LMFDB - Embedded newform 490.2.g.c.293.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(97,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("490.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.g (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:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			293.4
Root			$-0.587308 - 2.01725i$ of defining polynomial
Character	$\chi$	$=$	490.293
Dual form			490.2.g.c.97.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(2.05532 - 2.05532i) q^{3} -1.00000i q^{4} +(0.830578 + 2.07609i) q^{5} +2.90667i q^{6} +(0.707107 + 0.707107i) q^{8} -5.44871i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(2.05532 - 2.05532i) q^{3} -1.00000i q^{4} +(0.830578 + 2.07609i) q^{5} +2.90667i q^{6} +(0.707107 + 0.707107i) q^{8} -5.44871i q^{9} +(-2.05532 - 0.880708i) q^{10} +3.67114 q^{11} +(-2.05532 - 2.05532i) q^{12} +(0.830578 - 0.830578i) q^{13} +(5.97414 + 2.55992i) q^{15} -1.00000 q^{16} +(-0.557436 - 0.557436i) q^{17} +(3.85282 + 3.85282i) q^{18} -2.18923 q^{19} +(2.07609 - 0.830578i) q^{20} +(-2.59589 + 2.59589i) q^{22} +(3.32739 + 3.32739i) q^{23} +2.90667 q^{24} +(-3.62028 + 3.44871i) q^{25} +1.17462i q^{26} +(-5.03288 - 5.03288i) q^{27} -2.62236i q^{29} +(-6.03449 + 2.41421i) q^{30} +0.0415289i q^{31} +(0.707107 - 0.707107i) q^{32} +(7.54538 - 7.54538i) q^{33} +0.788333 q^{34} -5.44871 q^{36} +(0.181676 - 0.181676i) q^{37} +(1.54802 - 1.54802i) q^{38} -3.41421i q^{39} +(-0.880708 + 2.05532i) q^{40} -8.98026i q^{41} +(-0.474569 - 0.474569i) q^{43} -3.67114i q^{44} +(11.3120 - 4.52558i) q^{45} -4.70563 q^{46} +(-4.52558 - 4.52558i) q^{47} +(-2.05532 + 2.05532i) q^{48} +(0.121320 - 4.99853i) q^{50} -2.29142 q^{51} +(-0.830578 - 0.830578i) q^{52} +(5.59589 + 5.59589i) q^{53} +7.11757 q^{54} +(3.04917 + 7.62161i) q^{55} +(-4.49957 + 4.49957i) q^{57} +(1.85429 + 1.85429i) q^{58} -10.7123 q^{59} +(2.55992 - 5.97414i) q^{60} -1.99231i q^{61} +(-0.0293654 - 0.0293654i) q^{62} +1.00000i q^{64} +(2.41421 + 1.03449i) q^{65} +10.6708i q^{66} +(-4.68272 + 4.68272i) q^{67} +(-0.557436 + 0.557436i) q^{68} +13.6777 q^{69} +8.11777 q^{71} +(3.85282 - 3.85282i) q^{72} +(-6.97578 + 6.97578i) q^{73} +0.256928i q^{74} +(-0.352638 + 14.5291i) q^{75} +2.18923i q^{76} +(2.41421 + 2.41421i) q^{78} +13.4113i q^{79} +(-0.830578 - 2.07609i) q^{80} -4.34228 q^{81} +(6.35000 + 6.35000i) q^{82} +(-9.73033 + 9.73033i) q^{83} +(0.694291 - 1.62028i) q^{85} +0.671142 q^{86} +(-5.38980 - 5.38980i) q^{87} +(2.59589 + 2.59589i) q^{88} -1.43026 q^{89} +(-4.79872 + 11.1989i) q^{90} +(3.32739 - 3.32739i) q^{92} +(0.0853553 + 0.0853553i) q^{93} +6.40013 q^{94} +(-1.81832 - 4.54503i) q^{95} -2.90667i q^{96} +(-3.16693 - 3.16693i) q^{97} -20.0030i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 24 q^{11} + 16 q^{15} - 16 q^{16} + 16 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{25} - 40 q^{30} - 8 q^{36} - 8 q^{37} - 8 q^{43} + 16 q^{46} - 32 q^{50} + 32 q^{51} + 56 q^{53} + 8 q^{57} + 64 q^{58} - 16 q^{60} + 16 q^{65} - 64 q^{67} + 16 q^{71} + 16 q^{72} + 16 q^{78} + 24 q^{85} - 24 q^{86} + 8 q^{88} + 8 q^{92} - 56 q^{93} - 40 q^{95}+O(q^{100}) $ 16 * q + 24 * q^11 + 16 * q^15 - 16 * q^16 + 16 * q^18 - 8 * q^22 + 8 * q^23 - 24 * q^25 - 40 * q^30 - 8 * q^36 - 8 * q^37 - 8 * q^43 + 16 * q^46 - 32 * q^50 + 32 * q^51 + 56 * q^53 + 8 * q^57 + 64 * q^58 - 16 * q^60 + 16 * q^65 - 64 * q^67 + 16 * q^71 + 16 * q^72 + 16 * q^78 + 24 * q^85 - 24 * q^86 + 8 * q^88 + 8 * q^92 - 56 * q^93 - 40 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	2.05532	−	2.05532i	1.18664	−	1.18664i	0.208651	−	0.977990i	$-0.433093\pi$
$3$	2.05532	−	2.05532i	1.18664	−	1.18664i	0.977990	−	0.208651i	$-0.0669074\pi$
$4$		−	1.00000i		−	0.500000i
$5$	0.830578	+	2.07609i	0.371446	+	0.928455i
$5$	0.830578	+	2.07609i	0.371446	+	0.928455i
$6$			2.90667i			1.18664i
$7$		0			0
$7$		0			0
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		−	5.44871i		−	1.81624i
$10$	−2.05532	−	0.880708i	−0.649950	−	0.278504i
$11$	3.67114			1.10689			0.553445	−	0.832885i	$-0.313313\pi$
$11$	3.67114			1.10689			0.553445	+	0.832885i	$0.313313\pi$
$12$	−2.05532	−	2.05532i	−0.593321	−	0.593321i
$13$	0.830578	−	0.830578i	0.230361	−	0.230361i	−0.582482	−	0.812843i	$-0.697918\pi$
$13$	0.830578	−	0.830578i	0.230361	−	0.230361i	0.812843	+	0.582482i	$0.197918\pi$
$14$		0			0
$15$	5.97414	+	2.55992i	1.54252	+	0.660970i
$16$	−1.00000			−0.250000
$17$	−0.557436	−	0.557436i	−0.135198	−	0.135198i	0.636269	−	0.771467i	$-0.280477\pi$
$17$	−0.557436	−	0.557436i	−0.135198	−	0.135198i	−0.771467	+	0.636269i	$0.780477\pi$
$18$	3.85282	+	3.85282i	0.908118	+	0.908118i
$19$	−2.18923			−0.502243			−0.251122	−	0.967956i	$-0.580799\pi$
$19$	−2.18923			−0.502243			−0.251122	+	0.967956i	$0.580799\pi$
$20$	2.07609	−	0.830578i	0.464227	−	0.185723i
$21$		0			0
$22$	−2.59589	+	2.59589i	−0.553445	+	0.553445i
$23$	3.32739	+	3.32739i	0.693808	+	0.693808i	0.963068	−	0.269260i	$-0.0867790\pi$
$23$	3.32739	+	3.32739i	0.693808	+	0.693808i	−0.269260	+	0.963068i	$0.586779\pi$
$24$	2.90667			0.593321
$25$	−3.62028	+	3.44871i	−0.724056	+	0.689741i
$26$			1.17462i			0.230361i
$27$	−5.03288	−	5.03288i	−0.968579	−	0.968579i
$28$		0			0
$29$		−	2.62236i		−	0.486960i	−0.969906	−	0.243480i	$-0.921711\pi$
$29$		−	2.62236i		−	0.486960i	0.969906	−	0.243480i	$-0.0782891\pi$
$30$	−6.03449	+	2.41421i	−1.10174	+	0.440773i
$31$			0.0415289i			0.00745881i	0.999993	+	0.00372940i	$0.00118711\pi$
$31$			0.0415289i			0.00745881i	−0.999993	+	0.00372940i	$0.998813\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	7.54538	−	7.54538i	1.31348	−	1.31348i
$34$	0.788333			0.135198
$35$		0			0
$36$	−5.44871			−0.908118
$37$	0.181676	−	0.181676i	0.0298673	−	0.0298673i	−0.692015	−	0.721883i	$-0.743277\pi$
$37$	0.181676	−	0.181676i	0.0298673	−	0.0298673i	0.721883	+	0.692015i	$0.243277\pi$
$38$	1.54802	−	1.54802i	0.251122	−	0.251122i
$39$		−	3.41421i		−	0.546712i
$40$	−0.880708	+	2.05532i	−0.139252	+	0.324975i
$41$		−	8.98026i		−	1.40248i	−0.712925	−	0.701241i	$-0.752630\pi$
$41$		−	8.98026i		−	1.40248i	0.712925	−	0.701241i	$-0.247370\pi$
$42$		0			0
$43$	−0.474569	−	0.474569i	−0.0723711	−	0.0723711i	0.669995	−	0.742366i	$-0.266296\pi$
$43$	−0.474569	−	0.474569i	−0.0723711	−	0.0723711i	−0.742366	+	0.669995i	$0.766296\pi$
$44$		−	3.67114i		−	0.553445i
$45$	11.3120	−	4.52558i	1.68629	−	0.674633i
$46$	−4.70563			−0.693808
$47$	−4.52558	−	4.52558i	−0.660123	−	0.660123i	0.295286	−	0.955409i	$-0.404585\pi$
$47$	−4.52558	−	4.52558i	−0.660123	−	0.660123i	−0.955409	+	0.295286i	$0.904585\pi$
$48$	−2.05532	+	2.05532i	−0.296660	+	0.296660i
$49$		0			0
$50$	0.121320	−	4.99853i	0.0171573	−	0.706899i
$51$	−2.29142			−0.320863
$52$	−0.830578	−	0.830578i	−0.115180	−	0.115180i
$53$	5.59589	+	5.59589i	0.768654	+	0.768654i	0.977870	−	0.209215i	$-0.0670909\pi$
$53$	5.59589	+	5.59589i	0.768654	+	0.768654i	−0.209215	+	0.977870i	$0.567091\pi$
$54$	7.11757			0.968579
$55$	3.04917	+	7.62161i	0.411150	+	1.02770i
$56$		0			0
$57$	−4.49957	+	4.49957i	−0.595982	+	0.595982i
$58$	1.85429	+	1.85429i	0.243480	+	0.243480i
$59$	−10.7123			−1.39462			−0.697312	−	0.716768i	$-0.745621\pi$
$59$	−10.7123			−1.39462			−0.697312	+	0.716768i	$0.745621\pi$
$60$	2.55992	−	5.97414i	0.330485	−	0.771258i
$61$		−	1.99231i		−	0.255090i	−0.991833	−	0.127545i	$-0.959290\pi$
$61$		−	1.99231i		−	0.255090i	0.991833	−	0.127545i	$-0.0407097\pi$
$62$	−0.0293654	−	0.0293654i	−0.00372940	−	0.00372940i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	2.41421	+	1.03449i	0.299446	+	0.128313i
$66$			10.6708i			1.31348i
$67$	−4.68272	+	4.68272i	−0.572085	+	0.572085i	−0.932711	−	0.360626i	$-0.882563\pi$
$67$	−4.68272	+	4.68272i	−0.572085	+	0.572085i	0.360626	+	0.932711i	$0.382563\pi$
$68$	−0.557436	+	0.557436i	−0.0675990	+	0.0675990i
$69$	13.6777			1.64660
$70$		0			0
$71$	8.11777			0.963402			0.481701	−	0.876336i	$-0.340019\pi$
