	19.5530			1.12515
$303$	−2.20830	−	2.20830i	−0.126864	−	0.126864i
$304$		−	5.98141i		−	0.343057i
$305$	−32.6455			−1.86928
$306$	−4.12158	−	0.112193i	−0.235615	−	0.00641366i
$307$	−19.7432			−1.12680			−0.563402	−	0.826183i	$-0.690508\pi$
$307$	−19.7432			−1.12680			−0.563402	+	0.826183i	$0.690508\pi$
$308$			4.27120i			0.243374i
$309$	−12.0318	−	12.0318i	−0.684468	−	0.684468i
$310$	−8.85540			−0.502953
$311$	9.47953	+	9.47953i	0.537535	+	0.537535i	0.922804	−	0.385269i	$-0.125891\pi$
$311$	9.47953	+	9.47953i	0.537535	+	0.537535i	−0.385269	+	0.922804i	$0.625891\pi$
$312$	−0.792834	+	0.792834i	−0.0448854	+	0.0448854i
$313$	−14.2347	+	14.2347i	−0.804590	+	0.804590i	−0.983809	−	0.179219i	$-0.942643\pi$
$313$	−14.2347	+	14.2347i	−0.804590	+	0.804590i	0.179219	+	0.983809i	$0.442643\pi$
$314$		−	10.1767i		−	0.574304i
$315$			12.7727i			0.719662i
$316$	−3.01568	+	3.01568i	−0.169646	+	0.169646i
$317$	17.1970	−	17.1970i	0.965877	−	0.965877i	−0.0335597	−	0.999437i	$-0.510684\pi$
$317$	17.1970	−	17.1970i	0.965877	−	0.965877i	0.999437	+	0.0335597i	$0.0106844\pi$
$318$	9.71199	+	9.71199i	0.544621	+	0.544621i
$319$	0.595021			0.0333148
$320$	2.11456	+	2.11456i	0.118207	+	0.118207i
$321$			18.3029i			1.02157i
$322$	−34.4648			−1.92065
$323$	0.671073	−	24.6528i	0.0373395	−	1.37172i
$324$	1.00000			0.0555556
$325$		−	4.42068i		−	0.245215i
$326$	6.76244	+	6.76244i	0.374537	+	0.374537i
$327$	−8.12086			−0.449084
$328$	−4.14996	−	4.14996i	−0.229143	−	0.229143i
$329$	39.8763	−	39.8763i	2.19845	−	2.19845i
$330$	−2.11456	+	2.11456i	−0.116402	+	0.116402i
$331$		−	3.89510i		−	0.214094i	−0.994254	−	0.107047i	$-0.965860\pi$
$331$		−	3.89510i		−	0.214094i	0.994254	−	0.107047i	$-0.0341395\pi$
$332$		−	7.58758i		−	0.416423i
$333$	−1.97499	+	1.97499i	−0.108229	+	0.108229i
$334$	15.0285	−	15.0285i	0.822323	−	0.822323i
$335$	21.2027	+	21.2027i	1.15843	+	1.15843i
$336$	−4.27120			−0.233013
$337$	16.2724	+	16.2724i	0.886416	+	0.886416i	0.994177	−	0.107761i	$-0.0343682\pi$
$337$	16.2724	+	16.2724i	0.886416	+	0.886416i	−0.107761	+	0.994177i	$0.534368\pi$
$338$		−	11.7428i		−	0.638726i
$339$	−1.15246			−0.0625931
$340$	8.47807	+	8.95254i	0.459788	+	0.485520i
$341$	2.96124			0.160360
$342$			5.98141i			0.323437i
$343$	12.8152	+	12.8152i	0.691954	+	0.691954i
$344$	−5.97503			−0.322152
$345$	−17.0626	−	17.0626i	−0.918619	−	0.918619i
$346$	−6.29902	+	6.29902i	−0.338637	+	0.338637i
$347$	21.0523	−	21.0523i	1.13015	−	1.13015i	0.139996	−	0.990152i	$-0.455291\pi$
$347$	21.0523	−	21.0523i	1.13015	−	1.13015i	0.990152	−	0.139996i	$-0.0447088\pi$
$348$			0.595021i			0.0318965i
$349$			5.24483i			0.280749i	0.990098	+	0.140375i	$0.0448307\pi$
$349$			5.24483i			0.280749i	−0.990098	+	0.140375i	$0.955169\pi$
$350$	11.9077	−	11.9077i	0.636493	−	0.636493i
$351$	0.792834	−	0.792834i	0.0423183	−	0.0423183i
$352$	−0.707107	−	0.707107i	−0.0376889	−	0.0376889i
$353$	17.7879			0.946753			0.473376	−	0.880860i	$-0.343035\pi$
$353$	17.7879			0.946753			0.473376	+	0.880860i	$0.343035\pi$
$354$	−7.41124	−	7.41124i	−0.393903	−	0.393903i
$355$		−	1.39625i		−	0.0741051i
$356$	−11.0720			−0.586814
$357$	−17.6041	−	0.479200i	−0.931707	−	0.0253619i
$358$	15.9031			0.840507
$359$		−	1.85284i		−	0.0977892i	−0.998804	−	0.0488946i	$-0.984430\pi$
$359$		−	1.85284i		−	0.0977892i	0.998804	−	0.0488946i	$-0.0155698\pi$
$360$	−2.11456	−	2.11456i	−0.111447	−	0.111447i
$361$	−16.7772			−0.883011
$362$	−3.98836	−	3.98836i	−0.209623	−	0.209623i
$363$	0.707107	−	0.707107i	0.0371135	−	0.0371135i
$364$	−3.38635	+	3.38635i	−0.177493	+	0.177493i
$365$			39.4495i			2.06488i
$366$			10.9167i			0.570623i
$367$	−15.9943	+	15.9943i	−0.834896	+	0.834896i	−0.988182	−	0.153286i	$-0.951015\pi$
$367$	−15.9943	+	15.9943i	−0.834896	+	0.834896i	0.153286	+	0.988182i	$0.451015\pi$
$368$	5.70573	−	5.70573i	0.297432	−	0.297432i
$369$	4.14996	+	4.14996i	0.216039	+	0.216039i
$370$	8.35247			0.434224
$371$	41.4819	+	41.4819i	2.15363	+	2.15363i
$372$			2.96124i			0.153533i
$373$	−18.9111			−0.979180			−0.489590	−	0.871953i	$-0.662854\pi$
$373$	−18.9111			−0.979180			−0.489590	+	0.871953i	$0.662854\pi$
$374$	−2.83506	−	2.99373i	−0.146598	−	0.154802i
$375$	−3.16182			−0.163276
$376$			13.2032i			0.680904i
$377$	0.471752	+	0.471752i	0.0242965	+	0.0242965i
$378$	4.27120			0.219687
$379$	−7.35474	−	7.35474i	−0.377788	−	0.377788i	0.492516	−	0.870304i	$-0.336077\pi$
$379$	−7.35474	−	7.35474i	−0.377788	−	0.377788i	−0.870304	+	0.492516i	$0.836077\pi$
$380$	12.6480	−	12.6480i	0.648829	−	0.648829i
$381$	−5.15276	+	5.15276i	−0.263984	+	0.263984i
$382$			0.138993i			0.00711150i
$383$			34.1209i			1.74350i	0.489954	+	0.871748i	$0.337013\pi$
$383$			34.1209i			1.74350i	−0.489954	+	0.871748i	$0.662987\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	−9.03169	+	9.03169i	−0.460298	+	0.460298i
$386$	10.6849	+	10.6849i	0.543845	+	0.543845i
$387$	5.97503			0.303728
$388$	1.80211	+	1.80211i	0.0914882	+	0.0914882i
$389$		−	19.5017i		−	0.988774i	−0.869242	−	0.494387i	$-0.835393\pi$
$389$		−	19.5017i		−	0.988774i	0.869242	−	0.494387i	$-0.164607\pi$
$390$	−3.35298			−0.169785
$391$	24.1568	−	22.8765i	1.22166	−	1.15691i
$392$	−11.2432			−0.567865
$393$			13.8868i			0.700498i
$394$	14.6643	+	14.6643i	0.738776	+	0.738776i
$395$	−12.7537			−0.641706
$396$	0.707107	+	0.707107i	0.0355335	+	0.0355335i
$397$	−9.74740	+	9.74740i	−0.489208	+	0.489208i	−0.908056	−	0.418848i	$-0.862434\pi$
