LMFDB - Embedded newform 637.2.h.k.165.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(165,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 4]))

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

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

chi := DirichletCharacter("637.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.h (of order $3$, degree $2$, not 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1485512441856.7
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 24x^{6} + 455x^{4} + 2904x^{2} + 14641 $ x^8 + 24x^6 + 455x^4 + 2904*x^2 + 14641
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.4
Root			$2.04914 + 3.54921i$ of defining polynomial
Character	$\chi$	$=$	637.165
Dual form			637.2.h.k.471.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +(0.707107 + 1.22474i) q^{3} -1.00000 q^{4} +(2.04914 + 3.54921i) q^{5} +(0.707107 + 1.22474i) q^{6} -3.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(2.04914 + 3.54921i) q^{10} +(1.89792 + 3.28729i) q^{11} +(-0.707107 - 1.22474i) q^{12} +(0.634922 - 3.54921i) q^{13} +(-2.89792 + 5.01934i) q^{15} -1.00000 q^{16} +1.26984 q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.41421 + 2.44949i) q^{19} +(-2.04914 - 3.54921i) q^{20} +(1.89792 + 3.28729i) q^{22} -7.79583 q^{23} +(-2.12132 - 3.67423i) q^{24} +(-5.89792 + 10.2155i) q^{25} +(0.634922 - 3.54921i) q^{26} +5.65685 q^{27} +(-0.397916 + 0.689210i) q^{29} +(-2.89792 + 5.01934i) q^{30} +(-0.707107 + 1.22474i) q^{31} +5.00000 q^{32} +(-2.68406 + 4.64893i) q^{33} +1.26984 q^{34} +(-0.500000 + 0.866025i) q^{36} +2.79583 q^{37} +(-1.41421 + 2.44949i) q^{38} +(4.79583 - 1.73205i) q^{39} +(-6.14741 - 10.6476i) q^{40} +(1.48640 - 2.57452i) q^{41} +(-3.89792 - 6.75139i) q^{43} +(-1.89792 - 3.28729i) q^{44} +4.09827 q^{45} -7.79583 q^{46} +(1.41421 + 2.44949i) q^{47} +(-0.707107 - 1.22474i) q^{48} +(-5.89792 + 10.2155i) q^{50} +(0.897916 + 1.55524i) q^{51} +(-0.634922 + 3.54921i) q^{52} +(6.29583 - 10.9047i) q^{53} +5.65685 q^{54} +(-7.77817 + 13.4722i) q^{55} -4.00000 q^{57} +(-0.397916 + 0.689210i) q^{58} +12.4392 q^{59} +(2.89792 - 5.01934i) q^{60} +(4.17046 - 7.22344i) q^{61} +(-0.707107 + 1.22474i) q^{62} +7.00000 q^{64} +(13.8979 - 5.01934i) q^{65} +(-2.68406 + 4.64893i) q^{66} +(1.89792 + 3.28729i) q^{67} -1.26984 q^{68} +(-5.51249 - 9.54790i) q^{69} +(-3.00000 - 5.19615i) q^{71} +(-1.50000 + 2.59808i) q^{72} +(-6.29178 + 10.8977i) q^{73} +2.79583 q^{74} -16.6818 q^{75} +(1.41421 - 2.44949i) q^{76} +(4.79583 - 1.73205i) q^{78} +(1.10208 + 1.90887i) q^{79} +(-2.04914 - 3.54921i) q^{80} +(2.50000 + 4.33013i) q^{81} +(1.48640 - 2.57452i) q^{82} +9.89949 q^{83} +(2.60208 + 4.50694i) q^{85} +(-3.89792 - 6.75139i) q^{86} -1.12548 q^{87} +(-5.69375 - 9.86186i) q^{88} +14.9789 q^{89} +4.09827 q^{90} +7.79583 q^{92} -2.00000 q^{93} +(1.41421 + 2.44949i) q^{94} -11.5917 q^{95} +(3.53553 + 6.12372i) q^{96} +(-2.12132 - 3.67423i) q^{97} +3.79583 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 8 q^{4} - 24 q^{8} + 4 q^{9} - 4 q^{11} - 4 q^{15} - 8 q^{16} + 4 q^{18} - 4 q^{22} - 24 q^{23} - 28 q^{25} + 16 q^{29} - 4 q^{30} + 40 q^{32} - 4 q^{36} - 16 q^{37} - 12 q^{43} + 4 q^{44}+ \cdots - 8 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 - 8 * q^4 - 24 * q^8 + 4 * q^9 - 4 * q^11 - 4 * q^15 - 8 * q^16 + 4 * q^18 - 4 * q^22 - 24 * q^23 - 28 * q^25 + 16 * q^29 - 4 * q^30 + 40 * q^32 - 4 * q^36 - 16 * q^37 - 12 * q^43 + 4 * q^44 - 24 * q^46 - 28 * q^50 - 12 * q^51 + 12 * q^53 - 32 * q^57 + 16 * q^58 + 4 * q^60 + 56 * q^64 + 92 * q^65 - 4 * q^67 - 24 * q^71 - 12 * q^72 - 16 * q^74 + 28 * q^79 + 20 * q^81 + 40 * q^85 - 12 * q^86 + 12 * q^88 + 24 * q^92 - 16 * q^93 - 16 * q^95 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00000			0.707107			0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000			0.707107			0.353553	+	0.935414i	$0.384973\pi$
$3$	0.707107	+	1.22474i	0.408248	+	0.707107i	0.994694	−	0.102882i	$-0.0328064\pi$
$3$	0.707107	+	1.22474i	0.408248	+	0.707107i	−0.586445	+	0.809989i	$0.699473\pi$
$4$	−1.00000			−0.500000
$5$	2.04914	+	3.54921i	0.916401	+	1.58725i	0.804836	+	0.593497i	$0.202253\pi$
$5$	2.04914	+	3.54921i	0.916401	+	1.58725i	0.111565	+	0.993757i	$0.464414\pi$
$6$	0.707107	+	1.22474i	0.288675	+	0.500000i
$7$		0			0
$7$		0			0
$8$	−3.00000			−1.06066
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	2.04914	+	3.54921i	0.647994	+	1.12236i
$11$	1.89792	+	3.28729i	0.572243	+	0.991154i	0.996335	+	0.0855351i	$0.0272600\pi$
$11$	1.89792	+	3.28729i	0.572243	+	0.991154i	−0.424092	+	0.905619i	$0.639407\pi$
$12$	−0.707107	−	1.22474i	−0.204124	−	0.353553i
$13$	0.634922	−	3.54921i	0.176096	−	0.984373i
$13$	0.634922	−	3.54921i	0.176096	−	0.984373i
$14$		0			0
$15$	−2.89792	+	5.01934i	−0.748239	+	1.29599i
$16$	−1.00000			−0.250000
$17$	1.26984			0.307983			0.153991	−	0.988072i	$-0.450787\pi$
$17$	1.26984			0.307983			0.153991	+	0.988072i	$0.450787\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−1.41421	+	2.44949i	−0.324443	+	0.561951i	−0.981399	−	0.191977i	$-0.938510\pi$
$19$	−1.41421	+	2.44949i	−0.324443	+	0.561951i	0.656957	+	0.753928i	$0.271843\pi$
$20$	−2.04914	−	3.54921i	−0.458201	−	0.793627i
$21$		0			0
$22$	1.89792	+	3.28729i	0.404637	+	0.700852i
$23$	−7.79583			−1.62554			−0.812772	−	0.582582i	$-0.802042\pi$
$23$	−7.79583			−1.62554			−0.812772	+	0.582582i	$0.802042\pi$
$24$	−2.12132	−	3.67423i	−0.433013	−	0.750000i
$25$	−5.89792	+	10.2155i	−1.17958	+	2.04310i
$26$	0.634922	−	3.54921i	0.124519	−	0.696057i
$27$	5.65685			1.08866
$28$		0			0
$29$	−0.397916	+	0.689210i	−0.0738911	+	0.127983i	−0.900604	−	0.434642i	$-0.856875\pi$
$29$	−0.397916	+	0.689210i	−0.0738911	+	0.127983i	0.826712	+	0.562625i	$0.190208\pi$
$30$	−2.89792	+	5.01934i	−0.529085	+	0.916401i
$31$	−0.707107	+	1.22474i	−0.127000	+	0.219971i	−0.922513	−	0.385966i	$-0.873868\pi$
$31$	−0.707107	+	1.22474i	−0.127000	+	0.219971i	0.795513	+	0.605937i	$0.207202\pi$
$32$	5.00000			0.883883
$33$	−2.68406	+	4.64893i	−0.467235	+	0.809274i
$34$	1.26984			0.217777
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	2.79583			0.459632			0.229816	−	0.973234i	$-0.426188\pi$
$37$	2.79583			0.459632			0.229816	+	0.973234i	$0.426188\pi$
$38$	−1.41421	+	2.44949i	−0.229416	+	0.397360i
$39$	4.79583	−	1.73205i	0.767948	−	0.277350i
$40$	−6.14741	−	10.6476i	−0.971990	−	1.68354i
$41$	1.48640	−	2.57452i	0.232136	−	0.402072i	−0.726300	−	0.687378i	$-0.758762\pi$
$41$	1.48640	−	2.57452i	0.232136	−	0.402072i	0.958437	+	0.285306i	$0.0920951\pi$
$42$		0			0
$43$	−3.89792	−	6.75139i	−0.594427	−	1.02958i	−0.993628	−	0.112714i	$-0.964046\pi$
$43$	−3.89792	−	6.75139i	−0.594427	−	1.02958i	0.399201	−	0.916863i	$-0.369288\pi$
$44$	−1.89792	−	3.28729i	−0.286122	−	0.495577i
$45$	4.09827			0.610934
$46$	−7.79583			−1.14943
$47$	1.41421	+	2.44949i	0.206284	+	0.357295i	0.950541	−	0.310599i	$-0.100530\pi$
$47$	1.41421	+	2.44949i	0.206284	+	0.357295i	−0.744257	+	0.667893i	$0.767196\pi$
$48$	−0.707107	−	1.22474i	−0.102062	−	0.176777i
$49$		0			0
$50$	−5.89792	+	10.2155i	−0.834091	+	1.44469i
$51$	0.897916	+	1.55524i	0.125733	+	0.217777i
$52$	−0.634922	+	3.54921i	−0.0880479	+	0.492187i
$53$	6.29583	−	10.9047i	0.864799	−	1.49788i	−0.00244768	−	0.999997i	$-0.500779\pi$
$53$	6.29583	−	10.9047i	0.864799	−	1.49788i	0.867247	−	0.497879i	$-0.165888\pi$
$54$	5.65685			0.769800
$55$	−7.77817	+	13.4722i	−1.04881	+	1.81659i
$56$		0			0
$57$	−4.00000			−0.529813
$58$	−0.397916	+	0.689210i	−0.0522489	+	0.0904977i
$59$	12.4392			1.61944			0.809722	−	0.586814i	$-0.199618\pi$
$59$	12.4392			1.61944			0.809722	+	0.586814i	$0.199618\pi$
$60$	2.89792	−	5.01934i	0.374119	−	0.647994i
$61$	4.17046	−	7.22344i	0.533972	−	0.924867i	−0.465240	−	0.885185i	$-0.654032\pi$
$61$	4.17046	−	7.22344i	0.533972	−	0.924867i	0.999212	−	0.0396825i	$-0.0126346\pi$
$62$	−0.707107	+	1.22474i	−0.0898027	+	0.155543i
$63$		0			0
$64$	7.00000			0.875000
$65$	13.8979	−	5.01934i	1.72382	−	0.622572i
$66$	−2.68406	+	4.64893i	−0.330385	+	0.572243i
