LMFDB - Embedded newform 102.2.f.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [102,2,Mod(13,102)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(102, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("102.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 102 = 2 \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	102.f (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:	$0.814474100617$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.2
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	102.13
Dual form			102.2.f.a.55.2

$q$-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} +(0.414214 + 0.414214i) q^{5} +(0.707107 - 0.707107i) q^{6} +(3.41421 - 3.41421i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(0.414214 - 0.414214i) q^{10} +(-2.82843 + 2.82843i) q^{11} +(-0.707107 - 0.707107i) q^{12} -2.82843 q^{13} +(-3.41421 - 3.41421i) q^{14} +0.585786i q^{15} +1.00000 q^{16} +(-3.00000 - 2.82843i) q^{17} +1.00000 q^{18} +6.82843i q^{19} +(-0.414214 - 0.414214i) q^{20} +4.82843 q^{21} +(2.82843 + 2.82843i) q^{22} +(-2.24264 + 2.24264i) q^{23} +(-0.707107 + 0.707107i) q^{24} -4.65685i q^{25} +2.82843i q^{26} +(-0.707107 + 0.707107i) q^{27} +(-3.41421 + 3.41421i) q^{28} +(-0.414214 - 0.414214i) q^{29} +0.585786 q^{30} +(0.585786 + 0.585786i) q^{31} -1.00000i q^{32} -4.00000 q^{33} +(-2.82843 + 3.00000i) q^{34} +2.82843 q^{35} -1.00000i q^{36} +(-1.58579 - 1.58579i) q^{37} +6.82843 q^{38} +(-2.00000 - 2.00000i) q^{39} +(-0.414214 + 0.414214i) q^{40} +(-2.17157 + 2.17157i) q^{41} -4.82843i q^{42} +1.65685i q^{43} +(2.82843 - 2.82843i) q^{44} +(-0.414214 + 0.414214i) q^{45} +(2.24264 + 2.24264i) q^{46} +12.4853 q^{47} +(0.707107 + 0.707107i) q^{48} -16.3137i q^{49} -4.65685 q^{50} +(-0.121320 - 4.12132i) q^{51} +2.82843 q^{52} -2.82843i q^{53} +(0.707107 + 0.707107i) q^{54} -2.34315 q^{55} +(3.41421 + 3.41421i) q^{56} +(-4.82843 + 4.82843i) q^{57} +(-0.414214 + 0.414214i) q^{58} -12.4853i q^{59} -0.585786i q^{60} +(0.757359 - 0.757359i) q^{61} +(0.585786 - 0.585786i) q^{62} +(3.41421 + 3.41421i) q^{63} -1.00000 q^{64} +(-1.17157 - 1.17157i) q^{65} +4.00000i q^{66} +1.17157 q^{67} +(3.00000 + 2.82843i) q^{68} -3.17157 q^{69} -2.82843i q^{70} +(4.58579 + 4.58579i) q^{71} -1.00000 q^{72} +(6.65685 + 6.65685i) q^{73} +(-1.58579 + 1.58579i) q^{74} +(3.29289 - 3.29289i) q^{75} -6.82843i q^{76} +19.3137i q^{77} +(-2.00000 + 2.00000i) q^{78} +(-10.2426 + 10.2426i) q^{79} +(0.414214 + 0.414214i) q^{80} -1.00000 q^{81} +(2.17157 + 2.17157i) q^{82} -4.48528i q^{83} -4.82843 q^{84} +(-0.0710678 - 2.41421i) q^{85} +1.65685 q^{86} -0.585786i q^{87} +(-2.82843 - 2.82843i) q^{88} +(0.414214 + 0.414214i) q^{90} +(-9.65685 + 9.65685i) q^{91} +(2.24264 - 2.24264i) q^{92} +0.828427i q^{93} -12.4853i q^{94} +(-2.82843 + 2.82843i) q^{95} +(0.707107 - 0.707107i) q^{96} +(-9.48528 - 9.48528i) q^{97} -16.3137 q^{98} +(-2.82843 - 2.82843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 4 q^{5} + 8 q^{7} - 4 q^{10} - 8 q^{14} + 4 q^{16} - 12 q^{17} + 4 q^{18} + 4 q^{20} + 8 q^{21} + 8 q^{23} - 8 q^{28} + 4 q^{29} + 8 q^{30} + 8 q^{31} - 16 q^{33} - 12 q^{37} + 16 q^{38}+ \cdots - 20 q^{98}+O(q^{100}) $ 4 * q - 4 * q^4 - 4 * q^5 + 8 * q^7 - 4 * q^10 - 8 * q^14 + 4 * q^16 - 12 * q^17 + 4 * q^18 + 4 * q^20 + 8 * q^21 + 8 * q^23 - 8 * q^28 + 4 * q^29 + 8 * q^30 + 8 * q^31 - 16 * q^33 - 12 * q^37 + 16 * q^38 - 8 * q^39 + 4 * q^40 - 20 * q^41 + 4 * q^45 - 8 * q^46 + 16 * q^47 + 4 * q^50 + 8 * q^51 - 32 * q^55 + 8 * q^56 - 8 * q^57 + 4 * q^58 + 20 * q^61 + 8 * q^62 + 8 * q^63 - 4 * q^64 - 16 * q^65 + 16 * q^67 + 12 * q^68 - 24 * q^69 + 24 * q^71 - 4 * q^72 + 4 * q^73 - 12 * q^74 + 16 * q^75 - 8 * q^78 - 24 * q^79 - 4 * q^80 - 4 * q^81 + 20 * q^82 - 8 * q^84 + 28 * q^85 - 16 * q^86 - 4 * q^90 - 16 * q^91 - 8 * q^92 - 4 * q^97 - 20 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/102\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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
$5$	0.414214	+	0.414214i	0.185242	+	0.185242i	0.793635	−	0.608394i	$-0.208186\pi$
$5$	0.414214	+	0.414214i	0.185242	+	0.185242i	−0.608394	+	0.793635i	$0.708186\pi$
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	3.41421	−	3.41421i	1.29045	−	1.29045i	0.355944	−	0.934507i	$-0.384159\pi$
$7$	3.41421	−	3.41421i	1.29045	−	1.29045i	0.934507	−	0.355944i	$-0.115841\pi$
$8$			1.00000i			0.353553i
$9$			1.00000i			0.333333i
$10$	0.414214	−	0.414214i	0.130986	−	0.130986i
$11$	−2.82843	+	2.82843i	−0.852803	+	0.852803i	−0.990478	−	0.137675i	$-0.956037\pi$
$11$	−2.82843	+	2.82843i	−0.852803	+	0.852803i	0.137675	+	0.990478i	$0.456037\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	−2.82843			−0.784465			−0.392232	−	0.919866i	$-0.628297\pi$
$13$	−2.82843			−0.784465			−0.392232	+	0.919866i	$0.628297\pi$
$14$	−3.41421	−	3.41421i	−0.912487	−	0.912487i
$15$			0.585786i			0.151249i
$16$	1.00000			0.250000
$17$	−3.00000	−	2.82843i	−0.727607	−	0.685994i
$17$	−3.00000	−	2.82843i	−0.727607	−	0.685994i
$18$	1.00000			0.235702
$19$			6.82843i			1.56655i	0.621676	+	0.783274i	$0.286452\pi$
$19$			6.82843i			1.56655i	−0.621676	+	0.783274i	$0.713548\pi$
$20$	−0.414214	−	0.414214i	−0.0926210	−	0.0926210i
$21$	4.82843			1.05365
$22$	2.82843	+	2.82843i	0.603023	+	0.603023i
$23$	−2.24264	+	2.24264i	−0.467623	+	0.467623i	−0.901144	−	0.433521i	$-0.857271\pi$
$23$	−2.24264	+	2.24264i	−0.467623	+	0.467623i	0.433521	+	0.901144i	$0.357271\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$		−	4.65685i		−	0.931371i
$26$			2.82843i			0.554700i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−3.41421	+	3.41421i	−0.645226	+	0.645226i
$29$	−0.414214	−	0.414214i	−0.0769175	−	0.0769175i	0.667601	−	0.744519i	$-0.267321\pi$
$29$	−0.414214	−	0.414214i	−0.0769175	−	0.0769175i	−0.744519	+	0.667601i	$0.767321\pi$
$30$	0.585786			0.106949
$31$	0.585786	+	0.585786i	0.105210	+	0.105210i	0.757752	−	0.652542i	$-0.226297\pi$
$31$	0.585786	+	0.585786i	0.105210	+	0.105210i	−0.652542	+	0.757752i	$0.726297\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−4.00000			−0.696311
$34$	−2.82843	+	3.00000i	−0.485071	+	0.514496i
$35$	2.82843			0.478091
$36$		−	1.00000i		−	0.166667i
$37$	−1.58579	−	1.58579i	−0.260702	−	0.260702i	0.564637	−	0.825339i	$-0.309016\pi$
$37$	−1.58579	−	1.58579i	−0.260702	−	0.260702i	−0.825339	+	0.564637i	$0.809016\pi$
$38$	6.82843			1.10772
$39$	−2.00000	−	2.00000i	−0.320256	−	0.320256i
$40$	−0.414214	+	0.414214i	−0.0654929	+	0.0654929i
$41$	−2.17157	+	2.17157i	−0.339143	+	0.339143i	−0.856045	−	0.516902i	$-0.827085\pi$
$41$	−2.17157	+	2.17157i	−0.339143	+	0.339143i	0.516902	+	0.856045i	$0.327085\pi$
$42$		−	4.82843i		−	0.745042i
$43$			1.65685i			0.252668i	0.991988	+	0.126334i	$0.0403211\pi$
$43$			1.65685i			0.252668i	−0.991988	+	0.126334i	$0.959679\pi$
$44$	2.82843	−	2.82843i	0.426401	−	0.426401i
$45$	−0.414214	+	0.414214i	−0.0617473	+	0.0617473i
$46$	2.24264	+	2.24264i	0.330659	+	0.330659i
$47$	12.4853			1.82117			0.910583	−	0.413327i	$-0.135633\pi$
$47$	12.4853			1.82117			0.910583	+	0.413327i	$0.135633\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$		−	16.3137i		−	2.33053i
$50$	−4.65685			−0.658579
$51$	−0.121320	−	4.12132i	−0.0169882	−	0.577100i
$52$	2.82843			0.392232
$53$		−	2.82843i		−	0.388514i	−0.980951	−	0.194257i	$-0.937770\pi$
$53$		−	2.82843i		−	0.388514i	0.980951	−	0.194257i	$-0.0622296\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	−2.34315			−0.315950
$56$	3.41421	+	3.41421i	0.456243	+	0.456243i
$57$	−4.82843	+	4.82843i	−0.639541	+	0.639541i
$58$	−0.414214	+	0.414214i	−0.0543889	+	0.0543889i
$59$		−	12.4853i		−	1.62545i	−0.582651	−	0.812723i	$-0.697984\pi$
$59$		−	12.4853i		−	1.62545i	0.582651	−	0.812723i	$-0.302016\pi$
$60$		−	0.585786i		−	0.0756247i
$61$	0.757359	−	0.757359i	0.0969699	−	0.0969699i	−0.656958	−	0.753928i	$-0.728157\pi$
$61$	0.757359	−	0.757359i	0.0969699	−	0.0969699i	0.753928	+	0.656958i	$0.228157\pi$
$62$	0.585786	−	0.585786i	0.0743950	−	0.0743950i
$63$	3.41421	+	3.41421i	0.430150	+	0.430150i
$64$	−1.00000			−0.125000
$65$	−1.17157	−	1.17157i	−0.145316	−	0.145316i
$66$			4.00000i			0.492366i
$67$	1.17157			0.143130			0.0715652	−	0.997436i	$-0.477201\pi$