$397$	−9.74740	+	9.74740i	−0.489208	+	0.489208i	0.418848	+	0.908056i	$0.362434\pi$
$398$	−0.962297	+	0.962297i	−0.0482356	+	0.0482356i
$399$			25.5478i			1.27899i
$400$			3.94269i			0.197134i
$401$	−14.6397	+	14.6397i	−0.731071	+	0.731071i	−0.970832	−	0.239761i	$-0.922931\pi$
$401$	−14.6397	+	14.6397i	−0.731071	+	0.731071i	0.239761	+	0.970832i	$0.422931\pi$
$402$	7.09018	−	7.09018i	0.353626	−	0.353626i
$403$	2.34777	+	2.34777i	0.116951	+	0.116951i
$404$	3.12301			0.155376
$405$	2.11456	+	2.11456i	0.105073	+	0.105073i
$406$			2.54145i			0.126130i
$407$	−2.79306			−0.138447
$408$	2.99373	−	2.83506i	0.148212	−	0.140357i
$409$	17.8551			0.882877			0.441439	−	0.897291i	$-0.354468\pi$
$409$	17.8551			0.882877			0.441439	+	0.897291i	$0.354468\pi$
$410$		−	17.5507i		−	0.866765i
$411$	−7.87095	−	7.87095i	−0.388245	−	0.388245i
$412$	17.0156			0.838298
$413$	−31.6549	−	31.6549i	−1.55764	−	1.55764i
$414$	−5.70573	+	5.70573i	−0.280421	+	0.280421i
$415$	16.0444	−	16.0444i	0.787586	−	0.787586i
$416$		−	1.12124i		−	0.0549731i
$417$			9.47833i			0.464156i
$418$	−4.22949	+	4.22949i	−0.206871	+	0.206871i
$419$	−1.94511	+	1.94511i	−0.0950247	+	0.0950247i	−0.753021	−	0.657996i	$-0.771404\pi$
$419$	−1.94511	+	1.94511i	−0.0950247	+	0.0950247i	0.657996	+	0.753021i	$0.271404\pi$
$420$	−9.03169	−	9.03169i	−0.440701	−	0.440701i
$421$	−17.0084			−0.828939			−0.414469	−	0.910063i	$-0.636033\pi$
$421$	−17.0084			−0.828939			−0.414469	+	0.910063i	$0.636033\pi$
$422$	0.689718	+	0.689718i	0.0335749	+	0.0335749i
$423$		−	13.2032i		−	0.641962i
$424$	−13.7348			−0.667022
$425$	−0.442343	+	16.2501i	−0.0214568	+	0.788245i
$426$	−0.466904			−0.0226216
$427$			46.6272i			2.25645i
$428$	−12.9421	−	12.9421i	−0.625581	−	0.625581i
$429$	1.12124			0.0541338
$430$	−12.6345	−	12.6345i	−0.609291	−	0.609291i
$431$	11.6671	−	11.6671i	0.561986	−	0.561986i	−0.367885	−	0.929871i	$-0.619918\pi$
$431$	11.6671	−	11.6671i	0.561986	−	0.561986i	0.929871	+	0.367885i	$0.119918\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$			4.25797i			0.204625i	0.994752	+	0.102312i	$0.0326242\pi$
$433$			4.25797i			0.204625i	−0.994752	+	0.102312i	$0.967376\pi$
$434$			12.6481i			0.607127i
$435$	−1.25820	+	1.25820i	−0.0603263	+	0.0603263i
$436$	5.74231	−	5.74231i	0.275007	−	0.275007i
$437$	−34.1283	−	34.1283i	−1.63258	−	1.63258i
$438$	13.1919			0.630333
$439$	−17.3144	−	17.3144i	−0.826371	−	0.826371i	0.160642	−	0.987013i	$-0.448644\pi$
$439$	−17.3144	−	17.3144i	−0.826371	−	0.826371i	−0.987013	+	0.160642i	$0.948644\pi$
$440$		−	2.99043i		−	0.142563i
$441$	11.2432			0.535388
$442$	0.125795	−	4.62126i	0.00598346	−	0.219811i
$443$	3.16713			0.150475			0.0752375	−	0.997166i	$-0.476029\pi$
$443$	3.16713			0.150475			0.0752375	+	0.997166i	$0.476029\pi$
$444$		−	2.79306i		−	0.132553i
$445$	−23.4123	−	23.4123i	−1.10985	−	1.10985i
$446$	−0.0302217			−0.00143104
$447$	13.1664	+	13.1664i	0.622749	+	0.622749i
$448$	3.02020	−	3.02020i	0.142691	−	0.142691i
$449$	8.23576	−	8.23576i	0.388670	−	0.388670i	−0.485543	−	0.874213i	$-0.661378\pi$
$449$	8.23576	−	8.23576i	0.388670	−	0.388670i	0.874213	+	0.485543i	$0.161378\pi$
$450$		−	3.94269i		−	0.185860i
$451$			5.86894i			0.276357i
$452$	0.814913	−	0.814913i	0.0383303	−	0.0383303i
$453$	13.8261	−	13.8261i	0.649606	−	0.649606i
$454$	3.47082	+	3.47082i	0.162894	+	0.162894i
$455$	−14.3213			−0.671391
$456$	−4.22949	−	4.22949i	−0.198064	−	0.198064i
$457$			20.4839i			0.958198i	0.877761	+	0.479099i	$0.159036\pi$
$457$			20.4839i			0.958198i	−0.877761	+	0.479099i	$0.840964\pi$
$458$	18.0229			0.842156
$459$	−2.99373	+	2.83506i	−0.139735	+	0.132329i
$460$	24.1302			1.12507
$461$		−	14.8103i		−	0.689787i	−0.938642	−	0.344893i	$-0.887915\pi$
$461$		−	14.8103i		−	0.689787i	0.938642	−	0.344893i	$-0.112085\pi$
$462$	3.02020	+	3.02020i	0.140512	+	0.140512i
$463$	−30.5599			−1.42024			−0.710120	−	0.704081i	$-0.751359\pi$
$463$	−30.5599			−1.42024			−0.710120	+	0.704081i	$0.751359\pi$
$464$	−0.420743	−	0.420743i	−0.0195325	−	0.0195325i
$465$	−6.26172	+	6.26172i	−0.290380	+	0.290380i
$466$	16.9619	−	16.9619i	0.785743	−	0.785743i
$467$		−	7.23663i		−	0.334871i	−0.985883	−	0.167436i	$-0.946451\pi$
$467$		−	7.23663i		−	0.334871i	0.985883	−	0.167436i	$-0.0535487\pi$
$468$			1.12124i			0.0518292i
$469$	30.2836	−	30.2836i	1.39837	−	1.39837i
$470$	−27.9189	+	27.9189i	−1.28780	+	1.28780i
$471$	−7.19601	−	7.19601i	−0.331575	−	0.331575i
$472$	10.4811			0.482431
$473$	4.22498	+	4.22498i	0.194265	+	0.194265i
$474$			4.26482i			0.195890i
$475$	23.5828			1.08205
$476$	12.7868	−	12.1091i	0.586083	−	0.555021i
$477$	13.7348			0.628874
$478$		−	29.4171i		−	1.34551i
$479$	−3.82787	−	3.82787i	−0.174900	−	0.174900i	0.614229	−	0.789128i	$-0.289467\pi$
$479$	−3.82787	−	3.82787i	−0.174900	−	0.174900i	−0.789128	+	0.614229i	$0.789467\pi$
$480$	2.99043			0.136494
$481$	−2.21444	−	2.21444i	−0.100970	−	0.100970i
$482$	4.18761	−	4.18761i	0.190740	−	0.190740i
$483$	−24.3703	+	24.3703i	−1.10889	+	1.10889i
$484$			1.00000i			0.0454545i
$485$			7.62131i			0.346066i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$	3.82865	−	3.82865i	0.173493	−	0.173493i	−0.615019	−	0.788512i	$-0.710852\pi$
$487$	3.82865	−	3.82865i	0.173493	−	0.173493i	0.788512	+	0.615019i	$0.210852\pi$
$488$	−7.71924	−	7.71924i	−0.349434	−	0.349434i
$489$	9.56353			0.432478
$490$	−23.7743	−	23.7743i	−1.07401	−	1.07401i