$67$	1.89792	+	3.28729i	0.231867	+	0.401606i	0.958358	−	0.285571i	$-0.0921831\pi$
$67$	1.89792	+	3.28729i	0.231867	+	0.401606i	−0.726490	+	0.687177i	$0.758850\pi$
$68$	−1.26984			−0.153991
$69$	−5.51249	−	9.54790i	−0.663625	−	1.14943i
$70$		0			0
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	0.631260	−	0.775571i	$-0.282538\pi$
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	−0.987294	+	0.158901i	$0.949205\pi$
$72$	−1.50000	+	2.59808i	−0.176777	+	0.306186i
$73$	−6.29178	+	10.8977i	−0.736397	+	1.27548i	0.217711	+	0.976013i	$0.430141\pi$
$73$	−6.29178	+	10.8977i	−0.736397	+	1.27548i	−0.954108	+	0.299463i	$0.903192\pi$
$74$	2.79583			0.325009
$75$	−16.6818			−1.92625
$76$	1.41421	−	2.44949i	0.162221	−	0.280976i
$77$		0			0
$78$	4.79583	−	1.73205i	0.543021	−	0.196116i
$79$	1.10208	+	1.90887i	0.123994	+	0.214764i	0.921339	−	0.388759i	$-0.127096\pi$
$79$	1.10208	+	1.90887i	0.123994	+	0.214764i	−0.797345	+	0.603524i	$0.793763\pi$
$80$	−2.04914	−	3.54921i	−0.229100	−	0.396813i
$81$	2.50000	+	4.33013i	0.277778	+	0.481125i
$82$	1.48640	−	2.57452i	0.164145	−	0.284308i
$83$	9.89949			1.08661			0.543305	−	0.839535i	$-0.317173\pi$
$83$	9.89949			1.08661			0.543305	+	0.839535i	$0.317173\pi$
$84$		0			0
$85$	2.60208	+	4.50694i	0.282236	+	0.488847i
$86$	−3.89792	−	6.75139i	−0.420323	−	0.728021i
$87$	−1.12548			−0.120664
$88$	−5.69375	−	9.86186i	−0.606955	−	1.05128i
$89$	14.9789			1.58776			0.793879	−	0.608076i	$-0.208058\pi$
$89$	14.9789			1.58776			0.793879	+	0.608076i	$0.208058\pi$
$90$	4.09827			0.431996
$91$		0			0
$92$	7.79583			0.812772
$93$	−2.00000			−0.207390
$94$	1.41421	+	2.44949i	0.145865	+	0.252646i
$95$	−11.5917			−1.18928
$96$	3.53553	+	6.12372i	0.360844	+	0.625000i
$97$	−2.12132	−	3.67423i	−0.215387	−	0.373062i	0.738005	−	0.674795i	$-0.235768\pi$
$97$	−2.12132	−	3.67423i	−0.215387	−	0.373062i	−0.953392	+	0.301733i	$0.902435\pi$
$98$		0			0
$99$	3.79583			0.381495
$100$	5.89792	−	10.2155i	0.589792	−	1.02155i
$101$	−4.87756	−	8.44819i	−0.485336	−	0.840626i	0.514522	−	0.857477i	$-0.327969\pi$
$101$	−4.87756	−	8.44819i	−0.485336	−	0.840626i	−0.999858	+	0.0168509i	$0.994636\pi$
$102$	0.897916	+	1.55524i	0.0889069	+	0.153991i
$103$	2.68406	+	4.64893i	0.264468	+	0.458072i	0.967424	−	0.253161i	$-0.0814703\pi$
$103$	2.68406	+	4.64893i	0.264468	+	0.458072i	−0.702956	+	0.711233i	$0.748137\pi$
$104$	−1.90477	+	10.6476i	−0.186778	+	1.04409i
$105$		0			0
$106$	6.29583	−	10.9047i	0.611505	−	1.05916i
$107$	−6.00000			−0.580042			−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000			−0.580042			−0.290021	+	0.957020i	$0.593662\pi$
$108$	−5.65685			−0.544331
$109$	−0.795832	+	1.37842i	−0.0762268	+	0.132029i	−0.901619	−	0.432531i	$-0.857621\pi$
$109$	−0.795832	+	1.37842i	−0.0762268	+	0.132029i	0.825392	+	0.564560i	$0.190954\pi$
$110$	−7.77817	+	13.4722i	−0.741620	+	1.28452i
$111$	1.97695	+	3.42418i	0.187644	+	0.325009i
$112$		0			0
$113$	−1.29583	−	2.24445i	−0.121902	−	0.211140i	0.798616	−	0.601841i	$-0.205566\pi$
$113$	−1.29583	−	2.24445i	−0.121902	−	0.211140i	−0.920518	+	0.390701i	$0.872233\pi$
$114$	−4.00000			−0.374634
$115$	−15.9747	−	27.6690i	−1.48965	−	2.58015i
$116$	0.397916	−	0.689210i	0.0369456	−	0.0639916i
$117$	−2.75624	−	2.32446i	−0.254815	−	0.214897i
$118$	12.4392			1.14512
$119$		0			0
$120$	8.69375	−	15.0580i	0.793627	−	1.37460i
$121$	−1.70417	+	2.95171i	−0.154924	+	0.268337i
$122$	4.17046	−	7.22344i	0.377575	−	0.653980i
$123$	4.20417			0.379077
$124$	0.707107	−	1.22474i	0.0635001	−	0.109985i
$125$	−27.8512			−2.49108
$126$		0			0
$127$	5.79583	−	10.0387i	0.514297	−	0.890788i	−0.485566	−	0.874200i	$-0.661386\pi$
$127$	5.79583	−	10.0387i	0.514297	−	0.890788i	0.999862	−	0.0165881i	$-0.00528038\pi$
$128$	−3.00000			−0.265165
$129$	5.51249	−	9.54790i	0.485347	−	0.840646i
$130$	13.8979	−	5.01934i	1.21893	−	0.440225i
$131$	2.68406	+	4.64893i	0.234507	+	0.406178i	0.959129	−	0.282968i	$-0.0913190\pi$
$131$	2.68406	+	4.64893i	0.234507	+	0.406178i	−0.724622	+	0.689146i	$0.757986\pi$
$132$	2.68406	−	4.64893i	0.233617	−	0.404637i
$133$		0			0
$134$	1.89792	+	3.28729i	0.163955	+	0.283978i
$135$	11.5917	+	20.0773i	0.997652	+	1.72798i
$136$	−3.80953			−0.326665
$137$	−18.7958			−1.60584			−0.802918	−	0.596089i	$-0.796720\pi$
$137$	−18.7958			−1.60584			−0.802918	+	0.596089i	$0.796720\pi$
$138$	−5.51249	−	9.54790i	−0.469254	−	0.812772i
$139$	−0.851476	−	1.47480i	−0.0722212	−	0.125091i	0.827653	−	0.561240i	$-0.189675\pi$
$139$	−0.851476	−	1.47480i	−0.0722212	−	0.125091i	−0.899875	+	0.436149i	$0.856342\pi$
$140$		0			0
$141$	−2.00000	+	3.46410i	−0.168430	+	0.291730i
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$	12.8723	−	4.64893i	1.07644	−	0.388763i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−3.26153			−0.270856
$146$	−6.29178	+	10.8977i	−0.520711	+	0.901898i
$147$		0			0
$148$	−2.79583			−0.229816
$149$	7.29583	−	12.6368i	0.597698	−	1.03524i	−0.395462	−	0.918482i	$-0.629416\pi$
$149$	7.29583	−	12.6368i	0.597698	−	1.03524i	0.993160	−	0.116761i	$-0.0372511\pi$
$150$	−16.6818			−1.36207
$151$	−0.795832	+	1.37842i	−0.0647639	+	0.112174i	−0.896589	−	0.442863i	$-0.853963\pi$
$151$	−0.795832	+	1.37842i	−0.0647639	+	0.112174i	0.831825	+	0.555037i	$0.187296\pi$
$152$	4.24264	−	7.34847i	0.344124	−	0.596040i
$153$	0.634922	−	1.09972i	0.0513304	−	0.0889069i
$154$		0			0
$155$	−5.79583			−0.465532
$156$	−4.79583	+	1.73205i	−0.383974	+	0.138675i
$157$	−0.0721845	+	0.125027i	−0.00576095	+	0.00997825i	−0.868892	−	0.495003i	$-0.835167\pi$
$157$	−0.0721845	+	0.125027i	−0.00576095	+	0.00997825i	0.863131	+	0.504981i	$0.168500\pi$
$158$	1.10208	+	1.90887i	0.0876771	+	0.151861i
$159$	17.8073			1.41221
$160$	10.2457	+	17.7460i	0.809992	+	1.40295i
$161$		0			0
$162$	2.50000	+	4.33013i	0.196419	+	0.340207i
$163$	−7.69375	+	13.3260i	−0.602621	+	1.04377i	0.389802	+	0.920899i	$0.372543\pi$
$163$	−7.69375	+	13.3260i	−0.602621	+	1.04377i	−0.992423	+	0.122871i	$0.960790\pi$
$164$	−1.48640	+	2.57452i	−0.116068	+	0.201036i
$165$	−22.0000			−1.71270
$166$	9.89949			0.768350
$167$	0.851476	−	1.47480i	0.0658892	−	0.114123i	−0.831199	−	0.555975i	$-0.812345\pi$
$167$	0.851476	−	1.47480i	0.0658892	−	0.114123i	0.897088	+	0.441852i	$0.145678\pi$
$168$		0			0
$169$	−12.1937	−	4.50694i	−0.937981	−	0.346688i
$170$	2.60208	+	4.50694i	0.199571	+	0.345667i
$171$	1.41421	+	2.44949i	0.108148	+	0.187317i
$172$	3.89792	+	6.75139i	0.297213	+	0.514789i
$173$	−8.90365	+	15.4216i	−0.676932	+	1.17248i	0.298968	+	0.954263i	$0.403358\pi$
$173$	−8.90365	+	15.4216i	−0.676932	+	1.17248i	−0.975900	+	0.218218i	$0.929976\pi$
$174$	−1.12548			−0.0853221
$175$		0			0
$176$	−1.89792	−	3.28729i	−0.143061	−	0.247789i
$177$	8.79583	+	15.2348i	0.661135	+	1.14512i
$178$	14.9789			1.12271
$179$	9.79583	+	16.9669i	0.732175	+	1.26816i	0.955952	+	0.293524i	$0.0948279\pi$
$179$	9.79583	+	16.9669i	0.732175	+	1.26816i	−0.223777	+	0.974640i	$0.571839\pi$
$180$	−4.09827			−0.305467
$181$	−3.80953			−0.283160			−0.141580	−	0.989927i	$-0.545218\pi$
$181$	−3.80953			−0.283160			−0.141580	+	0.989927i	$0.545218\pi$
$182$		0			0
$183$	11.7958			0.871973
$184$	23.3875			1.72415
$185$	5.72904	+	9.92299i	0.421207	+	0.729552i
$186$	−2.00000			−0.146647
$187$	2.41006	+	4.17434i	0.176241	+	0.305258i
$188$	−1.41421	−	2.44949i	−0.103142	−	0.178647i
$189$		0			0
$190$	−11.5917			−0.840948
$191$	8.10208	−	14.0332i	0.586246	−	1.01541i	−0.408473	−	0.912771i	$-0.633938\pi$
$191$	8.10208	−	14.0332i	0.586246	−	1.01541i	0.994719	−	0.102638i	$-0.0327282\pi$
$192$	4.94975	+	8.57321i	0.357217	+	0.618718i
$193$	−11.2958	−	19.5650i	−0.813092	−	1.40832i	−0.910690	−	0.413090i	$-0.864449\pi$
$193$	−11.2958	−	19.5650i	−0.813092	−	1.40832i	0.0975983	−	0.995226i	$-0.468884\pi$
$194$	−2.12132	−	3.67423i	−0.152302	−	0.263795i
$195$	15.9747	+	13.4722i	1.14397	+	0.964764i
$196$		0			0
$197$	4.00000	−	6.92820i	0.284988	−	0.493614i	−0.687618	−	0.726073i	$-0.741344\pi$
$197$	4.00000	−	6.92820i	0.284988	−	0.493614i	0.972606	+	0.232458i	$0.0746770\pi$
$198$	3.79583			0.269758