$67$	1.17157			0.143130			0.0715652	+	0.997436i	$0.477201\pi$
$68$	3.00000	+	2.82843i	0.363803	+	0.342997i
$69$	−3.17157			−0.381813
$70$		−	2.82843i		−	0.338062i
$71$	4.58579	+	4.58579i	0.544233	+	0.544233i	0.924767	−	0.380534i	$-0.124260\pi$
$71$	4.58579	+	4.58579i	0.544233	+	0.544233i	−0.380534	+	0.924767i	$0.624260\pi$
$72$	−1.00000			−0.117851
$73$	6.65685	+	6.65685i	0.779126	+	0.779126i	0.979682	−	0.200556i	$-0.0642750\pi$
$73$	6.65685	+	6.65685i	0.779126	+	0.779126i	−0.200556	+	0.979682i	$0.564275\pi$
$74$	−1.58579	+	1.58579i	−0.184344	+	0.184344i
$75$	3.29289	−	3.29289i	0.380231	−	0.380231i
$76$		−	6.82843i		−	0.783274i
$77$			19.3137i			2.20100i
$78$	−2.00000	+	2.00000i	−0.226455	+	0.226455i
$79$	−10.2426	+	10.2426i	−1.15239	+	1.15239i	−0.166314	+	0.986073i	$0.553187\pi$
$79$	−10.2426	+	10.2426i	−1.15239	+	1.15239i	−0.986073	+	0.166314i	$0.946813\pi$
$80$	0.414214	+	0.414214i	0.0463105	+	0.0463105i
$81$	−1.00000			−0.111111
$82$	2.17157	+	2.17157i	0.239810	+	0.239810i
$83$		−	4.48528i		−	0.492324i	−0.969229	−	0.246162i	$-0.920831\pi$
$83$		−	4.48528i		−	0.492324i	0.969229	−	0.246162i	$-0.0791695\pi$
$84$	−4.82843			−0.526825
$85$	−0.0710678	−	2.41421i	−0.00770839	−	0.261858i
$86$	1.65685			0.178663
$87$		−	0.585786i		−	0.0628029i
$88$	−2.82843	−	2.82843i	−0.301511	−	0.301511i
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$	0.414214	+	0.414214i	0.0436619	+	0.0436619i
$91$	−9.65685	+	9.65685i	−1.01231	+	1.01231i
$92$	2.24264	−	2.24264i	0.233811	−	0.233811i
$93$			0.828427i			0.0859039i
$94$		−	12.4853i		−	1.28776i
$95$	−2.82843	+	2.82843i	−0.290191	+	0.290191i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	−9.48528	−	9.48528i	−0.963084	−	0.963084i	0.0362581	−	0.999342i	$-0.488456\pi$
$97$	−9.48528	−	9.48528i	−0.963084	−	0.963084i	−0.999342	+	0.0362581i	$0.988456\pi$
$98$	−16.3137			−1.64793
$99$	−2.82843	−	2.82843i	−0.284268	−	0.284268i
$100$			4.65685i			0.465685i
$101$	5.17157			0.514591			0.257295	−	0.966333i	$-0.417169\pi$
$101$	5.17157			0.514591			0.257295	+	0.966333i	$0.417169\pi$
$102$	−4.12132	+	0.121320i	−0.408072	+	0.0120125i
$103$	14.8284			1.46109			0.730544	−	0.682865i	$-0.239266\pi$
$103$	14.8284			1.46109			0.730544	+	0.682865i	$0.239266\pi$
$104$		−	2.82843i		−	0.277350i
$105$	2.00000	+	2.00000i	0.195180	+	0.195180i
$106$	−2.82843			−0.274721
$107$	9.65685	+	9.65685i	0.933563	+	0.933563i	0.997927	−	0.0643632i	$-0.0205016\pi$
$107$	9.65685	+	9.65685i	0.933563	+	0.933563i	−0.0643632	+	0.997927i	$0.520502\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	−2.75736	+	2.75736i	−0.264107	+	0.264107i	−0.826720	−	0.562613i	$-0.809796\pi$
$109$	−2.75736	+	2.75736i	−0.264107	+	0.264107i	0.562613	+	0.826720i	$0.309796\pi$
$110$			2.34315i			0.223410i
$111$		−	2.24264i		−	0.212862i
$112$	3.41421	−	3.41421i	0.322613	−	0.322613i
$113$	9.00000	−	9.00000i	0.846649	−	0.846649i	−0.143065	−	0.989713i	$-0.545696\pi$
$113$	9.00000	−	9.00000i	0.846649	−	0.846649i	0.989713	+	0.143065i	$0.0456957\pi$
$114$	4.82843	+	4.82843i	0.452224	+	0.452224i
$115$	−1.85786			−0.173247
$116$	0.414214	+	0.414214i	0.0384588	+	0.0384588i
$117$		−	2.82843i		−	0.261488i
$118$	−12.4853			−1.14936
$119$	−19.8995	+	0.585786i	−1.82418	+	0.0536990i
$120$	−0.585786			−0.0534747
$121$		−	5.00000i		−	0.454545i
$122$	−0.757359	−	0.757359i	−0.0685681	−	0.0685681i
$123$	−3.07107			−0.276909
$124$	−0.585786	−	0.585786i	−0.0526052	−	0.0526052i
$125$	4.00000	−	4.00000i	0.357771	−	0.357771i
$126$	3.41421	−	3.41421i	0.304162	−	0.304162i
$127$			13.6569i			1.21185i	0.795522	+	0.605925i	$0.207197\pi$
$127$			13.6569i			1.21185i	−0.795522	+	0.605925i	$0.792803\pi$
$128$			1.00000i			0.0883883i
$129$	−1.17157	+	1.17157i	−0.103151	+	0.103151i
$130$	−1.17157	+	1.17157i	−0.102754	+	0.102754i
$131$	−13.6569	−	13.6569i	−1.19320	−	1.19320i	−0.976162	−	0.217043i	$-0.930359\pi$
$131$	−13.6569	−	13.6569i	−1.19320	−	1.19320i	−0.217043	−	0.976162i	$-0.569641\pi$
$132$	4.00000			0.348155
$133$	23.3137	+	23.3137i	2.02155	+	2.02155i
$134$		−	1.17157i		−	0.101208i
$135$	−0.585786			−0.0504165
$136$	2.82843	−	3.00000i	0.242536	−	0.257248i
$137$	−17.6569			−1.50853			−0.754263	−	0.656572i	$-0.772006\pi$
$137$	−17.6569			−1.50853			−0.754263	+	0.656572i	$0.772006\pi$
$138$			3.17157i			0.269982i
$139$	4.48528	+	4.48528i	0.380437	+	0.380437i	0.871259	−	0.490823i	$-0.163304\pi$
$139$	4.48528	+	4.48528i	0.380437	+	0.380437i	−0.490823	+	0.871259i	$0.663304\pi$
$140$	−2.82843			−0.239046
$141$	8.82843	+	8.82843i	0.743488	+	0.743488i
$142$	4.58579	−	4.58579i	0.384831	−	0.384831i
$143$	8.00000	−	8.00000i	0.668994	−	0.668994i
$144$			1.00000i			0.0833333i
$145$		−	0.343146i		−	0.0284967i
$146$	6.65685	−	6.65685i	0.550925	−	0.550925i
$147$	11.5355	−	11.5355i	0.951435	−	0.951435i
$148$	1.58579	+	1.58579i	0.130351	+	0.130351i
$149$	10.0000			0.819232			0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000			0.819232			0.409616	+	0.912258i	$0.365663\pi$
$150$	−3.29289	−	3.29289i	−0.268864	−	0.268864i
$151$		−	13.6569i		−	1.11138i	−0.831390	−	0.555690i	$-0.812454\pi$
$151$		−	13.6569i		−	1.11138i	0.831390	−	0.555690i	$-0.187546\pi$
$152$	−6.82843			−0.553859
$153$	2.82843	−	3.00000i	0.228665	−	0.242536i
$154$	19.3137			1.55634
$155$			0.485281i			0.0389787i
$156$	2.00000	+	2.00000i	0.160128	+	0.160128i
$157$	6.00000			0.478852			0.239426	−	0.970915i	$-0.423041\pi$
$157$	6.00000			0.478852			0.239426	+	0.970915i	$0.423041\pi$
$158$	10.2426	+	10.2426i	0.814861	+	0.814861i
$159$	2.00000	−	2.00000i	0.158610	−	0.158610i
$160$	0.414214	−	0.414214i	0.0327465	−	0.0327465i
$161$			15.3137i			1.20689i
$162$			1.00000i			0.0785674i
$163$	1.65685	−	1.65685i	0.129775	−	0.129775i	−0.639236	−	0.769011i	$-0.720749\pi$
$163$	1.65685	−	1.65685i	0.129775	−	0.129775i	0.769011	+	0.639236i	$0.220749\pi$
$164$	2.17157	−	2.17157i	0.169571	−	0.169571i
$165$	−1.65685	−	1.65685i	−0.128986	−	0.128986i
$166$	−4.48528			−0.348125
$167$	−15.4142	−	15.4142i	−1.19279	−	1.19279i	−0.976281	−	0.216506i	$-0.930534\pi$
$167$	−15.4142	−	15.4142i	−1.19279	−	1.19279i	−0.216506	−	0.976281i	$-0.569466\pi$
$168$			4.82843i			0.372521i
$169$	−5.00000			−0.384615
$170$	−2.41421	+	0.0710678i	−0.185162	+	0.00545065i
$171$	−6.82843			−0.522183
$172$		−	1.65685i		−	0.126334i
$173$	2.89949	+	2.89949i	0.220445	+	0.220445i	0.808686	−	0.588241i	$-0.200179\pi$
$173$	2.89949	+	2.89949i	0.220445	+	0.220445i	−0.588241	+	0.808686i	$0.700179\pi$
$174$	−0.585786			−0.0444084
$175$	−15.8995	−	15.8995i	−1.20189	−	1.20189i
$176$	−2.82843	+	2.82843i	−0.213201	+	0.213201i
$177$	8.82843	−	8.82843i	0.663585	−	0.663585i
$178$		0			0
$179$		−	12.9706i		−	0.969465i	−0.874662	−	0.484733i	$-0.838917\pi$
$179$		−	12.9706i		−	0.969465i	0.874662	−	0.484733i	$-0.161083\pi$
$180$	0.414214	−	0.414214i	0.0308737	−	0.0308737i
$181$	−5.58579	+	5.58579i	−0.415188	+	0.415188i	−0.883541	−	0.468353i	$-0.844848\pi$
$181$	−5.58579	+	5.58579i	−0.415188	+	0.415188i	0.468353	+	0.883541i	$0.344848\pi$
$182$	9.65685	+	9.65685i	0.715814	+	0.715814i
$183$	1.07107			0.0791756
$184$	−2.24264	−	2.24264i	−0.165330	−	0.165330i
$185$		−	1.31371i		−	0.0965858i
$186$	0.828427			0.0607432
$187$	16.4853	−	0.485281i	1.20552	−	0.0354873i
$188$	−12.4853			−0.910583
$189$			4.82843i			0.351216i
$190$	2.82843	+	2.82843i	0.205196	+	0.205196i
$191$	1.17157			0.0847720			0.0423860	−	0.999101i	$-0.486504\pi$
$191$	1.17157			0.0847720			0.0423860	+	0.999101i	$0.486504\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	−4.17157	+	4.17157i	−0.300276	+	0.300276i	−0.841122	−	0.540846i	$-0.818104\pi$
$193$	−4.17157	+	4.17157i	−0.300276	+	0.300276i	0.540846	+	0.841122i	$0.318104\pi$
$194$	−9.48528	+	9.48528i	−0.681004	+	0.681004i
$195$		−	1.65685i		−	0.118650i
$196$			16.3137i			1.16526i
$197$	−7.24264	+	7.24264i	−0.516017	+	0.516017i	−0.916364	−	0.400347i	$-0.868890\pi$
$197$	−7.24264	+	7.24264i	−0.516017	+	0.516017i	0.400347	+	0.916364i	$0.368890\pi$
$198$	−2.82843	+	2.82843i	−0.201008	+	0.201008i
$199$	−0.585786	−	0.585786i	−0.0415253	−	0.0415253i	0.686039	−	0.727565i	$-0.259348\pi$
$199$	−0.585786	−	0.585786i	−0.0415253	−	0.0415253i	−0.727565	+	0.686039i	$0.759348\pi$
$200$	4.65685			0.329289