$491$			19.9571i			0.900653i	0.892864	+	0.450326i	$0.148692\pi$
$491$			19.9571i			0.900653i	−0.892864	+	0.450326i	$0.851308\pi$
$492$	−5.86894			−0.264592
$493$	−1.68692	−	1.78133i	−0.0759751	−	0.0802271i
$494$	−6.70657			−0.301743
$495$			2.99043i			0.134410i
$496$	−2.09392	−	2.09392i	−0.0940196	−	0.0940196i
$497$	−1.99424			−0.0894540
$498$	−5.36523	−	5.36523i	−0.240422	−	0.240422i
$499$	12.3020	−	12.3020i	0.550713	−	0.550713i	−0.375933	−	0.926647i	$-0.622678\pi$
$499$	12.3020	−	12.3020i	0.550713	−	0.550713i	0.926647	+	0.375933i	$0.122678\pi$
$500$	2.23575	−	2.23575i	0.0999856	−	0.0999856i
$501$		−	21.2535i		−	0.949537i
$502$			14.8831i			0.664267i
$503$	−3.02465	+	3.02465i	−0.134862	+	0.134862i	−0.771315	−	0.636453i	$-0.780401\pi$
$503$	−3.02465	+	3.02465i	−0.134862	+	0.134862i	0.636453	+	0.771315i	$0.280401\pi$
$504$	−3.02020	+	3.02020i	−0.134530	+	0.134530i
$505$	6.60378	+	6.60378i	0.293864	+	0.293864i
$506$	−8.06912			−0.358716
$507$	−8.30343	−	8.30343i	−0.368768	−	0.368768i
$508$		−	7.28710i		−	0.323313i
$509$	33.7726			1.49694			0.748471	−	0.663167i	$-0.230788\pi$
$509$	33.7726			1.49694			0.748471	+	0.663167i	$0.230788\pi$
$510$	12.3253	+	0.335506i	0.545774	+	0.0148565i
$511$	56.3452			2.49257
$512$			1.00000i			0.0441942i
$513$	4.22949	+	4.22949i	0.186737	+	0.186737i
$514$	4.23710			0.186890
$515$	35.9804	+	35.9804i	1.58549	+	1.58549i
$516$	−4.22498	+	4.22498i	−0.185994	+	0.185994i
$517$	9.33608	−	9.33608i	0.410600	−	0.410600i
$518$		−	11.9297i		−	0.524163i
$519$			8.90815i			0.391025i
$520$	2.37092	−	2.37092i	0.103972	−	0.103972i
$521$	−16.8109	+	16.8109i	−0.736497	+	0.736497i	−0.971898	−	0.235401i	$-0.924360\pi$
$521$	−16.8109	+	16.8109i	−0.736497	+	0.736497i	0.235401	+	0.971898i	$0.424360\pi$
$522$	0.420743	+	0.420743i	0.0184154	+	0.0184154i
$523$	−15.6990			−0.686468			−0.343234	−	0.939250i	$-0.611522\pi$
$523$	−15.6990			−0.686468			−0.343234	+	0.939250i	$0.611522\pi$
$524$	−9.81947	−	9.81947i	−0.428965	−	0.428965i
$525$		−	16.8400i		−	0.734958i
$526$	−3.40613			−0.148515
$527$	−8.39532	−	8.86516i	−0.365706	−	0.386173i
$528$	−1.00000			−0.0435194
$529$		−	42.1107i		−	1.83090i
$530$	−29.0430	−	29.0430i	−1.26155	−	1.26155i
$531$	−10.4811			−0.454840
$532$	−18.0650	−	18.0650i	−0.783218	−	0.783218i
$533$	−4.65309	+	4.65309i	−0.201548	+	0.201548i
$534$	−7.82907	+	7.82907i	−0.338797	+	0.338797i
$535$		−	54.7336i		−	2.36634i
$536$			10.0270i			0.433102i
$537$	11.2452	−	11.2452i	0.485267	−	0.485267i
$538$	20.6282	−	20.6282i	0.889346	−	0.889346i
$539$	7.95011	+	7.95011i	0.342436	+	0.342436i
$540$	−2.99043			−0.128688
$541$	−1.38048	−	1.38048i	−0.0593513	−	0.0593513i	0.676808	−	0.736159i	$-0.263363\pi$
$541$	−1.38048	−	1.38048i	−0.0593513	−	0.0593513i	−0.736159	+	0.676808i	$0.763363\pi$
$542$		−	5.75280i		−	0.247104i
$543$	−5.64039			−0.242052
$544$	−0.112193	+	4.12158i	−0.00481024	+	0.176711i
$545$	24.2849			1.04025
$546$			4.78903i			0.204951i
$547$	22.5809	+	22.5809i	0.965490	+	0.965490i	0.999424	−	0.0339345i	$-0.0108038\pi$
$547$	22.5809	+	22.5809i	0.965490	+	0.965490i	−0.0339345	+	0.999424i	$0.510804\pi$
$548$	11.1312			0.475502
$549$	7.71924	+	7.71924i	0.329449	+	0.329449i
$550$	2.78790	−	2.78790i	0.118876	−	0.118876i
$551$	−2.51664	+	2.51664i	−0.107212	+	0.107212i
$552$		−	8.06912i		−	0.343445i
$553$			18.2159i			0.774619i
$554$	−0.791792	+	0.791792i	−0.0336400	+	0.0336400i
$555$	5.90609	−	5.90609i	0.250699	−	0.250699i
$556$	−6.70219	−	6.70219i	−0.284236	−	0.284236i
$557$	26.1189			1.10669			0.553347	−	0.832951i	$-0.313350\pi$
$557$	26.1189			1.10669			0.553347	+	0.832951i	$0.313350\pi$
$558$	2.09392	+	2.09392i	0.0886425	+	0.0886425i
$559$			6.69942i			0.283355i
$560$	12.7727			0.539747
$561$	−4.12158	−	0.112193i	−0.174013	−	0.00473680i
$562$	11.5402			0.486792
$563$		−	8.78734i		−	0.370342i	−0.982706	−	0.185171i	$-0.940716\pi$
$563$		−	8.78734i		−	0.370342i	0.982706	−	0.185171i	$-0.0592839\pi$
$564$	9.33608	+	9.33608i	0.393120	+	0.393120i
$565$	3.44636			0.144989
$566$	6.51371	+	6.51371i	0.273792	+	0.273792i
$567$	3.02020	−	3.02020i	0.126836	−	0.126836i
$568$	0.330151	−	0.330151i	0.0138528	−	0.0138528i
$569$			2.61519i			0.109635i	0.998496	+	0.0548173i	$0.0174576\pi$
$569$			2.61519i			0.109635i	−0.998496	+	0.0548173i	$0.982542\pi$
$570$		−	17.8870i		−	0.749204i
$571$	14.2071	−	14.2071i	0.594549	−	0.594549i	−0.344308	−	0.938857i	$-0.611886\pi$
$571$	14.2071	−	14.2071i	0.594549	−	0.594549i	0.938857	+	0.344308i	$0.111886\pi$
$572$	−0.792834	+	0.792834i	−0.0331500	+	0.0331500i
$573$	0.0982828	+	0.0982828i	0.00410582	+	0.00410582i
$574$	−25.0674			−1.04629
$575$	22.4959	+	22.4959i	0.938144	+	0.938144i
$576$		−	1.00000i		−	0.0416667i
$577$	15.6246			0.650460			0.325230	−	0.945635i	$-0.394558\pi$
$577$	15.6246			0.650460			0.325230	+	0.945635i	$0.394558\pi$
$578$	−0.924826	+	16.9748i	−0.0384677	+	0.706060i
$579$	15.1107			0.627978
$580$		−	1.77937i		−	0.0738843i
$581$	−22.9160	−	22.9160i	−0.950715	−	0.950715i
$582$	2.54857			0.105641
$583$	9.71199	+	9.71199i	0.402229	+	0.402229i
$584$	−9.32808	+	9.32808i	−0.385999	+	0.385999i
$585$	−2.37092	+	2.37092i	−0.0980253	+	0.0980253i
$586$		−	4.11555i		−	0.170012i
$587$			7.75026i			0.319888i	0.987126	+	0.159944i	$0.0511313\pi$
$587$			7.75026i			0.319888i	−0.987126	+	0.159944i	$0.948869\pi$
$588$	−7.95011	+	7.95011i	−0.327857	+	0.327857i
$589$	−12.5246	+	12.5246i	−0.516066	+	0.516066i
$590$	22.1628	+	22.1628i	0.912429	+	0.912429i