$199$	−5.07938			−0.360068			−0.180034	−	0.983660i	$-0.557621\pi$
$199$	−5.07938			−0.360068			−0.180034	+	0.983660i	$0.557621\pi$
$200$	17.6937	−	30.6465i	1.25114	−	2.16703i
$201$	−2.68406	+	4.64893i	−0.189319	+	0.327910i
$202$	−4.87756	−	8.44819i	−0.343184	−	0.594412i
$203$		0			0
$204$	−0.897916	−	1.55524i	−0.0628667	−	0.108888i
$205$	12.1833			0.850920
$206$	2.68406	+	4.64893i	0.187007	+	0.323906i
$207$	−3.89792	+	6.75139i	−0.270924	+	0.469254i
$208$	−0.634922	+	3.54921i	−0.0440239	+	0.246093i
$209$	−10.7362			−0.742641
$210$		0			0
$211$	−3.89792	+	6.75139i	−0.268344	+	0.464785i	−0.968434	−	0.249269i	$-0.919810\pi$
$211$	−3.89792	+	6.75139i	−0.268344	+	0.464785i	0.700091	+	0.714054i	$0.253143\pi$
$212$	−6.29583	+	10.9047i	−0.432399	+	0.748938i
$213$	4.24264	−	7.34847i	0.290701	−	0.503509i
$214$	−6.00000			−0.410152
$215$	15.9747	−	27.6690i	1.08947	−	1.88701i
$216$	−16.9706			−1.15470
$217$		0			0
$218$	−0.795832	+	1.37842i	−0.0539005	+	0.0933584i
$219$	−17.7958			−1.20253
$220$	7.77817	−	13.4722i	0.524404	−	0.908295i
$221$	0.806253	−	4.50694i	0.0542344	−	0.303170i
$222$	1.97695	+	3.42418i	0.132684	+	0.229816i
$223$	−2.82843	+	4.89898i	−0.189405	+	0.328060i	−0.945052	−	0.326920i	$-0.893989\pi$
$223$	−2.82843	+	4.89898i	−0.189405	+	0.328060i	0.755647	+	0.654979i	$0.227323\pi$
$224$		0			0
$225$	5.89792	+	10.2155i	0.393194	+	0.681033i
$226$	−1.29583	−	2.24445i	−0.0861974	−	0.149298i
$227$	−7.35981			−0.488487			−0.244244	−	0.969714i	$-0.578540\pi$
$227$	−7.35981			−0.488487			−0.244244	+	0.969714i	$0.578540\pi$
$228$	4.00000			0.264906
$229$	6.36396	+	11.0227i	0.420542	+	0.728401i	0.995993	−	0.0894361i	$-0.0285065\pi$
$229$	6.36396	+	11.0227i	0.420542	+	0.728401i	−0.575450	+	0.817837i	$0.695173\pi$
$230$	−15.9747	−	27.6690i	−1.05334	−	1.82444i
$231$		0			0
$232$	1.19375	−	2.06763i	0.0783733	−	0.135747i
$233$	−8.59166	−	14.8812i	−0.562859	−	0.974900i	−0.997245	−	0.0741732i	$-0.976368\pi$
$233$	−8.59166	−	14.8812i	−0.562859	−	0.974900i	0.434387	−	0.900726i	$-0.356965\pi$
$234$	−2.75624	−	2.32446i	−0.180181	−	0.151955i
$235$	−5.79583	+	10.0387i	−0.378078	+	0.654851i
$236$	−12.4392			−0.809722
$237$	−1.55858	+	2.69954i	−0.101241	+	0.175354i
$238$		0			0
$239$	−10.2042			−0.660053			−0.330026	−	0.943972i	$-0.607058\pi$
$239$	−10.2042			−0.660053			−0.330026	+	0.943972i	$0.607058\pi$
$240$	2.89792	−	5.01934i	0.187060	−	0.323997i
$241$	−11.1693			−0.719480			−0.359740	−	0.933053i	$-0.617135\pi$
$241$	−11.1693			−0.719480			−0.359740	+	0.933053i	$0.617135\pi$
$242$	−1.70417	+	2.95171i	−0.109548	+	0.189743i
$243$	4.94975	−	8.57321i	0.317526	−	0.549972i
$244$	−4.17046	+	7.22344i	−0.266986	+	0.462433i
$245$		0			0
$246$	4.20417			0.268048
$247$	7.79583	+	6.57457i	0.496037	+	0.418330i
$248$	2.12132	−	3.67423i	0.134704	−	0.233314i
$249$	7.00000	+	12.1244i	0.443607	+	0.768350i
$250$	−27.8512			−1.76146
$251$	−8.34091	−	14.4469i	−0.526474	−	0.911879i	−0.999524	−	0.0308439i	$-0.990181\pi$
$251$	−8.34091	−	14.4469i	−0.526474	−	0.911879i	0.473050	−	0.881035i	$-0.343153\pi$
$252$		0			0
$253$	−14.7958	−	25.6271i	−0.930206	−	1.61116i
$254$	5.79583	−	10.0387i	0.363663	−	0.629882i
$255$	−3.67990	+	6.37378i	−0.230444	+	0.399142i
$256$	−17.0000			−1.06250
$257$	−8.62965			−0.538303			−0.269151	−	0.963098i	$-0.586743\pi$
$257$	−8.62965			−0.538303			−0.269151	+	0.963098i	$0.586743\pi$
$258$	5.51249	−	9.54790i	0.343192	−	0.594427i
$259$		0			0
$260$	−13.8979	+	5.01934i	−0.861912	+	0.311286i
$261$	0.397916	+	0.689210i	0.0246304	+	0.0426610i
$262$	2.68406	+	4.64893i	0.165822	+	0.287212i
$263$	−1.69375	−	2.93366i	−0.104441	−	0.180897i	0.809069	−	0.587714i	$-0.199972\pi$
$263$	−1.69375	−	2.93366i	−0.104441	−	0.180897i	−0.913510	+	0.406817i	$0.866639\pi$
$264$	8.05217	−	13.9468i	0.495577	−	0.858365i
$265$	51.6041			3.17001
$266$		0			0
$267$	10.5917	+	18.3453i	0.648199	+	1.12271i
$268$	−1.89792	−	3.28729i	−0.115934	−	0.200803i
$269$	−12.4392			−0.758430			−0.379215	−	0.925308i	$-0.623806\pi$
$269$	−12.4392			−0.758430			−0.379215	+	0.925308i	$0.623806\pi$
$270$	11.5917	+	20.0773i	0.705446	+	1.22187i
$271$	−17.5186			−1.06418			−0.532088	−	0.846689i	$-0.678593\pi$
$271$	−17.5186			−1.06418			−0.532088	+	0.846689i	$0.678593\pi$
$272$	−1.26984			−0.0769956
$273$		0			0
$274$	−18.7958			−1.13550
$275$	−44.7750			−2.70003
$276$	5.51249	+	9.54790i	0.331813	+	0.574716i
$277$	32.1833			1.93371			0.966854	−	0.255329i	$-0.0821837\pi$
$277$	32.1833			1.93371			0.966854	+	0.255329i	$0.0821837\pi$
$278$	−0.851476	−	1.47480i	−0.0510681	−	0.0884526i
$279$	0.707107	+	1.22474i	0.0423334	+	0.0733236i
$280$		0			0
$281$	24.7958			1.47920			0.739598	−	0.673049i	$-0.235016\pi$
$281$	24.7958			1.47920			0.739598	+	0.673049i	$0.235016\pi$
$282$	−2.00000	+	3.46410i	−0.119098	+	0.206284i
$283$	−7.92254	−	13.7222i	−0.470946	−	0.815703i	0.528501	−	0.848932i	$-0.322754\pi$
$283$	−7.92254	−	13.7222i	−0.470946	−	0.815703i	−0.999448	+	0.0332294i	$0.989421\pi$
$284$	3.00000	+	5.19615i	0.178017	+	0.308335i
$285$	−8.19654	−	14.1968i	−0.485521	−	0.840948i
$286$	12.8723	−	4.64893i	0.761155	−	0.274897i
$287$		0			0
$288$	2.50000	−	4.33013i	0.147314	−	0.255155i
$289$	−15.3875			−0.905147
$290$	−3.26153			−0.191524
$291$	3.00000	−	5.19615i	0.175863	−	0.304604i
$292$	6.29178	−	10.8977i	0.368198	−	0.637738i
$293$	−1.48640	−	2.57452i	−0.0868363	−	0.150405i	0.819336	−	0.573314i	$-0.194342\pi$
$293$	−1.48640	−	2.57452i	−0.0868363	−	0.150405i	−0.906172	+	0.422909i	$0.861009\pi$
$294$		0			0
$295$	25.4896	+	44.1492i	1.48406	+	2.57047i
$296$	−8.38749			−0.487513
$297$	10.7362	+	18.5957i	0.622979	+	1.07903i
$298$	7.29583	−	12.6368i	0.422636	−	0.732027i
$299$	−4.94975	+	27.6690i	−0.286251	+	1.60014i
$300$	16.6818			0.963126
$301$		0			0
$302$	−0.795832	+	1.37842i	−0.0457950	+	0.0793192i
$303$	6.89792	−	11.9475i	0.396275	−	0.686368i
$304$	1.41421	−	2.44949i	0.0811107	−	0.140488i
$305$	34.1833			1.95733
$306$	0.634922	−	1.09972i	0.0362961	−	0.0628667i
$307$	20.0583			1.14478			0.572392	−	0.819980i	$-0.306015\pi$
$307$	20.0583			1.14478			0.572392	+	0.819980i	$0.306015\pi$
$308$		0			0
$309$	−3.79583	+	6.57457i	−0.215937	+	0.374014i
$310$	−5.79583			−0.329181
$311$	−14.4161	+	24.9695i	−0.817464	+	1.41589i	0.0900809	+	0.995934i	$0.471287\pi$
$311$	−14.4161	+	24.9695i	−0.817464	+	1.41589i	−0.907545	+	0.419955i	$0.862046\pi$
$312$	−14.3875	+	5.19615i	−0.814531	+	0.294174i
$313$	7.63381	+	13.2221i	0.431488	+	0.747359i	0.997002	−	0.0773795i	$-0.0246553\pi$
$313$	7.63381	+	13.2221i	0.431488	+	0.747359i	−0.565514	+	0.824739i	$0.691322\pi$
$314$	−0.0721845	+	0.125027i	−0.00407360	+	0.00705569i
$315$		0			0
$316$	−1.10208	−	1.90887i	−0.0619971	−	0.107382i
$317$	−3.29583	−	5.70855i	−0.185112	−	0.320624i	0.758502	−	0.651671i	$-0.225932\pi$
$317$	−3.29583	−	5.70855i	−0.185112	−	0.320624i	−0.943614	+	0.331047i	$0.892598\pi$
$318$	17.8073			0.998584
$319$	−3.02084			−0.169135
$320$	14.3440	+	24.8445i	0.801851	+	1.38885i
$321$	−4.24264	−	7.34847i	−0.236801	−	0.410152i
$322$		0			0
$323$	−1.79583	+	3.11047i	−0.0999227	+	0.173071i
$324$	−2.50000	−	4.33013i	−0.138889	−	0.240563i
$325$	32.5122	+	27.4190i	1.80345	+	1.52093i
$326$	−7.69375	+	13.3260i	−0.426117	+	0.738057i
$327$	−2.25095			−0.124478
$328$	−4.45919	+	7.72355i	−0.246218	+	0.426462i
$329$		0			0
$330$	−22.0000			−1.21106
$331$	−14.6937	+	25.4503i	−0.807641	+	1.39888i	0.106852	+	0.994275i	$0.465923\pi$
$331$	−14.6937	+	25.4503i	−0.807641	+	1.39888i	−0.914493	+	0.404601i	$0.867410\pi$
$332$	−9.89949			−0.543305
$333$	1.39792	−	2.42126i	0.0766053	−	0.132684i
$334$	0.851476	−	1.47480i	0.0465907	−	0.0806974i
$335$	−7.77817	+	13.4722i	−0.424967	+	0.736065i
$336$		0			0
$337$	17.9792			0.979387			0.489694	−	0.871895i	$-0.337109\pi$
$337$	17.9792			0.979387			0.489694	+	0.871895i	$0.337109\pi$
$338$	−12.1937	−	4.50694i	−0.663252	−	0.245145i
$339$	1.83258	−	3.17413i	0.0995322	−	0.172395i
$340$	−2.60208	−	4.50694i	−0.141118	−	0.244423i
$341$	−5.36812			−0.290700
$342$	1.41421	+	2.44949i	0.0764719	+	0.132453i