$201$	0.828427	+	0.828427i	0.0584327	+	0.0584327i
$202$		−	5.17157i		−	0.363871i
$203$	−2.82843			−0.198517
$204$	0.121320	+	4.12132i	0.00849412	+	0.288550i
$205$	−1.79899			−0.125647
$206$		−	14.8284i		−	1.03315i
$207$	−2.24264	−	2.24264i	−0.155874	−	0.155874i
$208$	−2.82843			−0.196116
$209$	−19.3137	−	19.3137i	−1.33596	−	1.33596i
$210$	2.00000	−	2.00000i	0.138013	−	0.138013i
$211$	−20.4853	+	20.4853i	−1.41026	+	1.41026i	−0.652329	+	0.757936i	$0.726208\pi$
$211$	−20.4853	+	20.4853i	−1.41026	+	1.41026i	−0.757936	+	0.652329i	$0.773792\pi$
$212$			2.82843i			0.194257i
$213$			6.48528i			0.444364i
$214$	9.65685	−	9.65685i	0.660129	−	0.660129i
$215$	−0.686292	+	0.686292i	−0.0468047	+	0.0468047i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	4.00000			0.271538
$218$	2.75736	+	2.75736i	0.186752	+	0.186752i
$219$			9.41421i			0.636154i
$220$	2.34315			0.157975
$221$	8.48528	+	8.00000i	0.570782	+	0.538138i
$222$	−2.24264			−0.150516
$223$		−	6.82843i		−	0.457265i	−0.973513	−	0.228633i	$-0.926575\pi$
$223$		−	6.82843i		−	0.457265i	0.973513	−	0.228633i	$-0.0734255\pi$
$224$	−3.41421	−	3.41421i	−0.228122	−	0.228122i
$225$	4.65685			0.310457
$226$	−9.00000	−	9.00000i	−0.598671	−	0.598671i
$227$	−12.4853	+	12.4853i	−0.828677	+	0.828677i	−0.987334	−	0.158657i	$-0.949284\pi$
$227$	−12.4853	+	12.4853i	−0.828677	+	0.828677i	0.158657	+	0.987334i	$0.449284\pi$
$228$	4.82843	−	4.82843i	0.319770	−	0.319770i
$229$		−	14.0000i		−	0.925146i	−0.886581	−	0.462573i	$-0.846926\pi$
$229$		−	14.0000i		−	0.925146i	0.886581	−	0.462573i	$-0.153074\pi$
$230$			1.85786i			0.122504i
$231$	−13.6569	+	13.6569i	−0.898555	+	0.898555i
$232$	0.414214	−	0.414214i	0.0271945	−	0.0271945i
$233$	9.00000	+	9.00000i	0.589610	+	0.589610i	0.937526	−	0.347916i	$-0.113111\pi$
$233$	9.00000	+	9.00000i	0.589610	+	0.589610i	−0.347916	+	0.937526i	$0.613111\pi$
$234$	−2.82843			−0.184900
$235$	5.17157	+	5.17157i	0.337356	+	0.337356i
$236$			12.4853i			0.812723i
$237$	−14.4853			−0.940920
$238$	0.585786	+	19.8995i	0.0379709	+	1.28989i
$239$	12.4853			0.807606			0.403803	−	0.914846i	$-0.367688\pi$
$239$	12.4853			0.807606			0.403803	+	0.914846i	$0.367688\pi$
$240$			0.585786i			0.0378124i
$241$	−5.82843	−	5.82843i	−0.375442	−	0.375442i	0.494013	−	0.869455i	$-0.335530\pi$
$241$	−5.82843	−	5.82843i	−0.375442	−	0.375442i	−0.869455	+	0.494013i	$0.835530\pi$
$242$	−5.00000			−0.321412
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−0.757359	+	0.757359i	−0.0484850	+	0.0484850i
$245$	6.75736	−	6.75736i	0.431712	−	0.431712i
$246$			3.07107i			0.195804i
$247$		−	19.3137i		−	1.22890i
$248$	−0.585786	+	0.585786i	−0.0371975	+	0.0371975i
$249$	3.17157	−	3.17157i	0.200990	−	0.200990i
$250$	−4.00000	−	4.00000i	−0.252982	−	0.252982i
$251$	17.6569			1.11449			0.557245	−	0.830348i	$-0.311858\pi$
$251$	17.6569			1.11449			0.557245	+	0.830348i	$0.311858\pi$
$252$	−3.41421	−	3.41421i	−0.215075	−	0.215075i
$253$		−	12.6863i		−	0.797580i
$254$	13.6569			0.856907
$255$	1.65685	−	1.75736i	0.103756	−	0.110050i
$256$	1.00000			0.0625000
$257$			29.3137i			1.82854i	0.405107	+	0.914269i	$0.367234\pi$
$257$			29.3137i			1.82854i	−0.405107	+	0.914269i	$0.632766\pi$
$258$	1.17157	+	1.17157i	0.0729389	+	0.0729389i
$259$	−10.8284			−0.672846
$260$	1.17157	+	1.17157i	0.0726579	+	0.0726579i
$261$	0.414214	−	0.414214i	0.0256392	−	0.0256392i
$262$	−13.6569	+	13.6569i	−0.843723	+	0.843723i
$263$			10.1421i			0.625391i	0.949853	+	0.312695i	$0.101232\pi$
$263$			10.1421i			0.625391i	−0.949853	+	0.312695i	$0.898768\pi$
$264$		−	4.00000i		−	0.246183i
$265$	1.17157	−	1.17157i	0.0719691	−	0.0719691i
$266$	23.3137	−	23.3137i	1.42946	−	1.42946i
$267$		0			0
$268$	−1.17157			−0.0715652
$269$	−3.58579	−	3.58579i	−0.218629	−	0.218629i	0.589291	−	0.807921i	$-0.299407\pi$
$269$	−3.58579	−	3.58579i	−0.218629	−	0.218629i	−0.807921	+	0.589291i	$0.799407\pi$
$270$			0.585786i			0.0356498i
$271$	21.6569			1.31556			0.657780	−	0.753210i	$-0.271496\pi$
$271$	21.6569			1.31556			0.657780	+	0.753210i	$0.271496\pi$
$272$	−3.00000	−	2.82843i	−0.181902	−	0.171499i
$273$	−13.6569			−0.826550
$274$			17.6569i			1.06669i
$275$	13.1716	+	13.1716i	0.794276	+	0.794276i
$276$	3.17157			0.190906
$277$	−6.89949	−	6.89949i	−0.414550	−	0.414550i	0.468770	−	0.883320i	$-0.344697\pi$
$277$	−6.89949	−	6.89949i	−0.414550	−	0.414550i	−0.883320	+	0.468770i	$0.844697\pi$
$278$	4.48528	−	4.48528i	0.269009	−	0.269009i
$279$	−0.585786	+	0.585786i	−0.0350701	+	0.0350701i
$280$			2.82843i			0.169031i
$281$		−	19.3137i		−	1.15216i	−0.817394	−	0.576080i	$-0.804582\pi$
$281$		−	19.3137i		−	1.15216i	0.817394	−	0.576080i	$-0.195418\pi$
$282$	8.82843	−	8.82843i	0.525725	−	0.525725i
$283$	5.65685	−	5.65685i	0.336265	−	0.336265i	−0.518695	−	0.854960i	$-0.673582\pi$
$283$	5.65685	−	5.65685i	0.336265	−	0.336265i	0.854960	+	0.518695i	$0.173582\pi$
$284$	−4.58579	−	4.58579i	−0.272116	−	0.272116i
$285$	−4.00000			−0.236940
$286$	−8.00000	−	8.00000i	−0.473050	−	0.473050i
$287$			14.8284i			0.875294i
$288$	1.00000			0.0589256
$289$	1.00000	+	16.9706i	0.0588235	+	0.998268i
$290$	−0.343146			−0.0201502
$291$		−	13.4142i		−	0.786355i
$292$	−6.65685	−	6.65685i	−0.389563	−	0.389563i
$293$	9.31371			0.544113			0.272056	−	0.962281i	$-0.412296\pi$
$293$	9.31371			0.544113			0.272056	+	0.962281i	$0.412296\pi$
$294$	−11.5355	−	11.5355i	−0.672766	−	0.672766i
$295$	5.17157	−	5.17157i	0.301101	−	0.301101i
$296$	1.58579	−	1.58579i	0.0921720	−	0.0921720i
$297$		−	4.00000i		−	0.232104i
$298$		−	10.0000i		−	0.579284i
$299$	6.34315	−	6.34315i	0.366834	−	0.366834i
$300$	−3.29289	+	3.29289i	−0.190115	+	0.190115i
$301$	5.65685	+	5.65685i	0.326056	+	0.326056i
$302$	−13.6569			−0.785864
$303$	3.65685	+	3.65685i	0.210081	+	0.210081i
$304$			6.82843i			0.391637i
$305$	0.627417			0.0359258
$306$	−3.00000	−	2.82843i	−0.171499	−	0.161690i
$307$	−6.34315			−0.362022			−0.181011	−	0.983481i	$-0.557937\pi$
$307$	−6.34315			−0.362022			−0.181011	+	0.983481i	$0.557937\pi$
$308$		−	19.3137i		−	1.10050i
$309$	10.4853	+	10.4853i	0.596487	+	0.596487i
$310$	0.485281			0.0275621
$311$	0.585786	+	0.585786i	0.0332169	+	0.0332169i	0.723520	−	0.690303i	$-0.242523\pi$
$311$	0.585786	+	0.585786i	0.0332169	+	0.0332169i	−0.690303	+	0.723520i	$0.742523\pi$
$312$	2.00000	−	2.00000i	0.113228	−	0.113228i
$313$	7.14214	−	7.14214i	0.403697	−	0.403697i	−0.475836	−	0.879534i	$-0.657855\pi$
$313$	7.14214	−	7.14214i	0.403697	−	0.403697i	0.879534	+	0.475836i	$0.157855\pi$
$314$		−	6.00000i		−	0.338600i
$315$			2.82843i			0.159364i
$316$	10.2426	−	10.2426i	0.576194	−	0.576194i
$317$	−15.2426	+	15.2426i	−0.856112	+	0.856112i	−0.990878	−	0.134766i	$-0.956972\pi$
$317$	−15.2426	+	15.2426i	−0.856112	+	0.856112i	0.134766	+	0.990878i	$0.456972\pi$
$318$	−2.00000	−	2.00000i	−0.112154	−	0.112154i
$319$	2.34315			0.131191
$320$	−0.414214	−	0.414214i	−0.0231552	−	0.0231552i
$321$			13.6569i			0.762251i
$322$	15.3137			0.853400
$323$	19.3137	−	20.4853i	1.07464	−	1.13983i
$324$	1.00000			0.0555556
$325$			13.1716i			0.730627i
$326$	−1.65685	−	1.65685i	−0.0917647	−	0.0917647i
$327$	−3.89949			−0.215643
$328$	−2.17157	−	2.17157i	−0.119905	−	0.119905i
$329$	42.6274	−	42.6274i	2.35013	−	2.35013i
$330$	−1.65685	+	1.65685i	−0.0912068	+	0.0912068i
$331$			18.6274i			1.02386i	0.859029	+	0.511928i	$0.171068\pi$
$331$			18.6274i			1.02386i	−0.859029	+	0.511928i	$0.828932\pi$
$332$			4.48528i			0.246162i
$333$	1.58579	−	1.58579i	0.0869006	−	0.0869006i
$334$	−15.4142	+	15.4142i	−0.843428	+	0.843428i
$335$	0.485281	+	0.485281i	0.0265138	+	0.0265138i
$336$	4.82843			0.263412
$337$	9.00000	+	9.00000i	0.490261	+	0.490261i	0.908388	−	0.418127i	$-0.137313\pi$
$337$	9.00000	+	9.00000i	0.490261	+	0.490261i	−0.418127	+	0.908388i	$0.637313\pi$
$338$			5.00000i			0.271964i
$339$	12.7279			0.691286
$340$	0.0710678	+	2.41421i	0.00385419	+	0.130929i
$341$	−3.31371			−0.179447
$342$			6.82843i			0.369239i
$343$	−31.7990	−	31.7990i	−1.71698	−	1.71698i
$344$	−1.65685			−0.0893316
$345$	−1.31371	−	1.31371i	−0.0707277	−	0.0707277i
$346$	2.89949	−	2.89949i	0.155878	−	0.155878i
$347$	−8.00000	+	8.00000i	−0.429463	+	0.429463i	−0.888445	−	0.458983i	$-0.848214\pi$