$591$	20.7384			0.853065
$592$	1.97499	+	1.97499i	0.0811718	+	0.0811718i
$593$			21.8114i			0.895685i	0.894112	+	0.447843i	$0.147808\pi$
$593$			21.8114i			0.895685i	−0.894112	+	0.447843i	$0.852192\pi$
$594$	1.00000			0.0410305
$595$	52.6439	+	1.43301i	2.15819	+	0.0587478i
$596$	−18.6201			−0.762709
$597$			1.36089i			0.0556977i
$598$	−6.39747	−	6.39747i	−0.261612	−	0.261612i
$599$	8.15811			0.333331			0.166666	−	0.986013i	$-0.446700\pi$
$599$	8.15811			0.333331			0.166666	+	0.986013i	$0.446700\pi$
$600$	2.78790	+	2.78790i	0.113816	+	0.113816i
$601$	2.93219	−	2.93219i	0.119607	−	0.119607i	−0.644770	−	0.764377i	$-0.723047\pi$
$601$	2.93219	−	2.93219i	0.119607	−	0.119607i	0.764377	+	0.644770i	$0.223047\pi$
$602$	−18.0457	+	18.0457i	−0.735490	+	0.735490i
$603$		−	10.0270i		−	0.408332i
$604$			19.5530i			0.795601i
$605$	−2.11456	+	2.11456i	−0.0859689	+	0.0859689i
$606$	2.20830	−	2.20830i	0.0897062	−	0.0897062i
$607$	−3.77592	−	3.77592i	−0.153260	−	0.153260i	0.626312	−	0.779572i	$-0.284563\pi$
$607$	−3.77592	−	3.77592i	−0.153260	−	0.153260i	−0.779572	+	0.626312i	$0.784563\pi$
$608$	5.98141			0.242578
$609$	1.79708	+	1.79708i	0.0728213	+	0.0728213i
$610$		−	32.6455i		−	1.32178i
$611$	14.8039			0.598902
$612$	0.112193	−	4.12158i	0.00453514	−	0.166605i
$613$	−2.96313			−0.119680			−0.0598399	−	0.998208i	$-0.519059\pi$
$613$	−2.96313			−0.119680			−0.0598399	+	0.998208i	$0.519059\pi$
$614$		−	19.7432i		−	0.796771i
$615$	−12.4102	−	12.4102i	−0.500427	−	0.500427i
$616$	−4.27120			−0.172092
$617$	−17.5528	−	17.5528i	−0.706648	−	0.706648i	0.259181	−	0.965829i	$-0.416547\pi$
$617$	−17.5528	−	17.5528i	−0.706648	−	0.706648i	−0.965829	+	0.259181i	$0.916547\pi$
$618$	12.0318	−	12.0318i	0.483992	−	0.483992i
$619$	15.7107	−	15.7107i	0.631466	−	0.631466i	−0.316970	−	0.948436i	$-0.602665\pi$
$619$	15.7107	−	15.7107i	0.631466	−	0.631466i	0.948436	+	0.316970i	$0.102665\pi$
$620$		−	8.85540i		−	0.355642i
$621$			8.06912i			0.323803i
$622$	−9.47953	+	9.47953i	−0.380095	+	0.380095i
$623$	−33.4395	+	33.4395i	−1.33973	+	1.33973i
$624$	−0.792834	−	0.792834i	−0.0317387	−	0.0317387i
$625$	29.1687			1.16675
$626$	−14.2347	−	14.2347i	−0.568931	−	0.568931i
$627$			5.98141i			0.238874i
$628$	10.1767			0.406094
$629$	7.91852	+	8.36168i	0.315732	+	0.333402i
$630$	−12.7727			−0.508878
$631$			44.9639i			1.78998i	0.446082	+	0.894992i	$0.352819\pi$
$631$			44.9639i			1.78998i	−0.446082	+	0.894992i	$0.647181\pi$
$632$	−3.01568	−	3.01568i	−0.119958	−	0.119958i
$633$	0.975408			0.0387690
$634$	17.1970	+	17.1970i	0.682978	+	0.682978i
$635$	15.4090	−	15.4090i	0.611487	−	0.611487i
$636$	−9.71199	+	9.71199i	−0.385105	+	0.385105i
$637$			12.6062i			0.499477i
$638$			0.595021i			0.0235571i
$639$	−0.330151	+	0.330151i	−0.0130606	+	0.0130606i
$640$	−2.11456	+	2.11456i	−0.0835851	+	0.0835851i
$641$	−25.3010	−	25.3010i	−0.999328	−	0.999328i	0.000671831	−	1.00000i	$-0.499786\pi$
$641$	−25.3010	−	25.3010i	−0.999328	−	0.999328i	−1.00000		0.000671831i	$0.999786\pi$
$642$	−18.3029			−0.722358
$643$	17.4084	+	17.4084i	0.686519	+	0.686519i	0.961461	−	0.274942i	$-0.0886587\pi$
$643$	17.4084	+	17.4084i	0.686519	+	0.686519i	−0.274942	+	0.961461i	$0.588659\pi$
$644$		−	34.4648i		−	1.35810i
$645$	−17.8679			−0.703548
$646$	24.6528	+	0.671073i	0.969953	+	0.0264030i
$647$	−5.20422			−0.204599			−0.102300	−	0.994754i	$-0.532620\pi$
$647$	−5.20422			−0.204599			−0.102300	+	0.994754i	$0.532620\pi$
$648$			1.00000i			0.0392837i
$649$	−7.41124	−	7.41124i	−0.290917	−	0.290917i
$650$	4.42068			0.173393
$651$	8.94354	+	8.94354i	0.350525	+	0.350525i
$652$	−6.76244	+	6.76244i	−0.264837	+	0.264837i
$653$	1.58355	−	1.58355i	0.0619691	−	0.0619691i	−0.675443	−	0.737412i	$-0.736048\pi$
$653$	1.58355	−	1.58355i	0.0619691	−	0.0619691i	0.737412	+	0.675443i	$0.236048\pi$
$654$		−	8.12086i		−	0.317551i
$655$		−	41.5276i		−	1.62262i
$656$	4.14996	−	4.14996i	0.162029	−	0.162029i
$657$	9.32808	−	9.32808i	0.363923	−	0.363923i
$658$	39.8763	+	39.8763i	1.55454	+	1.55454i
$659$	29.5226			1.15004			0.575019	−	0.818140i	$-0.304994\pi$
$659$	29.5226			1.15004			0.575019	+	0.818140i	$0.304994\pi$
$660$	−2.11456	−	2.11456i	−0.0823089	−	0.0823089i
$661$			44.4435i			1.72865i	0.502932	+	0.864326i	$0.332255\pi$
$661$			44.4435i			1.72865i	−0.502932	+	0.864326i	$0.667745\pi$
$662$	3.89510			0.151387
$663$	−3.17878	−	3.35668i	−0.123453	−	0.130363i
$664$	7.58758			0.294455
$665$		−	76.3989i		−	2.96262i
$666$	−1.97499	−	1.97499i	−0.0765295	−	0.0765295i
$667$	−4.80129			−0.185907
$668$	15.0285	+	15.0285i	0.581470	+	0.581470i
$669$	−0.0213700	+	0.0213700i	−0.000826210	+	0.000826210i
$670$	−21.2027	+	21.2027i	−0.819132	+	0.819132i
$671$			10.9167i			0.421433i
$672$		−	4.27120i		−	0.164765i
$673$	1.11638	−	1.11638i	0.0430333	−	0.0430333i	−0.685263	−	0.728296i	$-0.740313\pi$
$673$	1.11638	−	1.11638i	0.0430333	−	0.0430333i	0.728296	+	0.685263i	$0.240313\pi$
$674$	−16.2724	+	16.2724i	−0.626791	+	0.626791i
$675$	−2.78790	−	2.78790i	−0.107306	−	0.107306i
$676$	11.7428			0.451647
$677$	−15.0131	−	15.0131i	−0.577000	−	0.577000i	0.357075	−	0.934076i	$-0.383774\pi$
$677$	−15.0131	−	15.0131i	−0.577000	−	0.577000i	−0.934076	+	0.357075i	$0.883774\pi$
$678$		−	1.15246i		−	0.0442600i
$679$	10.8854			0.417745
$680$	−8.95254	+	8.47807i	−0.343314	+	0.325119i
$681$	4.90848			0.188093
$682$			2.96124i			0.113392i