$71$	8.11777			0.963402			0.481701	+	0.876336i	$0.340019\pi$
$72$	3.85282	−	3.85282i	0.454059	−	0.454059i
$73$	−6.97578	+	6.97578i	−0.816454	+	0.816454i	−0.985592	−	0.169139i	$-0.945901\pi$
$73$	−6.97578	+	6.97578i	−0.816454	+	0.816454i	0.169139	+	0.985592i	$0.445901\pi$
$74$			0.256928i			0.0298673i
$75$	−0.352638	+	14.5291i	−0.0407191	+	1.67767i
$76$			2.18923i			0.251122i
$77$		0			0
$78$	2.41421	+	2.41421i	0.273356	+	0.273356i
$79$			13.4113i			1.50889i	0.656366	+	0.754443i	$0.272093\pi$
$79$			13.4113i			1.50889i	−0.656366	+	0.754443i	$0.727907\pi$
$80$	−0.830578	−	2.07609i	−0.0928615	−	0.232114i
$81$	−4.34228			−0.482476
$82$	6.35000	+	6.35000i	0.701241	+	0.701241i
$83$	−9.73033	+	9.73033i	−1.06804	+	1.06804i	−0.0705331	+	0.997509i	$0.522470\pi$
$83$	−9.73033	+	9.73033i	−1.06804	+	1.06804i	−0.997509	+	0.0705331i	$0.977530\pi$
$84$		0			0
$85$	0.694291	−	1.62028i	0.0753065	−	0.175744i
$86$	0.671142			0.0723711
$87$	−5.38980	−	5.38980i	−0.577847	−	0.577847i
$88$	2.59589	+	2.59589i	0.276723	+	0.276723i
$89$	−1.43026			−0.151607			−0.0758036	−	0.997123i	$-0.524152\pi$
$89$	−1.43026			−0.151607			−0.0758036	+	0.997123i	$0.524152\pi$
$90$	−4.79872	+	11.1989i	−0.505829	+	1.18046i
$91$		0			0
$92$	3.32739	−	3.32739i	0.346904	−	0.346904i
$93$	0.0853553	+	0.0853553i	0.00885093	+	0.00885093i
$94$	6.40013			0.660123
$95$	−1.81832	−	4.54503i	−0.186556	−	0.466310i
$96$		−	2.90667i		−	0.296660i
$97$	−3.16693	−	3.16693i	−0.321553	−	0.321553i	0.527810	−	0.849363i	$-0.323013\pi$
$97$	−3.16693	−	3.16693i	−0.321553	−	0.321553i	−0.849363	+	0.527810i	$0.823013\pi$
$98$		0			0
$99$		−	20.0030i		−	2.01037i
$100$	3.44871	+	3.62028i	0.344871	+	0.362028i
$101$		−	0.0719071i		−	0.00715503i	−0.999994	−	0.00357751i	$-0.998861\pi$
$101$		−	0.0719071i		−	0.00715503i	0.999994	−	0.00357751i	$-0.00113876\pi$
$102$	1.62028	−	1.62028i	0.160432	−	0.160432i
$103$	−11.7237	+	11.7237i	−1.15517	+	1.15517i	−0.169664	+	0.985502i	$0.554268\pi$
$103$	−11.7237	+	11.7237i	−1.15517	+	1.15517i	−0.985502	+	0.169664i	$0.945732\pi$
$104$	1.17462			0.115180
$105$		0			0
$106$	−7.91378			−0.768654
$107$	3.23107	−	3.23107i	0.312359	−	0.312359i	−0.533464	−	0.845823i	$-0.679110\pi$
$107$	3.23107	−	3.23107i	0.312359	−	0.312359i	0.845823	+	0.533464i	$0.179110\pi$
$108$	−5.03288	+	5.03288i	−0.484289	+	0.484289i
$109$		−	18.1026i		−	1.73392i	−0.498381	−	0.866958i	$-0.666072\pi$
$109$		−	18.1026i		−	1.73392i	0.498381	−	0.866958i	$-0.333928\pi$
$110$	−7.54538	−	3.23320i	−0.719424	−	0.308274i
$111$		−	0.746804i		−	0.0708835i
$112$		0			0
$113$	1.52064	+	1.52064i	0.143049	+	0.143049i	0.775005	−	0.631955i	$-0.217747\pi$
$113$	1.52064	+	1.52064i	0.143049	+	0.143049i	−0.631955	+	0.775005i	$0.717747\pi$
$114$		−	6.36335i		−	0.595982i
$115$	−4.14429	+	9.67160i	−0.386457	+	0.901881i
$116$	−2.62236			−0.243480
$117$	−4.52558	−	4.52558i	−0.418390	−	0.418390i
$118$	7.57475	−	7.57475i	0.697312	−	0.697312i
$119$		0			0
$120$	2.41421	+	6.03449i	0.220387	+	0.550871i
$121$	2.47728			0.225207
$122$	1.40878	+	1.40878i	0.127545	+	0.127545i
$123$	−18.4573	−	18.4573i	−1.66424	−	1.66424i
$124$	0.0415289			0.00372940
$125$	−10.1667	−	4.65160i	−0.909341	−	0.416051i
$126$		0			0
$127$	−13.2527	+	13.2527i	−1.17599	+	1.17599i	−0.195234	+	0.980757i	$0.562547\pi$
$127$	−13.2527	+	13.2527i	−1.17599	+	1.17599i	−0.980757	+	0.195234i	$0.937453\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−1.95078			−0.171757
$130$	−2.43860	+	0.975610i	−0.213880	+	0.0855666i
$131$		−	14.1946i		−	1.24019i	−0.784527	−	0.620095i	$-0.787094\pi$
$131$		−	14.1946i		−	1.24019i	0.784527	−	0.620095i	$-0.212906\pi$
$132$	−7.54538	−	7.54538i	−0.656741	−	0.656741i
$133$		0			0
$134$		−	6.62236i		−	0.572085i
$135$	6.26850	−	14.6289i	0.539507	−	1.25906i
$136$		−	0.788333i		−	0.0675990i
$137$	−13.4113	+	13.4113i	−1.14580	+	1.14580i	−0.158432	+	0.987370i	$0.550644\pi$
$137$	−13.4113	+	13.4113i	−1.14580	+	1.14580i	−0.987370	+	0.158432i	$0.949356\pi$
$138$	−9.67160	+	9.67160i	−0.823301	+	0.823301i
$139$	8.23706			0.698658			0.349329	−	0.937000i	$-0.386409\pi$
$139$	8.23706			0.698658			0.349329	+	0.937000i	$0.386409\pi$
$140$		0			0
$141$	−18.6030			−1.56666
$142$	−5.74013	+	5.74013i	−0.481701	+	0.481701i
$143$	3.04917	−	3.04917i	0.254984	−	0.254984i
$144$			5.44871i			0.454059i
$145$	5.44425	−	2.17808i	0.452120	−	0.180879i
$146$		−	9.86525i		−	0.816454i
$147$		0			0
$148$	−0.181676	−	0.181676i	−0.0149336	−	0.0149336i
$149$		−	4.84185i		−	0.396660i	−0.980135	−	0.198330i	$-0.936448\pi$
$149$		−	4.84185i		−	0.396660i	0.980135	−	0.198330i	$-0.0635518\pi$
$150$	−10.0242	−	10.5229i	−0.818476	−	0.859195i
$151$	10.0458			0.817519			0.408759	−	0.912642i	$-0.365962\pi$
$151$	10.0458			0.817519			0.408759	+	0.912642i	$0.365962\pi$
$152$	−1.54802	−	1.54802i	−0.125561	−	0.125561i
$153$	−3.03730	+	3.03730i	−0.245551	+	0.245551i
$154$		0			0
$155$	−0.0862176	+	0.0344930i	−0.00692516	+	0.00277054i
$156$	−3.41421			−0.273356
$157$	17.3147	+	17.3147i	1.38186	+	1.38186i	0.841310	+	0.540553i	$0.181785\pi$
$157$	17.3147	+	17.3147i	1.38186	+	1.38186i	0.540553	+	0.841310i	$0.318215\pi$
$158$	−9.48320	−	9.48320i	−0.754443	−	0.754443i
$159$	23.0027			1.82423
$160$	2.05532	+	0.880708i	0.162488	+	0.0696261i
$161$		0			0
$162$	3.07046	−	3.07046i	0.241238	−	0.241238i
$163$	−15.5320	−	15.5320i	−1.21656	−	1.21656i	−0.968829	−	0.247729i	$-0.920316\pi$
$163$	−15.5320	−	15.5320i	−1.21656	−	1.21656i	−0.247729	−	0.968829i	$-0.579684\pi$
$164$	−8.98026			−0.701241
$165$	21.9319	+	9.39784i	1.70740	+	0.731621i
$166$		−	13.7608i		−	1.06804i
$167$	−3.14616	−	3.14616i	−0.243457	−	0.243457i	0.574821	−	0.818279i	$-0.305072\pi$
$167$	−3.14616	−	3.14616i	−0.243457	−	0.243457i	−0.818279	+	0.574821i	$0.805072\pi$
$168$		0			0
$169$			11.6203i			0.893868i
$170$	0.654772	+	1.63665i	0.0502188	+	0.125525i
$171$			11.9285i			0.912192i
$172$	−0.474569	+	0.474569i	−0.0361855	+	0.0361855i
$173$	−3.69572	+	3.69572i	−0.280980	+	0.280980i	−0.833500	−	0.552520i	$-0.813666\pi$
$173$	−3.69572	+	3.69572i	−0.280980	+	0.280980i	0.552520	+	0.833500i	$0.313666\pi$
$174$	7.62233			0.577847
$175$		0			0
$176$	−3.67114			−0.276723
$177$	−22.0173	+	22.0173i	−1.65492	+	1.65492i
$178$	1.01135	−	1.01135i	0.0758036	−	0.0758036i
$179$			12.5686i			0.939418i	0.882821	+	0.469709i	$0.155641\pi$
$179$			12.5686i			0.939418i	−0.882821	+	0.469709i	$0.844359\pi$
$180$	−4.52558	−	11.3120i	−0.337317	−	0.843146i
$181$			11.6742i			0.867740i	0.900976	+	0.433870i	$0.142852\pi$
$181$			11.6742i			0.867740i	−0.900976	+	0.433870i	$0.857148\pi$
$182$		0			0
$183$	−4.09485	−	4.09485i	−0.302700	−	0.302700i
$184$			4.70563i			0.346904i
$185$	0.528070	+	0.226279i	0.0388245	+	0.0166363i
$186$	−0.120711			−0.00885093
$187$	−2.04643	−	2.04643i	−0.149649	−	0.149649i
$188$	−4.52558	+	4.52558i	−0.330062	+	0.330062i
$189$		0			0
$190$	4.49957	+	1.92807i	0.326433	+	0.139877i
$191$	15.5034			1.12179			0.560894	−	0.827888i	$-0.310458\pi$
$191$	15.5034			1.12179			0.560894	+	0.827888i	$0.310458\pi$
$192$	2.05532	+	2.05532i	0.148330	+	0.148330i
$193$	6.36249	+	6.36249i	0.457982	+	0.457982i	0.897993	−	0.440011i	$-0.145025\pi$
$193$	6.36249	+	6.36249i	0.457982	+	0.457982i	−0.440011	+	0.897993i	$0.645025\pi$
$194$	4.47871			0.321553
$195$	7.08821	−	2.83577i	0.507597	−	0.203074i
$196$		0			0
$197$	12.1951	−	12.1951i	0.868865	−	0.868865i	−0.123482	−	0.992347i	$-0.539406\pi$
$197$	12.1951	−	12.1951i	0.868865	−	0.868865i	0.992347	+	0.123482i	$0.0394061\pi$
$198$	14.1442	+	14.1442i	1.00519	+	1.00519i
$199$	−8.73115			−0.618935			−0.309467	−	0.950910i	$-0.600151\pi$
$199$	−8.73115			−0.618935			−0.309467	+	0.950910i	$0.600151\pi$
$200$	−4.99853	−	0.121320i	−0.353449	−	0.00857864i
$201$			19.2490i			1.35772i
$202$	0.0508460	+	0.0508460i	0.00357751	+	0.00357751i
$203$		0			0
$204$			2.29142i			0.160432i
$205$	18.6438	−	7.45881i	1.30214	−	0.520946i
$206$		−	16.5798i		−	1.15517i