$347$	−8.00000	+	8.00000i	−0.429463	+	0.429463i	0.458983	+	0.888445i	$0.348214\pi$
$348$			0.585786i			0.0314014i
$349$		−	10.8284i		−	0.579632i	−0.957082	−	0.289816i	$-0.906406\pi$
$349$		−	10.8284i		−	0.579632i	0.957082	−	0.289816i	$-0.0935942\pi$
$350$	−15.8995	+	15.8995i	−0.849864	+	0.849864i
$351$	2.00000	−	2.00000i	0.106752	−	0.106752i
$352$	2.82843	+	2.82843i	0.150756	+	0.150756i
$353$	−12.6274			−0.672090			−0.336045	−	0.941846i	$-0.609089\pi$
$353$	−12.6274			−0.672090			−0.336045	+	0.941846i	$0.609089\pi$
$354$	−8.82843	−	8.82843i	−0.469226	−	0.469226i
$355$			3.79899i			0.201629i
$356$		0			0
$357$	−14.4853	−	13.6569i	−0.766642	−	0.722797i
$358$	−12.9706			−0.685516
$359$			16.0000i			0.844448i	0.906492	+	0.422224i	$0.138750\pi$
$359$			16.0000i			0.844448i	−0.906492	+	0.422224i	$0.861250\pi$
$360$	−0.414214	−	0.414214i	−0.0218310	−	0.0218310i
$361$	−27.6274			−1.45407
$362$	5.58579	+	5.58579i	0.293582	+	0.293582i
$363$	3.53553	−	3.53553i	0.185567	−	0.185567i
$364$	9.65685	−	9.65685i	0.506157	−	0.506157i
$365$			5.51472i			0.288654i
$366$		−	1.07107i		−	0.0559856i
$367$	−12.3848	+	12.3848i	−0.646480	+	0.646480i	−0.952141	−	0.305661i	$-0.901123\pi$
$367$	−12.3848	+	12.3848i	−0.646480	+	0.646480i	0.305661	+	0.952141i	$0.401123\pi$
$368$	−2.24264	+	2.24264i	−0.116906	+	0.116906i
$369$	−2.17157	−	2.17157i	−0.113048	−	0.113048i
$370$	−1.31371			−0.0682965
$371$	−9.65685	−	9.65685i	−0.501359	−	0.501359i
$372$		−	0.828427i		−	0.0429519i
$373$	19.7990			1.02515			0.512576	−	0.858642i	$-0.328691\pi$
$373$	19.7990			1.02515			0.512576	+	0.858642i	$0.328691\pi$
$374$	−0.485281	−	16.4853i	−0.0250933	−	0.852434i
$375$	5.65685			0.292119
$376$			12.4853i			0.643879i
$377$	1.17157	+	1.17157i	0.0603391	+	0.0603391i
$378$	4.82843			0.248347
$379$	17.6569	+	17.6569i	0.906972	+	0.906972i	0.996027	−	0.0890550i	$-0.0283847\pi$
$379$	17.6569	+	17.6569i	0.906972	+	0.906972i	−0.0890550	+	0.996027i	$0.528385\pi$
$380$	2.82843	−	2.82843i	0.145095	−	0.145095i
$381$	−9.65685	+	9.65685i	−0.494736	+	0.494736i
$382$		−	1.17157i		−	0.0599429i
$383$			23.7990i			1.21607i	0.793910	+	0.608036i	$0.208042\pi$
$383$			23.7990i			1.21607i	−0.793910	+	0.608036i	$0.791958\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	−8.00000	+	8.00000i	−0.407718	+	0.407718i
$386$	4.17157	+	4.17157i	0.212327	+	0.212327i
$387$	−1.65685			−0.0842226
$388$	9.48528	+	9.48528i	0.481542	+	0.481542i
$389$			36.6274i			1.85708i	0.371228	+	0.928542i	$0.378937\pi$
$389$			36.6274i			1.85708i	−0.371228	+	0.928542i	$0.621063\pi$
$390$	−1.65685			−0.0838981
$391$	13.0711	−	0.384776i	0.661032	−	0.0194590i
$392$	16.3137			0.823967
$393$		−	19.3137i		−	0.974248i
$394$	7.24264	+	7.24264i	0.364879	+	0.364879i
$395$	−8.48528			−0.426941
$396$	2.82843	+	2.82843i	0.142134	+	0.142134i
$397$	23.3848	−	23.3848i	1.17365	−	1.17365i	0.192315	−	0.981333i	$-0.438400\pi$
$397$	23.3848	−	23.3848i	1.17365	−	1.17365i	0.981333	−	0.192315i	$-0.0615995\pi$
$398$	−0.585786	+	0.585786i	−0.0293628	+	0.0293628i
$399$			32.9706i			1.65059i
$400$		−	4.65685i		−	0.232843i
$401$	−6.17157	+	6.17157i	−0.308194	+	0.308194i	−0.844209	−	0.536015i	$-0.819929\pi$
$401$	−6.17157	+	6.17157i	−0.308194	+	0.308194i	0.536015	+	0.844209i	$0.319929\pi$
$402$	0.828427	−	0.828427i	0.0413182	−	0.0413182i
$403$	−1.65685	−	1.65685i	−0.0825338	−	0.0825338i
$404$	−5.17157			−0.257295
$405$	−0.414214	−	0.414214i	−0.0205824	−	0.0205824i
$406$			2.82843i			0.140372i
$407$	8.97056			0.444654
$408$	4.12132	−	0.121320i	0.204036	−	0.00600625i
$409$	−14.0000			−0.692255			−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000			−0.692255			−0.346128	+	0.938187i	$0.612504\pi$
$410$			1.79899i			0.0888458i
$411$	−12.4853	−	12.4853i	−0.615854	−	0.615854i
$412$	−14.8284			−0.730544
$413$	−42.6274	−	42.6274i	−2.09756	−	2.09756i
$414$	−2.24264	+	2.24264i	−0.110220	+	0.110220i
$415$	1.85786	−	1.85786i	0.0911990	−	0.0911990i
$416$			2.82843i			0.138675i
$417$			6.34315i			0.310625i
$418$	−19.3137	+	19.3137i	−0.944664	+	0.944664i
$419$	1.17157	−	1.17157i	0.0572351	−	0.0572351i	−0.677910	−	0.735145i	$-0.737114\pi$
$419$	1.17157	−	1.17157i	0.0572351	−	0.0572351i	0.735145	+	0.677910i	$0.237114\pi$
$420$	−2.00000	−	2.00000i	−0.0975900	−	0.0975900i
$421$	−15.5147			−0.756141			−0.378071	−	0.925777i	$-0.623412\pi$
$421$	−15.5147			−0.756141			−0.378071	+	0.925777i	$0.623412\pi$
$422$	20.4853	+	20.4853i	0.997208	+	0.997208i
$423$			12.4853i			0.607055i
$424$	2.82843			0.137361
$425$	−13.1716	+	13.9706i	−0.638915	+	0.677672i
$426$	6.48528			0.314213
$427$		−	5.17157i		−	0.250270i
$428$	−9.65685	−	9.65685i	−0.466782	−	0.466782i
$429$	11.3137			0.546231
$430$	0.686292	+	0.686292i	0.0330959	+	0.0330959i
$431$	−14.2426	+	14.2426i	−0.686044	+	0.686044i	−0.961355	−	0.275311i	$-0.911219\pi$
$431$	−14.2426	+	14.2426i	−0.686044	+	0.686044i	0.275311	+	0.961355i	$0.411219\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$		−	16.6274i		−	0.799063i	−0.916720	−	0.399531i	$-0.869173\pi$
$433$		−	16.6274i		−	0.799063i	0.916720	−	0.399531i	$-0.130827\pi$
$434$		−	4.00000i		−	0.192006i
$435$	0.242641	−	0.242641i	0.0116337	−	0.0116337i
$436$	2.75736	−	2.75736i	0.132054	−	0.132054i
$437$	−15.3137	−	15.3137i	−0.732554	−	0.732554i
$438$	9.41421			0.449829
$439$	−9.55635	−	9.55635i	−0.456100	−	0.456100i	0.441273	−	0.897373i	$-0.354527\pi$
$439$	−9.55635	−	9.55635i	−0.456100	−	0.456100i	−0.897373	+	0.441273i	$0.854527\pi$
$440$		−	2.34315i		−	0.111705i
$441$	16.3137			0.776843
$442$	8.00000	−	8.48528i	0.380521	−	0.403604i
$443$	−28.9706			−1.37643			−0.688216	−	0.725505i	$-0.741606\pi$
$443$	−28.9706			−1.37643			−0.688216	+	0.725505i	$0.741606\pi$
$444$			2.24264i			0.106431i
$445$		0			0
$446$	−6.82843			−0.323335
$447$	7.07107	+	7.07107i	0.334450	+	0.334450i
$448$	−3.41421	+	3.41421i	−0.161306	+	0.161306i
$449$	8.51472	−	8.51472i	0.401834	−	0.401834i	−0.477045	−	0.878879i	$-0.658292\pi$
$449$	8.51472	−	8.51472i	0.401834	−	0.401834i	0.878879	+	0.477045i	$0.158292\pi$
$450$		−	4.65685i		−	0.219526i
$451$		−	12.2843i		−	0.578444i
$452$	−9.00000	+	9.00000i	−0.423324	+	0.423324i
$453$	9.65685	−	9.65685i	0.453719	−	0.453719i
$454$	12.4853	+	12.4853i	0.585963	+	0.585963i
$455$	−8.00000			−0.375046
$456$	−4.82843	−	4.82843i	−0.226112	−	0.226112i
$457$			2.68629i			0.125659i	0.998024	+	0.0628297i	$0.0200125\pi$
$457$			2.68629i			0.125659i	−0.998024	+	0.0628297i	$0.979988\pi$
$458$	−14.0000			−0.654177
$459$	4.12132	−	0.121320i	0.192367	−	0.00566275i
$460$	1.85786			0.0866234
$461$		−	25.4558i		−	1.18560i	−0.805351	−	0.592798i	$-0.798023\pi$
$461$		−	25.4558i		−	1.18560i	0.805351	−	0.592798i	$-0.201977\pi$
$462$	13.6569	+	13.6569i	0.635374	+	0.635374i
$463$	6.82843			0.317344			0.158672	−	0.987331i	$-0.449279\pi$
$463$	6.82843			0.317344			0.158672	+	0.987331i	$0.449279\pi$
$464$	−0.414214	−	0.414214i	−0.0192294	−	0.0192294i
$465$	−0.343146	+	0.343146i	−0.0159130	+	0.0159130i
$466$	9.00000	−	9.00000i	0.416917	−	0.416917i
$467$		−	28.0000i		−	1.29569i	−0.761774	−	0.647843i	$-0.775671\pi$
$467$		−	28.0000i		−	1.29569i	0.761774	−	0.647843i	$-0.224329\pi$
$468$			2.82843i			0.130744i
$469$	4.00000	−	4.00000i	0.184703	−	0.184703i
$470$	5.17157	−	5.17157i	0.238547	−	0.238547i
$471$	4.24264	+	4.24264i	0.195491	+	0.195491i
$472$	12.4853			0.574682
$473$	−4.68629	−	4.68629i	−0.215476	−	0.215476i
$474$			14.4853i			0.665331i
$475$	31.7990			1.45904
$476$	19.8995	−	0.585786i	0.912092	−	0.0268495i
$477$	2.82843			0.129505
$478$		−	12.4853i		−	0.571063i
$479$	−5.07107	−	5.07107i	−0.231703	−	0.231703i	0.581700	−	0.813403i	$-0.302388\pi$
$479$	−5.07107	−	5.07107i	−0.231703	−	0.231703i	−0.813403	+	0.581700i	$0.802388\pi$
$480$	0.585786			0.0267374
$481$	4.48528	+	4.48528i	0.204511	+	0.204511i
$482$	−5.82843	+	5.82843i	−0.265478	+	0.265478i
$483$	−10.8284	+	10.8284i	−0.492710	+	0.492710i
$484$			5.00000i			0.227273i
$485$		−	7.85786i		−	0.356807i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	29.0711	−	29.0711i	1.31734	−	1.31734i	0.401459	−	0.915877i	$-0.368503\pi$
$487$	29.0711	−	29.0711i	1.31734	−	1.31734i	0.915877	−	0.401459i	$-0.131497\pi$
$488$	0.757359	+	0.757359i	0.0342840	+	0.0342840i
$489$	2.34315			0.105961
$490$	−6.75736	−	6.75736i	−0.305266	−	0.305266i