$683$	2.77997	+	2.77997i	0.106373	+	0.106373i	0.758290	−	0.651917i	$-0.226035\pi$
$683$	2.77997	+	2.77997i	0.106373	+	0.106373i	−0.651917	+	0.758290i	$0.726035\pi$
$684$	−5.98141			−0.228705
$685$	23.5375	+	23.5375i	0.899323	+	0.899323i
$686$	−12.8152	+	12.8152i	−0.489285	+	0.489285i
$687$	12.7441	−	12.7441i	0.486219	−	0.486219i
$688$		−	5.97503i		−	0.227796i
$689$			15.4000i			0.586693i
$690$	17.0626	−	17.0626i	0.649562	−	0.649562i
$691$	−18.1438	+	18.1438i	−0.690222	+	0.690222i	−0.962281	−	0.272059i	$-0.912295\pi$
$691$	−18.1438	+	18.1438i	−0.690222	+	0.690222i	0.272059	+	0.962281i	$0.412295\pi$
$692$	−6.29902	−	6.29902i	−0.239453	−	0.239453i
$693$	4.27120			0.162250
$694$	21.0523	+	21.0523i	0.799135	+	0.799135i
$695$		−	28.3443i		−	1.07516i
$696$	−0.595021			−0.0225542
$697$	17.5700	−	16.6388i	0.665511	−	0.630240i
$698$	−5.24483			−0.198520
$699$		−	23.9877i		−	0.907298i
$700$	11.9077	+	11.9077i	0.450068	+	0.450068i
$701$	2.91819			0.110219			0.0551093	−	0.998480i	$-0.482449\pi$
$701$	2.91819			0.110219			0.0551093	+	0.998480i	$0.482449\pi$
$702$	0.792834	+	0.792834i	0.0299236	+	0.0299236i
$703$	11.8132	−	11.8132i	0.445545	−	0.445545i
$704$	0.707107	−	0.707107i	0.0266501	−	0.0266501i
$705$			39.4833i			1.48703i
$706$			17.7879i			0.669455i
$707$	9.43211	−	9.43211i	0.354731	−	0.354731i
$708$	7.41124	−	7.41124i	0.278531	−	0.278531i
$709$	15.6387	+	15.6387i	0.587322	+	0.587322i	0.936905	−	0.349583i	$-0.113677\pi$
$709$	15.6387	+	15.6387i	0.587322	+	0.587322i	−0.349583	+	0.936905i	$0.613677\pi$
$710$	1.39625			0.0524002
$711$	3.01568	+	3.01568i	0.113097	+	0.113097i
$712$		−	11.0720i		−	0.414940i
$713$	−23.8946			−0.894861
$714$	0.479200	−	17.6041i	0.0179336	−	0.658817i
$715$	−3.35298			−0.125394
$716$			15.9031i			0.594328i
$717$	−20.8010	−	20.8010i	−0.776828	−	0.776828i
$718$	1.85284			0.0691474
$719$	5.84729	+	5.84729i	0.218067	+	0.218067i	0.807683	−	0.589616i	$-0.200721\pi$
$719$	5.84729	+	5.84729i	0.218067	+	0.218067i	−0.589616	+	0.807683i	$0.700721\pi$
$720$	2.11456	−	2.11456i	0.0788048	−	0.0788048i
$721$	51.3904	−	51.3904i	1.91388	−	1.91388i
$722$		−	16.7772i		−	0.624383i
$723$		−	5.92217i		−	0.220248i
$724$	3.98836	−	3.98836i	0.148226	−	0.148226i
$725$	1.65886	−	1.65886i	0.0616085	−	0.0616085i
$726$	0.707107	+	0.707107i	0.0262432	+	0.0262432i
$727$	4.14506			0.153732			0.0768659	−	0.997041i	$-0.475509\pi$
$727$	4.14506			0.153732			0.0768659	+	0.997041i	$0.475509\pi$
$728$	−3.38635	−	3.38635i	−0.125507	−	0.125507i
$729$		−	1.00000i		−	0.0370370i
$730$	−39.4495			−1.46009
$731$	0.670357	−	24.6265i	0.0247941	−	0.910846i
$732$	−10.9167			−0.403491
$733$		−	14.4474i		−	0.533627i	−0.963748	−	0.266813i	$-0.914029\pi$
$733$		−	14.4474i		−	0.533627i	0.963748	−	0.266813i	$-0.0859707\pi$
$734$	−15.9943	−	15.9943i	−0.590361	−	0.590361i
$735$	−33.6219			−1.24016
$736$	5.70573	+	5.70573i	0.210316	+	0.210316i
$737$	7.09018	−	7.09018i	0.261170	−	0.261170i
$738$	−4.14996	+	4.14996i	−0.152762	+	0.152762i
$739$			44.6137i			1.64114i	0.571545	+	0.820571i	$0.306344\pi$
$739$			44.6137i			1.64114i	−0.571545	+	0.820571i	$0.693656\pi$
$740$			8.35247i			0.307043i
$741$	−4.74226	+	4.74226i	−0.174211	+	0.174211i
$742$	−41.4819	+	41.4819i	−1.52285	+	1.52285i
$743$	35.2174	+	35.2174i	1.29200	+	1.29200i	0.933547	+	0.358455i	$0.116696\pi$
$743$	35.2174	+	35.2174i	1.29200	+	1.29200i	0.358455	+	0.933547i	$0.383304\pi$
$744$	−2.96124			−0.108565
$745$	−39.3732	−	39.3732i	−1.44252	−	1.44252i
$746$		−	18.9111i		−	0.692385i
$747$	−7.58758			−0.277615
$748$	2.99373	−	2.83506i	0.109462	−	0.103660i
$749$	−78.1754			−2.85647
$750$		−	3.16182i		−	0.115453i
$751$	32.1769	+	32.1769i	1.17415	+	1.17415i	0.981210	+	0.192943i	$0.0618034\pi$
$751$	32.1769	+	32.1769i	1.17415	+	1.17415i	0.192943	+	0.981210i	$0.438197\pi$
$752$	−13.2032			−0.481472
$753$	10.5240	+	10.5240i	0.383515	+	0.383515i
$754$	−0.471752	+	0.471752i	−0.0171802	+	0.0171802i
$755$	−41.3459	+	41.3459i	−1.50473	+	1.50473i
$756$			4.27120i			0.155342i
$757$			23.6107i			0.858147i	0.903270	+	0.429073i	$0.141160\pi$
$757$			23.6107i			0.858147i	−0.903270	+	0.429073i	$0.858840\pi$
$758$	7.35474	−	7.35474i	0.267136	−	0.267136i
$759$	−5.70573	+	5.70573i	−0.207105	+	0.207105i
$760$	12.6480	+	12.6480i	0.458792	+	0.458792i
$761$	29.5287			1.07042			0.535208	−	0.844721i	$-0.320233\pi$
$761$	29.5287			1.07042			0.535208	+	0.844721i	$0.320233\pi$
$762$	−5.15276	−	5.15276i	−0.186665	−	0.186665i
$763$		−	34.6858i		−	1.25571i
$764$	−0.138993			−0.00502859
$765$	8.95254	−	8.47807i	0.323680	−	0.306525i
$766$	−34.1209			−1.23284
$767$		−	11.7518i		−	0.424332i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	−29.0500			−1.04757			−0.523784	−	0.851851i	$-0.675480\pi$
$769$	−29.0500			−1.04757			−0.523784	+	0.851851i	$0.675480\pi$
$770$	−9.03169	−	9.03169i	−0.325480	−	0.325480i
$771$	2.99608	−	2.99608i	0.107901	−	0.107901i
$772$	−10.6849	+	10.6849i	−0.384557	+	0.384557i
$773$			25.3965i			0.913448i	0.889608	+	0.456724i	$0.150977\pi$
$773$			25.3965i			0.913448i	−0.889608	+	0.456724i	$0.849023\pi$
$774$			5.97503i			0.214768i
$775$	8.25566	−	8.25566i	0.296552	−	0.296552i
$776$	−1.80211	+	1.80211i	−0.0646919	+	0.0646919i
$777$	−8.43560	−	8.43560i	−0.302625	−	0.302625i
$778$	19.5017			0.699169
$779$	−24.8226	−	24.8226i	−0.889363	−	0.889363i
$780$		−	3.35298i		−	0.120056i
$781$	−0.466904			−0.0167072
$782$	22.8765	+	24.1568i	0.818061	+	0.863844i
$783$	0.595021			0.0212643