$343$		0			0
$344$	11.6937	+	20.2542i	0.630485	+	1.09203i
$345$	22.5917	−	39.1299i	1.21629	−	2.10668i
$346$	−8.90365	+	15.4216i	−0.478663	+	0.829069i
$347$	−32.9792			−1.77041			−0.885207	−	0.465197i	$-0.845983\pi$
$347$	−32.9792			−1.77041			−0.885207	+	0.465197i	$0.845983\pi$
$348$	1.12548			0.0603318
$349$	13.2907	−	23.0201i	0.711433	−	1.23224i	−0.252887	−	0.967496i	$-0.581380\pi$
$349$	13.2907	−	23.0201i	0.711433	−	1.23224i	0.964319	−	0.264742i	$-0.0852867\pi$
$350$		0			0
$351$	3.59166	−	20.0773i	0.191709	−	1.07165i
$352$	9.48958	+	16.4364i	0.505796	+	0.876065i
$353$	2.61187	+	4.52390i	0.139016	+	0.240783i	0.927124	−	0.374754i	$-0.122273\pi$
$353$	2.61187	+	4.52390i	0.139016	+	0.240783i	−0.788108	+	0.615536i	$0.788939\pi$
$354$	8.79583	+	15.2348i	0.467493	+	0.809722i
$355$	12.2948	−	21.2952i	0.652541	−	1.13023i
$356$	−14.9789			−0.793879
$357$		0			0
$358$	9.79583	+	16.9669i	0.517726	+	0.896727i
$359$	2.00000	+	3.46410i	0.105556	+	0.182828i	0.913965	−	0.405793i	$-0.133004\pi$
$359$	2.00000	+	3.46410i	0.105556	+	0.182828i	−0.808409	+	0.588621i	$0.799671\pi$
$360$	−12.2948			−0.647994
$361$	5.50000	+	9.52628i	0.289474	+	0.501383i
$362$	−3.80953			−0.200225
$363$	−4.82012			−0.252990
$364$		0			0
$365$	−51.5708			−2.69934
$366$	11.7958			0.616578
$367$	10.6066	+	18.3712i	0.553660	+	0.958967i	0.998006	+	0.0631123i	$0.0201026\pi$
$367$	10.6066	+	18.3712i	0.553660	+	0.958967i	−0.444346	+	0.895855i	$0.646564\pi$
$368$	7.79583			0.406386
$369$	−1.48640	−	2.57452i	−0.0773788	−	0.134024i
$370$	5.72904	+	9.92299i	0.297839	+	0.515871i
$371$		0			0
$372$	2.00000			0.103695
$373$	−3.29583	+	5.70855i	−0.170652	+	0.295577i	−0.938648	−	0.344877i	$-0.887921\pi$
$373$	−3.29583	+	5.70855i	−0.170652	+	0.295577i	0.767996	+	0.640454i	$0.221254\pi$
$374$	2.41006	+	4.17434i	0.124621	+	0.215850i
$375$	−19.6937	−	34.1106i	−1.01698	−	1.76146i
$376$	−4.24264	−	7.34847i	−0.218797	−	0.378968i
$377$	2.19350	+	1.84988i	0.112971	+	0.0952737i
$378$		0			0
$379$	−12.6937	+	21.9862i	−0.652034	+	1.12936i	0.330595	+	0.943773i	$0.392751\pi$
$379$	−12.6937	+	21.9862i	−0.652034	+	1.12936i	−0.982629	+	0.185583i	$0.940583\pi$
$380$	11.5917			0.594640
$381$	16.3931			0.839843
$382$	8.10208	−	14.0332i	0.414539	−	0.718002i
$383$	6.07522	−	10.5226i	0.310429	−	0.537680i	−0.668026	−	0.744138i	$-0.732860\pi$
$383$	6.07522	−	10.5226i	0.310429	−	0.537680i	0.978455	+	0.206458i	$0.0661938\pi$
$384$	−2.12132	−	3.67423i	−0.108253	−	0.187500i
$385$		0			0
$386$	−11.2958	−	19.5650i	−0.574943	−	0.995830i
$387$	−7.79583			−0.396284
$388$	2.12132	+	3.67423i	0.107694	+	0.186531i
$389$	0.193747	−	0.335580i	0.00982338	−	0.0170146i	−0.861072	−	0.508483i	$-0.830206\pi$
$389$	0.193747	−	0.335580i	0.00982338	−	0.0170146i	0.870895	+	0.491469i	$0.163540\pi$
$390$	15.9747	+	13.4722i	0.808911	+	0.682191i
$391$	−9.89949			−0.500639
$392$		0			0
$393$	−3.79583	+	6.57457i	−0.191474	+	0.331643i
$394$	4.00000	−	6.92820i	0.201517	−	0.349038i
$395$	−4.51664	+	7.82305i	−0.227257	+	0.393620i
$396$	−3.79583			−0.190748
$397$	3.53553	−	6.12372i	0.177443	−	0.307341i	−0.763561	−	0.645736i	$-0.776551\pi$
$397$	3.53553	−	6.12372i	0.177443	−	0.307341i	0.941004	+	0.338395i	$0.109884\pi$
$398$	−5.07938			−0.254606
$399$		0			0
$400$	5.89792	−	10.2155i	0.294896	−	0.510774i
$401$	−4.38749			−0.219101			−0.109551	−	0.993981i	$-0.534941\pi$
$401$	−4.38749			−0.219101			−0.109551	+	0.993981i	$0.534941\pi$
$402$	−2.68406	+	4.64893i	−0.133869	+	0.231867i
$403$	3.89792	+	3.28729i	0.194169	+	0.163751i
$404$	4.87756	+	8.44819i	0.242668	+	0.420313i
$405$	−10.2457	+	17.7460i	−0.509112	+	0.881808i
$406$		0			0
$407$	5.30625	+	9.19070i	0.263021	+	0.455566i
$408$	−2.69375	−	4.66571i	−0.133360	−	0.230987i
$409$	−18.7884			−0.929027			−0.464513	−	0.885566i	$-0.653771\pi$
$409$	−18.7884			−0.929027			−0.464513	+	0.885566i	$0.653771\pi$
$410$	12.1833			0.601692
$411$	−13.2907	−	23.0201i	−0.655580	−	1.13550i
$412$	−2.68406	−	4.64893i	−0.132234	−	0.229036i
$413$		0			0
$414$	−3.89792	+	6.75139i	−0.191572	+	0.331813i
$415$	20.2854	+	35.1354i	0.995772	+	1.72473i
$416$	3.17461	−	17.7460i	0.155648	−	0.870071i
$417$	1.20417	−	2.08568i	0.0589684	−	0.102136i
$418$	−10.7362			−0.525126
$419$	−12.8576	+	22.2699i	−0.628133	+	1.08796i	0.359794	+	0.933032i	$0.382847\pi$
$419$	−12.8576	+	22.2699i	−0.628133	+	1.08796i	−0.987926	+	0.154926i	$0.950486\pi$
$420$		0			0
$421$	12.5917			0.613680			0.306840	−	0.951761i	$-0.400728\pi$
$421$	12.5917			0.613680			0.306840	+	0.951761i	$0.400728\pi$
$422$	−3.89792	+	6.75139i	−0.189748	+	0.328652i
$423$	2.82843			0.137523
$424$	−18.8875	+	32.7141i	−0.917258	+	1.58874i
$425$	−7.48944	+	12.9721i	−0.363291	+	0.629239i
$426$	4.24264	−	7.34847i	0.205557	−	0.356034i
$427$		0			0
$428$	6.00000			0.290021
$429$	14.7958	+	12.4780i	0.714349	+	0.602443i
$430$	15.9747	−	27.6690i	0.770369	−	1.33432i
$431$	−16.5917	−	28.7376i	−0.799192	−	1.38424i	−0.920143	−	0.391583i	$-0.871928\pi$
$431$	−16.5917	−	28.7376i	−0.799192	−	1.38424i	0.120950	−	0.992659i	$-0.461406\pi$
$432$	−5.65685			−0.272166
$433$	−10.2457	−	17.7460i	−0.492376	−	0.852820i	0.507586	−	0.861601i	$-0.330538\pi$
$433$	−10.2457	−	17.7460i	−0.492376	−	0.852820i	−0.999961	+	0.00878126i	$0.997205\pi$
$434$		0			0
$435$	−2.30625	−	3.99455i	−0.110576	−	0.191524i
$436$	0.795832	−	1.37842i	0.0381134	−	0.0660144i
$437$	11.0250	−	19.0958i	0.527396	−	0.913476i
$438$	−17.7958			−0.850318
$439$	20.0583			0.957328			0.478664	−	0.877998i	$-0.341121\pi$
$439$	20.0583			0.957328			0.478664	+	0.877998i	$0.341121\pi$
$440$	23.3345	−	40.4166i	1.11243	−	1.92678i
$441$		0			0
$442$	0.806253	−	4.50694i	0.0383495	−	0.214373i
$443$	−5.00000	−	8.66025i	−0.237557	−	0.411461i	0.722456	−	0.691417i	$-0.243013\pi$
$443$	−5.00000	−	8.66025i	−0.237557	−	0.411461i	−0.960013	+	0.279956i	$0.909680\pi$
$444$	−1.97695	−	3.42418i	−0.0938220	−	0.162504i
$445$	30.6937	+	53.1631i	1.45502	+	2.52017i
$446$	−2.82843	+	4.89898i	−0.133930	+	0.231973i
$447$	20.6357			0.976036
$448$		0			0
$449$	−11.7958	−	20.4310i	−0.556680	−	0.964198i	−0.997771	−	0.0667352i	$-0.978742\pi$
$449$	−11.7958	−	20.4310i	−0.556680	−	0.964198i	0.441091	−	0.897462i	$-0.354592\pi$
$450$	5.89792	+	10.2155i	0.278030	+	0.481563i
$451$	11.2842			0.531354
$452$	1.29583	+	2.24445i	0.0609508	+	0.105570i
$453$	−2.25095			−0.105759
$454$	−7.35981			−0.345413
$455$		0			0
$456$	12.0000			0.561951
$457$	4.59166			0.214789			0.107394	−	0.994216i	$-0.465749\pi$
$457$	4.59166			0.214789			0.107394	+	0.994216i	$0.465749\pi$
$458$	6.36396	+	11.0227i	0.297368	+	0.515057i
$459$	7.18333			0.335289
$460$	15.9747	+	27.6690i	0.744825	+	1.29007i
$461$	12.0930	+	20.9457i	0.563227	+	0.975538i	0.997212	+	0.0746180i	$0.0237737\pi$
$461$	12.0930	+	20.9457i	0.563227	+	0.975538i	−0.433985	+	0.900920i	$0.642893\pi$
$462$		0			0
$463$	−17.3875			−0.808065			−0.404033	−	0.914745i	$-0.632392\pi$
$463$	−17.3875			−0.808065			−0.404033	+	0.914745i	$0.632392\pi$
$464$	0.397916	−	0.689210i	0.0184728	−	0.0319958i
$465$	−4.09827	−	7.09841i	−0.190053	−	0.329181i
$466$	−8.59166	−	14.8812i	−0.398001	−	0.689358i
$467$	−15.9747	−	27.6690i	−0.739222	−	1.28037i	−0.952846	−	0.303454i	$-0.901860\pi$
$467$	−15.9747	−	27.6690i	−0.739222	−	1.28037i	0.213624	−	0.976916i	$-0.431473\pi$
$468$	2.75624	+	2.32446i	0.127407	+	0.107448i
$469$		0			0
$470$	−5.79583	+	10.0387i	−0.267342	+	0.463050i
$471$	−0.204168			−0.00940759
$472$	−37.3176			−1.71768
$473$	14.7958	−	25.6271i	0.680313	−	1.17834i
$474$	−1.55858	+	2.69954i	−0.0715881	+	0.123994i
$475$	−16.6818	−	28.8938i	−0.765415	−	1.32574i
$476$		0			0
$477$	−6.29583	−	10.9047i	−0.288266	−	0.499292i
$478$	−10.2042			−0.466728
$479$	−10.4622	−	18.1211i	−0.478032	−	0.827975i	0.521651	−	0.853159i	$-0.325316\pi$
$479$	−10.4622	−	18.1211i	−0.478032	−	0.827975i	−0.999683	+	0.0251838i	$0.991983\pi$
$480$	−14.4896	+	25.0967i	−0.661356	+	1.14550i
$481$	1.77514	−	9.92299i	0.0809392	−	0.452449i
$482$	−11.1693			−0.508749
$483$		0			0
$484$	1.70417	−	2.95171i	0.0774622	−	0.134168i