$207$	18.1300	−	18.1300i	1.26012	−	1.26012i
$208$	−0.830578	+	0.830578i	−0.0575902	+	0.0575902i
$209$	−8.03696			−0.555928
$210$		0			0
$211$	−11.1745			−0.769288			−0.384644	−	0.923065i	$-0.625676\pi$
$211$	−11.1745			−0.769288			−0.384644	+	0.923065i	$0.625676\pi$
$212$	5.59589	−	5.59589i	0.384327	−	0.384327i
$213$	16.6846	−	16.6846i	1.14321	−	1.14321i
$214$			4.56942i			0.312359i
$215$	0.591080	−	1.37941i	0.0403113	−	0.0940752i
$216$		−	7.11757i		−	0.484289i
$217$		0			0
$218$	12.8005	+	12.8005i	0.866958	+	0.866958i
$219$			28.6750i			1.93768i
$220$	7.62161	−	3.04917i	0.513849	−	0.205575i
$221$	−0.925988			−0.0622887
$222$	0.528070	+	0.528070i	0.0354418	+	0.0354418i
$223$	0.746804	−	0.746804i	0.0500097	−	0.0500097i	−0.681660	−	0.731669i	$-0.738742\pi$
$223$	0.746804	−	0.746804i	0.0500097	−	0.0500097i	0.731669	+	0.681660i	$0.238742\pi$
$224$		0			0
$225$	18.7910	+	19.7258i	1.25273	+	1.31506i
$226$	−2.15051			−0.143049
$227$	−2.20643	−	2.20643i	−0.146446	−	0.146446i	0.630082	−	0.776528i	$-0.283021\pi$
$227$	−2.20643	−	2.20643i	−0.146446	−	0.146446i	−0.776528	+	0.630082i	$0.783021\pi$
$228$	4.49957	+	4.49957i	0.297991	+	0.297991i
$229$	−8.42181			−0.556529			−0.278264	−	0.960504i	$-0.589759\pi$
$229$	−8.42181			−0.556529			−0.278264	+	0.960504i	$0.589759\pi$
$230$	−3.90840	−	9.76931i	−0.257712	−	0.644169i
$231$		0			0
$232$	1.85429	−	1.85429i	0.121740	−	0.121740i
$233$	−16.1198	−	16.1198i	−1.05605	−	1.05605i	−0.998333	−	0.0577132i	$-0.981619\pi$
$233$	−16.1198	−	16.1198i	−1.05605	−	1.05605i	−0.0577132	−	0.998333i	$-0.518381\pi$
$234$	6.40013			0.418390
$235$	5.63665	−	13.1543i	0.367694	−	0.858095i
$236$			10.7123i			0.697312i
$237$	27.5645	+	27.5645i	1.79051	+	1.79051i
$238$		0			0
$239$		−	23.9971i		−	1.55224i	−0.630585	−	0.776120i	$-0.717185\pi$
$239$		−	23.9971i		−	1.55224i	0.630585	−	0.776120i	$-0.282815\pi$
$240$	−5.97414	−	2.55992i	−0.385629	−	0.165242i
$241$		−	24.7875i		−	1.59670i	−0.602194	−	0.798350i	$-0.705706\pi$
$241$		−	24.7875i		−	1.59670i	0.602194	−	0.798350i	$-0.294294\pi$
$242$	−1.75170	+	1.75170i	−0.112604	+	0.112604i
$243$	6.17385	−	6.17385i	0.396053	−	0.396053i
$244$	−1.99231			−0.127545
$245$		0			0
$246$	26.1026			1.66424
$247$	−1.81832	+	1.81832i	−0.115697	+	0.115697i
$248$	−0.0293654	+	0.0293654i	−0.00186470	+	0.00186470i
$249$			39.9979i			2.53477i
$250$	10.4781	−	3.89980i	0.662696	−	0.246645i
$251$		−	11.1158i		−	0.701623i	−0.936446	−	0.350811i	$-0.885906\pi$
$251$		−	11.1158i		−	0.701623i	0.936446	−	0.350811i	$-0.114094\pi$
$252$		0			0
$253$	12.2153	+	12.2153i	0.767970	+	0.767970i
$254$		−	18.7422i		−	1.17599i
$255$	−1.90320	−	4.75719i	−0.119183	−	0.297907i
$256$	1.00000			0.0625000
$257$	17.8850	+	17.8850i	1.11564	+	1.11564i	0.992374	+	0.123262i	$0.0393355\pi$
$257$	17.8850	+	17.8850i	1.11564	+	1.11564i	0.123262	+	0.992374i	$0.460664\pi$
$258$	1.37941	−	1.37941i	0.0858785	−	0.0858785i
$259$		0			0
$260$	1.03449	−	2.41421i	0.0641565	−	0.149723i
$261$	−14.2885			−0.884435
$262$	10.0371	+	10.0371i	0.620095	+	0.620095i
$263$	8.02292	+	8.02292i	0.494714	+	0.494714i	0.909788	−	0.415074i	$-0.136244\pi$
$263$	8.02292	+	8.02292i	0.494714	+	0.494714i	−0.415074	+	0.909788i	$0.636244\pi$
$264$	10.6708			0.656741
$265$	−6.96973	+	16.2654i	−0.428147	+	0.999174i
$266$		0			0
$267$	−2.93964	+	2.93964i	−0.179903	+	0.179903i
$268$	4.68272	+	4.68272i	0.286042	+	0.286042i
$269$	8.06692			0.491849			0.245924	−	0.969289i	$-0.420908\pi$
$269$	8.06692			0.491849			0.245924	+	0.969289i	$0.420908\pi$
$270$	5.91170	+	14.7767i	0.359775	+	0.899281i
$271$		−	8.39951i		−	0.510234i	−0.966910	−	0.255117i	$-0.917886\pi$
$271$		−	8.39951i		−	0.510234i	0.966910	−	0.255117i	$-0.0821140\pi$
$272$	0.557436	+	0.557436i	0.0337995	+	0.0337995i
$273$		0			0
$274$		−	18.9664i		−	1.14580i
$275$	−13.2906	+	12.6607i	−0.801451	+	0.763468i
$276$		−	13.6777i		−	0.823301i
$277$	4.01637	−	4.01637i	0.241320	−	0.241320i	−0.576076	−	0.817396i	$-0.695417\pi$
$277$	4.01637	−	4.01637i	0.241320	−	0.241320i	0.817396	+	0.576076i	$0.195417\pi$
$278$	−5.82448	+	5.82448i	−0.349329	+	0.349329i
$279$	0.226279			0.0135470
$280$		0			0
$281$	7.27627			0.434066			0.217033	−	0.976164i	$-0.430362\pi$
$281$	7.27627			0.434066			0.217033	+	0.976164i	$0.430362\pi$
$282$	13.1543	−	13.1543i	0.783330	−	0.783330i
$283$	5.45180	−	5.45180i	0.324076	−	0.324076i	−0.526253	−	0.850328i	$-0.676403\pi$
$283$	5.45180	−	5.45180i	0.324076	−	0.324076i	0.850328	+	0.526253i	$0.176403\pi$
$284$		−	8.11777i		−	0.481701i
$285$	−13.0787	−	5.60425i	−0.774718	−	0.331967i
$286$			4.31218i			0.254984i
$287$		0			0
$288$	−3.85282	−	3.85282i	−0.227029	−	0.227029i
$289$		−	16.3785i		−	0.963443i
$290$	−2.30953	+	5.38980i	−0.135621	+	0.316500i
$291$	−13.0181			−0.763136
$292$	6.97578	+	6.97578i	0.408227	+	0.408227i
$293$	3.35198	−	3.35198i	0.195824	−	0.195824i	−0.602383	−	0.798207i	$-0.705782\pi$
$293$	3.35198	−	3.35198i	0.195824	−	0.195824i	0.798207	+	0.602383i	$0.205782\pi$
$294$		0			0
$295$	−8.89741	−	22.2397i	−0.518027	−	1.29485i
$296$	0.256928			0.0149336
$297$	−18.4764	−	18.4764i	−1.07211	−	1.07211i
$298$	3.42371	+	3.42371i	0.198330	+	0.198330i
$299$	5.52731			0.319653
$300$	14.5291	+	0.352638i	0.838835	+	0.0203595i
$301$		0			0
$302$	−7.10348	+	7.10348i	−0.408759	+	0.408759i
$303$	−0.147792	−	0.147792i	−0.00849045	−	0.00849045i
$304$	2.18923			0.125561
$305$	4.13622	−	1.65477i	0.236839	−	0.0947520i
$306$		−	4.29540i		−	0.245551i
$307$	−1.06546	−	1.06546i	−0.0608089	−	0.0608089i	0.676048	−	0.736857i	$-0.263691\pi$
$307$	−1.06546	−	1.06546i	−0.0608089	−	0.0608089i	−0.736857	+	0.676048i	$0.763691\pi$
$308$		0			0
$309$			48.1918i			2.74154i
$310$	0.0365748	−	0.0853553i	0.00207731	−	0.00484785i
$311$			13.8083i			0.782999i	0.920178	+	0.391500i	$0.128044\pi$
$311$			13.8083i			0.782999i	−0.920178	+	0.391500i	$0.871956\pi$
$312$	2.41421	−	2.41421i	0.136678	−	0.136678i
$313$	16.5089	−	16.5089i	0.933136	−	0.933136i	−0.0647646	−	0.997901i	$-0.520630\pi$
$313$	16.5089	−	16.5089i	0.933136	−	0.933136i	0.997901	+	0.0647646i	$0.0206296\pi$
$314$	−24.4867			−1.38186
$315$		0			0
$316$	13.4113			0.754443
$317$	9.32591	−	9.32591i	0.523796	−	0.523796i	−0.394920	−	0.918716i	$-0.629228\pi$
$317$	9.32591	−	9.32591i	0.523796	−	0.523796i	0.918716	+	0.394920i	$0.129228\pi$
$318$	−16.2654	+	16.2654i	−0.912117	+	0.912117i
$319$		−	9.62706i		−	0.539012i
$320$	−2.07609	+	0.830578i	−0.116057	+	0.0464307i
$321$		−	13.2818i		−	0.741316i
$322$		0			0
$323$	1.22035	+	1.22035i	0.0679023	+	0.0679023i
$324$			4.34228i			0.241238i
$325$	−0.142505	+	5.87135i	−0.00790474	+	0.325684i
$326$	21.9655			1.21656
$327$	−37.2067	−	37.2067i	−2.05754	−	2.05754i
$328$	6.35000	−	6.35000i	0.350620	−	0.350620i
$329$		0			0
$330$	−22.1535	+	8.86292i	−1.21951	+	0.487888i
$331$	−19.0960			−1.04961			−0.524805	−	0.851223i	$-0.675862\pi$
$331$	−19.0960			−1.04961			−0.524805	+	0.851223i	$0.675862\pi$
$332$	9.73033	+	9.73033i	0.534021	+	0.534021i
$333$	−0.989897	−	0.989897i	−0.0542460	−	0.0542460i
$334$	4.44935			0.243457
$335$	−13.6111	−	5.83237i	−0.743653	−	0.318656i
$336$		0			0
$337$	0.488226	−	0.488226i	0.0265953	−	0.0265953i	−0.693684	−	0.720279i	$-0.744014\pi$
$337$	0.488226	−	0.488226i	0.0265953	−	0.0265953i	0.720279	+	0.693684i	$0.244014\pi$
$338$	−8.21678	−	8.21678i	−0.446934	−	0.446934i
$339$	6.25080			0.339497
$340$	−1.62028	−	0.694291i	−0.0878720	−	0.0376532i
$341$			0.152458i			0.00825609i
$342$	−8.43469	−	8.43469i	−0.456096	−	0.456096i
$343$		0			0
$344$		−	0.671142i		−	0.0361855i
$345$	11.3604	+	28.3961i	0.611624	+	1.52880i
$346$		−	5.22653i		−	0.280980i
$347$	2.69406	−	2.69406i	0.144625	−	0.144625i	−0.631087	−	0.775712i	$-0.717391\pi$
$347$	2.69406	−	2.69406i	0.144625	−	0.144625i	0.775712	+	0.631087i	$0.217391\pi$
$348$	−5.38980	+	5.38980i	−0.288924	+	0.288924i
$349$	−7.91303			−0.423575			−0.211787	−	0.977316i	$-0.567928\pi$
$349$	−7.91303			−0.423575			−0.211787	+	0.977316i	$0.567928\pi$