$784$		−	11.2432i		−	0.401541i
$785$	21.5192	+	21.5192i	0.768053	+	0.768053i
$786$	−13.8868			−0.495327
$787$	−16.9590	−	16.9590i	−0.604524	−	0.604524i	0.336986	−	0.941510i	$-0.390593\pi$
$787$	−16.9590	−	16.9590i	−0.604524	−	0.604524i	−0.941510	+	0.336986i	$0.890593\pi$
$788$	−14.6643	+	14.6643i	−0.522393	+	0.522393i
$789$	−2.40850	+	2.40850i	−0.0857449	+	0.0857449i
$790$		−	12.7537i		−	0.453755i
$791$		−	4.92239i		−	0.175020i
$792$	−0.707107	+	0.707107i	−0.0251259	+	0.0251259i
$793$	−8.65509	+	8.65509i	−0.307351	+	0.307351i
$794$	−9.74740	−	9.74740i	−0.345922	−	0.345922i
$795$	−41.0731			−1.45671
$796$	−0.962297	−	0.962297i	−0.0341077	−	0.0341077i
$797$			42.7690i			1.51495i	0.652862	+	0.757477i	$0.273568\pi$
$797$			42.7690i			1.51495i	−0.652862	+	0.757477i	$0.726432\pi$
$798$	−25.5478			−0.904382
$799$	−54.4181	−	1.48131i	−1.92517	−	0.0524050i
$800$	−3.94269			−0.139395
$801$			11.0720i			0.391209i
$802$	−14.6397	−	14.6397i	−0.516945	−	0.516945i
$803$	13.1919			0.465532
$804$	7.09018	+	7.09018i	0.250051	+	0.250051i
$805$	72.8778	−	72.8778i	2.56860	−	2.56860i
$806$	−2.34777	+	2.34777i	−0.0826968	+	0.0826968i
$807$		−	29.1727i		−	1.02693i
$808$			3.12301i			0.109867i
$809$	−0.233700	+	0.233700i	−0.00821645	+	0.00821645i	−0.711203	−	0.702987i	$-0.751849\pi$
$809$	−0.233700	+	0.233700i	−0.00821645	+	0.00821645i	0.702987	+	0.711203i	$0.251849\pi$
$810$	−2.11456	+	2.11456i	−0.0742979	+	0.0742979i
$811$	17.7990	+	17.7990i	0.625009	+	0.625009i	0.946808	−	0.321799i	$-0.104288\pi$
$811$	17.7990	+	17.7990i	0.625009	+	0.625009i	−0.321799	+	0.946808i	$0.604288\pi$
$812$	−2.54145			−0.0891875
$813$	−4.06784	−	4.06784i	−0.142665	−	0.142665i
$814$		−	2.79306i		−	0.0978968i
$815$	−28.5991			−1.00178
$816$	2.83506	+	2.99373i	0.0992471	+	0.104801i
$817$	−35.7391			−1.25035
$818$			17.8551i			0.624288i
$819$	3.38635	+	3.38635i	0.118329	+	0.118329i
$820$	17.5507			0.612896
$821$	35.9613	+	35.9613i	1.25506	+	1.25506i	0.953423	+	0.301637i	$0.0975329\pi$
$821$	35.9613	+	35.9613i	1.25506	+	1.25506i	0.301637	+	0.953423i	$0.402467\pi$
$822$	7.87095	−	7.87095i	0.274531	−	0.274531i
$823$	−19.2350	+	19.2350i	−0.670489	+	0.670489i	−0.957829	−	0.287339i	$-0.907229\pi$
$823$	−19.2350	+	19.2350i	−0.670489	+	0.670489i	0.287339	+	0.957829i	$0.407229\pi$
$824$			17.0156i			0.592766i
$825$		−	3.94269i		−	0.137267i
$826$	31.6549	−	31.6549i	1.10141	−	1.10141i
$827$	−28.0245	+	28.0245i	−0.974507	+	0.974507i	−0.999683	−	0.0251762i	$-0.991985\pi$
$827$	−28.0245	+	28.0245i	−0.974507	+	0.974507i	0.0251762	+	0.999683i	$0.491985\pi$
$828$	−5.70573	−	5.70573i	−0.198288	−	0.198288i
$829$	−8.45503			−0.293655			−0.146828	−	0.989162i	$-0.546906\pi$
$829$	−8.45503			−0.293655			−0.146828	+	0.989162i	$0.546906\pi$
$830$	16.0444	+	16.0444i	0.556908	+	0.556908i
$831$			1.11976i			0.0388442i
$832$	1.12124			0.0388719
$833$	1.26141	−	46.3396i	0.0437051	−	1.60557i
$834$	−9.47833			−0.328208
$835$			63.5572i			2.19949i
$836$	−4.22949	−	4.22949i	−0.146280	−	0.146280i
$837$	2.96124			0.102356
$838$	−1.94511	−	1.94511i	−0.0671926	−	0.0671926i
$839$	3.82983	−	3.82983i	0.132221	−	0.132221i	−0.637899	−	0.770120i	$-0.720196\pi$
$839$	3.82983	−	3.82983i	0.132221	−	0.132221i	0.770120	+	0.637899i	$0.220196\pi$
$840$	9.03169	−	9.03169i	0.311623	−	0.311623i
$841$		−	28.6460i		−	0.987791i
$842$		−	17.0084i		−	0.586148i
$843$	8.16012	−	8.16012i	0.281050	−	0.281050i
$844$	−0.689718	+	0.689718i	−0.0237411	+	0.0237411i
$845$	24.8309	+	24.8309i	0.854208	+	0.854208i
$846$	13.2032			0.453936
$847$	3.02020	+	3.02020i	0.103775	+	0.103775i
$848$		−	13.7348i		−	0.471656i
$849$	9.21177			0.316147
$850$	−16.2501	−	0.442343i	−0.557374	−	0.0151722i
$851$	22.5376			0.772578
$852$		−	0.466904i		−	0.0159959i
$853$	26.8885	+	26.8885i	0.920645	+	0.920645i	0.997075	−	0.0764301i	$-0.0243522\pi$
$853$	26.8885	+	26.8885i	0.920645	+	0.920645i	−0.0764301	+	0.997075i	$0.524352\pi$
$854$	−46.6272			−1.59555
$855$	−12.6480	−	12.6480i	−0.432553	−	0.432553i
$856$	12.9421	−	12.9421i	0.442352	−	0.442352i
$857$	−0.411018	+	0.411018i	−0.0140401	+	0.0140401i	−0.714092	−	0.700052i	$-0.753160\pi$
$857$	−0.411018	+	0.411018i	−0.0140401	+	0.0140401i	0.700052	+	0.714092i	$0.253160\pi$
$858$			1.12124i			0.0382784i
$859$		−	13.5632i		−	0.462771i	−0.972862	−	0.231385i	$-0.925674\pi$
$859$		−	13.5632i		−	0.462771i	0.972862	−	0.231385i	$-0.0743258\pi$
$860$	12.6345	−	12.6345i	0.430834	−	0.430834i
$861$	−17.7253	+	17.7253i	−0.604078	+	0.604078i
$862$	11.6671	+	11.6671i	0.397384	+	0.397384i
$863$	−32.6188			−1.11036			−0.555179	−	0.831731i	$-0.687350\pi$
$863$	−32.6188			−1.11036			−0.555179	+	0.831731i	$0.687350\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$		−	26.6392i		−	0.905761i
$866$	−4.25797			−0.144692
$867$	11.3491	+	12.6570i	0.385434	+	0.429853i
$868$	−12.6481			−0.429304
$869$			4.26482i			0.144674i
$870$	−1.25820	−	1.25820i	−0.0426571	−	0.0426571i
$871$	11.2427			0.380943
$872$	5.74231	+	5.74231i	0.194459	+	0.194459i
$873$	1.80211	−	1.80211i	0.0609921	−	0.0609921i
$874$	34.1283	−	34.1283i	1.15441	−	1.15441i
$875$		−	13.5048i		−	0.456545i
$876$			13.1919i			0.445713i
$877$	7.51510	−	7.51510i	0.253767	−	0.253767i	−0.568746	−	0.822513i	$-0.692571\pi$
$877$	7.51510	−	7.51510i	0.253767	−	0.253767i	0.822513	+	0.568746i	$0.192571\pi$
$878$	17.3144	−	17.3144i	0.584332	−	0.584332i
$879$	−2.91013	−	2.91013i	−0.0981564	−	0.0981564i