$485$	8.69375	−	15.0580i	0.394763	−	0.683749i
$486$	4.94975	−	8.57321i	0.224525	−	0.388889i
$487$	0.408337			0.0185035			0.00925176	−	0.999957i	$-0.497055\pi$
$487$	0.408337			0.0185035			0.00925176	+	0.999957i	$0.497055\pi$
$488$	−12.5114	+	21.6703i	−0.566363	+	0.980970i
$489$	−21.7612			−0.984076
$490$		0			0
$491$	−4.79583	+	8.30662i	−0.216433	+	0.374873i	−0.953715	−	0.300712i	$-0.902776\pi$
$491$	−4.79583	+	8.30662i	−0.216433	+	0.374873i	0.737282	+	0.675585i	$0.236109\pi$
$492$	−4.20417			−0.189539
$493$	−0.505291	+	0.875190i	−0.0227572	+	0.0394166i
$494$	7.79583	+	6.57457i	0.350751	+	0.295804i
$495$	7.77817	+	13.4722i	0.349603	+	0.605530i
$496$	0.707107	−	1.22474i	0.0317500	−	0.0549927i
$497$		0			0
$498$	7.00000	+	12.1244i	0.313678	+	0.543305i
$499$	−12.8979	−	22.3398i	−0.577390	−	1.00007i	−0.995777	−	0.0918002i	$-0.970738\pi$
$499$	−12.8979	−	22.3398i	−0.577390	−	1.00007i	0.418387	−	0.908269i	$-0.362595\pi$
$500$	27.8512			1.24554
$501$	2.40834			0.107597
$502$	−8.34091	−	14.4469i	−0.372273	−	0.644796i
$503$	12.8576	+	22.2699i	0.573290	+	0.992967i	0.996225	+	0.0868074i	$0.0276665\pi$
$503$	12.8576	+	22.2699i	0.573290	+	0.992967i	−0.422935	+	0.906160i	$0.639000\pi$
$504$		0			0
$505$	19.9896	−	34.6230i	0.889525	−	1.54070i
$506$	−14.7958	−	25.6271i	−0.657755	−	1.13926i
$507$	−3.10243	−	18.1211i	−0.137784	−	0.804787i
$508$	−5.79583	+	10.0387i	−0.257148	+	0.445394i
$509$	−6.08996			−0.269933			−0.134966	−	0.990850i	$-0.543093\pi$
$509$	−6.08996			−0.269933			−0.134966	+	0.990850i	$0.543093\pi$
$510$	−3.67990	+	6.37378i	−0.162949	+	0.282236i
$511$		0			0
$512$	−11.0000			−0.486136
$513$	−8.00000	+	13.8564i	−0.353209	+	0.611775i
$514$	−8.62965			−0.380638
$515$	−11.0000	+	19.0526i	−0.484718	+	0.839556i
$516$	−5.51249	+	9.54790i	−0.242674	+	0.420323i
$517$	−5.36812	+	9.29785i	−0.236089	+	0.408919i
$518$		0			0
$519$	−25.1833			−1.10543
$520$	−41.6937	+	15.0580i	−1.82839	+	0.660338i
$521$	2.33787	−	4.04932i	0.102424	−	0.177404i	−0.810259	−	0.586072i	$-0.800673\pi$
$521$	2.33787	−	4.04932i	0.102424	−	0.177404i	0.912683	+	0.408669i	$0.134007\pi$
$522$	0.397916	+	0.689210i	0.0174163	+	0.0301659i
$523$	−42.1377			−1.84255			−0.921276	−	0.388910i	$-0.872852\pi$
$523$	−42.1377			−1.84255			−0.921276	+	0.388910i	$0.872852\pi$
$524$	−2.68406	−	4.64893i	−0.117254	−	0.203089i
$525$		0			0
$526$	−1.69375	−	2.93366i	−0.0738509	−	0.127913i
$527$	−0.897916	+	1.55524i	−0.0391138	+	0.0677471i
$528$	2.68406	−	4.64893i	0.116809	−	0.202318i
$529$	37.7750			1.64239
$530$	51.6041			2.24154
$531$	6.21959	−	10.7726i	0.269907	−	0.467493i
$532$		0			0
$533$	−8.19375	−	6.91015i	−0.354911	−	0.299312i
$534$	10.5917	+	18.3453i	0.458346	+	0.793879i
$535$	−12.2948	−	21.2952i	−0.531551	−	0.920674i
$536$	−5.69375	−	9.86186i	−0.245932	−	0.425967i
$537$	−13.8534	+	23.9948i	−0.597818	+	1.03545i
$538$	−12.4392			−0.536291
$539$		0			0
$540$	−11.5917	−	20.0773i	−0.498826	−	0.863992i
$541$	−3.29583	−	5.70855i	−0.141699	−	0.245430i	0.786438	−	0.617670i	$-0.211923\pi$
$541$	−3.29583	−	5.70855i	−0.141699	−	0.245430i	−0.928136	+	0.372240i	$0.878590\pi$
$542$	−17.5186			−0.752487
$543$	−2.69375	−	4.66571i	−0.115600	−	0.200225i
$544$	6.34922			0.272221
$545$	−6.52307			−0.279418
$546$		0			0
$547$	10.9792			0.469435			0.234717	−	0.972064i	$-0.424584\pi$
$547$	10.9792			0.469435			0.234717	+	0.972064i	$0.424584\pi$
$548$	18.7958			0.802918
$549$	−4.17046	−	7.22344i	−0.177991	−	0.308289i
$550$	−44.7750			−1.90921
$551$	−1.12548	−	1.94938i	−0.0479469	−	0.0830464i
$552$	16.5375	+	28.6437i	0.703881	+	1.21916i
$553$		0			0
$554$	32.1833			1.36734
$555$	−8.10208	+	14.0332i	−0.343914	+	0.595677i
$556$	0.851476	+	1.47480i	0.0361106	+	0.0625454i
$557$	−0.704168	−	1.21966i	−0.0298366	−	0.0516785i	0.850722	−	0.525617i	$-0.176165\pi$
$557$	−0.704168	−	1.21966i	−0.0298366	−	0.0516785i	−0.880558	+	0.473938i	$0.842832\pi$
$558$	0.707107	+	1.22474i	0.0299342	+	0.0518476i
$559$	−26.4370	+	9.54790i	−1.11816	+	0.403833i
$560$		0			0
$561$	−3.40834	+	5.90341i	−0.143900	+	0.249242i
$562$	24.7958			1.04595
$563$	−12.4392			−0.524249			−0.262125	−	0.965034i	$-0.584423\pi$
$563$	−12.4392			−0.524249			−0.262125	+	0.965034i	$0.584423\pi$
$564$	2.00000	−	3.46410i	0.0842152	−	0.145865i
$565$	5.31067	−	9.19835i	0.223422	−	0.386977i
$566$	−7.92254	−	13.7222i	−0.333009	−	0.576789i
$567$		0			0
$568$	9.00000	+	15.5885i	0.377632	+	0.654077i
$569$	25.5917			1.07286			0.536429	−	0.843945i	$-0.319773\pi$
$569$	25.5917			1.07286			0.536429	+	0.843945i	$0.319773\pi$
$570$	−8.19654	−	14.1968i	−0.343315	−	0.594640i
$571$	11.5917	−	20.0773i	0.485096	−	0.840211i	−0.514757	−	0.857336i	$-0.672118\pi$
$571$	11.5917	−	20.0773i	0.485096	−	0.840211i	0.999853	+	0.0171250i	$0.00545132\pi$
$572$	−12.8723	+	4.64893i	−0.538218	+	0.194381i
$573$	22.9162			0.957336
$574$		0			0
$575$	45.9792	−	79.6382i	1.91746	−	3.32114i
$576$	3.50000	−	6.06218i	0.145833	−	0.252591i
$577$	12.3670	−	21.4203i	0.514845	−	0.891738i	−0.485007	−	0.874510i	$-0.661183\pi$
$577$	12.3670	−	21.4203i	0.514845	−	0.891738i	0.999852	−	0.0172271i	$-0.00548384\pi$
$578$	−15.3875			−0.640035
$579$	15.9747	−	27.6690i	0.663887	−	1.14989i
$580$	3.26153			0.135428
$581$		0			0
$582$	3.00000	−	5.19615i	0.124354	−	0.215387i
$583$	47.7958			1.97950
$584$	18.8753	−	32.6930i	0.781067	−	1.35285i
$585$	2.60208	−	14.5456i	0.107583	−	0.601387i
$586$	−1.48640	−	2.57452i	−0.0614025	−	0.106352i
$587$	8.34091	−	14.4469i	0.344266	−	0.596287i	−0.640954	−	0.767579i	$-0.721461\pi$
$587$	8.34091	−	14.4469i	0.344266	−	0.596287i	0.985220	+	0.171293i	$0.0547944\pi$
$588$		0			0
$589$	−2.00000	−	3.46410i	−0.0824086	−	0.142736i
$590$	25.4896	+	44.1492i	1.04939	+	1.81760i
$591$	11.3137			0.465384
$592$	−2.79583			−0.114908
$593$	−4.17046	−	7.22344i	−0.171260	−	0.296631i	0.767601	−	0.640929i	$-0.221451\pi$
$593$	−4.17046	−	7.22344i	−0.171260	−	0.296631i	−0.938861	+	0.344297i	$0.888117\pi$
$594$	10.7362	+	18.5957i	0.440513	+	0.762991i
$595$		0			0
$596$	−7.29583	+	12.6368i	−0.298849	+	0.517621i
$597$	−3.59166	−	6.22094i	−0.146997	−	0.254606i
$598$	−4.94975	+	27.6690i	−0.202410	+	1.13147i
$599$	16.7958	−	29.0912i	0.686259	−	1.18864i	−0.286780	−	0.957996i	$-0.592585\pi$
$599$	16.7958	−	29.0912i	0.686259	−	1.18864i	0.973039	−	0.230639i	$-0.0740817\pi$
$600$	50.0455			2.04310
$601$	−12.0930	+	20.9457i	−0.493284	+	0.854393i	−0.999970	−	0.00773797i	$-0.997537\pi$
$601$	−12.0930	+	20.9457i	−0.493284	+	0.854393i	0.506686	+	0.862130i	$0.330870\pi$
$602$		0			0
$603$	3.79583			0.154578
$604$	0.795832	−	1.37842i	0.0323819	−	0.0560871i
$605$	−13.9683			−0.567892
$606$	6.89792	−	11.9475i	0.280209	−	0.485336i
$607$	2.39532	−	4.14882i	0.0972231	−	0.168395i	−0.813311	−	0.581829i	$-0.802337\pi$
$607$	2.39532	−	4.14882i	0.0972231	−	0.168395i	0.910534	+	0.413434i	$0.135671\pi$
$608$	−7.07107	+	12.2474i	−0.286770	+	0.496700i
$609$		0			0
$610$	34.1833			1.38404
$611$	9.59166	−	3.46410i	0.388037	−	0.140143i
$612$	−0.634922	+	1.09972i	−0.0256652	+	0.0444535i
$613$	−20.9896	−	36.3550i	−0.847761	−	1.46837i	−0.883202	−	0.468994i	$-0.844617\pi$
$613$	−20.9896	−	36.3550i	−0.847761	−	1.46837i	0.0354405	−	0.999372i	$-0.488717\pi$
$614$	20.0583			0.809485
$615$	8.61491	+	14.9215i	0.347387	+	0.601692i
$616$		0			0
$617$	−2.19375	−	3.79968i	−0.0883169	−	0.152969i	0.818483	−	0.574531i	$-0.194815\pi$
$617$	−2.19375	−	3.79968i	−0.0883169	−	0.152969i	−0.906800	+	0.421561i	$0.861482\pi$
$618$	−3.79583	+	6.57457i	−0.152691	+	0.264468i
$619$	−16.9558	+	29.3684i	−0.681512	+	1.18041i	0.293007	+	0.956110i	$0.405344\pi$
$619$	−16.9558	+	29.3684i	−0.681512	+	1.18041i	−0.974519	+	0.224303i	$0.927989\pi$
$620$	5.79583			0.232766
$621$	−44.0999			−1.76967
$622$	−14.4161	+	24.9695i	−0.578034	+	1.00118i
$623$		0			0
$624$	−4.79583	+	1.73205i	−0.191987	+	0.0693375i
$625$	−27.5812	−	47.7721i	−1.10325	−	1.91088i
$626$	7.63381	+	13.2221i	0.305108	+	0.528463i
$627$	−7.59166	−	13.1491i	−0.303182	−	0.525126i
$628$	0.0721845	−	0.125027i	0.00288047	−	0.00498913i
$629$	3.55027			0.141559
$630$		0			0