$350$		0			0
$351$	−8.36041			−0.446246
$352$	2.59589	−	2.59589i	0.138361	−	0.138361i
$353$	18.2283	−	18.2283i	0.970196	−	0.970196i	−0.0293725	−	0.999569i	$-0.509351\pi$
$353$	18.2283	−	18.2283i	0.970196	−	0.970196i	0.999569	+	0.0293725i	$0.00935090\pi$
$354$		−	31.1371i		−	1.65492i
$355$	6.74244	+	16.8532i	0.357852	+	0.894475i
$356$			1.43026i			0.0758036i
$357$		0			0
$358$	−8.88731	−	8.88731i	−0.469709	−	0.469709i
$359$		−	10.3865i		−	0.548179i	−0.961704	−	0.274089i	$-0.911624\pi$
$359$		−	10.3865i		−	0.548179i	0.961704	−	0.274089i	$-0.0883764\pi$
$360$	11.1989	+	4.79872i	0.590231	+	0.252915i
$361$	−14.2073			−0.747752
$362$	−8.25494	−	8.25494i	−0.433870	−	0.433870i
$363$	5.09161	−	5.09161i	0.267240	−	0.267240i
$364$		0			0
$365$	−20.2763	−	8.68840i	−1.06131	−	0.454772i
$366$	5.79099			0.302700
$367$	−6.14194	−	6.14194i	−0.320607	−	0.320607i	0.528393	−	0.849000i	$-0.322795\pi$
$367$	−6.14194	−	6.14194i	−0.320607	−	0.320607i	−0.849000	+	0.528393i	$0.822795\pi$
$368$	−3.32739	−	3.32739i	−0.173452	−	0.173452i
$369$	−48.9308			−2.54724
$370$	−0.533405	+	0.213399i	−0.0277304	+	0.0110941i
$371$		0			0
$372$	0.0853553	−	0.0853553i	0.00442546	−	0.00442546i
$373$	9.41127	+	9.41127i	0.487297	+	0.487297i	0.907452	−	0.420155i	$-0.138024\pi$
$373$	9.41127	+	9.41127i	0.487297	+	0.487297i	−0.420155	+	0.907452i	$0.638024\pi$
$374$	2.89408			0.149649
$375$	−30.4565	+	11.3354i	−1.57277	+	0.585358i
$376$		−	6.40013i		−	0.330062i
$377$	−2.17808	−	2.17808i	−0.112177	−	0.112177i
$378$		0			0
$379$			25.3453i			1.30190i	0.759121	+	0.650949i	$0.225629\pi$
$379$			25.3453i			1.30190i	−0.759121	+	0.650949i	$0.774371\pi$
$380$	−4.54503	+	1.81832i	−0.233155	+	0.0932781i
$381$			54.4773i			2.79096i
$382$	−10.9626	+	10.9626i	−0.560894	+	0.560894i
$383$	13.0114	−	13.0114i	0.664852	−	0.664852i	−0.291668	−	0.956520i	$-0.594210\pi$
$383$	13.0114	−	13.0114i	0.664852	−	0.664852i	0.956520	+	0.291668i	$0.0942101\pi$
$384$	−2.90667			−0.148330
$385$		0			0
$386$	−8.99792			−0.457982
$387$	−2.58579	+	2.58579i	−0.131443	+	0.131443i
$388$	−3.16693	+	3.16693i	−0.160776	+	0.160776i
$389$		−	22.3575i		−	1.13357i	−0.823866	−	0.566784i	$-0.808187\pi$
$389$		−	22.3575i		−	1.13357i	0.823866	−	0.566784i	$-0.191813\pi$
$390$	−3.00693	+	7.01731i	−0.152262	+	0.355335i
$391$		−	3.70961i		−	0.187603i
$392$		0			0
$393$	−29.1745	−	29.1745i	−1.47166	−	1.47166i
$394$			17.2465i			0.868865i
$395$	−27.8430	+	11.1391i	−1.40093	+	0.560469i
$396$	−20.0030			−1.00519
$397$	11.1609	+	11.1609i	0.560151	+	0.560151i	0.929350	−	0.369199i	$-0.120368\pi$
$397$	11.1609	+	11.1609i	0.560151	+	0.560151i	−0.369199	+	0.929350i	$0.620368\pi$
$398$	6.17385	−	6.17385i	0.309467	−	0.309467i
$399$		0			0
$400$	3.62028	−	3.44871i	0.181014	−	0.172435i
$401$	13.9706			0.697657			0.348828	−	0.937187i	$-0.386580\pi$
$401$	13.9706			0.697657			0.348828	+	0.937187i	$0.386580\pi$
$402$	−13.6111	−	13.6111i	−0.678860	−	0.678860i
$403$	0.0344930	+	0.0344930i	0.00171822	+	0.00171822i
$404$	−0.0719071			−0.00357751
$405$	−3.60661	−	9.01496i	−0.179214	−	0.447957i
$406$		0			0
$407$	0.666957	−	0.666957i	0.0330598	−	0.0330598i
$408$	−1.62028	−	1.62028i	−0.0802158	−	0.0802158i
$409$	0.313362			0.0154947			0.00774737	−	0.999970i	$-0.497534\pi$
$409$	0.313362			0.0154947			0.00774737	+	0.999970i	$0.497534\pi$
$410$	−7.90899	+	18.4573i	−0.390597	+	0.911543i
$411$			55.1290i			2.71931i
$412$	11.7237	+	11.7237i	0.577583	+	0.577583i
$413$		0			0
$414$			25.6396i			1.26012i
$415$	−28.2828	−	12.1192i	−1.38835	−	0.594909i
$416$		−	1.17462i		−	0.0575902i
$417$	16.9298	−	16.9298i	0.829057	−	0.829057i
$418$	5.68299	−	5.68299i	0.277964	−	0.277964i
$419$	31.6254			1.54500			0.772501	−	0.635014i	$-0.219006\pi$
$419$	31.6254			1.54500			0.772501	+	0.635014i	$0.219006\pi$
$420$		0			0
$421$	24.2137			1.18011			0.590053	−	0.807365i	$-0.299107\pi$
$421$	24.2137			1.18011			0.590053	+	0.807365i	$0.299107\pi$
$422$	7.90160	−	7.90160i	0.384644	−	0.384644i
$423$	−24.6585	+	24.6585i	−1.19894	+	1.19894i
$424$			7.91378i			0.384327i
$425$	3.94051	+	0.0956409i	0.191143	+	0.00463926i
$426$			23.5956i			1.14321i
$427$		0			0
$428$	−3.23107	−	3.23107i	−0.156179	−	0.156179i
$429$		−	12.5341i		−	0.605150i
$430$	0.557436	+	1.39335i	0.0268819	+	0.0671933i
$431$	1.55807			0.0750498			0.0375249	−	0.999296i	$-0.488053\pi$
$431$	1.55807			0.0750498			0.0375249	+	0.999296i	$0.488053\pi$
$432$	5.03288	+	5.03288i	0.242145	+	0.242145i
$433$	6.28166	−	6.28166i	0.301877	−	0.301877i	−0.539871	−	0.841748i	$-0.681527\pi$
$433$	6.28166	−	6.28166i	0.301877	−	0.301877i	0.841748	+	0.539871i	$0.181527\pi$
$434$		0			0
$435$	6.71305	−	15.6663i	0.321866	−	0.751144i
$436$	−18.1026			−0.866958
$437$	−7.28440	−	7.28440i	−0.348460	−	0.348460i
$438$	−20.2763	−	20.2763i	−0.968838	−	0.968838i
$439$	−23.9142			−1.14136			−0.570681	−	0.821172i	$-0.693321\pi$
$439$	−23.9142			−1.14136			−0.570681	+	0.821172i	$0.693321\pi$
$440$	−3.23320	+	7.54538i	−0.154137	+	0.359712i
$441$		0			0
$442$	0.654772	−	0.654772i	0.0311443	−	0.0311443i
$443$	9.09485	+	9.09485i	0.432109	+	0.432109i	0.889345	−	0.457236i	$-0.151161\pi$
$443$	9.09485	+	9.09485i	0.432109	+	0.432109i	−0.457236	+	0.889345i	$0.651161\pi$
$444$	−0.746804			−0.0354418
$445$	−1.18794	−	2.96934i	−0.0563139	−	0.140760i
$446$			1.05614i			0.0500097i
$447$	−9.95157	−	9.95157i	−0.470693	−	0.470693i
$448$		0			0
$449$		−	17.8932i		−	0.844435i	−0.906495	−	0.422217i	$-0.861252\pi$
$449$		−	17.8932i		−	0.844435i	0.906495	−	0.422217i	$-0.138748\pi$
$450$	−27.2355	−	0.661039i	−1.28389	−	0.0311617i
$451$		−	32.9678i		−	1.55239i
$452$	1.52064	−	1.52064i	0.0715247	−	0.0715247i
$453$	20.6474	−	20.6474i	0.970101	−	0.970101i
$454$	3.12036			0.146446
$455$		0			0
$456$	−6.36335			−0.297991
$457$	24.1909	−	24.1909i	1.13160	−	1.13160i	0.141693	−	0.989911i	$-0.454746\pi$
$457$	24.1909	−	24.1909i	1.13160	−	1.13160i	0.989911	−	0.141693i	$-0.0452545\pi$
$458$	5.95512	−	5.95512i	0.278264	−	0.278264i
$459$			5.61102i			0.261900i
$460$	9.67160	+	4.14429i	0.450941	+	0.193229i
$461$			23.3471i			1.08738i	0.839286	+	0.543690i	$0.182973\pi$
$461$			23.3471i			1.08738i	−0.839286	+	0.543690i	$0.817027\pi$
$462$		0			0
$463$	3.98510	+	3.98510i	0.185203	+	0.185203i	0.793619	−	0.608415i	$-0.208195\pi$
$463$	3.98510	+	3.98510i	0.185203	+	0.185203i	−0.608415	+	0.793619i	$0.708195\pi$
$464$			2.62236i			0.121740i
$465$	−0.106311	+	0.248099i	−0.00493004	+	0.0115053i
$466$	22.7969			1.05605
$467$	3.45478	+	3.45478i	0.159868	+	0.159868i	0.782508	−	0.622640i	$-0.213940\pi$
$467$	3.45478	+	3.45478i	0.159868	+	0.159868i	−0.622640	+	0.782508i	$0.713940\pi$
$468$	−4.52558	+	4.52558i	−0.209195	+	0.209195i
$469$		0			0
$470$	5.31581	+	13.2872i	0.245200	+	0.612895i
$471$	71.1746			3.27955
$472$	−7.57475	−	7.57475i	−0.348656	−	0.348656i
$473$	−1.74221	−	1.74221i	−0.0801069	−	0.0801069i
$474$	−38.9821			−1.79051
$475$	7.92561	−	7.55000i	0.363652	−	0.346418i
$476$		0			0
$477$	30.4904	−	30.4904i	1.39606	−	1.39606i
$478$	16.9685	+	16.9685i	0.776120	+	0.776120i
$479$	17.1114			0.781841			0.390921	−	0.920424i	$-0.372157\pi$
$479$	17.1114			0.781841			0.390921	+	0.920424i	$0.372157\pi$
$480$	6.03449	−	2.41421i	0.275436	−	0.110193i
$481$		−	0.301792i		−	0.0137605i
$482$	17.5274	+	17.5274i	0.798350	+	0.798350i
$483$		0			0
$484$		−	2.47728i		−	0.112604i
$485$	3.94444	−	9.20520i	0.179108	−	0.417987i
$486$			8.73115i			0.396053i
$487$	0.0921357	−	0.0921357i	0.00417507	−	0.00417507i	−0.705016	−	0.709191i	$-0.749060\pi$
$487$	0.0921357	−	0.0921357i	0.00417507	−	0.00417507i	0.709191	+	0.705016i	$0.249060\pi$
$488$	1.40878	−	1.40878i	0.0637724	−	0.0637724i
$489$	−63.8465			−2.88724
$490$		0			0
$491$	26.9895			1.21802			0.609011	−	0.793162i	$-0.291567\pi$
$491$	26.9895			1.21802			0.609011	+	0.793162i	$0.291567\pi$
$492$	−18.4573	+	18.4573i	−0.832121	+	0.832121i
$493$	−1.46180	+	1.46180i	−0.0658361	+	0.0658361i
$494$		−	2.57150i		−	0.115697i