$491$			16.2843i			0.734899i	0.930043	+	0.367449i	$0.119769\pi$
$491$			16.2843i			0.734899i	−0.930043	+	0.367449i	$0.880231\pi$
$492$	3.07107			0.138454
$493$	0.0710678	+	2.41421i	0.00320073	+	0.108731i
$494$	−19.3137			−0.868965
$495$		−	2.34315i		−	0.105317i
$496$	0.585786	+	0.585786i	0.0263026	+	0.0263026i
$497$	31.3137			1.40461
$498$	−3.17157	−	3.17157i	−0.142122	−	0.142122i
$499$	−17.6569	+	17.6569i	−0.790429	+	0.790429i	−0.981564	−	0.191135i	$-0.938783\pi$
$499$	−17.6569	+	17.6569i	−0.790429	+	0.790429i	0.191135	+	0.981564i	$0.438783\pi$
$500$	−4.00000	+	4.00000i	−0.178885	+	0.178885i
$501$		−	21.7990i		−	0.973907i
$502$		−	17.6569i		−	0.788064i
$503$	6.72792	−	6.72792i	0.299983	−	0.299983i	−0.541024	−	0.841007i	$-0.681963\pi$
$503$	6.72792	−	6.72792i	0.299983	−	0.299983i	0.841007	+	0.541024i	$0.181963\pi$
$504$	−3.41421	+	3.41421i	−0.152081	+	0.152081i
$505$	2.14214	+	2.14214i	0.0953238	+	0.0953238i
$506$	−12.6863			−0.563974
$507$	−3.53553	−	3.53553i	−0.157019	−	0.157019i
$508$		−	13.6569i		−	0.605925i
$509$	2.68629			0.119068			0.0595339	−	0.998226i	$-0.481039\pi$
$509$	2.68629			0.119068			0.0595339	+	0.998226i	$0.481039\pi$
$510$	−1.75736	−	1.65685i	−0.0778172	−	0.0733667i
$511$	45.4558			2.01085
$512$		−	1.00000i		−	0.0441942i
$513$	−4.82843	−	4.82843i	−0.213180	−	0.213180i
$514$	29.3137			1.29297
$515$	6.14214	+	6.14214i	0.270655	+	0.270655i
$516$	1.17157	−	1.17157i	0.0515756	−	0.0515756i
$517$	−35.3137	+	35.3137i	−1.55310	+	1.55310i
$518$			10.8284i			0.475774i
$519$			4.10051i			0.179992i
$520$	1.17157	−	1.17157i	0.0513769	−	0.0513769i
$521$	−5.48528	+	5.48528i	−0.240315	+	0.240315i	−0.816980	−	0.576666i	$-0.804354\pi$
$521$	−5.48528	+	5.48528i	−0.240315	+	0.240315i	0.576666	+	0.816980i	$0.304354\pi$
$522$	−0.414214	−	0.414214i	−0.0181296	−	0.0181296i
$523$	−18.1421			−0.793300			−0.396650	−	0.917970i	$-0.629827\pi$
$523$	−18.1421			−0.793300			−0.396650	+	0.917970i	$0.629827\pi$
$524$	13.6569	+	13.6569i	0.596602	+	0.596602i
$525$		−	22.4853i		−	0.981338i
$526$	10.1421			0.442218
$527$	−0.100505	−	3.41421i	−0.00437807	−	0.148725i
$528$	−4.00000			−0.174078
$529$			12.9411i			0.562658i
$530$	−1.17157	−	1.17157i	−0.0508899	−	0.0508899i
$531$	12.4853			0.541815
$532$	−23.3137	−	23.3137i	−1.01078	−	1.01078i
$533$	6.14214	−	6.14214i	0.266045	−	0.266045i
$534$		0			0
$535$			8.00000i			0.345870i
$536$			1.17157i			0.0506042i
$537$	9.17157	−	9.17157i	0.395783	−	0.395783i
$538$	−3.58579	+	3.58579i	−0.154594	+	0.154594i
$539$	46.1421	+	46.1421i	1.98748	+	1.98748i
$540$	0.585786			0.0252082
$541$	−12.8995	−	12.8995i	−0.554593	−	0.554593i	0.373170	−	0.927763i	$-0.378271\pi$
$541$	−12.8995	−	12.8995i	−0.554593	−	0.554593i	−0.927763	+	0.373170i	$0.878271\pi$
$542$		−	21.6569i		−	0.930242i
$543$	−7.89949			−0.339000
$544$	−2.82843	+	3.00000i	−0.121268	+	0.128624i
$545$	−2.28427			−0.0978474
$546$			13.6569i			0.584459i
$547$	−13.1716	−	13.1716i	−0.563176	−	0.563176i	0.367032	−	0.930208i	$-0.380374\pi$
$547$	−13.1716	−	13.1716i	−0.563176	−	0.563176i	−0.930208	+	0.367032i	$0.880374\pi$
$548$	17.6569			0.754263
$549$	0.757359	+	0.757359i	0.0323233	+	0.0323233i
$550$	13.1716	−	13.1716i	0.561638	−	0.561638i
$551$	2.82843	−	2.82843i	0.120495	−	0.120495i
$552$		−	3.17157i		−	0.134991i
$553$			69.9411i			2.97420i
$554$	−6.89949	+	6.89949i	−0.293131	+	0.293131i
$555$	0.928932	−	0.928932i	0.0394310	−	0.0394310i
$556$	−4.48528	−	4.48528i	−0.190218	−	0.190218i
$557$	8.48528			0.359533			0.179766	−	0.983709i	$-0.442466\pi$
$557$	8.48528			0.359533			0.179766	+	0.983709i	$0.442466\pi$
$558$	0.585786	+	0.585786i	0.0247983	+	0.0247983i
$559$		−	4.68629i		−	0.198209i
$560$	2.82843			0.119523
$561$	12.0000	+	11.3137i	0.506640	+	0.477665i
$562$	−19.3137			−0.814700
$563$			3.51472i			0.148128i	0.997254	+	0.0740639i	$0.0235969\pi$
$563$			3.51472i			0.148128i	−0.997254	+	0.0740639i	$0.976403\pi$
$564$	−8.82843	−	8.82843i	−0.371744	−	0.371744i
$565$	7.45584			0.313670
$566$	−5.65685	−	5.65685i	−0.237775	−	0.237775i
$567$	−3.41421	+	3.41421i	−0.143383	+	0.143383i
$568$	−4.58579	+	4.58579i	−0.192415	+	0.192415i
$569$		−	12.9706i		−	0.543754i	−0.962332	−	0.271877i	$-0.912356\pi$
$569$		−	12.9706i		−	0.543754i	0.962332	−	0.271877i	$-0.0876444\pi$
$570$			4.00000i			0.167542i
$571$	6.14214	−	6.14214i	0.257040	−	0.257040i	−0.566809	−	0.823849i	$-0.691822\pi$
$571$	6.14214	−	6.14214i	0.257040	−	0.257040i	0.823849	+	0.566809i	$0.191822\pi$
$572$	−8.00000	+	8.00000i	−0.334497	+	0.334497i
$573$	0.828427	+	0.828427i	0.0346080	+	0.0346080i
$574$	14.8284			0.618927
$575$	10.4437	+	10.4437i	0.435530	+	0.435530i
$576$		−	1.00000i		−	0.0416667i
$577$	−3.31371			−0.137951			−0.0689757	−	0.997618i	$-0.521973\pi$
$577$	−3.31371			−0.137951			−0.0689757	+	0.997618i	$0.521973\pi$
$578$	16.9706	−	1.00000i	0.705882	−	0.0415945i
$579$	−5.89949			−0.245175
$580$			0.343146i			0.0142484i
$581$	−15.3137	−	15.3137i	−0.635320	−	0.635320i
$582$	−13.4142			−0.556037
$583$	8.00000	+	8.00000i	0.331326	+	0.331326i
$584$	−6.65685	+	6.65685i	−0.275463	+	0.275463i
$585$	1.17157	−	1.17157i	0.0484386	−	0.0484386i
$586$		−	9.31371i		−	0.384746i
$587$		−	36.9706i		−	1.52594i	−0.646435	−	0.762969i	$-0.723741\pi$
$587$		−	36.9706i		−	1.52594i	0.646435	−	0.762969i	$-0.276259\pi$
$588$	−11.5355	+	11.5355i	−0.475717	+	0.475717i
$589$	−4.00000	+	4.00000i	−0.164817	+	0.164817i
$590$	−5.17157	−	5.17157i	−0.212910	−	0.212910i
$591$	−10.2426			−0.421326
$592$	−1.58579	−	1.58579i	−0.0651754	−	0.0651754i
$593$		−	4.00000i		−	0.164260i	−0.996622	−	0.0821302i	$-0.973828\pi$
$593$		−	4.00000i		−	0.164260i	0.996622	−	0.0821302i	$-0.0261723\pi$
$594$	−4.00000			−0.164122
$595$	−8.48528	−	8.00000i	−0.347863	−	0.327968i
$596$	−10.0000			−0.409616
$597$		−	0.828427i		−	0.0339053i
$598$	−6.34315	−	6.34315i	−0.259391	−	0.259391i
$599$	−30.6274			−1.25140			−0.625701	−	0.780063i	$-0.715187\pi$
$599$	−30.6274			−1.25140			−0.625701	+	0.780063i	$0.715187\pi$
$600$	3.29289	+	3.29289i	0.134432	+	0.134432i
$601$	−4.65685	+	4.65685i	−0.189957	+	0.189957i	−0.795678	−	0.605720i	$-0.792885\pi$
$601$	−4.65685	+	4.65685i	−0.189957	+	0.189957i	0.605720	+	0.795678i	$0.292885\pi$
$602$	5.65685	−	5.65685i	0.230556	−	0.230556i
$603$			1.17157i			0.0477101i
$604$			13.6569i			0.555690i
$605$	2.07107	−	2.07107i	0.0842009	−	0.0842009i
$606$	3.65685	−	3.65685i	0.148550	−	0.148550i
$607$	7.41421	+	7.41421i	0.300934	+	0.300934i	0.841379	−	0.540445i	$-0.181744\pi$
$607$	7.41421	+	7.41421i	0.300934	+	0.300934i	−0.540445	+	0.841379i	$0.681744\pi$
$608$	6.82843			0.276929
$609$	−2.00000	−	2.00000i	−0.0810441	−	0.0810441i
$610$		−	0.627417i		−	0.0254034i
$611$	−35.3137			−1.42864
$612$	−2.82843	+	3.00000i	−0.114332	+	0.121268i
$613$	−21.3137			−0.860853			−0.430426	−	0.902626i	$-0.641637\pi$
$613$	−21.3137			−0.860853			−0.430426	+	0.902626i	$0.641637\pi$
$614$			6.34315i			0.255989i
$615$	−1.27208	−	1.27208i	−0.0512951	−	0.0512951i
$616$	−19.3137			−0.778171
$617$	10.6569	+	10.6569i	0.429029	+	0.429029i	0.888297	−	0.459269i	$-0.151888\pi$
$617$	10.6569	+	10.6569i	0.429029	+	0.429029i	−0.459269	+	0.888297i	$0.651888\pi$
$618$	10.4853	−	10.4853i	0.421780	−	0.421780i
$619$	−16.9706	+	16.9706i	−0.682105	+	0.682105i	−0.960474	−	0.278370i	$-0.910206\pi$
$619$	−16.9706	+	16.9706i	−0.682105	+	0.682105i	0.278370	+	0.960474i	$0.410206\pi$
$620$		−	0.485281i		−	0.0194894i
$621$		−	3.17157i		−	0.127271i
$622$	0.585786	−	0.585786i	0.0234879	−	0.0234879i
$623$		0			0
$624$	−2.00000	−	2.00000i	−0.0800641	−	0.0800641i
$625$	−19.9706			−0.798823
$626$	−7.14214	−	7.14214i	−0.285457	−	0.285457i
$627$		−	27.3137i		−	1.09080i
$628$	−6.00000			−0.239426
$629$	0.272078	+	9.24264i	0.0108485	+	0.368528i
$630$	2.82843			0.112687
$631$		−	26.1421i		−	1.04070i	−0.853952	−	0.520351i	$-0.825801\pi$
$631$		−	26.1421i		−	1.04070i	0.853952	−	0.520351i	$-0.174199\pi$
$632$	−10.2426	−	10.2426i	−0.407430	−	0.407430i
$633$	−28.9706			−1.15148
$634$	15.2426	+	15.2426i	0.605363	+	0.605363i
$635$	−5.65685	+	5.65685i	−0.224485	+	0.224485i
$636$	−2.00000	+	2.00000i	−0.0793052	+	0.0793052i
$637$			46.1421i			1.82822i
$638$		−	2.34315i		−	0.0927660i
$639$	−4.58579	+	4.58579i	−0.181411	+	0.181411i