$631$	19.7958	+	34.2874i	0.788060	+	1.36496i	0.927154	+	0.374680i	$0.122247\pi$
$631$	19.7958	+	34.2874i	0.788060	+	1.36496i	−0.139095	+	0.990279i	$0.544419\pi$
$632$	−3.30625	−	5.72660i	−0.131516	−	0.227792i
$633$	−11.0250			−0.438203
$634$	−3.29583	−	5.70855i	−0.130894	−	0.226715i
$635$	47.5058			1.88521
$636$	−17.8073			−0.706105
$637$		0			0
$638$	−3.02084			−0.119596
$639$	−6.00000			−0.237356
$640$	−6.14741	−	10.6476i	−0.242998	−	0.420884i
$641$	−4.79583			−0.189424			−0.0947120	−	0.995505i	$-0.530193\pi$
$641$	−4.79583			−0.189424			−0.0947120	+	0.995505i	$0.530193\pi$
$642$	−4.24264	−	7.34847i	−0.167444	−	0.290021i
$643$	2.82843	+	4.89898i	0.111542	+	0.193197i	0.916392	−	0.400281i	$-0.131088\pi$
$643$	2.82843	+	4.89898i	0.111542	+	0.193197i	−0.804850	+	0.593478i	$0.797754\pi$
$644$		0			0
$645$	45.1833			1.77909
$646$	−1.79583	+	3.11047i	−0.0706560	+	0.122380i
$647$	19.3659	+	33.5427i	0.761351	+	1.31870i	0.942154	+	0.335180i	$0.108797\pi$
$647$	19.3659	+	33.5427i	0.761351	+	1.31870i	−0.180803	+	0.983519i	$0.557870\pi$
$648$	−7.50000	−	12.9904i	−0.294628	−	0.510310i
$649$	23.6085	+	40.8912i	0.926716	+	1.60512i
$650$	32.5122	+	27.4190i	1.27523	+	1.07546i
$651$		0			0
$652$	7.69375	−	13.3260i	0.301310	−	0.521885i
$653$	−13.1833			−0.515903			−0.257952	−	0.966158i	$-0.583048\pi$
$653$	−13.1833			−0.515903			−0.257952	+	0.966158i	$0.583048\pi$
$654$	−2.25095			−0.0880192
$655$	−11.0000	+	19.0526i	−0.429806	+	0.744445i
$656$	−1.48640	+	2.57452i	−0.0580341	+	0.100518i
$657$	6.29178	+	10.8977i	0.245466	+	0.425159i
$658$		0			0
$659$	9.20417	+	15.9421i	0.358543	+	0.621016i	0.987718	−	0.156249i	$-0.0499401\pi$
$659$	9.20417	+	15.9421i	0.358543	+	0.621016i	−0.629174	+	0.777264i	$0.716607\pi$
$660$	22.0000			0.856349
$661$	3.75209	+	6.49881i	0.145939	+	0.252774i	0.929723	−	0.368260i	$-0.120046\pi$
$661$	3.75209	+	6.49881i	0.145939	+	0.252774i	−0.783784	+	0.621034i	$0.786713\pi$
$662$	−14.6937	+	25.4503i	−0.571089	+	0.989155i
$663$	6.08996	−	2.19944i	0.236514	−	0.0854190i
$664$	−29.6985			−1.15252
$665$		0			0
$666$	1.39792	−	2.42126i	0.0541681	−	0.0938220i
$667$	3.10208	−	5.37297i	0.120113	−	0.208042i
$668$	−0.851476	+	1.47480i	−0.0329446	+	0.0570617i
$669$	−8.00000			−0.309298
$670$	−7.77817	+	13.4722i	−0.300497	+	0.520476i
$671$	31.6607			1.22225
$672$		0			0
$673$	11.9896	−	20.7666i	0.462164	−	0.800492i	−0.536904	−	0.843643i	$-0.680406\pi$
$673$	11.9896	−	20.7666i	0.462164	−	0.800492i	0.999069	+	0.0431511i	$0.0137397\pi$
$674$	17.9792			0.692531
$675$	−33.3636	+	57.7875i	−1.28417	+	2.22424i
$676$	12.1937	+	4.50694i	0.468990	+	0.173344i
$677$	3.82427	+	6.62383i	0.146979	+	0.254575i	0.930109	−	0.367283i	$-0.119712\pi$
$677$	3.82427	+	6.62383i	0.146979	+	0.254575i	−0.783131	+	0.621857i	$0.786378\pi$
$678$	1.83258	−	3.17413i	0.0703799	−	0.121902i
$679$		0			0
$680$	−7.80625	−	13.5208i	−0.299356	−	0.518500i
$681$	−5.20417	−	9.01388i	−0.199424	−	0.345413i
$682$	−5.36812			−0.205556
$683$	−6.77499			−0.259238			−0.129619	−	0.991564i	$-0.541375\pi$
$683$	−6.77499			−0.259238			−0.129619	+	0.991564i	$0.541375\pi$
$684$	−1.41421	−	2.44949i	−0.0540738	−	0.0936586i
$685$	−38.5152	−	66.7103i	−1.47159	−	2.54887i
$686$		0			0
$687$	−9.00000	+	15.5885i	−0.343371	+	0.594737i
$688$	3.89792	+	6.75139i	0.148607	+	0.257394i
$689$	−34.7057	−	29.2688i	−1.32218	−	1.11505i
$690$	22.5917	−	39.1299i	0.860050	−	1.48965i
$691$	2.53969			0.0966143			0.0483072	−	0.998833i	$-0.484617\pi$
$691$	2.53969			0.0966143			0.0483072	+	0.998833i	$0.484617\pi$
$692$	8.90365	−	15.4216i	0.338466	−	0.586240i
$693$		0			0
$694$	−32.9792			−1.25187
$695$	3.48958	−	6.04413i	0.132367	−	0.229267i
$696$	3.37643			0.127983
$697$	1.88749	−	3.26924i	0.0714940	−	0.123831i
$698$	13.2907	−	23.0201i	0.503059	−	0.871324i
$699$	12.1504	−	21.0452i	0.459572	−	0.796002i
$700$		0			0
$701$	−29.5917			−1.11766			−0.558831	−	0.829282i	$-0.688750\pi$
$701$	−29.5917			−1.11766			−0.558831	+	0.829282i	$0.688750\pi$
$702$	3.59166	−	20.0773i	0.135559	−	0.757771i
$703$	−3.95390	+	6.84836i	−0.149124	+	0.258291i
$704$	13.2854	+	23.0110i	0.500713	+	0.867260i
$705$	−16.3931			−0.617399
$706$	2.61187	+	4.52390i	0.0982992	+	0.170259i
$707$		0			0
$708$	−8.79583	−	15.2348i	−0.330568	−	0.572560i
$709$	4.60208	−	7.97104i	0.172835	−	0.299359i	−0.766575	−	0.642155i	$-0.778041\pi$
$709$	4.60208	−	7.97104i	0.172835	−	0.299359i	0.939410	+	0.342796i	$0.111374\pi$
$710$	12.2948	−	21.2952i	0.461416	−	0.799196i
$711$	2.20417			0.0826628
$712$	−44.9366			−1.68407
$713$	5.51249	−	9.54790i	0.206444	−	0.357572i
$714$		0			0
$715$	42.8771	+	36.1602i	1.60351	+	1.35231i
$716$	−9.79583	−	16.9669i	−0.366087	−	0.634082i
$717$	−7.21544	−	12.4975i	−0.269465	−	0.466728i
$718$	2.00000	+	3.46410i	0.0746393	+	0.129279i
$719$	0.995845	−	1.72485i	0.0371387	−	0.0643262i	−0.846859	−	0.531818i	$-0.821509\pi$
$719$	0.995845	−	1.72485i	0.0371387	−	0.0643262i	0.883997	+	0.467492i	$0.154842\pi$
$720$	−4.09827			−0.152734
$721$		0			0
$722$	5.50000	+	9.52628i	0.204689	+	0.354531i
$723$	−7.89792	−	13.6796i	−0.293727	−	0.508749i
$724$	3.80953			0.141580
$725$	−4.69375	−	8.12981i	−0.174321	−	0.301934i
$726$	−4.82012			−0.178891
$727$	−32.4974			−1.20526			−0.602632	−	0.798020i	$-0.705881\pi$
$727$	−32.4974			−1.20526			−0.602632	+	0.798020i	$0.705881\pi$
$728$		0			0
$729$	29.0000			1.07407
$730$	−51.5708			−1.90872
$731$	−4.94975	−	8.57321i	−0.183073	−	0.317092i
$732$	−11.7958			−0.435986
$733$	−16.6096	−	28.7687i	−0.613491	−	1.06260i	−0.990647	−	0.136448i	$-0.956431\pi$
$733$	−16.6096	−	28.7687i	−0.613491	−	1.06260i	0.377156	−	0.926150i	$-0.376902\pi$
$734$	10.6066	+	18.3712i	0.391497	+	0.678092i
$735$		0			0
$736$	−38.9792			−1.43679
$737$	−7.20417	+	12.4780i	−0.265369	+	0.459633i
$738$	−1.48640	−	2.57452i	−0.0547151	−	0.0947693i
$739$	11.5917	+	20.0773i	0.426406	+	0.738557i	0.996551	−	0.0829873i	$-0.0264461\pi$
$739$	11.5917	+	20.0773i	0.426406	+	0.738557i	−0.570144	+	0.821545i	$0.693113\pi$
$740$	−5.72904	−	9.92299i	−0.210604	−	0.364776i
$741$	−2.53969	+	14.1968i	−0.0932978	+	0.521534i
$742$		0			0
$743$	14.5917	−	25.2735i	0.535316	−	0.927195i	−0.463832	−	0.885923i	$-0.653526\pi$
$743$	14.5917	−	25.2735i	0.535316	−	0.927195i	0.999148	−	0.0412716i	$-0.0131409\pi$
$744$	6.00000			0.219971
$745$	59.8006			2.19092
$746$	−3.29583	+	5.70855i	−0.120669	+	0.209005i
$747$	4.94975	−	8.57321i	0.181102	−	0.313678i
$748$	−2.41006	−	4.17434i	−0.0881205	−	0.152629i
$749$		0			0
$750$	−19.6937	−	34.1106i	−0.719114	−	1.24554i
$751$	−7.79583			−0.284474			−0.142237	−	0.989833i	$-0.545430\pi$
$751$	−7.79583			−0.284474			−0.142237	+	0.989833i	$0.545430\pi$
$752$	−1.41421	−	2.44949i	−0.0515711	−	0.0893237i
$753$	11.7958	−	20.4310i	0.429864	−	0.744546i
$754$	2.19350	+	1.84988i	0.0798827	+	0.0673687i
$755$	−6.52307			−0.237399
$756$		0			0
$757$	−6.59166	+	11.4171i	−0.239578	+	0.414961i	−0.960593	−	0.277958i	$-0.910342\pi$
$757$	−6.59166	+	11.4171i	−0.239578	+	0.414961i	0.721015	+	0.692919i	$0.243676\pi$
$758$	−12.6937	+	21.9862i	−0.461058	+	0.798575i
$759$	20.9245	−	36.2422i	0.759510	−	1.31551i
$760$	34.7750			1.26142
$761$	−8.90365	+	15.4216i	−0.322757	+	0.559032i	−0.981056	−	0.193725i	$-0.937943\pi$
$761$	−8.90365	+	15.4216i	−0.322757	+	0.559032i	0.658299	+	0.752757i	$0.271276\pi$
$762$	16.3931			0.593859
$763$		0			0
$764$	−8.10208	+	14.0332i	−0.293123	+	0.507704i
$765$	5.20417			0.188157
$766$	6.07522	−	10.5226i	0.219507	−	0.380197i
$767$	7.89792	−	44.1492i	0.285177	−	1.59414i
$768$	−12.0208	−	20.8207i	−0.433764	−	0.751301i
$769$	2.12132	−	3.67423i	0.0764968	−	0.132496i	−0.825239	−	0.564783i	$-0.808960\pi$
$769$	2.12132	−	3.67423i	0.0764968	−	0.132496i	0.901736	+	0.432287i	$0.142293\pi$
$770$		0			0
$771$	−6.10208	−	10.5691i	−0.219761	−	0.380638i
$772$	11.2958	+	19.5650i	0.406546	+	0.704158i
$773$	−34.7779			−1.25087			−0.625436	−	0.780275i	$-0.715079\pi$
$773$	−34.7779			−1.25087			−0.625436	+	0.780275i	$0.715079\pi$
$774$	−7.79583			−0.280215
$775$	−8.34091	−	14.4469i	−0.299614	−	0.518947i