$495$	41.5279	−	16.6140i	1.86654	−	0.746745i
$496$		−	0.0415289i		−	0.00186470i
$497$		0			0
$498$	−28.2828	−	28.2828i	−1.26738	−	1.26738i
$499$			0.0962993i			0.00431095i	0.999998	+	0.00215548i	$0.000686110\pi$
$499$			0.0962993i			0.00431095i	−0.999998	+	0.00215548i	$0.999314\pi$
$500$	−4.65160	+	10.1667i	−0.208026	+	0.454671i
$501$	−12.9328			−0.577793
$502$	7.86005	+	7.86005i	0.350811	+	0.350811i
$503$	−13.6334	+	13.6334i	−0.607883	+	0.607883i	−0.942392	−	0.334509i	$-0.891429\pi$
$503$	−13.6334	+	13.6334i	−0.607883	+	0.607883i	0.334509	+	0.942392i	$0.391429\pi$
$504$		0			0
$505$	0.149286	−	0.0597245i	0.00664312	−	0.00265771i
$506$	−17.2751			−0.767970
$507$	23.8834	+	23.8834i	1.06070	+	1.06070i
$508$	13.2527	+	13.2527i	0.587995	+	0.587995i
$509$	12.3273			0.546399			0.273199	−	0.961957i	$-0.411918\pi$
$509$	12.3273			0.546399			0.273199	+	0.961957i	$0.411918\pi$
$510$	4.70961	+	2.01807i	0.208545	+	0.0893618i
$511$		0			0
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	11.0181	+	11.0181i	0.486462	+	0.486462i
$514$	−25.2932			−1.11564
$515$	−34.0768	−	14.6019i	−1.50160	−	0.643438i
$516$			1.95078i			0.0858785i
$517$	−16.6140	−	16.6140i	−0.730684	−	0.730684i
$518$		0			0
$519$			15.1918i			0.666845i
$520$	0.975610	+	2.43860i	0.0427833	+	0.106940i
$521$			16.3292i			0.715396i	0.933837	+	0.357698i	$0.116438\pi$
$521$			16.3292i			0.715396i	−0.933837	+	0.357698i	$0.883562\pi$
$522$	10.1035	−	10.1035i	0.442217	−	0.442217i
$523$	−19.3776	+	19.3776i	−0.847323	+	0.847323i	−0.989798	−	0.142475i	$-0.954494\pi$
$523$	−19.3776	+	19.3776i	−0.847323	+	0.847323i	0.142475	+	0.989798i	$0.454494\pi$
$524$	−14.1946			−0.620095
$525$		0			0
$526$	−11.3461			−0.494714
$527$	0.0231497	−	0.0231497i	0.00100842	−	0.00100842i
$528$	−7.54538	+	7.54538i	−0.328371	+	0.328371i
$529$		−	0.857002i		−	0.0372610i
$530$	−6.57302	−	16.4297i	−0.285514	−	0.713661i
$531$			58.3682i			2.53297i
$532$		0			0
$533$	−7.45881	−	7.45881i	−0.323077	−	0.323077i
$534$		−	4.15729i		−	0.179903i
$535$	9.39163	+	4.02432i	0.406036	+	0.173987i
$536$	−6.62236			−0.286042
$537$	25.8324	+	25.8324i	1.11475	+	1.11475i
$538$	−5.70417	+	5.70417i	−0.245924	+	0.245924i
$539$		0			0
$540$	−14.6289	−	6.26850i	−0.629528	−	0.269753i
$541$	−41.1547			−1.76938			−0.884689	−	0.466181i	$-0.845630\pi$
$541$	−41.1547			−1.76938			−0.884689	+	0.466181i	$0.845630\pi$
$542$	5.93935	+	5.93935i	0.255117	+	0.255117i
$543$	23.9943	+	23.9943i	1.02970	+	1.02970i
$544$	−0.788333			−0.0337995
$545$	37.5826	−	15.0356i	1.60986	−	0.644056i
$546$		0			0
$547$	8.06541	−	8.06541i	0.344852	−	0.344852i	−0.513336	−	0.858188i	$-0.671590\pi$
$547$	8.06541	−	8.06541i	0.344852	−	0.344852i	0.858188	+	0.513336i	$0.171590\pi$
$548$	13.4113	+	13.4113i	0.572901	+	0.572901i
$549$	−10.8555			−0.463303
$550$	0.445384	−	18.3503i	0.0189912	−	0.782460i
$551$			5.74094i			0.244572i
$552$	9.67160	+	9.67160i	0.411651	+	0.411651i
$553$		0			0
$554$			5.68000i			0.241320i
$555$	1.55043	−	0.620279i	0.0658121	−	0.0263294i
$556$		−	8.23706i		−	0.349329i
$557$	−18.1422	+	18.1422i	−0.768708	+	0.768708i	−0.977879	−	0.209171i	$-0.932923\pi$
$557$	−18.1422	+	18.1422i	−0.768708	+	0.768708i	0.209171	+	0.977879i	$0.432923\pi$
$558$	−0.160003	+	0.160003i	−0.00677348	+	0.00677348i
$559$	−0.788333			−0.0333429
$560$		0			0
$561$	−8.41213			−0.355160
$562$	−5.14510	+	5.14510i	−0.217033	+	0.217033i
$563$	9.05904	−	9.05904i	0.381793	−	0.381793i	−0.489955	−	0.871748i	$-0.662987\pi$
$563$	9.05904	−	9.05904i	0.381793	−	0.381793i	0.871748	+	0.489955i	$0.162987\pi$
$564$			18.6030i			0.783330i
$565$	−1.89397	+	4.41998i	−0.0796798	+	0.185950i
$566$			7.71000i			0.324076i
$567$		0			0
$568$	5.74013	+	5.74013i	0.240850	+	0.240850i
$569$			34.4437i			1.44395i	0.691917	+	0.721977i	$0.256766\pi$
$569$			34.4437i			1.44395i	−0.691917	+	0.721977i	$0.743234\pi$
$570$	13.2109	−	5.28526i	0.553343	−	0.221375i
$571$	−8.23970			−0.344821			−0.172410	−	0.985025i	$-0.555155\pi$
$571$	−8.23970			−0.344821			−0.172410	+	0.985025i	$0.555155\pi$
$572$	−3.04917	−	3.04917i	−0.127492	−	0.127492i
$573$	31.8645	−	31.8645i	1.33116	−	1.33116i
$574$		0			0
$575$	−23.5212	−	0.570889i	−0.980904	−	0.0238077i
$576$	5.44871			0.227029
$577$	−2.48640	−	2.48640i	−0.103510	−	0.103510i	0.653455	−	0.756965i	$-0.273319\pi$
$577$	−2.48640	−	2.48640i	−0.103510	−	0.103510i	−0.756965	+	0.653455i	$0.773319\pi$
$578$	11.5814	+	11.5814i	0.481721	+	0.481721i
$579$	26.1539			1.08692
$580$	−2.17808	−	5.44425i	−0.0904397	−	0.226060i
$581$		0			0
$582$	9.20520	−	9.20520i	0.381568	−	0.381568i
$583$	20.5433	+	20.5433i	0.850817	+	0.850817i
$584$	−9.86525			−0.408227
$585$	5.63665	−	13.1543i	0.233047	−	0.543865i
$586$			4.74041i			0.195824i
$587$	−5.37485	−	5.37485i	−0.221844	−	0.221844i	0.587431	−	0.809275i	$-0.300139\pi$
$587$	−5.37485	−	5.37485i	−0.221844	−	0.221844i	−0.809275	+	0.587431i	$0.800139\pi$
$588$		0			0
$589$		−	0.0909162i		−	0.00374613i
$590$	22.0173	+	9.43442i	0.906436	+	0.388409i
$591$		−	50.1297i		−	2.06206i
$592$	−0.181676	+	0.181676i	−0.00746682	+	0.00746682i
$593$	0.519513	−	0.519513i	0.0213338	−	0.0213338i	−0.696359	−	0.717693i	$-0.745198\pi$
$593$	0.519513	−	0.519513i	0.0213338	−	0.0213338i	0.717693	+	0.696359i	$0.245198\pi$
$594$	26.1296			1.07211
$595$		0			0
$596$	−4.84185			−0.198330
$597$	−17.9453	+	17.9453i	−0.734454	+	0.734454i
$598$	−3.90840	+	3.90840i	−0.159826	+	0.159826i
$599$			8.35746i			0.341477i	0.985316	+	0.170738i	$0.0546153\pi$
$599$			8.35746i			0.341477i	−0.985316	+	0.170738i	$0.945385\pi$
$600$	−10.5229	+	10.0242i	−0.429597	+	0.409238i
$601$		−	39.9236i		−	1.62852i	−0.580501	−	0.814259i	$-0.697143\pi$
$601$		−	39.9236i		−	1.62852i	0.580501	−	0.814259i	$-0.302857\pi$
$602$		0			0
$603$	25.5147	+	25.5147i	1.03904	+	1.03904i
$604$		−	10.0458i		−	0.408759i
$605$	2.05758	+	5.14305i	0.0836524	+	0.209095i
$606$	0.209010			0.00849045
$607$	−24.3596	−	24.3596i	−0.988726	−	0.988726i	0.0112116	−	0.999937i	$-0.496431\pi$
$607$	−24.3596	−	24.3596i	−0.988726	−	0.988726i	−0.999937	+	0.0112116i	$0.996431\pi$
$608$	−1.54802	+	1.54802i	−0.0627804	+	0.0627804i
$609$		0			0
$610$	−1.75465	+	4.09485i	−0.0710436	+	0.165796i
$611$	−7.51769			−0.304133
$612$	3.03730	+	3.03730i	0.122776	+	0.122776i
$613$	−23.1359	−	23.1359i	−0.934449	−	0.934449i	0.0635309	−	0.997980i	$-0.479764\pi$
$613$	−23.1359	−	23.1359i	−0.934449	−	0.934449i	−0.997980	+	0.0635309i	$0.979764\pi$
$614$	1.50679			0.0608089
$615$	22.9888	−	53.6493i	0.926997	−	2.16335i
$616$		0			0
$617$	−15.5005	+	15.5005i	−0.624025	+	0.624025i	−0.946558	−	0.322533i	$-0.895466\pi$
$617$	−15.5005	+	15.5005i	−0.624025	+	0.624025i	0.322533	+	0.946558i	$0.395466\pi$
$618$	−34.0768	−	34.0768i	−1.37077	−	1.37077i
$619$	−8.62275			−0.346578			−0.173289	−	0.984871i	$-0.555439\pi$
$619$	−8.62275			−0.346578			−0.173289	+	0.984871i	$0.555439\pi$
$620$	0.0344930	+	0.0862176i	0.00138527	+	0.00346258i
$621$		−	33.4927i		−	1.34402i
$622$	−9.76397	−	9.76397i	−0.391500	−	0.391500i
$623$		0			0
$624$			3.41421i			0.136678i
$625$	1.21285	−	24.9706i	0.0485138	−	0.998823i
$626$			23.3471i			0.933136i
$627$	−16.5186	+	16.5186i	−0.659688	+	0.659688i
$628$	17.3147	−	17.3147i	0.690931	−	0.690931i
$629$	−0.202545			−0.00807600
$630$		0			0
$631$	−4.13675			−0.164682			−0.0823408	−	0.996604i	$-0.526240\pi$
$631$	−4.13675			−0.164682			−0.0823408	+	0.996604i	$0.526240\pi$
$632$	−9.48320	+	9.48320i	−0.377221	+	0.377221i
$633$	−22.9673	+	22.9673i	−0.912868	+	0.912868i
$634$			13.1888i			0.523796i
$635$	−38.5213	−	16.5064i	−1.52867	−	0.655037i
$636$		−	23.0027i		−	0.912117i
$637$		0			0
$638$	6.80736	+	6.80736i	0.269506	+	0.269506i
$639$		−	44.2313i		−	1.74976i
$640$	0.880708	−	2.05532i	0.0348130	−	0.0812438i
$641$	10.8561			0.428792			0.214396	−	0.976747i	$-0.431222\pi$
$641$	10.8561			0.428792			0.214396	+	0.976747i	$0.431222\pi$
$642$	9.39163	+	9.39163i	0.370658	+	0.370658i