$880$	2.99043			0.100807
$881$	−36.5663	−	36.5663i	−1.23195	−	1.23195i	−0.963214	−	0.268736i	$-0.913394\pi$
$881$	−36.5663	−	36.5663i	−1.23195	−	1.23195i	−0.268736	−	0.963214i	$-0.586606\pi$
$882$			11.2432i			0.378577i
$883$	30.1755			1.01549			0.507743	−	0.861509i	$-0.330480\pi$
$883$	30.1755			1.01549			0.507743	+	0.861509i	$0.330480\pi$
$884$	4.62126	+	0.125795i	0.155430	+	0.00423094i
$885$	31.3430			1.05358
$886$			3.16713i			0.106402i
$887$	−27.3655	−	27.3655i	−0.918844	−	0.918844i	0.0781018	−	0.996945i	$-0.475114\pi$
$887$	−27.3655	−	27.3655i	−0.918844	−	0.918844i	−0.996945	+	0.0781018i	$0.975114\pi$
$888$	2.79306			0.0937291
$889$	−22.0085	−	22.0085i	−0.738140	−	0.738140i
$890$	23.4123	−	23.4123i	0.784783	−	0.784783i
$891$	0.707107	−	0.707107i	0.0236890	−	0.0236890i
$892$		−	0.0302217i		−	0.00101190i
$893$			78.9738i			2.64276i
$894$	−13.1664	+	13.1664i	−0.440350	+	0.440350i
$895$	−33.6280	+	33.6280i	−1.12406	+	1.12406i
$896$	3.02020	+	3.02020i	0.100898	+	0.100898i
$897$	−9.04739			−0.302083
$898$	8.23576	+	8.23576i	0.274831	+	0.274831i
$899$			1.76200i			0.0587661i
$900$	3.94269			0.131423
$901$	1.54095	−	56.6092i	0.0513366	−	1.88592i
$902$	−5.86894			−0.195414
$903$			25.5205i			0.849270i
$904$	0.814913	+	0.814913i	0.0271036	+	0.0271036i
$905$	16.8672			0.560685
$906$	13.8261	+	13.8261i	0.459341	+	0.459341i
$907$	−17.2373	+	17.2373i	−0.572356	+	0.572356i	−0.932786	−	0.360430i	$-0.882630\pi$
$907$	−17.2373	+	17.2373i	−0.572356	+	0.572356i	0.360430	+	0.932786i	$0.382630\pi$
$908$	−3.47082	+	3.47082i	−0.115183	+	0.115183i
$909$		−	3.12301i		−	0.103584i
$910$		−	14.3213i		−	0.474745i
$911$	−8.37784	+	8.37784i	−0.277570	+	0.277570i	−0.832138	−	0.554568i	$-0.812884\pi$
$911$	−8.37784	+	8.37784i	−0.277570	+	0.277570i	0.554568	+	0.832138i	$0.312884\pi$
$912$	4.22949	−	4.22949i	0.140052	−	0.140052i
$913$	−5.36523	−	5.36523i	−0.177563	−	0.177563i
$914$	−20.4839			−0.677548
$915$	−23.0839	−	23.0839i	−0.763129	−	0.763129i
$916$			18.0229i			0.595494i
$917$	−59.3134			−1.95870
$918$	−2.83506	−	2.99373i	−0.0935711	−	0.0988078i
$919$	−56.9896			−1.87991			−0.939957	−	0.341292i	$-0.889135\pi$
$919$	−56.9896			−1.87991			−0.939957	+	0.341292i	$0.889135\pi$
$920$			24.1302i			0.795548i
$921$	−13.9606	−	13.9606i	−0.460016	−	0.460016i
$922$	14.8103			0.487753
$923$	−0.370178	−	0.370178i	−0.0121845	−	0.0121845i
$924$	−3.02020	+	3.02020i	−0.0993571	+	0.0993571i
$925$	−7.78679	+	7.78679i	−0.256028	+	0.256028i
$926$		−	30.5599i		−	1.00426i
$927$		−	17.0156i		−	0.558865i
$928$	0.420743	−	0.420743i	0.0138116	−	0.0138116i
$929$	−24.2275	+	24.2275i	−0.794878	+	0.794878i	−0.982283	−	0.187405i	$-0.939992\pi$
$929$	−24.2275	+	24.2275i	−0.794878	+	0.794878i	0.187405	+	0.982283i	$0.439992\pi$
$930$	−6.26172	−	6.26172i	−0.205330	−	0.205330i
$931$	−67.2499			−2.20403
$932$	16.9619	+	16.9619i	0.555604	+	0.555604i
$933$			13.4061i			0.438896i
$934$	7.23663			0.236790
$935$	12.3253	+	0.335506i	0.403081	+	0.0109722i
$936$	−1.12124			−0.0366488
$937$		−	19.9459i		−	0.651604i	−0.945438	−	0.325802i	$-0.894366\pi$
$937$		−	19.9459i		−	0.651604i	0.945438	−	0.325802i	$-0.105634\pi$
$938$	30.2836	+	30.2836i	0.988794	+	0.988794i
$939$	−20.1308			−0.656945
$940$	−27.9189	−	27.9189i	−0.910615	−	0.910615i
$941$	21.8964	−	21.8964i	0.713802	−	0.713802i	−0.253527	−	0.967328i	$-0.581591\pi$
$941$	21.8964	−	21.8964i	0.713802	−	0.713802i	0.967328	+	0.253527i	$0.0815905\pi$
$942$	7.19601	−	7.19601i	0.234459	−	0.234459i
$943$		−	47.3571i		−	1.54216i
$944$			10.4811i			0.341130i
$945$	−9.03169	+	9.03169i	−0.293801	+	0.293801i
$946$	−4.22498	+	4.22498i	−0.137366	+	0.137366i
$947$	36.2745	+	36.2745i	1.17876	+	1.17876i	0.980060	+	0.198704i	$0.0636732\pi$
$947$	36.2745	+	36.2745i	1.17876	+	1.17876i	0.198704	+	0.980060i	$0.436327\pi$
$948$	−4.26482			−0.138515
$949$	10.4590	+	10.4590i	0.339513	+	0.339513i
$950$			23.5828i			0.765127i
$951$	24.3202			0.788635
$952$	12.1091	+	12.7868i	0.392459	+	0.414423i
$953$	−7.70698			−0.249653			−0.124827	−	0.992179i	$-0.539837\pi$
$953$	−7.70698			−0.249653			−0.124827	+	0.992179i	$0.539837\pi$
$954$			13.7348i			0.444681i
$955$	−0.293908	−	0.293908i	−0.00951065	−	0.00951065i
$956$	29.4171			0.951416
$957$	0.420743	+	0.420743i	0.0136007	+	0.0136007i
$958$	3.82787	−	3.82787i	0.123673	−	0.123673i
$959$	33.6184	−	33.6184i	1.08560	−	1.08560i
$960$			2.99043i			0.0965158i
$961$		−	22.2310i		−	0.717130i
$962$	2.21444	−	2.21444i	0.0713963	−	0.0713963i
$963$	−12.9421	+	12.9421i	−0.417054	+	0.417054i
$964$	4.18761	+	4.18761i	0.134874	+	0.134874i
$965$	−45.1875			−1.45464
$966$	−24.3703	−	24.3703i	−0.784102	−	0.784102i
$967$		−	60.3430i		−	1.94050i	−0.242102	−	0.970251i	$-0.577837\pi$
$967$		−	60.3430i		−	1.94050i	0.242102	−	0.970251i	$-0.422163\pi$
$968$	−1.00000			−0.0321412
$969$	17.9067	−	16.9577i	0.575246	−	0.544759i
$970$	−7.62131			−0.244706
$971$		−	39.4228i		−	1.26514i	−0.774504	−	0.632569i	$-0.782000\pi$
$971$		−	39.4228i		−	1.26514i	0.774504	−	0.632569i	$-0.218000\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	−40.4838			−1.29785
$974$	3.82865	+	3.82865i	0.122678	+	0.122678i
$975$	3.12590	−	3.12590i	0.100109	−	0.100109i
$976$	7.71924	−	7.71924i	0.247087	−	0.247087i
$977$			13.6923i			0.438056i	0.975719	+	0.219028i	$0.0702887\pi$
$977$			13.6923i			0.438056i	−0.975719	+	0.219028i	$0.929711\pi$
$978$			9.56353i			0.305808i