$776$	6.36396	+	11.0227i	0.228453	+	0.395692i
$777$		0			0
$778$	0.193747	−	0.335580i	0.00694618	−	0.0120311i
$779$	4.20417	+	7.28183i	0.150630	+	0.260899i
$780$	−15.9747	−	13.4722i	−0.571987	−	0.482382i
$781$	11.3875	−	19.7237i	0.407477	−	0.705770i
$782$	−9.89949			−0.354005
$783$	−2.25095	+	3.89876i	−0.0804424	+	0.139330i
$784$		0			0
$785$	−0.591663			−0.0211174
$786$	−3.79583	+	6.57457i	−0.135393	+	0.234507i
$787$	42.3969			1.51129			0.755644	−	0.654983i	$-0.227324\pi$
$787$	42.3969			1.51129			0.755644	+	0.654983i	$0.227324\pi$
$788$	−4.00000	+	6.92820i	−0.142494	+	0.246807i
$789$	2.39532	−	4.14882i	0.0852757	−	0.147702i
$790$	−4.51664	+	7.82305i	−0.160695	+	0.278332i
$791$		0			0
$792$	−11.3875			−0.404637
$793$	−22.9896	−	19.3881i	−0.816384	−	0.688493i
$794$	3.53553	−	6.12372i	0.125471	−	0.217323i
$795$	36.4896	+	63.2018i	1.29415	+	2.24154i
$796$	5.07938			0.180034
$797$	0.418369	+	0.724636i	0.0148194	+	0.0256679i	0.873340	−	0.487111i	$-0.161949\pi$
$797$	0.418369	+	0.724636i	0.0148194	+	0.0256679i	−0.858521	+	0.512779i	$0.828616\pi$
$798$		0			0
$799$	1.79583	+	3.11047i	0.0635320	+	0.110041i
$800$	−29.4896	+	51.0774i	−1.04261	+	1.80586i
$801$	7.48944	−	12.9721i	0.264626	−	0.458346i
$802$	−4.38749			−0.154928
$803$	−47.7650			−1.68559
$804$	2.68406	−	4.64893i	0.0946594	−	0.163955i
$805$		0			0
$806$	3.89792	+	3.28729i	0.137298	+	0.115790i
$807$	−8.79583	−	15.2348i	−0.309628	−	0.536291i
$808$	14.6327	+	25.3446i	0.514776	+	0.891619i
$809$	18.6833	+	32.3605i	0.656871	+	1.13773i	0.981421	+	0.191865i	$0.0614536\pi$
$809$	18.6833	+	32.3605i	0.656871	+	1.13773i	−0.324551	+	0.945868i	$0.605213\pi$
$810$	−10.2457	+	17.7460i	−0.359996	+	0.623532i
$811$	52.0372			1.82727			0.913636	−	0.406533i	$-0.133262\pi$
$811$	52.0372			1.82727			0.913636	+	0.406533i	$0.133262\pi$
$812$		0			0
$813$	−12.3875	−	21.4558i	−0.434448	−	0.752487i
$814$	5.30625	+	9.19070i	0.185984	+	0.322134i
$815$	−63.0621			−2.20897
$816$	−0.897916	−	1.55524i	−0.0314333	−	0.0544441i
$817$	22.0499			0.771430
$818$	−18.7884			−0.656921
$819$		0			0
$820$	−12.1833			−0.425460
$821$	36.3667			1.26920			0.634602	−	0.772839i	$-0.281164\pi$
$821$	36.3667			1.26920			0.634602	+	0.772839i	$0.281164\pi$
$822$	−13.2907	−	23.0201i	−0.463565	−	0.802918i
$823$	−20.7750			−0.724171			−0.362085	−	0.932145i	$-0.617935\pi$
$823$	−20.7750			−0.724171			−0.362085	+	0.932145i	$0.617935\pi$
$824$	−8.05217	−	13.9468i	−0.280511	−	0.485859i
$825$	−31.6607	−	54.8379i	−1.10228	−	1.90921i
$826$		0			0
$827$	−20.9792			−0.729517			−0.364758	−	0.931102i	$-0.618848\pi$
$827$	−20.9792			−0.729517			−0.364758	+	0.931102i	$0.618848\pi$
$828$	3.89792	−	6.75139i	0.135462	−	0.234627i
$829$	−13.6368	−	23.6197i	−0.473627	−	0.820346i	0.525917	−	0.850536i	$-0.323722\pi$
$829$	−13.6368	−	23.6197i	−0.473627	−	0.820346i	−0.999544	+	0.0301895i	$0.990389\pi$
$830$	20.2854	+	35.1354i	0.704117	+	1.21957i
$831$	22.7570	+	39.4164i	0.789433	+	1.36734i
$832$	4.44446	−	24.8445i	0.154084	−	0.861326i
$833$		0			0
$834$	1.20417	−	2.08568i	0.0416969	−	0.0722212i
$835$	6.97916			0.241524
$836$	10.7362			0.371320
$837$	−4.00000	+	6.92820i	−0.138260	+	0.239474i
$838$	−12.8576	+	22.2699i	−0.444157	+	0.769302i
$839$	2.82843	+	4.89898i	0.0976481	+	0.169132i	0.910711	−	0.413045i	$-0.135535\pi$
$839$	2.82843	+	4.89898i	0.0976481	+	0.169132i	−0.813063	+	0.582176i	$0.802201\pi$
$840$		0			0
$841$	14.1833	+	24.5662i	0.489080	+	0.847112i
$842$	12.5917			0.433937
$843$	17.5333	+	30.3686i	0.603879	+	1.04595i
$844$	3.89792	−	6.75139i	0.134172	−	0.232392i
$845$	−8.99057	−	52.5135i	−0.309285	−	1.80652i
$846$	2.82843			0.0972433
$847$		0			0
$848$	−6.29583	+	10.9047i	−0.216200	+	0.374469i
$849$	11.2042	−	19.4062i	0.384526	−	0.666019i
$850$	−7.48944	+	12.9721i	−0.256886	+	0.444939i
$851$	−21.7958			−0.747151
$852$	−4.24264	+	7.34847i	−0.145350	+	0.251754i
$853$	33.5080			1.14729			0.573646	−	0.819103i	$-0.305528\pi$
$853$	33.5080			1.14729			0.573646	+	0.819103i	$0.305528\pi$
$854$		0			0
$855$	−5.79583	+	10.0387i	−0.198213	+	0.343315i
$856$	18.0000			0.615227
$857$	−8.70183	+	15.0720i	−0.297249	+	0.514850i	−0.975506	−	0.219975i	$-0.929402\pi$
$857$	−8.70183	+	15.0720i	−0.297249	+	0.514850i	0.678257	+	0.734825i	$0.262736\pi$
$858$	14.7958	+	12.4780i	0.505121	+	0.425991i
$859$	5.09412	+	8.82327i	0.173809	+	0.301046i	0.939748	−	0.341867i	$-0.111059\pi$
$859$	5.09412	+	8.82327i	0.173809	+	0.301046i	−0.765939	+	0.642913i	$0.777726\pi$
$860$	−15.9747	+	27.6690i	−0.544733	+	0.943506i
$861$		0			0
$862$	−16.5917	−	28.7376i	−0.565114	−	0.978807i
$863$	−4.10208	−	7.10502i	−0.139637	−	0.241858i	0.787723	−	0.616030i	$-0.211260\pi$
$863$	−4.10208	−	7.10502i	−0.139637	−	0.241858i	−0.927359	+	0.374173i	$0.877927\pi$
$864$	28.2843			0.962250
$865$	−72.9792			−2.48137
$866$	−10.2457	−	17.7460i	−0.348162	−	0.603035i
$867$	−10.8806	−	18.8458i	−0.369525	−	0.640035i
$868$		0			0
$869$	−4.18333	+	7.24573i	−0.141910	+	0.245795i
$870$	−2.30625	−	3.99455i	−0.0781893	−	0.135428i
$871$	12.8723	−	4.64893i	0.436161	−	0.157523i
$872$	2.38749	−	4.13526i	0.0808508	−	0.140038i
$873$	−4.24264			−0.143592
$874$	11.0250	−	19.0958i	0.372925	−	0.645925i
$875$		0			0
$876$	17.7958			0.601265
$877$	−2.39792	+	4.15331i	−0.0809719	+	0.140247i	−0.903668	−	0.428235i	$-0.859136\pi$
$877$	−2.39792	+	4.15331i	−0.0809719	+	0.140247i	0.822696	+	0.568482i	$0.192469\pi$
$878$	20.0583			0.676933
$879$	2.10208	−	3.64092i	0.0709015	−	0.122805i
$880$	7.77817	−	13.4722i	0.262202	−	0.454148i
$881$	5.29593	−	9.17282i	0.178424	−	0.309040i	−0.762917	−	0.646497i	$-0.776233\pi$
$881$	5.29593	−	9.17282i	0.178424	−	0.309040i	0.941341	+	0.337457i	$0.109567\pi$
$882$		0			0
$883$	−45.3875			−1.52741			−0.763705	−	0.645565i	$-0.776622\pi$
$883$	−45.3875			−1.52741			−0.763705	+	0.645565i	$0.776622\pi$
$884$	−0.806253	+	4.50694i	−0.0271172	+	0.151585i
$885$	−36.0477	+	62.4365i	−1.21173	+	2.09878i
$886$	−5.00000	−	8.66025i	−0.167978	−	0.290947i
$887$	42.1377			1.41484			0.707422	−	0.706791i	$-0.249858\pi$
$887$	42.1377			1.41484			0.707422	+	0.706791i	$0.249858\pi$
$888$	−5.93085	−	10.2725i	−0.199026	−	0.344724i
$889$		0			0
$890$	30.6937	+	53.1631i	1.02886	+	1.78203i
$891$	−9.48958	+	16.4364i	−0.317913	+	0.550641i
$892$	2.82843	−	4.89898i	0.0947027	−	0.164030i
$893$	−8.00000			−0.267710
$894$	20.6357			0.690162
$895$	−40.1460	+	69.5349i	−1.34193	+	2.32429i
$896$		0			0
$897$	−37.3875	+	13.5028i	−1.24833	+	0.450845i
$898$	−11.7958	−	20.4310i	−0.393632	−	0.681791i
$899$	−0.562738	−	0.974691i	−0.0187684	−	0.0325078i
$900$	−5.89792	−	10.2155i	−0.196597	−	0.340516i
$901$	7.99473	−	13.8473i	0.266343	−	0.461320i
$902$	11.2842			0.375724
$903$		0			0
$904$	3.88749	+	6.73334i	0.129296	+	0.223947i
$905$	−7.80625	−	13.5208i	−0.259489	−	0.449447i
$906$	−2.25095			−0.0747829
$907$	−10.3063	−	17.8510i	−0.342214	−	0.592731i	0.642630	−	0.766177i	$-0.277843\pi$
$907$	−10.3063	−	17.8510i	−0.342214	−	0.592731i	−0.984843	+	0.173446i	$0.944510\pi$
$908$	7.35981			0.244244
$909$	−9.75513			−0.323557
$910$		0			0
$911$	−4.81667			−0.159584			−0.0797918	−	0.996812i	$-0.525426\pi$
$911$	−4.81667			−0.159584			−0.0797918	+	0.996812i	$0.525426\pi$
$912$	4.00000			0.132453
$913$	18.7884	+	32.5425i	0.621806	+	1.07700i
$914$	4.59166			0.151879
$915$	24.1713	+	41.8659i	0.799077	+	1.38404i
$916$	−6.36396	−	11.0227i	−0.210271	−	0.364200i
$917$		0			0
$918$	7.18333			0.237085
$919$	−5.00000	+	8.66025i	−0.164935	+	0.285675i	−0.936632	−	0.350315i	$-0.886075\pi$
$919$	−5.00000	+	8.66025i	−0.164935	+	0.285675i	0.771697	+	0.635990i	$0.219408\pi$
$920$	47.9242	+	83.0071i	1.58001	+	2.73666i
$921$	14.1833	+	24.5662i	0.467356	+	0.809485i
$922$	12.0930	+	20.9457i	0.398262	+	0.689810i
$923$	−20.3470	+	7.34847i	−0.669729	+	0.241878i
$924$		0			0
$925$	−16.4896	+	28.5608i	−0.542174	+	0.939073i
$926$	−17.3875			−0.571389
$927$	5.36812			0.176312
$928$	−1.98958	+	3.44605i	−0.0653111	+	0.113122i
$929$	−10.6788	+	18.4962i	−0.350360	+	0.606841i	−0.986312	−	0.164887i	$-0.947274\pi$