$643$	−8.06230	+	8.06230i	−0.317946	+	0.317946i	−0.847978	−	0.530032i	$-0.822180\pi$
$643$	−8.06230	+	8.06230i	−0.317946	+	0.317946i	0.530032	+	0.847978i	$0.322180\pi$
$644$		0			0
$645$	−1.62028	−	4.05000i	−0.0637984	−	0.159469i
$646$	−1.72584			−0.0679023
$647$	−7.37284	−	7.37284i	−0.289856	−	0.289856i	0.547167	−	0.837023i	$-0.315706\pi$
$647$	−7.37284	−	7.37284i	−0.289856	−	0.289856i	−0.837023	+	0.547167i	$0.815706\pi$
$648$	−3.07046	−	3.07046i	−0.120619	−	0.120619i
$649$	−39.3264			−1.54370
$650$	−4.05090	−	4.25243i	−0.158889	−	0.166794i
$651$		0			0
$652$	−15.5320	+	15.5320i	−0.608279	+	0.608279i
$653$	−4.69937	−	4.69937i	−0.183900	−	0.183900i	0.609153	−	0.793053i	$-0.291510\pi$
$653$	−4.69937	−	4.69937i	−0.183900	−	0.183900i	−0.793053	+	0.609153i	$0.791510\pi$
$654$	52.6183			2.05754
$655$	29.4693	−	11.7897i	1.15146	−	0.460664i
$656$			8.98026i			0.350620i
$657$	38.0090	+	38.0090i	1.48287	+	1.48287i
$658$		0			0
$659$			22.0345i			0.858343i	0.903223	+	0.429172i	$0.141194\pi$
$659$			22.0345i			0.858343i	−0.903223	+	0.429172i	$0.858806\pi$
$660$	9.39784	−	21.9319i	0.365811	−	0.853698i
$661$		−	11.4809i		−	0.446557i	−0.974755	−	0.223278i	$-0.928324\pi$
$661$		−	11.4809i		−	0.446557i	0.974755	−	0.223278i	$-0.0716759\pi$
$662$	13.5029	−	13.5029i	0.524805	−	0.524805i
$663$	−1.90320	+	1.90320i	−0.0739143	+	0.0739143i
$664$	−13.7608			−0.534021
$665$		0			0
$666$	1.39993			0.0542460
$667$	8.72561	−	8.72561i	0.337857	−	0.337857i
$668$	−3.14616	+	3.14616i	−0.121729	+	0.121729i
$669$		−	3.06985i		−	0.118687i
$670$	13.7486	−	5.50039i	0.531155	−	0.212499i
$671$		−	7.31407i		−	0.282356i
$672$		0			0
$673$	−15.2073	−	15.2073i	−0.586198	−	0.586198i	0.350402	−	0.936600i	$-0.386045\pi$
$673$	−15.2073	−	15.2073i	−0.586198	−	0.586198i	−0.936600	+	0.350402i	$0.886045\pi$
$674$			0.690455i			0.0265953i
$675$	35.5774	+	0.863506i	1.36937	+	0.0332364i
$676$	11.6203			0.446934
$677$	4.05773	+	4.05773i	0.155951	+	0.155951i	0.780770	−	0.624819i	$-0.214827\pi$
$677$	4.05773	+	4.05773i	0.155951	+	0.155951i	−0.624819	+	0.780770i	$0.714827\pi$
$678$	−4.41998	+	4.41998i	−0.169748	+	0.169748i
$679$		0			0
$680$	1.63665	−	0.654772i	0.0627626	−	0.0251094i
$681$	−9.06985			−0.347557
$682$	−0.107804	−	0.107804i	−0.00412804	−	0.00412804i
$683$	13.7395	+	13.7395i	0.525727	+	0.525727i	0.919295	−	0.393568i	$-0.128759\pi$
$683$	13.7395	+	13.7395i	0.525727	+	0.525727i	−0.393568	+	0.919295i	$0.628759\pi$
$684$	11.9285			0.456096
$685$	−38.9821	−	16.7039i	−1.48943	−	0.638222i
$686$		0			0
$687$	−17.3095	+	17.3095i	−0.660400	+	0.660400i
$688$	0.474569	+	0.474569i	0.0180928	+	0.0180928i
$689$	9.29565			0.354136
$690$	−28.1121	−	12.0461i	−1.07021	−	0.458586i
$691$		−	22.0448i		−	0.838624i	−0.907842	−	0.419312i	$-0.862271\pi$
$691$		−	22.0448i		−	0.838624i	0.907842	−	0.419312i	$-0.137729\pi$
$692$	3.69572	+	3.69572i	0.140490	+	0.140490i
$693$		0			0
$694$			3.80998i			0.144625i
$695$	6.84152	+	17.1009i	0.259514	+	0.648673i
$696$		−	7.62233i		−	0.288924i
$697$	−5.00592	+	5.00592i	−0.189613	+	0.189613i
$698$	5.59536	−	5.59536i	0.211787	−	0.211787i
$699$	−66.2630			−2.50630
$700$		0			0
$701$	−18.0270			−0.680870			−0.340435	−	0.940268i	$-0.610574\pi$
$701$	−18.0270			−0.680870			−0.340435	+	0.940268i	$0.610574\pi$
$702$	5.91170	−	5.91170i	0.223123	−	0.223123i
$703$	−0.397729	+	0.397729i	−0.0150006	+	0.0150006i
$704$			3.67114i			0.138361i
$705$	−15.4513	−	38.6216i	−0.581929	−	1.45457i
$706$			25.7787i			0.970196i
$707$		0			0
$708$	22.0173	+	22.0173i	0.827459	+	0.827459i
$709$			42.7949i			1.60719i	0.595173	+	0.803597i	$0.297083\pi$
$709$			42.7949i			1.60719i	−0.595173	+	0.803597i	$0.702917\pi$
$710$	−16.6846	−	7.14938i	−0.626163	−	0.268312i
$711$	73.0741			2.74049
$712$	−1.01135	−	1.01135i	−0.0379018	−	0.0379018i
$713$	−0.138183	+	0.138183i	−0.00517498	+	0.00517498i
$714$		0			0
$715$	8.86292	+	3.79777i	0.331454	+	0.142029i
$716$	12.5686			0.469709
$717$	−49.3217	−	49.3217i	−1.84195	−	1.84195i
$718$	7.34437	+	7.34437i	0.274089	+	0.274089i
$719$	5.45382			0.203393			0.101697	−	0.994815i	$-0.467573\pi$
$719$	5.45382			0.203393			0.101697	+	0.994815i	$0.467573\pi$
$720$	−11.3120	+	4.52558i	−0.421573	+	0.168658i
$721$		0			0
$722$	10.0461	−	10.0461i	0.373876	−	0.373876i
$723$	−50.9462	−	50.9462i	−1.89471	−	1.89471i
$724$	11.6742			0.433870
$725$	9.04375	+	9.49368i	0.335877	+	0.352586i
$726$			7.20063i			0.267240i
$727$	16.6781	+	16.6781i	0.618555	+	0.618555i	0.945161	−	0.326606i	$-0.105905\pi$
$727$	16.6781	+	16.6781i	0.618555	+	0.618555i	−0.326606	+	0.945161i	$0.605905\pi$
$728$		0			0
$729$		−	38.4054i		−	1.42242i
$730$	20.4811	−	8.19386i	0.758040	−	0.303268i
$731$			0.529083i			0.0195689i
$732$	−4.09485	+	4.09485i	−0.151350	+	0.151350i
$733$	−24.0409	+	24.0409i	−0.887973	+	0.887973i	−0.994328	−	0.106356i	$-0.966082\pi$
$733$	−24.0409	+	24.0409i	−0.887973	+	0.887973i	0.106356	+	0.994328i	$0.466082\pi$
$734$	8.68601			0.320607
$735$		0			0
$736$	4.70563			0.173452
$737$	−17.1909	+	17.1909i	−0.633236	+	0.633236i
$738$	34.5993	−	34.5993i	1.27362	−	1.27362i
$739$			28.9521i			1.06502i	0.846424	+	0.532510i	$0.178751\pi$
$739$			28.9521i			1.06502i	−0.846424	+	0.532510i	$0.821249\pi$
$740$	0.226279	−	0.528070i	0.00831817	−	0.0194123i
$741$			7.47449i			0.274582i
$742$		0			0
$743$	34.0351	+	34.0351i	1.24863	+	1.24863i	0.956327	+	0.292300i	$0.0944206\pi$
$743$	34.0351	+	34.0351i	1.24863	+	1.24863i	0.292300	+	0.956327i	$0.405579\pi$
$744$			0.120711i			0.00442546i
$745$	10.0521	−	4.02154i	0.368281	−	0.147338i
$746$	−13.3095			−0.487297
$747$	53.0177	+	53.0177i	1.93982	+	1.93982i
$748$	−2.04643	+	2.04643i	−0.0748247	+	0.0748247i
$749$		0			0
$750$	13.5206	−	29.5513i	0.493704	−	1.07906i
$751$	−18.6114			−0.679139			−0.339569	−	0.940581i	$-0.610281\pi$
$751$	−18.6114			−0.679139			−0.339569	+	0.940581i	$0.610281\pi$
$752$	4.52558	+	4.52558i	0.165031	+	0.165031i
$753$	−22.8466	−	22.8466i	−0.832575	−	0.832575i
$754$	3.08027			0.112177
$755$	8.34385	+	20.8560i	0.303664	+	0.759029i
$756$		0			0
$757$	29.7422	−	29.7422i	1.08100	−	1.08100i	0.0845825	−	0.996416i	$-0.473044\pi$
$757$	29.7422	−	29.7422i	1.08100	−	1.08100i	0.996416	−	0.0845825i	$-0.0269557\pi$
$758$	−17.9218	−	17.9218i	−0.650949	−	0.650949i
$759$	50.2128			1.82261
$760$	1.92807	−	4.49957i	0.0699384	−	0.163217i
$761$		−	20.3775i		−	0.738682i	−0.929294	−	0.369341i	$-0.879583\pi$
$761$		−	20.3775i		−	0.738682i	0.929294	−	0.369341i	$-0.120417\pi$
$762$	−38.5213	−	38.5213i	−1.39548	−	1.39548i
$763$		0			0
$764$		−	15.5034i		−	0.560894i
$765$	−8.82843	−	3.78299i	−0.319192	−	0.136774i
$766$			18.4009i			0.664852i
$767$	−8.89741	+	8.89741i	−0.321267	+	0.321267i
$768$	2.05532	−	2.05532i	0.0741651	−	0.0741651i
$769$	40.9728			1.47752			0.738759	−	0.673970i	$-0.235412\pi$
$769$	40.9728			1.47752			0.738759	+	0.673970i	$0.235412\pi$
$770$		0			0
$771$	73.5189			2.64772
$772$	6.36249	−	6.36249i	0.228991	−	0.228991i
$773$	−17.4650	+	17.4650i	−0.628174	+	0.628174i	−0.947608	−	0.319435i	$-0.896507\pi$
$773$	−17.4650	+	17.4650i	−0.628174	+	0.628174i	0.319435	+	0.947608i	$0.396507\pi$
$774$		−	3.65685i		−	0.131443i
$775$	−0.143221	−	0.150346i	−0.00514465	−	0.00540059i
$776$		−	4.47871i		−	0.160776i
$777$		0			0
$778$	15.8091	+	15.8091i	0.566784	+	0.566784i
$779$			19.6598i			0.704386i
$780$	−2.83577	−	7.08821i	−0.101537	−	0.253799i
$781$	29.8015			1.06638
$782$	2.62309	+	2.62309i	0.0938015	+	0.0938015i
$783$	−13.1980	+	13.1980i	−0.471659	+	0.471659i
$784$		0			0
$785$	−21.5656	+	50.3280i	−0.769710	+	1.79628i
$786$	41.2590			1.47166
$787$	5.80401	+	5.80401i	0.206891	+	0.206891i	0.802945	−	0.596054i	$-0.203265\pi$
$787$	5.80401	+	5.80401i	0.206891	+	0.206891i	−0.596054	+	0.802945i	$0.703265\pi$
$788$	−12.1951	−	12.1951i	−0.434432	−	0.434432i
$789$	32.9794			1.17410
$790$	11.8114	−	27.5645i	0.420231	−	0.980701i
$791$		0			0
$792$	14.1442	−	14.1442i	0.502594	−	0.502594i
$793$	−1.65477	−	1.65477i	−0.0587627	−	0.0587627i