$640$	−0.414214	+	0.414214i	−0.0163732	+	0.0163732i
$641$	13.4853	+	13.4853i	0.532637	+	0.532637i	0.921356	−	0.388720i	$-0.127082\pi$
$641$	13.4853	+	13.4853i	0.532637	+	0.532637i	−0.388720	+	0.921356i	$0.627082\pi$
$642$	13.6569			0.538993
$643$	0.485281	+	0.485281i	0.0191376	+	0.0191376i	0.716611	−	0.697473i	$-0.245692\pi$
$643$	0.485281	+	0.485281i	0.0191376	+	0.0191376i	−0.697473	+	0.716611i	$0.745692\pi$
$644$		−	15.3137i		−	0.603445i
$645$	−0.970563			−0.0382159
$646$	−20.4853	−	19.3137i	−0.805983	−	0.759888i
$647$	38.4264			1.51070			0.755349	−	0.655323i	$-0.227467\pi$
$647$	38.4264			1.51070			0.755349	+	0.655323i	$0.227467\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	35.3137	+	35.3137i	1.38618	+	1.38618i
$650$	13.1716			0.516632
$651$	2.82843	+	2.82843i	0.110855	+	0.110855i
$652$	−1.65685	+	1.65685i	−0.0648874	+	0.0648874i
$653$	22.2132	−	22.2132i	0.869270	−	0.869270i	−0.123122	−	0.992392i	$-0.539291\pi$
$653$	22.2132	−	22.2132i	0.869270	−	0.869270i	0.992392	+	0.123122i	$0.0392906\pi$
$654$			3.89949i			0.152482i
$655$		−	11.3137i		−	0.442063i
$656$	−2.17157	+	2.17157i	−0.0847857	+	0.0847857i
$657$	−6.65685	+	6.65685i	−0.259709	+	0.259709i
$658$	−42.6274	−	42.6274i	−1.66179	−	1.66179i
$659$	3.51472			0.136914			0.0684570	−	0.997654i	$-0.478192\pi$
$659$	3.51472			0.136914			0.0684570	+	0.997654i	$0.478192\pi$
$660$	1.65685	+	1.65685i	0.0644930	+	0.0644930i
$661$			30.1421i			1.17239i	0.810169	+	0.586197i	$0.199375\pi$
$661$			30.1421i			1.17239i	−0.810169	+	0.586197i	$0.800625\pi$
$662$	18.6274			0.723975
$663$	0.343146	+	11.6569i	0.0133267	+	0.452715i
$664$	4.48528			0.174063
$665$			19.3137i			0.748953i
$666$	−1.58579	−	1.58579i	−0.0614480	−	0.0614480i
$667$	1.85786			0.0719368
$668$	15.4142	+	15.4142i	0.596394	+	0.596394i
$669$	4.82843	−	4.82843i	0.186678	−	0.186678i
$670$	0.485281	−	0.485281i	0.0187481	−	0.0187481i
$671$			4.28427i			0.165392i
$672$		−	4.82843i		−	0.186261i
$673$	25.1421	−	25.1421i	0.969158	−	0.969158i	−0.0303803	−	0.999538i	$-0.509672\pi$
$673$	25.1421	−	25.1421i	0.969158	−	0.969158i	0.999538	+	0.0303803i	$0.00967184\pi$
$674$	9.00000	−	9.00000i	0.346667	−	0.346667i
$675$	3.29289	+	3.29289i	0.126744	+	0.126744i
$676$	5.00000			0.192308
$677$	20.0711	+	20.0711i	0.771394	+	0.771394i	0.978350	−	0.206956i	$-0.0663558\pi$
$677$	20.0711	+	20.0711i	0.771394	+	0.771394i	−0.206956	+	0.978350i	$0.566356\pi$
$678$		−	12.7279i		−	0.488813i
$679$	−64.7696			−2.48563
$680$	2.41421	−	0.0710678i	0.0925809	−	0.00272533i
$681$	−17.6569			−0.676612
$682$			3.31371i			0.126888i
$683$	14.3431	+	14.3431i	0.548825	+	0.548825i	0.926101	−	0.377276i	$-0.123139\pi$
$683$	14.3431	+	14.3431i	0.548825	+	0.548825i	−0.377276	+	0.926101i	$0.623139\pi$
$684$	6.82843			0.261091
$685$	−7.31371	−	7.31371i	−0.279442	−	0.279442i
$686$	−31.7990	+	31.7990i	−1.21409	+	1.21409i
$687$	9.89949	−	9.89949i	0.377689	−	0.377689i
$688$			1.65685i			0.0631670i
$689$			8.00000i			0.304776i
$690$	−1.31371	+	1.31371i	−0.0500120	+	0.0500120i
$691$	−9.17157	+	9.17157i	−0.348903	+	0.348903i	−0.859701	−	0.510798i	$-0.829350\pi$
$691$	−9.17157	+	9.17157i	−0.348903	+	0.348903i	0.510798	+	0.859701i	$0.329350\pi$
$692$	−2.89949	−	2.89949i	−0.110222	−	0.110222i
$693$	−19.3137			−0.733667
$694$	8.00000	+	8.00000i	0.303676	+	0.303676i
$695$			3.71573i			0.140946i
$696$	0.585786			0.0222042
$697$	12.6569	−	0.372583i	0.479413	−	0.0141126i
$698$	−10.8284			−0.409862
$699$			12.7279i			0.481414i
$700$	15.8995	+	15.8995i	0.600944	+	0.600944i
$701$	−23.5147			−0.888139			−0.444069	−	0.895992i	$-0.646466\pi$
$701$	−23.5147			−0.888139			−0.444069	+	0.895992i	$0.646466\pi$
$702$	−2.00000	−	2.00000i	−0.0754851	−	0.0754851i
$703$	10.8284	−	10.8284i	0.408402	−	0.408402i
$704$	2.82843	−	2.82843i	0.106600	−	0.106600i
$705$			7.31371i			0.275450i
$706$			12.6274i			0.475239i
$707$	17.6569	−	17.6569i	0.664054	−	0.664054i
$708$	−8.82843	+	8.82843i	−0.331793	+	0.331793i
$709$	−23.5858	−	23.5858i	−0.885783	−	0.885783i	0.108332	−	0.994115i	$-0.465449\pi$
$709$	−23.5858	−	23.5858i	−0.885783	−	0.885783i	−0.994115	+	0.108332i	$0.965449\pi$
$710$	3.79899			0.142574
$711$	−10.2426	−	10.2426i	−0.384129	−	0.384129i
$712$		0			0
$713$	−2.62742			−0.0983975
$714$	−13.6569	+	14.4853i	−0.511095	+	0.542098i
$715$	6.62742			0.247851
$716$			12.9706i			0.484733i
$717$	8.82843	+	8.82843i	0.329704	+	0.329704i
$718$	16.0000			0.597115
$719$	7.21320	+	7.21320i	0.269007	+	0.269007i	0.828700	−	0.559693i	$-0.189081\pi$
$719$	7.21320	+	7.21320i	0.269007	+	0.269007i	−0.559693	+	0.828700i	$0.689081\pi$
$720$	−0.414214	+	0.414214i	−0.0154368	+	0.0154368i
$721$	50.6274	−	50.6274i	1.88546	−	1.88546i
$722$			27.6274i			1.02819i
$723$		−	8.24264i		−	0.306547i
$724$	5.58579	−	5.58579i	0.207594	−	0.207594i
$725$	−1.92893	+	1.92893i	−0.0716387	+	0.0716387i
$726$	−3.53553	−	3.53553i	−0.131216	−	0.131216i
$727$	−10.3431			−0.383606			−0.191803	−	0.981433i	$-0.561433\pi$
$727$	−10.3431			−0.383606			−0.191803	+	0.981433i	$0.561433\pi$
$728$	−9.65685	−	9.65685i	−0.357907	−	0.357907i
$729$		−	1.00000i		−	0.0370370i
$730$	5.51472			0.204109
$731$	4.68629	−	4.97056i	0.173329	−	0.183843i
$732$	−1.07107			−0.0395878
$733$		−	41.4558i		−	1.53121i	−0.643313	−	0.765603i	$-0.722441\pi$
$733$		−	41.4558i		−	1.53121i	0.643313	−	0.765603i	$-0.277559\pi$
$734$	12.3848	+	12.3848i	0.457130	+	0.457130i
$735$	9.55635			0.352491
$736$	2.24264	+	2.24264i	0.0826648	+	0.0826648i
$737$	−3.31371	+	3.31371i	−0.122062	+	0.122062i
$738$	−2.17157	+	2.17157i	−0.0799367	+	0.0799367i
$739$		−	9.17157i		−	0.337382i	−0.985669	−	0.168691i	$-0.946046\pi$
$739$		−	9.17157i		−	0.337382i	0.985669	−	0.168691i	$-0.0539540\pi$
$740$			1.31371i			0.0482929i
$741$	13.6569	−	13.6569i	0.501697	−	0.501697i
$742$	−9.65685	+	9.65685i	−0.354514	+	0.354514i
$743$	−22.2426	−	22.2426i	−0.816003	−	0.816003i	0.169523	−	0.985526i	$-0.445777\pi$
$743$	−22.2426	−	22.2426i	−0.816003	−	0.816003i	−0.985526	+	0.169523i	$0.945777\pi$
$744$	−0.828427			−0.0303716
$745$	4.14214	+	4.14214i	0.151756	+	0.151756i
$746$		−	19.7990i		−	0.724893i
$747$	4.48528			0.164108
$748$	−16.4853	+	0.485281i	−0.602762	+	0.0177436i
$749$	65.9411			2.40944
$750$		−	5.65685i		−	0.206559i
$751$	8.10051	+	8.10051i	0.295592	+	0.295592i	0.839284	−	0.543693i	$-0.182974\pi$
$751$	8.10051	+	8.10051i	0.295592	+	0.295592i	−0.543693	+	0.839284i	$0.682974\pi$
$752$	12.4853			0.455291
$753$	12.4853	+	12.4853i	0.454989	+	0.454989i
$754$	1.17157	−	1.17157i	0.0426662	−	0.0426662i
$755$	5.65685	−	5.65685i	0.205874	−	0.205874i
$756$		−	4.82843i		−	0.175608i
$757$		−	6.00000i		−	0.218074i	−0.994038	−	0.109037i	$-0.965223\pi$
$757$		−	6.00000i		−	0.218074i	0.994038	−	0.109037i	$-0.0347767\pi$
$758$	17.6569	−	17.6569i	0.641326	−	0.641326i
$759$	8.97056	−	8.97056i	0.325611	−	0.325611i
$760$	−2.82843	−	2.82843i	−0.102598	−	0.102598i
$761$	1.65685			0.0600609			0.0300305	−	0.999549i	$-0.490440\pi$
$761$	1.65685			0.0600609			0.0300305	+	0.999549i	$0.490440\pi$
$762$	9.65685	+	9.65685i	0.349831	+	0.349831i
$763$			18.8284i			0.681635i
$764$	−1.17157			−0.0423860
$765$	2.41421	−	0.0710678i	0.0872861	−	0.00256946i
$766$	23.7990			0.859892
$767$			35.3137i			1.27510i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	40.9706			1.47744			0.738718	−	0.674014i	$-0.235431\pi$
$769$	40.9706			1.47744			0.738718	+	0.674014i	$0.235431\pi$
$770$	8.00000	+	8.00000i	0.288300	+	0.288300i
$771$	−20.7279	+	20.7279i	−0.746498	+	0.746498i
$772$	4.17157	−	4.17157i	0.150138	−	0.150138i
$773$		−	44.6274i		−	1.60514i	−0.596560	−	0.802568i	$-0.703466\pi$
$773$		−	44.6274i		−	1.60514i	0.596560	−	0.802568i	$-0.296534\pi$
$774$			1.65685i			0.0595544i
$775$	2.72792	−	2.72792i	0.0979899	−	0.0979899i
$776$	9.48528	−	9.48528i	0.340502	−	0.340502i
$777$	−7.65685	−	7.65685i	−0.274688	−	0.274688i
$778$	36.6274			1.31316
$779$	−14.8284	−	14.8284i	−0.531284	−	0.531284i
$780$			1.65685i			0.0593249i
$781$	−25.9411			−0.928246
$782$	−0.384776	−	13.0711i	−0.0137596	−	0.467420i
$783$	0.585786			0.0209343
$784$		−	16.3137i		−	0.582632i
$785$	2.48528	+	2.48528i	0.0887035	+	0.0887035i
$786$	−19.3137			−0.688897