$929$	−10.6788	+	18.4962i	−0.350360	+	0.606841i	0.635953	+	0.771728i	$0.280607\pi$
$930$	−4.09827	−	7.09841i	−0.134388	−	0.232766i
$931$		0			0
$932$	8.59166	+	14.8812i	0.281429	+	0.487450i
$933$	−40.7750			−1.33491
$934$	−15.9747	−	27.6690i	−0.522709	−	0.905358i
$935$	−9.87707	+	17.1076i	−0.323015	+	0.559478i
$936$	8.26873	+	6.97339i	0.270272	+	0.227932i
$937$	13.7090			0.447854			0.223927	−	0.974606i	$-0.428112\pi$
$937$	13.7090			0.447854			0.223927	+	0.974606i	$0.428112\pi$
$938$		0			0
$939$	−10.7958	+	18.6989i	−0.352309	+	0.610216i
$940$	5.79583	−	10.0387i	0.189039	−	0.327425i
$941$	1.83258	−	3.17413i	0.0597405	−	0.103474i	−0.834608	−	0.550844i	$-0.814306\pi$
$941$	1.83258	−	3.17413i	0.0597405	−	0.103474i	0.894349	+	0.447370i	$0.147639\pi$
$942$	−0.204168			−0.00665217
$943$	−11.5877	+	20.0705i	−0.377348	+	0.653585i
$944$	−12.4392			−0.404861
$945$		0			0
$946$	14.7958	−	25.6271i	0.481054	−	0.833210i
$947$	37.7958			1.22820			0.614100	−	0.789228i	$-0.289519\pi$
$947$	37.7958			1.22820			0.614100	+	0.789228i	$0.289519\pi$
$948$	1.55858	−	2.69954i	0.0506204	−	0.0876771i
$949$	34.6833	+	29.2500i	1.12587	+	0.949495i
$950$	−16.6818	−	28.8938i	−0.541230	−	0.937438i
$951$	4.66101	−	8.07311i	0.151144	−	0.261788i
$952$		0			0
$953$	21.5917	+	37.3979i	0.699423	+	1.21144i	0.968667	+	0.248364i	$0.0798928\pi$
$953$	21.5917	+	37.3979i	0.699423	+	1.21144i	−0.269244	+	0.963072i	$0.586774\pi$
$954$	−6.29583	−	10.9047i	−0.203835	−	0.353053i
$955$	66.4091			2.14895
$956$	10.2042			0.330026
$957$	−2.13606	−	3.69976i	−0.0690490	−	0.119596i
$958$	−10.4622	−	18.1211i	−0.338019	−	0.585467i
$959$		0			0
$960$	−20.2854	+	35.1354i	−0.654709	+	1.13399i
$961$	14.5000	+	25.1147i	0.467742	+	0.810153i
$962$	1.77514	−	9.92299i	0.0572327	−	0.319930i
$963$	−3.00000	+	5.19615i	−0.0966736	+	0.167444i
$964$	11.1693			0.359740
$965$	46.2934	−	80.1825i	1.49024	−	2.58117i
$966$		0			0
$967$	−17.3875			−0.559144			−0.279572	−	0.960125i	$-0.590193\pi$
$967$	−17.3875			−0.559144			−0.279572	+	0.960125i	$0.590193\pi$
$968$	5.11251	−	8.85512i	0.164322	−	0.284614i
$969$	−5.07938			−0.163173
$970$	8.69375	−	15.0580i	0.279139	−	0.483484i
$971$	−11.3137	+	19.5959i	−0.363074	+	0.628863i	−0.988465	−	0.151449i	$-0.951606\pi$
$971$	−11.3137	+	19.5959i	−0.363074	+	0.628863i	0.625391	+	0.780312i	$0.284940\pi$
$972$	−4.94975	+	8.57321i	−0.158763	+	0.274986i
$973$		0			0
$974$	0.408337			0.0130840
$975$	−10.5917	+	59.2073i	−0.339205	+	1.89615i
$976$	−4.17046	+	7.22344i	−0.133493	+	0.231217i
$977$	14.1937	+	24.5843i	0.454098	+	0.786521i	0.998636	−	0.0522152i	$-0.0166282\pi$
$977$	14.1937	+	24.5843i	0.454098	+	0.786521i	−0.544538	+	0.838736i	$0.683295\pi$
$978$	−21.7612			−0.695847
$979$	28.4286	+	49.2398i	0.908583	+	1.57371i
$980$		0			0
$981$	0.795832	+	1.37842i	0.0254089	+	0.0440096i
$982$	−4.79583	+	8.30662i	−0.153041	+	0.265075i
$983$	0.433107	−	0.750163i	0.0138140	−	0.0239265i	−0.859036	−	0.511916i	$-0.828936\pi$
$983$	0.433107	−	0.750163i	0.0138140	−	0.0239265i	0.872850	+	0.487989i	$0.162269\pi$
$984$	−12.6125			−0.402072
$985$	32.7862			1.04465
$986$	−0.505291	+	0.875190i	−0.0160918	+	0.0278717i
$987$		0			0
$988$	−7.79583	−	6.57457i	−0.248018	−	0.209165i
$989$	30.3875	+	52.6327i	0.966266	+	1.67362i
$990$	7.77817	+	13.4722i	0.247207	+	0.428174i
$991$	−13.8979	−	24.0719i	−0.441482	−	0.764669i	0.556318	−	0.830970i	$-0.312214\pi$
$991$	−13.8979	−	24.0719i	−0.441482	−	0.764669i	−0.997800	+	0.0663006i	$0.978880\pi$
$992$	−3.53553	+	6.12372i	−0.112253	+	0.194428i
$993$	−41.5602			−1.31887
$994$		0			0
$995$	−10.4083	−	18.0278i	−0.329966	−	0.571519i
$996$	−7.00000	−	12.1244i	−0.221803	−	0.384175i
$997$	−1.26984			−0.0402164			−0.0201082	−	0.999798i	$-0.506401\pi$
$997$	−1.26984			−0.0402164			−0.0201082	+	0.999798i	$0.506401\pi$
$998$	−12.8979	−	22.3398i	−0.408276	−	0.707155i
$999$	15.8156			0.500384

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.h.k.165.4		8
7.2	even	3		637.2.g.h.373.2		8
7.3	odd	6		637.2.f.g.295.2	✓	8
7.4	even	3		637.2.f.g.295.3	yes	8
7.5	odd	6		637.2.g.h.373.3		8
7.6	odd	2	inner	637.2.h.k.165.1		8
13.3	even	3		637.2.g.h.263.2		8
91.3	odd	6		637.2.f.g.393.2	yes	8
91.4	even	6		8281.2.a.bn.1.2		4
91.16	even	3	inner	637.2.h.k.471.4		8
91.17	odd	6		8281.2.a.bn.1.3		4
91.55	odd	6		637.2.g.h.263.3		8
91.68	odd	6	inner	637.2.h.k.471.1		8
91.74	even	3		8281.2.a.bv.1.1		4
91.81	even	3		637.2.f.g.393.3	yes	8
91.87	odd	6		8281.2.a.bv.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.g.295.2	✓	8	7.3	odd	6
637.2.f.g.295.3	yes	8	7.4	even	3
637.2.f.g.393.2	yes	8	91.3	odd	6
637.2.f.g.393.3	yes	8	91.81	even	3
637.2.g.h.263.2		8	13.3	even	3
637.2.g.h.263.3		8	91.55	odd	6
637.2.g.h.373.2		8	7.2	even	3
637.2.g.h.373.3		8	7.5	odd	6
637.2.h.k.165.1		8	7.6	odd	2	inner
637.2.h.k.165.4		8	1.1	even	1	trivial
637.2.h.k.471.1		8	91.68	odd	6	inner
637.2.h.k.471.4		8	91.16	even	3	inner
8281.2.a.bn.1.2		4	91.4	even	6
8281.2.a.bn.1.3		4	91.17	odd	6
8281.2.a.bv.1.1		4	91.74	even	3
8281.2.a.bv.1.4		4	91.87	odd	6

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.707107 + 1.22474i) q^{3} -1.00000 q^{4} +(2.04914 + 3.54921i) q^{5} +(0.707107 + 1.22474i) q^{6} -3.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(2.04914 + 3.54921i) q^{10} +(1.89792 + 3.28729i) q^{11} +(-0.707107 - 1.22474i) q^{12} +(0.634922 - 3.54921i) q^{13} +(-2.89792 + 5.01934i) q^{15} -1.00000 q^{16} +1.26984 q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.41421 + 2.44949i) q^{19} +(-2.04914 - 3.54921i) q^{20} +(1.89792 + 3.28729i) q^{22} -7.79583 q^{23} +(-2.12132 - 3.67423i) q^{24} +(-5.89792 + 10.2155i) q^{25} +(0.634922 - 3.54921i) q^{26} +5.65685 q^{27} +(-0.397916 + 0.689210i) q^{29} +(-2.89792 + 5.01934i) q^{30} +(-0.707107 + 1.22474i) q^{31} +5.00000 q^{32} +(-2.68406 + 4.64893i) q^{33} +1.26984 q^{34} +(-0.500000 + 0.866025i) q^{36} +2.79583 q^{37} +(-1.41421 + 2.44949i) q^{38} +(4.79583 - 1.73205i) q^{39} +(-6.14741 - 10.6476i) q^{40} +(1.48640 - 2.57452i) q^{41} +(-3.89792 - 6.75139i) q^{43} +(-1.89792 - 3.28729i) q^{44} +4.09827 q^{45} -7.79583 q^{46} +(1.41421 + 2.44949i) q^{47} +(-0.707107 - 1.22474i) q^{48} +(-5.89792 + 10.2155i) q^{50} +(0.897916 + 1.55524i) q^{51} +(-0.634922 + 3.54921i) q^{52} +(6.29583 - 10.9047i) q^{53} +5.65685 q^{54} +(-7.77817 + 13.4722i) q^{55} -4.00000 q^{57} +(-0.397916 + 0.689210i) q^{58} +12.4392 q^{59} +(2.89792 - 5.01934i) q^{60} +(4.17046 - 7.22344i) q^{61} +(-0.707107 + 1.22474i) q^{62} +7.00000 q^{64} +(13.8979 - 5.01934i) q^{65} +(-2.68406 + 4.64893i) q^{66} +(1.89792 + 3.28729i) q^{67} -1.26984 q^{68} +(-5.51249 - 9.54790i) q^{69} +(-3.00000 - 5.19615i) q^{71} +(-1.50000 + 2.59808i) q^{72} +(-6.29178 + 10.8977i) q^{73} +2.79583 q^{74} -16.6818 q^{75} +(1.41421 - 2.44949i) q^{76} +(4.79583 - 1.73205i) q^{78} +(1.10208 + 1.90887i) q^{79} +(-2.04914 - 3.54921i) q^{80} +(2.50000 + 4.33013i) q^{81} +(1.48640 - 2.57452i) q^{82} +9.89949 q^{83} +(2.60208 + 4.50694i) q^{85} +(-3.89792 - 6.75139i) q^{86} -1.12548 q^{87} +(-5.69375 - 9.86186i) q^{88} +14.9789 q^{89} +4.09827 q^{90} +7.79583 q^{92} -2.00000 q^{93} +(1.41421 + 2.44949i) q^{94} -11.5917 q^{95} +(3.53553 + 6.12372i) q^{96} +(-2.12132 - 3.67423i) q^{97} +3.79583 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 8 q^{4} - 24 q^{8} + 4 q^{9} - 4 q^{11} - 4 q^{15} - 8 q^{16} + 4 q^{18} - 4 q^{22} - 24 q^{23} - 28 q^{25} + 16 q^{29} - 4 q^{30} + 40 q^{32} - 4 q^{36} - 16 q^{37} - 12 q^{43} + 4 q^{44}+ \cdots - 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 8 * q^4 - 24 * q^8 + 4 * q^9 - 4 * q^11 - 4 * q^15 - 8 * q^16 + 4 * q^18 - 4 * q^22 - 24 * q^23 - 28 * q^25 + 16 * q^29 - 4 * q^30 + 40 * q^32 - 4 * q^36 - 16 * q^37 - 12 * q^43 + 4 * q^44 - 24 * q^46 - 28 * q^50 - 12 * q^51 + 12 * q^53 - 32 * q^57 + 16 * q^58 + 4 * q^60 + 56 * q^64 + 92 * q^65 - 4 * q^67 - 24 * q^71 - 12 * q^72 - 16 * q^74 + 28 * q^79 + 20 * q^81 + 40 * q^85 - 12 * q^86 + 12 * q^88 + 24 * q^92 - 16 * q^93 - 16 * q^95 - 8 * q^99

Introduction

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