$979$	−7.82907	+	7.82907i	−0.250218	+	0.250218i
$980$	23.7743	−	23.7743i	0.759441	−	0.759441i
$981$	−5.74231	−	5.74231i	−0.183338	−	0.183338i
$982$	−19.9571			−0.636858
$983$	14.3329	+	14.3329i	0.457150	+	0.457150i	0.897719	−	0.440569i	$-0.145223\pi$
$983$	14.3329	+	14.3329i	0.457150	+	0.457150i	−0.440569	+	0.897719i	$0.645223\pi$
$984$		−	5.86894i		−	0.187095i
$985$	−62.0169			−1.97602
$986$	1.78133	−	1.68692i	0.0567291	−	0.0537225i
$987$	56.3936			1.79503
$988$		−	6.70657i		−	0.213364i
$989$	−34.0919	−	34.0919i	−1.08406	−	1.08406i
$990$	−2.99043			−0.0950422
$991$	26.0708	+	26.0708i	0.828167	+	0.828167i	0.987263	−	0.159096i	$-0.0508579\pi$
$991$	26.0708	+	26.0708i	0.828167	+	0.828167i	−0.159096	+	0.987263i	$0.550858\pi$
$992$	2.09392	−	2.09392i	0.0664819	−	0.0664819i
$993$	2.75425	−	2.75425i	0.0874035	−	0.0874035i
$994$		−	1.99424i		−	0.0632535i
$995$		−	4.06966i		−	0.129017i
$996$	5.36523	−	5.36523i	0.170004	−	0.170004i
$997$	−13.9753	+	13.9753i	−0.442602	+	0.442602i	−0.892885	−	0.450284i	$-0.851323\pi$
$997$	−13.9753	+	13.9753i	−0.442602	+	0.442602i	0.450284	+	0.892885i	$0.351323\pi$
$998$	12.3020	+	12.3020i	0.389413	+	0.389413i
$999$	−2.79306			−0.0883686

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1122.2.l.g.727.7	yes	20
17.4	even	4	inner	1122.2.l.g.463.7	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1122.2.l.g.463.7	✓	20	17.4	even	4	inner
1122.2.l.g.727.7	yes	20	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:	\( N \)	\(=\)	\( 1122 = 2 \cdot 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1122.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.11456 - 2.11456i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-3.02020 + 3.02020i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.11456 - 2.11456i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-3.02020 + 3.02020i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(2.11456 - 2.11456i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(-0.707107 - 0.707107i) q^{12} -1.12124 q^{13} +(-3.02020 - 3.02020i) q^{14} -2.99043i q^{15} +1.00000 q^{16} +(4.12158 + 0.112193i) q^{17} -1.00000 q^{18} -5.98141i q^{19} +(2.11456 + 2.11456i) q^{20} -4.27120 q^{21} +(-0.707107 - 0.707107i) q^{22} +(5.70573 - 5.70573i) q^{23} +(0.707107 - 0.707107i) q^{24} +3.94269i q^{25} -1.12124i q^{26} +(-0.707107 + 0.707107i) q^{27} +(3.02020 - 3.02020i) q^{28} +(-0.420743 - 0.420743i) q^{29} +2.99043 q^{30} +(-2.09392 - 2.09392i) q^{31} +1.00000i q^{32} -1.00000 q^{33} +(-0.112193 + 4.12158i) q^{34} +12.7727 q^{35} -1.00000i q^{36} +(1.97499 + 1.97499i) q^{37} +5.98141 q^{38} +(-0.792834 - 0.792834i) q^{39} +(-2.11456 + 2.11456i) q^{40} +(4.14996 - 4.14996i) q^{41} -4.27120i q^{42} -5.97503i q^{43} +(0.707107 - 0.707107i) q^{44} +(2.11456 - 2.11456i) q^{45} +(5.70573 + 5.70573i) q^{46} -13.2032 q^{47} +(0.707107 + 0.707107i) q^{48} -11.2432i q^{49} -3.94269 q^{50} +(2.83506 + 2.99373i) q^{51} +1.12124 q^{52} -13.7348i q^{53} +(-0.707107 - 0.707107i) q^{54} +2.99043 q^{55} +(3.02020 + 3.02020i) q^{56} +(4.22949 - 4.22949i) q^{57} +(0.420743 - 0.420743i) q^{58} +10.4811i q^{59} +2.99043i q^{60} +(7.71924 - 7.71924i) q^{61} +(2.09392 - 2.09392i) q^{62} +(-3.02020 - 3.02020i) q^{63} -1.00000 q^{64} +(2.37092 + 2.37092i) q^{65} -1.00000i q^{66} -10.0270 q^{67} +(-4.12158 - 0.112193i) q^{68} +8.06912 q^{69} +12.7727i q^{70} +(0.330151 + 0.330151i) q^{71} +1.00000 q^{72} +(-9.32808 - 9.32808i) q^{73} +(-1.97499 + 1.97499i) q^{74} +(-2.78790 + 2.78790i) q^{75} +5.98141i q^{76} -4.27120i q^{77} +(0.792834 - 0.792834i) q^{78} +(3.01568 - 3.01568i) q^{79} +(-2.11456 - 2.11456i) q^{80} -1.00000 q^{81} +(4.14996 + 4.14996i) q^{82} +7.58758i q^{83} +4.27120 q^{84} +(-8.47807 - 8.95254i) q^{85} +5.97503 q^{86} -0.595021i q^{87} +(0.707107 + 0.707107i) q^{88} +11.0720 q^{89} +(2.11456 + 2.11456i) q^{90} +(3.38635 - 3.38635i) q^{91} +(-5.70573 + 5.70573i) q^{92} -2.96124i q^{93} -13.2032i q^{94} +(-12.6480 + 12.6480i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(-1.80211 - 1.80211i) q^{97} +11.2432 q^{98} +(-0.707107 - 0.707107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{4} - 4 q^{5}+O(q^{10}) \) 20 * q - 20 * q^4 - 4 * q^5	\( 20 q - 20 q^{4} - 4 q^{5} + 4 q^{10} + 20 q^{16} - 12 q^{17} - 20 q^{18} + 4 q^{20} + 16 q^{23} + 4 q^{29} - 8 q^{31} - 20 q^{33} + 16 q^{35} - 20 q^{37} + 8 q^{39} - 4 q^{40} + 20 q^{41} + 4 q^{45} + 16 q^{46} - 16 q^{47} - 68 q^{50} + 8 q^{57} - 4 q^{58} - 20 q^{61} + 8 q^{62} - 20 q^{64} + 8 q^{65} - 48 q^{67} + 12 q^{68} - 32 q^{71} + 20 q^{72} + 20 q^{73} + 20 q^{74} - 8 q^{75} - 8 q^{78} - 16 q^{79} - 4 q^{80} - 20 q^{81} + 20 q^{82} - 4 q^{85} - 16 q^{86} + 4 q^{90} + 88 q^{91} - 16 q^{92} - 48 q^{95} + 4 q^{97} + 36 q^{98}+O(q^{100}) \) 20 * q - 20 * q^4 - 4 * q^5 + 4 * q^10 + 20 * q^16 - 12 * q^17 - 20 * q^18 + 4 * q^20 + 16 * q^23 + 4 * q^29 - 8 * q^31 - 20 * q^33 + 16 * q^35 - 20 * q^37 + 8 * q^39 - 4 * q^40 + 20 * q^41 + 4 * q^45 + 16 * q^46 - 16 * q^47 - 68 * q^50 + 8 * q^57 - 4 * q^58 - 20 * q^61 + 8 * q^62 - 20 * q^64 + 8 * q^65 - 48 * q^67 + 12 * q^68 - 32 * q^71 + 20 * q^72 + 20 * q^73 + 20 * q^74 - 8 * q^75 - 8 * q^78 - 16 * q^79 - 4 * q^80 - 20 * q^81 + 20 * q^82 - 4 * q^85 - 16 * q^86 + 4 * q^90 + 88 * q^91 - 16 * q^92 - 48 * q^95 + 4 * q^97 + 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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