$794$	−15.7839			−0.560151
$795$	19.1056	+	47.7557i	0.677604	+	1.69372i
$796$			8.73115i			0.309467i
$797$	11.7928	+	11.7928i	0.417722	+	0.417722i	0.884418	−	0.466696i	$-0.154556\pi$
$797$	11.7928	+	11.7928i	0.417722	+	0.417722i	−0.466696	+	0.884418i	$0.654556\pi$
$798$		0			0
$799$			5.04544i			0.178495i
$800$	−0.121320	+	4.99853i	−0.00428932	+	0.176725i
$801$			7.79306i			0.275354i
$802$	−9.87868	+	9.87868i	−0.348828	+	0.348828i
$803$	−25.6091	+	25.6091i	−0.903725	+	0.903725i
$804$	19.2490			0.678860
$805$		0			0
$806$	−0.0487805			−0.00171822
$807$	16.5801	−	16.5801i	0.583648	−	0.583648i
$808$	0.0508460	−	0.0508460i	0.00178876	−	0.00178876i
$809$		−	33.3128i		−	1.17122i	−0.810594	−	0.585609i	$-0.800856\pi$
$809$		−	33.3128i		−	1.17122i	0.810594	−	0.585609i	$-0.199144\pi$
$810$	8.92480	+	3.82428i	0.313585	+	0.134372i
$811$			55.2368i			1.93963i	0.243850	+	0.969813i	$0.421590\pi$
$811$			55.2368i			1.93963i	−0.243850	+	0.969813i	$0.578410\pi$
$812$		0			0
$813$	−17.2637	−	17.2637i	−0.605465	−	0.605465i
$814$			0.943220i			0.0330598i
$815$	19.3452	−	45.1463i	0.677634	−	1.58141i
$816$	2.29142			0.0802158
$817$	1.03894	+	1.03894i	0.0363479	+	0.0363479i
$818$	−0.221580	+	0.221580i	−0.00774737	+	0.00774737i
$819$		0			0
$820$	−7.45881	−	18.6438i	−0.260473	−	0.651070i
$821$	18.6291			0.650162			0.325081	−	0.945686i	$-0.394609\pi$
$821$	18.6291			0.650162			0.325081	+	0.945686i	$0.394609\pi$
$822$	−38.9821	−	38.9821i	−1.35966	−	1.35966i
$823$	−11.9426	−	11.9426i	−0.416294	−	0.416294i	0.467631	−	0.883924i	$-0.345108\pi$
$823$	−11.9426	−	11.9426i	−0.416294	−	0.416294i	−0.883924	+	0.467631i	$0.845108\pi$
$824$	−16.5798			−0.577583
$825$	−1.29458	+	53.3382i	−0.0450716	+	1.85700i
$826$		0			0
$827$	−5.62716	+	5.62716i	−0.195675	+	0.195675i	−0.798143	−	0.602468i	$-0.794184\pi$
$827$	−5.62716	+	5.62716i	−0.195675	+	0.195675i	0.602468	+	0.798143i	$0.294184\pi$
$828$	−18.1300	−	18.1300i	−0.630059	−	0.630059i
$829$	−6.59513			−0.229058			−0.114529	−	0.993420i	$-0.536536\pi$
$829$	−6.59513			−0.229058			−0.114529	+	0.993420i	$0.536536\pi$
$830$	28.5686	−	11.4294i	0.991629	−	0.396720i
$831$		−	16.5099i		−	0.572721i
$832$	0.830578	+	0.830578i	0.0287951	+	0.0287951i
$833$		0			0
$834$			23.9424i			0.829057i
$835$	3.91858	−	9.14485i	0.135608	−	0.316471i
$836$			8.03696i			0.277964i
$837$	0.209010	−	0.209010i	0.00722444	−	0.00722444i
$838$	−22.3625	+	22.3625i	−0.772501	+	0.772501i
$839$	46.0930			1.59131			0.795654	−	0.605752i	$-0.207128\pi$
$839$	46.0930			1.59131			0.795654	+	0.605752i	$0.207128\pi$
$840$		0			0
$841$	22.1232			0.762870
$842$	−17.1217	+	17.1217i	−0.590053	+	0.590053i
$843$	14.9551	−	14.9551i	0.515081	−	0.515081i
$844$			11.1745i			0.384644i
$845$	−24.1247	+	9.65155i	−0.829916	+	0.332023i
$846$		−	34.8724i		−	1.19894i
$847$		0			0
$848$	−5.59589	−	5.59589i	−0.192164	−	0.192164i
$849$		−	22.4104i		−	0.769123i
$850$	−2.85399	+	2.71873i	−0.0978909	+	0.0932517i
$851$	1.20901			0.0414443
$852$	−16.6846	−	16.6846i	−0.571606	−	0.571606i
$853$	14.9594	−	14.9594i	0.512200	−	0.512200i	−0.403000	−	0.915200i	$-0.632032\pi$
$853$	14.9594	−	14.9594i	0.512200	−	0.512200i	0.915200	+	0.403000i	$0.132032\pi$
$854$		0			0
$855$	−24.7645	+	9.90752i	−0.846929	+	0.338830i
$856$	4.56942			0.156179
$857$	8.52770	+	8.52770i	0.291301	+	0.291301i	0.837594	−	0.546293i	$-0.183962\pi$
$857$	8.52770	+	8.52770i	0.291301	+	0.291301i	−0.546293	+	0.837594i	$0.683962\pi$
$858$	8.86292	+	8.86292i	0.302575	+	0.302575i
$859$	5.80123			0.197935			0.0989677	−	0.995091i	$-0.468446\pi$
$859$	5.80123			0.197935			0.0989677	+	0.995091i	$0.468446\pi$
$860$	−1.37941	−	0.591080i	−0.0470376	−	0.0201557i
$861$		0			0
$862$	−1.10172	+	1.10172i	−0.0375249	+	0.0375249i
$863$	−2.12724	−	2.12724i	−0.0724120	−	0.0724120i	0.669973	−	0.742385i	$-0.266306\pi$
$863$	−2.12724	−	2.12724i	−0.0724120	−	0.0724120i	−0.742385	+	0.669973i	$0.766306\pi$
$864$	−7.11757			−0.242145
$865$	−10.7422	−	4.60305i	−0.365246	−	0.156508i
$866$			8.88361i			0.301877i
$867$	−33.6632	−	33.6632i	−1.14326	−	1.14326i
$868$		0			0
$869$			49.2347i			1.67017i
$870$	6.33094	+	15.8246i	0.214639	+	0.536505i
$871$			7.77873i			0.263572i
$872$	12.8005	−	12.8005i	0.433479	−	0.433479i
$873$	−17.2557	+	17.2557i	−0.584016	+	0.584016i
$874$	10.3017			0.348460
$875$		0			0
$876$	28.6750			0.968838
$877$	24.7859	−	24.7859i	0.836962	−	0.836962i	−0.151496	−	0.988458i	$-0.548409\pi$
$877$	24.7859	−	24.7859i	0.836962	−	0.836962i	0.988458	+	0.151496i	$0.0484091\pi$
$878$	16.9099	−	16.9099i	0.570681	−	0.570681i
$879$		−	13.7788i		−	0.464747i
$880$	−3.04917	−	7.62161i	−0.102788	−	0.256924i
$881$		−	23.7116i		−	0.798864i	−0.916763	−	0.399432i	$-0.869207\pi$
$881$		−	23.7116i		−	0.798864i	0.916763	−	0.399432i	$-0.130793\pi$
$882$		0			0
$883$	−7.95370	−	7.95370i	−0.267663	−	0.267663i	0.560495	−	0.828158i	$-0.310611\pi$
$883$	−7.95370	−	7.95370i	−0.267663	−	0.267663i	−0.828158	+	0.560495i	$0.810611\pi$
$884$			0.925988i			0.0311443i
$885$	−63.9968	−	27.4227i	−2.15123	−	0.921804i
$886$	−12.8621			−0.432109
$887$	14.4181	+	14.4181i	0.484111	+	0.484111i	0.906442	−	0.422331i	$-0.138788\pi$
$887$	14.4181	+	14.4181i	0.484111	+	0.484111i	−0.422331	+	0.906442i	$0.638788\pi$
$888$	0.528070	−	0.528070i	0.0177209	−	0.0177209i
$889$		0			0
$890$	2.93964	+	1.25964i	0.0985371	+	0.0422233i
$891$	−15.9411			−0.534048
$892$	−0.746804	−	0.746804i	−0.0250049	−	0.0250049i
$893$	9.90752	+	9.90752i	0.331542	+	0.331542i
$894$	14.0736			0.470693
$895$	−26.0934	+	10.4392i	−0.872207	+	0.348943i
$896$		0			0
$897$	11.3604	−	11.3604i	0.379313	−	0.379313i
$898$	12.6524	+	12.6524i	0.422217	+	0.422217i
$899$	0.108904			0.00363214
$900$	19.7258	−	18.7910i	0.657528	−	0.626366i
$901$		−	6.23870i		−	0.207841i
$902$	23.3118	+	23.3118i	0.776197	+	0.776197i
$903$		0			0
$904$			2.15051i			0.0715247i
$905$	−24.2368	+	9.69637i	−0.805657	+	0.322318i
$906$			29.1999i			0.970101i
$907$	−4.60662	+	4.60662i	−0.152960	+	0.152960i	−0.779439	−	0.626478i	$-0.784496\pi$
$907$	−4.60662	+	4.60662i	−0.152960	+	0.152960i	0.626478	+	0.779439i	$0.284496\pi$
$908$	−2.20643	+	2.20643i	−0.0732229	+	0.0732229i
$909$	−0.391801			−0.0129952
$910$		0			0
$911$	−24.2528			−0.803531			−0.401765	−	0.915743i	$-0.631603\pi$
$911$	−24.2528			−0.803531			−0.401765	+	0.915743i	$0.631603\pi$
$912$	4.49957	−	4.49957i	0.148996	−	0.148996i
$913$	−35.7214	+	35.7214i	−1.18221	+	1.18221i
$914$			34.2111i			1.13160i
$915$	5.10017	−	11.9024i	0.168606	−	0.393480i
$916$			8.42181i			0.278264i
$917$		0			0
$918$	−3.96759	−	3.96759i	−0.130950	−	0.130950i
$919$			36.0892i			1.19047i	0.803551	+	0.595236i	$0.202942\pi$
$919$			36.0892i			1.19047i	−0.803551	+	0.595236i	$0.797058\pi$
$920$	−9.76931	+	3.90840i	−0.322085	+	0.128856i
$921$	−4.37972			−0.144317
$922$	−16.5089	−	16.5089i	−0.543690	−	0.543690i
$923$	6.74244	−	6.74244i	0.221930	−	0.221930i
$924$		0			0
$925$	−0.0311706	+	1.28426i	−0.00102488	+	0.0422263i
$926$	−5.63579			−0.185203
$927$	63.8788	+	63.8788i	2.09805	+	2.09805i
$928$	−1.85429	−	1.85429i	−0.0608700	−	0.0608700i
$929$	42.4083			1.39137			0.695685	−	0.718347i	$-0.255101\pi$
$929$	42.4083			1.39137			0.695685	+	0.718347i	$0.255101\pi$
$930$	−0.100260	−	0.250606i	−0.00328764	−	0.00821769i
$931$		0			0
$932$	−16.1198	+	16.1198i	−0.528023	+	0.528023i
$933$	28.3806	+	28.3806i	0.929140	+	0.929140i
$934$	−4.88580			−0.159868
$935$	2.54884	−	5.94828i	0.0833561	−	0.194529i
$936$		−	6.40013i		−	0.209195i
$937$	4.06709	+	4.06709i	0.132866	+	0.132866i	0.770412	−	0.637546i	$-0.220050\pi$
$937$	4.06709	+	4.06709i	0.132866	+	0.132866i	−0.637546	+	0.770412i	$0.720050\pi$
$938$		0			0
$939$		−	67.8621i		−	2.21460i
$940$	−13.1543	−	5.63665i	−0.429047	−	0.183847i
$941$		−	20.1000i		−	0.655241i	−0.944809	−	0.327621i	$-0.893753\pi$
$941$		−	20.1000i		−	0.655241i	0.944809	−	0.327621i	$-0.106247\pi$
$942$	−50.3280	+	50.3280i	−1.63978	+	1.63978i