$787$	−15.5147	−	15.5147i	−0.553040	−	0.553040i	0.374277	−	0.927317i	$-0.377891\pi$
$787$	−15.5147	−	15.5147i	−0.553040	−	0.553040i	−0.927317	+	0.374277i	$0.877891\pi$
$788$	7.24264	−	7.24264i	0.258008	−	0.258008i
$789$	−7.17157	+	7.17157i	−0.255315	+	0.255315i
$790$			8.48528i			0.301893i
$791$		−	61.4558i		−	2.18512i
$792$	2.82843	−	2.82843i	0.100504	−	0.100504i
$793$	−2.14214	+	2.14214i	−0.0760695	+	0.0760695i
$794$	−23.3848	−	23.3848i	−0.829895	−	0.829895i
$795$	1.65685			0.0587626
$796$	0.585786	+	0.585786i	0.0207626	+	0.0207626i
$797$		−	21.1716i		−	0.749936i	−0.927038	−	0.374968i	$-0.877654\pi$
$797$		−	21.1716i		−	0.749936i	0.927038	−	0.374968i	$-0.122346\pi$
$798$	32.9706			1.16715
$799$	−37.4558	−	35.3137i	−1.32509	−	1.24931i
$800$	−4.65685			−0.164645
$801$		0			0
$802$	6.17157	+	6.17157i	0.217926	+	0.217926i
$803$	−37.6569			−1.32888
$804$	−0.828427	−	0.828427i	−0.0292164	−	0.0292164i
$805$	−6.34315	+	6.34315i	−0.223567	+	0.223567i
$806$	−1.65685	+	1.65685i	−0.0583602	+	0.0583602i
$807$		−	5.07107i		−	0.178510i
$808$			5.17157i			0.181935i
$809$	−31.4853	+	31.4853i	−1.10696	+	1.10696i	−0.113416	+	0.993548i	$0.536179\pi$
$809$	−31.4853	+	31.4853i	−1.10696	+	1.10696i	−0.993548	+	0.113416i	$0.963821\pi$
$810$	−0.414214	+	0.414214i	−0.0145540	+	0.0145540i
$811$	20.4853	+	20.4853i	0.719336	+	0.719336i	0.968469	−	0.249134i	$-0.0801458\pi$
$811$	20.4853	+	20.4853i	0.719336	+	0.719336i	−0.249134	+	0.968469i	$0.580146\pi$
$812$	2.82843			0.0992583
$813$	15.3137	+	15.3137i	0.537075	+	0.537075i
$814$		−	8.97056i		−	0.314418i
$815$	1.37258			0.0480795
$816$	−0.121320	−	4.12132i	−0.00424706	−	0.144275i
$817$	−11.3137			−0.395817
$818$			14.0000i			0.489499i
$819$	−9.65685	−	9.65685i	−0.337438	−	0.337438i
$820$	1.79899			0.0628235
$821$	9.72792	+	9.72792i	0.339507	+	0.339507i	0.856182	−	0.516675i	$-0.172830\pi$
$821$	9.72792	+	9.72792i	0.339507	+	0.339507i	−0.516675	+	0.856182i	$0.672830\pi$
$822$	−12.4853	+	12.4853i	−0.435474	+	0.435474i
$823$	22.0416	−	22.0416i	0.768323	−	0.768323i	−0.209488	−	0.977811i	$-0.567180\pi$
$823$	22.0416	−	22.0416i	0.768323	−	0.768323i	0.977811	+	0.209488i	$0.0671798\pi$
$824$			14.8284i			0.516573i
$825$			18.6274i			0.648523i
$826$	−42.6274	+	42.6274i	−1.48320	+	1.48320i
$827$	−26.8284	+	26.8284i	−0.932916	+	0.932916i	−0.997887	−	0.0649713i	$-0.979304\pi$
$827$	−26.8284	+	26.8284i	−0.932916	+	0.932916i	0.0649713	+	0.997887i	$0.479304\pi$
$828$	2.24264	+	2.24264i	0.0779372	+	0.0779372i
$829$	−27.9411			−0.970435			−0.485218	−	0.874393i	$-0.661260\pi$
$829$	−27.9411			−0.970435			−0.485218	+	0.874393i	$0.661260\pi$
$830$	−1.85786	−	1.85786i	−0.0644874	−	0.0644874i
$831$		−	9.75736i		−	0.338479i
$832$	2.82843			0.0980581
$833$	−46.1421	+	48.9411i	−1.59873	+	1.69571i
$834$	6.34315			0.219645
$835$		−	12.7696i		−	0.441909i
$836$	19.3137	+	19.3137i	0.667979	+	0.667979i
$837$	−0.828427			−0.0286346
$838$	−1.17157	−	1.17157i	−0.0404713	−	0.0404713i
$839$	1.75736	−	1.75736i	0.0606708	−	0.0606708i	−0.676120	−	0.736791i	$-0.736340\pi$
$839$	1.75736	−	1.75736i	0.0606708	−	0.0606708i	0.736791	+	0.676120i	$0.236340\pi$
$840$	−2.00000	+	2.00000i	−0.0690066	+	0.0690066i
$841$		−	28.6569i		−	0.988167i
$842$			15.5147i			0.534673i
$843$	13.6569	−	13.6569i	0.470367	−	0.470367i
$844$	20.4853	−	20.4853i	0.705132	−	0.705132i
$845$	−2.07107	−	2.07107i	−0.0712469	−	0.0712469i
$846$	12.4853			0.429253
$847$	−17.0711	−	17.0711i	−0.586569	−	0.586569i
$848$		−	2.82843i		−	0.0971286i
$849$	8.00000			0.274559
$850$	13.9706	+	13.1716i	0.479186	+	0.451781i
$851$	7.11270			0.243820
$852$		−	6.48528i		−	0.222182i
$853$	34.2132	+	34.2132i	1.17144	+	1.17144i	0.981867	+	0.189571i	$0.0607096\pi$
$853$	34.2132	+	34.2132i	1.17144	+	1.17144i	0.189571	+	0.981867i	$0.439290\pi$
$854$	−5.17157			−0.176968
$855$	−2.82843	−	2.82843i	−0.0967302	−	0.0967302i
$856$	−9.65685	+	9.65685i	−0.330064	+	0.330064i
$857$	−11.1421	+	11.1421i	−0.380608	+	0.380608i	−0.871321	−	0.490713i	$-0.836736\pi$
$857$	−11.1421	+	11.1421i	−0.380608	+	0.380608i	0.490713	+	0.871321i	$0.336736\pi$
$858$		−	11.3137i		−	0.386244i
$859$		−	1.65685i		−	0.0565311i	−0.999600	−	0.0282656i	$-0.991002\pi$
$859$		−	1.65685i		−	0.0565311i	0.999600	−	0.0282656i	$-0.00899841\pi$
$860$	0.686292	−	0.686292i	0.0234023	−	0.0234023i
$861$	−10.4853	+	10.4853i	−0.357337	+	0.357337i
$862$	14.2426	+	14.2426i	0.485106	+	0.485106i
$863$	5.65685			0.192562			0.0962808	−	0.995354i	$-0.469305\pi$
$863$	5.65685			0.192562			0.0962808	+	0.995354i	$0.469305\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$			2.40202i			0.0816711i
$866$	−16.6274			−0.565023
$867$	−11.2929	+	12.7071i	−0.383527	+	0.431556i
$868$	−4.00000			−0.135769
$869$		−	57.9411i		−	1.96552i
$870$	−0.242641	−	0.242641i	−0.00822629	−	0.00822629i
$871$	−3.31371			−0.112281
$872$	−2.75736	−	2.75736i	−0.0933760	−	0.0933760i
$873$	9.48528	−	9.48528i	0.321028	−	0.321028i
$874$	−15.3137	+	15.3137i	−0.517994	+	0.517994i
$875$		−	27.3137i		−	0.923372i
$876$		−	9.41421i		−	0.318077i
$877$	8.55635	−	8.55635i	0.288927	−	0.288927i	−0.547729	−	0.836656i	$-0.684507\pi$
$877$	8.55635	−	8.55635i	0.288927	−	0.288927i	0.836656	+	0.547729i	$0.184507\pi$
$878$	−9.55635	+	9.55635i	−0.322511	+	0.322511i
$879$	6.58579	+	6.58579i	0.222133	+	0.222133i
$880$	−2.34315			−0.0789874
$881$	20.6569	+	20.6569i	0.695947	+	0.695947i	0.963534	−	0.267587i	$-0.0862262\pi$
$881$	20.6569	+	20.6569i	0.695947	+	0.695947i	−0.267587	+	0.963534i	$0.586226\pi$
$882$		−	16.3137i		−	0.549311i
$883$	−48.7696			−1.64123			−0.820613	−	0.571484i	$-0.806368\pi$
$883$	−48.7696			−1.64123			−0.820613	+	0.571484i	$0.806368\pi$
$884$	−8.48528	−	8.00000i	−0.285391	−	0.269069i
$885$	7.31371			0.245848
$886$			28.9706i			0.973285i
$887$	−1.27208	−	1.27208i	−0.0427122	−	0.0427122i	0.685428	−	0.728140i	$-0.259615\pi$
$887$	−1.27208	−	1.27208i	−0.0427122	−	0.0427122i	−0.728140	+	0.685428i	$0.759615\pi$
$888$	2.24264			0.0752581
$889$	46.6274	+	46.6274i	1.56383	+	1.56383i
$890$		0			0
$891$	2.82843	−	2.82843i	0.0947559	−	0.0947559i
$892$			6.82843i			0.228633i
$893$			85.2548i			2.85294i
$894$	7.07107	−	7.07107i	0.236492	−	0.236492i
$895$	5.37258	−	5.37258i	0.179586	−	0.179586i
$896$	3.41421	+	3.41421i	0.114061	+	0.114061i
$897$	8.97056			0.299518
$898$	−8.51472	−	8.51472i	−0.284140	−	0.284140i
$899$		−	0.485281i		−	0.0161850i
$900$	−4.65685			−0.155228
$901$	−8.00000	+	8.48528i	−0.266519	+	0.282686i
$902$	−12.2843			−0.409021
$903$			8.00000i			0.266223i
$904$	9.00000	+	9.00000i	0.299336	+	0.299336i
$905$	−4.62742			−0.153821
$906$	−9.65685	−	9.65685i	−0.320827	−	0.320827i
$907$	−8.97056	+	8.97056i	−0.297863	+	0.297863i	−0.840176	−	0.542314i	$-0.817548\pi$
$907$	−8.97056	+	8.97056i	−0.297863	+	0.297863i	0.542314	+	0.840176i	$0.317548\pi$
$908$	12.4853	−	12.4853i	0.414339	−	0.414339i
$909$			5.17157i			0.171530i
$910$			8.00000i			0.265197i
$911$	20.5858	−	20.5858i	0.682038	−	0.682038i	−0.278421	−	0.960459i	$-0.589811\pi$
$911$	20.5858	−	20.5858i	0.682038	−	0.682038i	0.960459	+	0.278421i	$0.0898112\pi$
$912$	−4.82843	+	4.82843i	−0.159885	+	0.159885i
$913$	12.6863	+	12.6863i	0.419855	+	0.419855i
$914$	2.68629			0.0888546
$915$	0.443651	+	0.443651i	0.0146666	+	0.0146666i
$916$			14.0000i			0.462573i
$917$	−93.2548			−3.07955
$918$	−0.121320	−	4.12132i	−0.00400417	−	0.136024i
$919$	−18.3431			−0.605085			−0.302542	−	0.953136i	$-0.597835\pi$
$919$	−18.3431			−0.605085			−0.302542	+	0.953136i	$0.597835\pi$
$920$		−	1.85786i		−	0.0612520i
$921$	−4.48528	−	4.48528i	−0.147795	−	0.147795i
$922$	−25.4558			−0.838344
$923$	−12.9706	−	12.9706i	−0.426931	−	0.426931i
$924$	13.6569	−	13.6569i	0.449278	−	0.449278i
$925$	−7.38478	+	7.38478i	−0.242810	+	0.242810i
$926$		−	6.82843i		−	0.224396i
$927$			14.8284i			0.487029i
$928$	−0.414214	+	0.414214i	−0.0135972	+	0.0135972i
$929$	30.1127	−	30.1127i	0.987966	−	0.987966i	−0.0119629	−	0.999928i	$-0.503808\pi$
$929$	30.1127	−	30.1127i	0.987966	−	0.987966i	0.999928	+	0.0119629i	$0.00380799\pi$
$930$	0.343146	+	0.343146i	0.0112522	+	0.0112522i
$931$	111.397			3.65089
$932$	−9.00000	−	9.00000i	−0.294805	−	0.294805i
$933$			0.828427i			0.0271215i
$934$	−28.0000			−0.916188
$935$	7.02944	+	6.62742i	0.229887	+	0.216740i
$936$	2.82843			0.0924500
$937$			4.00000i			0.130674i	0.997863	+	0.0653372i	$0.0208123\pi$
$937$			4.00000i			0.130674i	−0.997863	+	0.0653372i	$0.979188\pi$
$938$	−4.00000	−	4.00000i	−0.130605	−	0.130605i
$939$	10.1005			0.329618
$940$	−5.17157	−	5.17157i	−0.168678	−	0.168678i
$941$	−24.2132	+	24.2132i	−0.789328	+	0.789328i	−0.981384	−	0.192056i	$-0.938484\pi$
$941$	−24.2132	+	24.2132i	−0.789328	+	0.789328i	0.192056	+	0.981384i	$0.438484\pi$
$942$	4.24264	−	4.24264i	0.138233	−	0.138233i
$943$		−	9.74012i		−	0.317182i
$944$		−	12.4853i		−	0.406361i
$945$	−2.00000	+	2.00000i	−0.0650600	+	0.0650600i
$946$	−4.68629	+	4.68629i	−0.152364	+	0.152364i
$947$	−15.5147	−	15.5147i	−0.504161	−	0.504161i	0.408567	−	0.912728i	$-0.366028\pi$
$947$	−15.5147	−	15.5147i	−0.504161	−	0.504161i	−0.912728	+	0.408567i	$0.866028\pi$
$948$	14.4853			0.470460
$949$	−18.8284	−	18.8284i	−0.611197	−	0.611197i
$950$		−	31.7990i		−	1.03170i
$951$	−21.5563			−0.699013
$952$	−0.585786	−	19.8995i	−0.0189854	−	0.644946i
$953$	7.02944			0.227706			0.113853	−	0.993498i	$-0.463681\pi$
$953$	7.02944			0.227706			0.113853	+	0.993498i	$0.463681\pi$
$954$		−	2.82843i		−	0.0915737i
$955$	0.485281	+	0.485281i	0.0157033	+	0.0157033i
$956$	−12.4853			−0.403803
$957$	1.65685	+	1.65685i	0.0535585	+	0.0535585i
$958$	−5.07107	+	5.07107i	−0.163839	+	0.163839i
$959$	−60.2843	+	60.2843i	−1.94668	+	1.94668i
$960$		−	0.585786i		−	0.0189062i
$961$		−	30.3137i		−	0.977862i
$962$	4.48528	−	4.48528i	0.144611	−	0.144611i
$963$	−9.65685	+	9.65685i	−0.311188	+	0.311188i
$964$	5.82843	+	5.82843i	0.187721	+	0.187721i
$965$	−3.45584			−0.111248
$966$	10.8284	+	10.8284i	0.348399	+	0.348399i
$967$			18.1421i			0.583412i	0.956508	+	0.291706i	$0.0942228\pi$
$967$			18.1421i			0.583412i	−0.956508	+	0.291706i	$0.905777\pi$
$968$	5.00000			0.160706
$969$	28.1421	−	0.828427i	0.904056	−	0.0266129i
$970$	−7.85786			−0.252301
$971$			20.4853i			0.657404i	0.944434	+	0.328702i	$0.106611\pi$
$971$			20.4853i			0.657404i	−0.944434	+	0.328702i	$0.893389\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	30.6274			0.981870
$974$	−29.0711	−	29.0711i	−0.931497	−	0.931497i
$975$	−9.31371	+	9.31371i	−0.298277	+	0.298277i
$976$	0.757359	−	0.757359i	0.0242425	−	0.0242425i
$977$		−	0.284271i		−	0.00909464i	−0.999990	−	0.00454732i	$-0.998553\pi$
$977$		−	0.284271i		−	0.00909464i	0.999990	−	0.00454732i	$-0.00144746\pi$
$978$		−	2.34315i		−	0.0749255i
$979$		0			0
$980$	−6.75736	+	6.75736i	−0.215856	+	0.215856i
$981$	−2.75736	−	2.75736i	−0.0880357	−	0.0880357i
$982$	16.2843			0.519652
$983$	3.41421	+	3.41421i	0.108897	+	0.108897i	0.759456	−	0.650559i	$-0.225465\pi$
$983$	3.41421	+	3.41421i	0.108897	+	0.108897i	−0.650559	+	0.759456i	$0.725465\pi$
$984$		−	3.07107i		−	0.0979021i
$985$	−6.00000			−0.191176
$986$	2.41421	−	0.0710678i	0.0768842	−	0.00226326i
$987$	60.2843			1.91887
$988$			19.3137i			0.614451i
$989$	−3.71573	−	3.71573i	−0.118153	−	0.118153i
$990$	−2.34315			−0.0744701
$991$	38.5269	+	38.5269i	1.22385	+	1.22385i	0.966253	+	0.257595i	$0.0829299\pi$
$991$	38.5269	+	38.5269i	1.22385	+	1.22385i	0.257595	+	0.966253i	$0.417070\pi$
$992$	0.585786	−	0.585786i	0.0185987	−	0.0185987i
$993$	−13.1716	+	13.1716i	−0.417987	+	0.417987i
$994$		−	31.3137i		−	0.993211i
$995$		−	0.485281i		−	0.0153845i
$996$	−3.17157	+	3.17157i	−0.100495	+	0.100495i
$997$	32.8995	−	32.8995i	1.04194	−	1.04194i	0.0428562	−	0.999081i	$-0.486354\pi$
$997$	32.8995	−	32.8995i	1.04194	−	1.04194i	0.999081	−	0.0428562i	$-0.0136457\pi$
$998$	17.6569	+	17.6569i	0.558918	+	0.558918i
$999$	2.24264			0.0709540

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	102.2.f.a.13.2	✓	4
3.2	odd	2		306.2.g.g.217.1		4
4.3	odd	2		816.2.bd.a.625.1		4
12.11	even	2		2448.2.be.t.1441.1		4
17.2	even	8		1734.2.a.o.1.2		2
17.4	even	4	inner	102.2.f.a.55.2	yes	4
17.8	even	8		1734.2.b.h.577.1		4
17.9	even	8		1734.2.b.h.577.4		4
17.13	even	4		1734.2.f.i.1483.1		4
17.15	even	8		1734.2.a.n.1.1		2
17.16	even	2		1734.2.f.i.829.1		4
51.2	odd	8		5202.2.a.x.1.1		2
51.32	odd	8		5202.2.a.o.1.2		2
51.38	odd	4		306.2.g.g.55.1		4
68.55	odd	4		816.2.bd.a.769.1		4
204.191	even	4		2448.2.be.t.1585.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.2.f.a.13.2	✓	4	1.1	even	1	trivial
102.2.f.a.55.2	yes	4	17.4	even	4	inner
306.2.g.g.55.1		4	51.38	odd	4
306.2.g.g.217.1		4	3.2	odd	2
816.2.bd.a.625.1		4	4.3	odd	2
816.2.bd.a.769.1		4	68.55	odd	4
1734.2.a.n.1.1		2	17.15	even	8
1734.2.a.o.1.2		2	17.2	even	8
1734.2.b.h.577.1		4	17.8	even	8
1734.2.b.h.577.4		4	17.9	even	8
1734.2.f.i.829.1		4	17.16	even	2
1734.2.f.i.1483.1		4	17.13	even	4
2448.2.be.t.1441.1		4	12.11	even	2
2448.2.be.t.1585.1		4	204.191	even	4
5202.2.a.o.1.2		2	51.32	odd	8
5202.2.a.x.1.1		2	51.2	odd	8

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:	\( N \)	\(=\)	\( 102 = 2 \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	102.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(0.414214 + 0.414214i) q^{5} +(0.707107 - 0.707107i) q^{6} +(3.41421 - 3.41421i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(0.414214 - 0.414214i) q^{10} +(-2.82843 + 2.82843i) q^{11} +(-0.707107 - 0.707107i) q^{12} -2.82843 q^{13} +(-3.41421 - 3.41421i) q^{14} +0.585786i q^{15} +1.00000 q^{16} +(-3.00000 - 2.82843i) q^{17} +1.00000 q^{18} +6.82843i q^{19} +(-0.414214 - 0.414214i) q^{20} +4.82843 q^{21} +(2.82843 + 2.82843i) q^{22} +(-2.24264 + 2.24264i) q^{23} +(-0.707107 + 0.707107i) q^{24} -4.65685i q^{25} +2.82843i q^{26} +(-0.707107 + 0.707107i) q^{27} +(-3.41421 + 3.41421i) q^{28} +(-0.414214 - 0.414214i) q^{29} +0.585786 q^{30} +(0.585786 + 0.585786i) q^{31} -1.00000i q^{32} -4.00000 q^{33} +(-2.82843 + 3.00000i) q^{34} +2.82843 q^{35} -1.00000i q^{36} +(-1.58579 - 1.58579i) q^{37} +6.82843 q^{38} +(-2.00000 - 2.00000i) q^{39} +(-0.414214 + 0.414214i) q^{40} +(-2.17157 + 2.17157i) q^{41} -4.82843i q^{42} +1.65685i q^{43} +(2.82843 - 2.82843i) q^{44} +(-0.414214 + 0.414214i) q^{45} +(2.24264 + 2.24264i) q^{46} +12.4853 q^{47} +(0.707107 + 0.707107i) q^{48} -16.3137i q^{49} -4.65685 q^{50} +(-0.121320 - 4.12132i) q^{51} +2.82843 q^{52} -2.82843i q^{53} +(0.707107 + 0.707107i) q^{54} -2.34315 q^{55} +(3.41421 + 3.41421i) q^{56} +(-4.82843 + 4.82843i) q^{57} +(-0.414214 + 0.414214i) q^{58} -12.4853i q^{59} -0.585786i q^{60} +(0.757359 - 0.757359i) q^{61} +(0.585786 - 0.585786i) q^{62} +(3.41421 + 3.41421i) q^{63} -1.00000 q^{64} +(-1.17157 - 1.17157i) q^{65} +4.00000i q^{66} +1.17157 q^{67} +(3.00000 + 2.82843i) q^{68} -3.17157 q^{69} -2.82843i q^{70} +(4.58579 + 4.58579i) q^{71} -1.00000 q^{72} +(6.65685 + 6.65685i) q^{73} +(-1.58579 + 1.58579i) q^{74} +(3.29289 - 3.29289i) q^{75} -6.82843i q^{76} +19.3137i q^{77} +(-2.00000 + 2.00000i) q^{78} +(-10.2426 + 10.2426i) q^{79} +(0.414214 + 0.414214i) q^{80} -1.00000 q^{81} +(2.17157 + 2.17157i) q^{82} -4.48528i q^{83} -4.82843 q^{84} +(-0.0710678 - 2.41421i) q^{85} +1.65685 q^{86} -0.585786i q^{87} +(-2.82843 - 2.82843i) q^{88} +(0.414214 + 0.414214i) q^{90} +(-9.65685 + 9.65685i) q^{91} +(2.24264 - 2.24264i) q^{92} +0.828427i q^{93} -12.4853i q^{94} +(-2.82843 + 2.82843i) q^{95} +(0.707107 - 0.707107i) q^{96} +(-9.48528 - 9.48528i) q^{97} -16.3137 q^{98} +(-2.82843 - 2.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 4 q^{5} + 8 q^{7} - 4 q^{10} - 8 q^{14} + 4 q^{16} - 12 q^{17} + 4 q^{18} + 4 q^{20} + 8 q^{21} + 8 q^{23} - 8 q^{28} + 4 q^{29} + 8 q^{30} + 8 q^{31} - 16 q^{33} - 12 q^{37} + 16 q^{38}+ \cdots - 20 q^{98}+O(q^{100}) \) 4 * q - 4 * q^4 - 4 * q^5 + 8 * q^7 - 4 * q^10 - 8 * q^14 + 4 * q^16 - 12 * q^17 + 4 * q^18 + 4 * q^20 + 8 * q^21 + 8 * q^23 - 8 * q^28 + 4 * q^29 + 8 * q^30 + 8 * q^31 - 16 * q^33 - 12 * q^37 + 16 * q^38 - 8 * q^39 + 4 * q^40 - 20 * q^41 + 4 * q^45 - 8 * q^46 + 16 * q^47 + 4 * q^50 + 8 * q^51 - 32 * q^55 + 8 * q^56 - 8 * q^57 + 4 * q^58 + 20 * q^61 + 8 * q^62 + 8 * q^63 - 4 * q^64 - 16 * q^65 + 16 * q^67 + 12 * q^68 - 24 * q^69 + 24 * q^71 - 4 * q^72 + 4 * q^73 - 12 * q^74 + 16 * q^75 - 8 * q^78 - 24 * q^79 - 4 * q^80 - 4 * q^81 + 20 * q^82 - 8 * q^84 + 28 * q^85 - 16 * q^86 - 4 * q^90 - 16 * q^91 - 8 * q^92 - 4 * q^97 - 20 * q^98

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