$943$	29.8808	−	29.8808i	0.973053	−	0.973053i
$944$	10.7123			0.348656
$945$		0			0
$946$	2.46386			0.0801069
$947$	−41.6866	+	41.6866i	−1.35463	+	1.35463i	−0.474232	+	0.880400i	$0.657274\pi$
$947$	−41.6866	+	41.6866i	−1.35463	+	1.35463i	−0.880400	+	0.474232i	$0.842726\pi$
$948$	27.5645	−	27.5645i	0.895253	−	0.895253i
$949$			11.5879i			0.376158i
$950$	−0.265598	+	10.9429i	−0.00861713	+	0.355035i
$951$		−	38.3355i		−	1.24311i
$952$		0			0
$953$	−31.1044	−	31.1044i	−1.00757	−	1.00757i	−0.999971	−	0.00759828i	$-0.997581\pi$
$953$	−31.1044	−	31.1044i	−1.00757	−	1.00757i	−0.00759828	−	0.999971i	$-0.502419\pi$
$954$			43.1199i			1.39606i
$955$	12.8768	+	32.1864i	0.416683	+	1.04153i
$956$	−23.9971			−0.776120
$957$	−19.7867	−	19.7867i	−0.639614	−	0.639614i
$958$	−12.0996	+	12.0996i	−0.390921	+	0.390921i
$959$		0			0
$960$	−2.55992	+	5.97414i	−0.0826212	+	0.192814i
$961$	30.9983			0.999944
$962$	0.213399	+	0.213399i	0.00688026	+	0.00688026i
$963$	−17.6051	−	17.6051i	−0.567317	−	0.567317i
$964$	−24.7875			−0.798350
$965$	−7.92454	+	18.4936i	−0.255100	+	0.595331i
$966$		0			0
$967$	−21.5036	+	21.5036i	−0.691510	+	0.691510i	−0.962564	−	0.271054i	$-0.912628\pi$
$967$	−21.5036	+	21.5036i	−0.691510	+	0.691510i	0.271054	+	0.962564i	$0.412628\pi$
$968$	1.75170	+	1.75170i	0.0563019	+	0.0563019i
$969$	5.01644			0.161151
$970$	3.71992	+	9.29820i	0.119440	+	0.298547i
$971$			52.3118i			1.67877i	0.543540	+	0.839384i	$0.317084\pi$
$971$			52.3118i			1.67877i	−0.543540	+	0.839384i	$0.682916\pi$
$972$	−6.17385	−	6.17385i	−0.198026	−	0.198026i
$973$		0			0
$974$			0.130300i			0.00417507i
$975$	11.7746	+	12.3604i	0.377090	+	0.395850i
$976$			1.99231i			0.0637724i
$977$	40.0182	−	40.0182i	1.28029	−	1.28029i	0.339794	−	0.940500i	$-0.389643\pi$
$977$	40.0182	−	40.0182i	1.28029	−	1.28029i	0.940500	−	0.339794i	$-0.110357\pi$
$978$	45.1463	−	45.1463i	1.44362	−	1.44362i
$979$	−5.25068			−0.167813
$980$		0			0
$981$	−98.6358			−3.14920
$982$	−19.0845	+	19.0845i	−0.609011	+	0.609011i
$983$	−10.9452	+	10.9452i	−0.349097	+	0.349097i	−0.859773	−	0.510676i	$-0.829395\pi$
$983$	−10.9452	+	10.9452i	−0.349097	+	0.349097i	0.510676	+	0.859773i	$0.329395\pi$
$984$		−	26.1026i		−	0.832121i
$985$	35.4471	+	15.1891i	1.12944	+	0.483965i
$986$		−	2.06729i		−	0.0658361i
$987$		0			0
$988$	1.81832	+	1.81832i	0.0578486	+	0.0578486i
$989$		−	3.15815i		−	0.100423i
$990$	−17.6168	+	41.1126i	−0.559898	+	1.30664i
$991$	−53.7295			−1.70678			−0.853388	−	0.521277i	$-0.825456\pi$
$991$	−53.7295			−1.70678			−0.853388	+	0.521277i	$0.825456\pi$
$992$	0.0293654	+	0.0293654i	0.000932351	+	0.000932351i
$993$	−39.2484	+	39.2484i	−1.24551	+	1.24551i
$994$		0			0
$995$	−7.25190	−	18.1266i	−0.229901	−	0.574653i
$996$	39.9979			1.26738
$997$	27.2445	+	27.2445i	0.862842	+	0.862842i	0.991667	−	0.128826i	$-0.0411208\pi$
$997$	27.2445	+	27.2445i	0.862842	+	0.862842i	−0.128826	+	0.991667i	$0.541121\pi$
$998$	−0.0680939	−	0.0680939i	−0.00215548	−	0.00215548i
$999$	−1.82870			−0.0578577

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.g.c.293.4		16
5.2	odd	4	inner	490.2.g.c.97.1		16
7.2	even	3		490.2.l.c.423.4		16
7.3	odd	6		490.2.l.c.313.2		16
7.4	even	3		70.2.k.a.33.1	yes	16
7.5	odd	6		70.2.k.a.3.3	✓	16
7.6	odd	2	inner	490.2.g.c.293.1		16
21.5	even	6		630.2.bv.c.73.1		16
21.11	odd	6		630.2.bv.c.523.4		16
28.11	odd	6		560.2.ci.c.33.4		16
28.19	even	6		560.2.ci.c.353.4		16
35.2	odd	12		490.2.l.c.227.2		16
35.4	even	6		350.2.o.c.243.4		16
35.12	even	12		70.2.k.a.17.1	yes	16
35.17	even	12		490.2.l.c.117.4		16
35.18	odd	12		350.2.o.c.257.2		16
35.19	odd	6		350.2.o.c.143.2		16
35.27	even	4	inner	490.2.g.c.97.4		16
35.32	odd	12		70.2.k.a.47.3	yes	16
35.33	even	12		350.2.o.c.157.4		16
105.32	even	12		630.2.bv.c.397.1		16
105.47	odd	12		630.2.bv.c.577.4		16
140.47	odd	12		560.2.ci.c.17.4		16
140.67	even	12		560.2.ci.c.257.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.3	✓	16	7.5	odd	6
70.2.k.a.17.1	yes	16	35.12	even	12
70.2.k.a.33.1	yes	16	7.4	even	3
70.2.k.a.47.3	yes	16	35.32	odd	12
350.2.o.c.143.2		16	35.19	odd	6
350.2.o.c.157.4		16	35.33	even	12
350.2.o.c.243.4		16	35.4	even	6
350.2.o.c.257.2		16	35.18	odd	12
490.2.g.c.97.1		16	5.2	odd	4	inner
490.2.g.c.97.4		16	35.27	even	4	inner
490.2.g.c.293.1		16	7.6	odd	2	inner
490.2.g.c.293.4		16	1.1	even	1	trivial
490.2.l.c.117.4		16	35.17	even	12
490.2.l.c.227.2		16	35.2	odd	12
490.2.l.c.313.2		16	7.3	odd	6
490.2.l.c.423.4		16	7.2	even	3
560.2.ci.c.17.4		16	140.47	odd	12
560.2.ci.c.33.4		16	28.11	odd	6
560.2.ci.c.257.4		16	140.67	even	12
560.2.ci.c.353.4		16	28.19	even	6
630.2.bv.c.73.1		16	21.5	even	6
630.2.bv.c.397.1		16	105.32	even	12
630.2.bv.c.523.4		16	21.11	odd	6
630.2.bv.c.577.4		16	105.47	odd	12

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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(2.05532 - 2.05532i) q^{3} -1.00000i q^{4} +(0.830578 + 2.07609i) q^{5} +2.90667i q^{6} +(0.707107 + 0.707107i) q^{8} -5.44871i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(2.05532 - 2.05532i) q^{3} -1.00000i q^{4} +(0.830578 + 2.07609i) q^{5} +2.90667i q^{6} +(0.707107 + 0.707107i) q^{8} -5.44871i q^{9} +(-2.05532 - 0.880708i) q^{10} +3.67114 q^{11} +(-2.05532 - 2.05532i) q^{12} +(0.830578 - 0.830578i) q^{13} +(5.97414 + 2.55992i) q^{15} -1.00000 q^{16} +(-0.557436 - 0.557436i) q^{17} +(3.85282 + 3.85282i) q^{18} -2.18923 q^{19} +(2.07609 - 0.830578i) q^{20} +(-2.59589 + 2.59589i) q^{22} +(3.32739 + 3.32739i) q^{23} +2.90667 q^{24} +(-3.62028 + 3.44871i) q^{25} +1.17462i q^{26} +(-5.03288 - 5.03288i) q^{27} -2.62236i q^{29} +(-6.03449 + 2.41421i) q^{30} +0.0415289i q^{31} +(0.707107 - 0.707107i) q^{32} +(7.54538 - 7.54538i) q^{33} +0.788333 q^{34} -5.44871 q^{36} +(0.181676 - 0.181676i) q^{37} +(1.54802 - 1.54802i) q^{38} -3.41421i q^{39} +(-0.880708 + 2.05532i) q^{40} -8.98026i q^{41} +(-0.474569 - 0.474569i) q^{43} -3.67114i q^{44} +(11.3120 - 4.52558i) q^{45} -4.70563 q^{46} +(-4.52558 - 4.52558i) q^{47} +(-2.05532 + 2.05532i) q^{48} +(0.121320 - 4.99853i) q^{50} -2.29142 q^{51} +(-0.830578 - 0.830578i) q^{52} +(5.59589 + 5.59589i) q^{53} +7.11757 q^{54} +(3.04917 + 7.62161i) q^{55} +(-4.49957 + 4.49957i) q^{57} +(1.85429 + 1.85429i) q^{58} -10.7123 q^{59} +(2.55992 - 5.97414i) q^{60} -1.99231i q^{61} +(-0.0293654 - 0.0293654i) q^{62} +1.00000i q^{64} +(2.41421 + 1.03449i) q^{65} +10.6708i q^{66} +(-4.68272 + 4.68272i) q^{67} +(-0.557436 + 0.557436i) q^{68} +13.6777 q^{69} +8.11777 q^{71} +(3.85282 - 3.85282i) q^{72} +(-6.97578 + 6.97578i) q^{73} +0.256928i q^{74} +(-0.352638 + 14.5291i) q^{75} +2.18923i q^{76} +(2.41421 + 2.41421i) q^{78} +13.4113i q^{79} +(-0.830578 - 2.07609i) q^{80} -4.34228 q^{81} +(6.35000 + 6.35000i) q^{82} +(-9.73033 + 9.73033i) q^{83} +(0.694291 - 1.62028i) q^{85} +0.671142 q^{86} +(-5.38980 - 5.38980i) q^{87} +(2.59589 + 2.59589i) q^{88} -1.43026 q^{89} +(-4.79872 + 11.1989i) q^{90} +(3.32739 - 3.32739i) q^{92} +(0.0853553 + 0.0853553i) q^{93} +6.40013 q^{94} +(-1.81832 - 4.54503i) q^{95} -2.90667i q^{96} +(-3.16693 - 3.16693i) q^{97} -20.0030i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 24 q^{11} + 16 q^{15} - 16 q^{16} + 16 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{25} - 40 q^{30} - 8 q^{36} - 8 q^{37} - 8 q^{43} + 16 q^{46} - 32 q^{50} + 32 q^{51} + 56 q^{53} + 8 q^{57} + 64 q^{58} - 16 q^{60} + 16 q^{65} - 64 q^{67} + 16 q^{71} + 16 q^{72} + 16 q^{78} + 24 q^{85} - 24 q^{86} + 8 q^{88} + 8 q^{92} - 56 q^{93} - 40 q^{95}+O(q^{100}) \) 16 * q + 24 * q^11 + 16 * q^15 - 16 * q^16 + 16 * q^18 - 8 * q^22 + 8 * q^23 - 24 * q^25 - 40 * q^30 - 8 * q^36 - 8 * q^37 - 8 * q^43 + 16 * q^46 - 32 * q^50 + 32 * q^51 + 56 * q^53 + 8 * q^57 + 64 * q^58 - 16 * q^60 + 16 * q^65 - 64 * q^67 + 16 * q^71 + 16 * q^72 + 16 * q^78 + 24 * q^85 - 24 * q^86 + 8 * q^88 + 8 * q^92 - 56 * q^93 - 40 * q^95

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